aspects of disc brake judder - universiti teknologi malaysiaarahim/jacobsson.pdf · 419 aspects of...

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419 Aspects of disc brake judder H Jacobsson* Machine and Vehicle Systems, Chalmers University of Technology, S-412 96 Go ¨ teborg, Sweden Abstract: Brake judder is a braking induced, forced vibration occurring in di erent types of vehicles. The judder frequency is directly proportional to the revolution speed of the wheel and therefore also to the velocity of the vehicle. The driver experiences judder as vibrations in the steering wheel, brake pedal and oor. In the higher frequency range, the structural vibrations are accompanied by a sound. Brake judder primarily a ects the comfort but could, when confronting an inexperienced driver for the rst time, lead to faulty reactions and reduced driving safety. Furthermore, a speci c type of judder, so-called hot judder, is related to disc cracking. There are numerous publications available dealing with high frequency vibrations, such as brake squeal, including mathematical models for analysis and simulation. However, low frequency phenomena, such as brake judder and groan, have received much less attention. There is a growing interest from the automotive industry concerning brake judder. Even though few companies would admit that they have the problem, it is not unusual to meet people who have experienced the problem in their own passenger cars. Much of the knowledge concerning brake judder remains within the companies. Hence, very few people have the full picture. The purpose of the present paper is to give an overview of the brake judder problem. Keywords: brake torque variation, brake pressure variation, brake roughness, cold judder, disc thickness variation, disc brake, hot judder, hot spots, judder, thermoelastic instability NOTATION BPV brake pressure variation BTV brake torque variation C equivalent viscous damping (N ms/rad) CFD computational uid dynamics DOF degree of freedom DTV disc thickness variation E envelope of Q ¨ C (rad/s2 ) FE nite element J C inertia moment of stator (kg m2 ) J D inertia moment of front rotor (kg m2 ) K angular sti ness of stator (N m/rad) LO lower order M brake torque (N m) MBS multibody system t physical time (s) t cr critical time (s) TEI thermoelastic instability Q C vibration of caliper (rad) Q ¨ C second derivative of Q C with respect to t (rad/s2 ) The MS was received on 15 October 2002 and was accepted after revision for publication on 16 January 2003. * Corresponding author: email: heja@mvs.chalmers.se D12302 © IMechE 2003 Proc. Instn Mech. Engrs Vol. 217 Part D: J. Automobile Engineering Q D vibration of disc (rad) W ideal wheel motion (rad) W C ideal caliper motion (rad) 1 INTRODUCTION In the low frequency domain, there are two fundamen- tally di erent types of structural vibrations, namely judder and groan, and their associated airborne noise called hum and moan respectively. Even though the fre- quency of judder is normally lower than that of groan, and groan is lower than squeal, the frequency ranges overlap in the region 400–500 Hz. Anyhow, brake judder is easily recognized, as its frequency is proportional to the vehicle speed. The frequency of brake squeal is independent of the speed of the vehicle. While judder is a forced vibration mostly due to geo- metrical deviations (including spatial variations of the coe cient of friction) of the brake disc, groan is an instability phenomenon occurring as a result of speci c types of friction–velocity characteristics. Squeal, on the other hand, involves bending modes of the brake components [ 1 ].

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Page 1: Aspects of disc brake judder - Universiti Teknologi Malaysiaarahim/jacobsson.pdf · 419 Aspects of disc brake judder HJacobsson* Machine and Vehicle Systems, Chalmers University of

419

Aspects of disc brake judder

H JacobssonMachine and Vehicle Systems Chalmers University of Technology S-412 96 Goteborg Sweden

Abstract Brake judder is a braking induced forced vibration occurring in di erent types of vehiclesThe judder frequency is directly proportional to the revolution speed of the wheel and therefore alsoto the velocity of the vehicle The driver experiences judder as vibrations in the steering wheel brakepedal and oor In the higher frequency range the structural vibrations are accompanied by a soundBrake judder primarily a ects the comfort but could when confronting an inexperienced driver forthe rst time lead to faulty reactions and reduced driving safety Furthermore a speci c type ofjudder so-called hot judder is related to disc cracking There are numerous publications availabledealing with high frequency vibrations such as brake squeal including mathematical models foranalysis and simulation However low frequency phenomena such as brake judder and groan havereceived much less attention There is a growing interest from the automotive industry concerningbrake judder Even though few companies would admit that they have the problem it is not unusualto meet people who have experienced the problem in their own passenger cars Much of the knowledgeconcerning brake judder remains within the companies Hence very few people have the full pictureThe purpose of the present paper is to give an overview of the brake judder problem

Keywords brake torque variation brake pressure variation brake roughness cold judder discthickness variation disc brake hot judder hot spots judder thermoelastic instability

NOTATION

BPV brake pressure variationBTV brake torque variationC equivalent viscous damping (N msrad)CFD computational uid dynamicsDOF degree of freedomDTV disc thickness variationE envelope of QC (rads2)FE nite elementJC inertia moment of stator (kg m2)JD inertia moment of front rotor (kg m2)

K angular sti ness of stator (N mrad)LO lower orderM brake torque (N m)MBS multibody systemt physical time (s)tcr critical time (s)

TEI thermoelastic instability

QC vibration of caliper (rad)QC second derivative of QC with respect to t

(rads2)

The MS was received on 15 October 2002 and was accepted after revisionfor publication on 16 January 2003 Corresponding author email hejamvschalmersse

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

QD vibration of disc (rad)W ideal wheel motion (rad)WC ideal caliper motion (rad)

1 INTRODUCTION

In the low frequency domain there are two fundamen-tally di erent types of structural vibrations namelyjudder and groan and their associated airborne noisecalled hum and moan respectively Even though the fre-quency of judder is normally lower than that of groanand groan is lower than squeal the frequency rangesoverlap in the region 400ndash500 Hz Anyhow brake judderis easily recognized as its frequency is proportional tothe vehicle speed The frequency of brake squeal isindependent of the speed of the vehicle

While judder is a forced vibration mostly due to geo-metrical deviations (including spatial variations of thecoe cient of friction) of the brake disc groan is aninstability phenomenon occurring as a result of speci ctypes of frictionndashvelocity characteristics Squeal on theother hand involves bending modes of the brakecomponents [1 ]

420 H JACOBSSON

11 Traditional classi cation

Traditionally brake noise and vibrations are classi edaccording to their dominant frequencies with thosebelow a certain limit (100 500 or 1000 Hz) being calledjudder or hum Above this limit the vibrations areregarded as high frequency noise including squeal Themain disadvantage with this classi cation is that onephysical phenomenon can be split into two di erentclasses and at the same time fundamentally di erentphenomena will be included in the same term Howeverthe classi cation is related to the way in which the phen-omena are experienced by the driver and passengers

Thermal or hot judder is caused by the following

(a) thermal deformation for example coning andwaving of a disc

(b) uneven thermal expansion(c) phase transformation of disc material

Cold judder is caused by geometrical irregularities dueto machining mounting uneven wear uneven corrosionor uneven friction lm generation Normally judderconsists of a combination of cold and hot judder andhence the terms lsquohotrsquo and lsquocoldrsquo are somewhat mis-leading For example a high disc thickness variation(DTV) level may indeed induce friction level variationssince a locally thicker area of the disc will be exposed toa locally higher contact pressure and become hotterFurthermore such areas will become hotter and expandmore [2 3 ]

12 Phenomenological classi cation

The classi cation of braking-induced noise andvibrations suggested by the author is as follows [4 5 ]

1 Forced vibrations These include brake juddervibration and its associated brake noise called hum

2 Vibrations primarily caused by friction characteristicsThe group includes creep groan and dynamic groanvibration and their associated moan noise Creepgroan which is related to stickndashslip motion is causedby a static coe cient of friction that is higher thanthe dynamic one Dynamic groan on the other handis an instability phenomenon occurring as a result ofa speci c type of frictionndashvelocity characteristic usu-ally known as lsquonegative dampingrsquo Groan is discussedin more detail in references [4 ] and [5 ]

3 Vibrations primarily caused by resonances of the brakecomponents Noises in this class are squeal and wirebrush noises etc The corresponding vibrationspropagate through the air rather than through thevehicle structure

This is similar to the classi cation by Abdelhamid [6 ]One of the bene ts of the classi cation is that it iscoupled to the way of modelling the vibrations Anotherbene t is the connection to appropriate experimental

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

tools In addition the classi cation separates the twofundamentally di erent brake vibrations judder andgroan from each other

The vibration frequency of brake judder is directlyproportional to the wheel speed and therefore also tothe velocity of the vehicle Hence it is common to relatethe judder frequencies to the wheel speed for examplefrequencies at twice the number of wheel rotationsper second are called second-order judder Two maingroups of judder are identi ed [4 ] according to theirvibration order

1 Normally there are some more or less static(ie lsquocoldrsquo) pronounced deviations from the idealgeometry of the lower order (LO) type with avibration order from 1 to 5 The disturbed geometrywill result in uneven contact pressure and temperature elds as well as uneven thermal expansion especiallyat long or repeated brake applications [7 ] Hence thestatic deviations will be reinforced during braking

2 Superimposed on the LO variations of for instancea brake disc there are higher-order geometricalandor frictional deviations with low static ampli-tudes However especially for long low intensitybrakings the temperature and pressure eld willgradually become more and more localized as thebraking continues Hot bands are generated on thepad and disc leading to a number (usually 6ndash20 [8 ] )of hot spots on the disc The dominant judder orderand the actual number of hot spots normally coincide[9 10] As for LO judder an uneven heating of thedisc will cause a temporary DTV and also often shapedeformation (eg coning and buckling) At su c-iently high local temperatures remaining discolouredareas [10] with locally di erent speci c volume wearand friction characteristics will occur

When de ning brake judder as braking-induced forcedvibrations the upper limit of its frequency is determinedby the maximal vehicle speed the wheel radius andjudder order For instance let a passenger car brakefrom 170 kmh down to zero Then the 20th-order juddervibrations will sweep from 500 Hz while the upper limitof the rst-order vibration will be only 25 Hz owingto the maximum revolution speed of the wheelsConsequently resonances above 100 Hz will not inpractice be excited by the rst-order disturbances

2 PHYSICAL EFFECTS CAUSING BRAKETORQUE VARIATION AND BRAKE PRESSUREVARIATION

There are several physical e ects causing brake torquevariation (BTV) and brake pressure variation (BPV )and hence judder The ones discussed in this work (seeFig 1) are geometrical irregularities uneven wear of thebrake rotor uneven friction lm between rotor and

421ASPECTS OF DISC BRAKE JUDDER

Fig 1 Physical e ects causing BTVBPV

lining uneven heating of the rotor uneven pressure dis-tribution the friction characteristic and friction leveland external forces The di erent e ects or sources aregenerally not independent of each other There arestrong couplings between geometrical irregularitiesuneven wear and uneven heating

21 Geometrical irregularities

For disc brake judder the most important geometricalproperties are DTV and run-out of the disc In additionto geometrical irregularities of a static or remainingnature there can be a dynamic and reversible variationof disc geometry (thermal DTV etc)

Because of the oating calliper normally used inmodern disc brakes an increase of the pad normal forceon one side is compensated (at least partly) by a decreaseon the opposite side Hence de ections from idealshapes such as run-out etc do not contribute to BTVand BPV (and judder) except at the extreme values wherenon-linearities inertia forces and unbalances becomeimportant [11] However run-out can indirectly causevibrations by the increase of DTV due to uneven wear[8 ]

The magnitude of the run-out is determined by discmachining and mounting tolerances bearing clearancesand disc distortion during braking In addition externalforces such as tyre forces and unbalances a ect therun-out

A DTV of 15 iacutem (measured in cold conditions) isobservable as brake judder to an experienced driver ina sensitive car under certain braking conditionsConsequently to achieve safety margins the initial DTVlevel varies between 6 and 10 iacutem for most manufacturers[11 12] On a long time scale DTV is known to growasymptotically from its initial value to a maximumbecause of wear [13] the higher the initial disc run-outthe faster the DTV growth [13] DTV can also be causedby uneven corrosion of the rotor when parked since thepads partly lsquoprotectrsquo the disc surface

Kao et al [7 ] found a considerable thermal coningand thermal growth of DTV ( rst and second order)when measuring the instantaneous disc surface de ectionduring a brake stop using capacitive transducers TheDTV level (and hence BTV ) increased linearly with timeduring braking The brake application time [7 11] and

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

how often the braking is repeated [2 ] are also importantfactors for brake judder to develop

Experimental investigations [11 12] have shown thatthe instantaneous DTV is the primary contributor todisc brake judder on passenger cars DTV is a verycomplex phenomenon consisting of the following

1 Initial DTV arises from manufacturing andmounting

2 Wear and cleaning processes produce DTV3 There are more or less permanent areas with locally

di erent speci c volume friction and wear propertiescaused by phase transformations when locallyoverheating the disc This DTV remains after coolingof the disc

4 Temporary thermal growth of DTV takes placeduring each brake application owing to unevenheating and localized contact area and pressureie thermoelastic instability (TEI) processes [7 11]Thermal expansion due to a local temperature di er-ence of 200ndash300 degC directly causes a di erence ofDTV amplitude of the order of 10 iacutem ConsequentlyDTV increases with braking time especially forlsquohardrsquo pads

5 Uneven friction lm thickness may contribute sev-eral iacutem

6 Uneven corrosion and deposition of heated padmaterial on the disc could occur

22 Uneven wear

O -brake wear sometimes called lsquocold erosionrsquo iscoupled to DTV and can lead to lsquocold judderrsquo Brakediscs can develop DTV because the brake pads in theo -brake mode lightly touch the rotors in some sectorsbut not at all in others resulting in non-uniform wearThe o -brake wear may be caused by disc run-out andcan be reduced by increasing the distance that the cal-liper piston is retarded after application of the brakethe so-called rollback [8 ]

The DTV created by pad contact has two phases gen-eration and cleaning The ratio between generation andcleaning is in uenced by the selection of the frictionmaterial Friction materials which generate DTV in theo -brake mode will usually have the ability to eliminateDTV by a higher disc wear in the on-brake mode Inparticular an increase of the high temperature and press-ure pad wear could be used to reduce hot spot develop-ment by counteracting localization of the contactpressure on the friction surface [3 14] Howeverincreased wear will also speed up the motion of the hotbands [3 14 15] which is believed to be a cause ofthermal fatigue of the disc [16 ]

Careful drivers may experience brake judder morequickly than sporty drivers since slow application of thebrakes at low brake pad pressures prevents lsquocleaningrsquoof the disc Discs causing BTV and hence judder can

422 H JACOBSSON

sometimes be cured by making several hard stopsHowever the relative amount of motorway driving is amuch more important factor for DTV generation thanthe driving style [17]

During long brake applications wear especially padwear becomes substantial Generally wear results in amore even temperature distribution and lower tempera-ture maxima [14] However the high wear will move thecontact surface (ie moving hot spotsbands) whichmight contribute to thermal fatigue of discs Simulations[3 14] and measurements [18] show that an increase ofthe hot pad wear could be used to reduce hot spot devel-opment by counteracting localization of the contactpressure on the friction surface

23 Uneven friction lms

The third-body layer friction lm or transfer lm is a lm a few iacutem thick consisting of material produced byattrition [19] The ferrous particles produced by the wearof the cast-iron disc are transformed and oxidized by theatmospheric oxygen and deposited as a greyndashblack layeron the braking surface of the disc This layer togetherwith the corresponding layers on the pads determinesthe frictional behaviour of the brake

When hot brakes are applied on a stationary vehiclesticking of the pad to the rotor can occur At veryhigh temperatures perhaps 500 degC the melted frictionmaterial can be lsquoburntrsquo into the disc

24 Uneven heating

Thermal deformation of a disc consists of the following

1 Waving or warping of the disc2 Coning of the disc This can lead to high run-out

Inoue [2 ] found that thermal run-out can be avoidedby a disc design that is stable to coning

3 Uneven thermal expansion A temperature di erenceof 250 degC which is not unusual causes a DTV ampli-tude of 10 iacutem [2 ] Even if no visible hot spots (orblue areas caused by phase transformations) occurduring braking this phenomenon is still importantfor brake judder occurrence by causing temporarygrowth of geometrical disturbances

4 Phase transformation5 Deposition of heated pad material on the disc

In disc brakes the rubbing speed and the frictional heatgenerated increase with the radius Hence the tempera-ture and pressure elds tend to be localized into band(s)near the outer radius even if the pad and disc are initiallyperfectly at and parallel with evenly distributedcoe cient of friction [3 ] The hot bands or rings maydevelop into hot spots as the rotor buckles [7 20] Themaximum disc temperature of the spots increases withpad sti ness [15] Measurements show that a local hot

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

spot can have a temperature of over 700ndash800 degC and thatthere can be a temperature di erence of over 300ndash600 degCbetween the hottest and the coldest local areas of thesame disc [2 3 21] Hot spots are usually more or lessbut not fully uniformly distributed [2 21]

The thicker areas of a brake disc become hotter thanthe thinner ones which causes thermal deformation ofthe brake disc (thermal coning and buckling [2 7 ] ) andalso uneven thermal expansion ie thermal DTV Theprocess can become unstable and is then de ned as aTEI TEI leads to a more and more localized brake press-ure and temperature eld as the braking continues Inthe extreme case especially at higher order (6ndash20) discdisturbances the disc will crack

Studies by Ste en and Bruns [22] have led to theexpected result that small dimensions (ie disc and padthickness and diameter of friction ring) increase the tend-ency towards hot spotting Also a higher revolutionspeed (ie higher energy level ) of the disc was found toincrease the hot spot generation

It is the temperature gradients and not the increase inabsolute temperature level that cause the increasingjudder level during long or repeated braking see refer-ence [23] The temperature gradients cause temporaryDTV owing to uneven thermal expansion of the discmaterial [2 ] The DTV level (and hence BTV ) increasesoften more or less linearly with time while braking [7 ]especially for lsquohardrsquo pads and at the outer radius Hencethe brake application time [7 11] and how often thebraking is repeated [23] are important factors for brakejudder development Hot spotting and thermal DTVbecome worse for low torque long duration applicationsthan for high torque ones [15] A light long applicationtime (20ndash45 s) gives substantially higher temperatureand pressure gradients than heavy shorter ones (3ndash4 s)[7 15 16 ]

Also a higher revolution speed (ie higher energylevel ) of the disc was found to increase the hot spotgeneration [11 22] In addition the localization process(and the correlated thermal DTV ) is particularly pro-nounced at high speed above 100 kmh [11] This mightbe explained by the fact that the TEI process demandsa minimal lsquocriticalrsquo speed to develop As a consequenceof this it is essential to test friction material at speedsabove the limit 100 kmh (60 milesh) which is usuallystandard

25 Uneven pressure

In a conventional disc brake analysis the interfacepressure is assumed to be either constant (ie constantpressure assumption) or inversely proportional to theradius (ie constant wear assumption) However underdynamic braking conditions the contact area and brakepressure distribution varies continuously with timebecause of

423ASPECTS OF DISC BRAKE JUDDER

(a) thermal distortion arising from the friction heatgeneration

(b) mechanical distortion due to the applied actuationforce

(c) wear of the friction pair material and formation offriction lm

(d) initial DTV and run-out

Conventional brake analysis gives an even temperatureand pressure distribution as well as maximal tempera-ture pressure and stress levels which are much lowerthan their actual peak values [3 ]

26 Friction characteristics and level

The variation of friction with velocity has historicallybeen regarded as the source of all kinds of braking-induced vibrations including brake judder Jacobsson[24] analytically showed that even a constant coe cientof friction may generate judder No speci c frictioncharacteristics are needed for the phenomenon to occurHowever a negative brake fade or a friction coe cientthat increases with brake pressure may increase the prob-lems To achieve a given brake torque a pad materialwith a lower friction coe cient needs a higher brakepressure level This induces more evenly distributedpressure and temperature elds on the contact surface[16 ] Consequently a reduction of the friction coe cientlevel decreases the judder problems and at the same timereduces the crack probability Also the relation betweenBTV and BPV is a ected by the absolute friction levelThis is because BTV is proportional to the coe cient offriction [11] while BPV is independent of friction

27 External forces

Unbalances and tyre force variations may induce a tum-bling rigid body motion of the disc as a result of elas-ticities of the wheel hub and bearing unit [13] Suchdynamic de ections cause the same type of vibrations(with a frequency that is an integer multiple of the instan-taneous brake rotor frequency) as geometrical irregu-larities Hence they may contribute to judder The wheelhubndashbearing design and sti ness contribute to themagnitude of the disc deviation [11] When the judderis due to the tyre force variation or imbalance the termbrake judder is misleading because it suggests that theexcitation force originates from the brakes

3 VEHICLE COMPONENTS

BTV and BPV are usually produced by geometrical orother irregularities of the brake components and furthertransmitted to and ampli ed in the wheel suspension andhydraulic system as outlined in Fig 2

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

Fig 2 Brake vibrations are transmitted to di erent vehiclecomponents

Theoretically a spatial friction coe cient variationaround the disc may occur without corresponding vari-ation of the hydraulic pressure (ie BPV) Howeverphysical e ects that generate friction variation such asphase transformation uneven transfer lm generationcorrosion etc will also generate geometrical irregularit-ies (DTV etc) with normal force variation and BPVHence it is often meaningful to consider BTV and BPVas an entity However their relative magnitudes arefunctions of the actual friction coe cient

Independently of how and where the disturbance isproduced it is transmitted and ampli ed in the sameway The wheel suspension ampli es the vibrationsespecially the frequencies near its eigenfrequenciesUsually there is a second ampli cation of the vibrationin for instance the steering system

An obvious way of reducing the judder is to reducethe BTVBPV which is the source of the vibrations Thistraditional approach will place the focus on the brakecomponents ie pad and disc

An alternative strategy especially with severe steeringwheel vibrations is to reduce the ampli cation eitherthe primary ampli cation in the wheel suspension ora relevant secondary ampli cation at the steeringsystem This can e ectively be achieved by introductionof the brake-by-wire and steering-by-wire techniquesSimulations and measurements by Jacobsson [23] dem-onstrate that the ampli cation is relatively low in thesubcritical region as indicated in Fig 6 Hence thevibration is reduced if the eigenfrequencies of the compo-nents in the transfer path are shifted above the frequencyrange of the rst wheel order excitation (above 25ndash30 Hzor vehicle speeds above 170ndash200 kmh) which was sug-gested by Engel et al [25] Also modal separation ofeigenfrequencies in the transfer path should be ensured

31 Pads

When developing or choosing a pad material more than20 properties are considered [26 ] Everything from den-sity melting point strength (tensile compressive ex-ural and shear) machinability environmental impactsqueal probability etc should be considered Withrespect to judder properties of interest are sti ness

424 H JACOBSSON

coe cient of friction coe cient of thermal expansionthermal conductivity corrosion and porosity

The most important pad property for judder reductionis the compressive sti ness [11] The BTV level can varyby a factor of 2ndash3 (with the same DTV ) depending onthe pad composition [21 27] The pad compressivesti ness should also be as low as possible to promoteuniform contact pressure [3 8 ] and to avoid TEI pro-cesses such as hot banding and thermal DTV This will atthe same time reduce eventual brake squeal problems [1 ]

The relation between the BTVBPV level and the padsti ness of modern passenger cars is non-linear [11] Inparticular during compression the material becomesprogressively sti er as the load is applied [15] For theseprogressive materials the same DTV level will result ina higher BTV level for hard than for light brakings

To achieve a good lsquopedal feelrsquo and positive retractionthe sti ness should be reasonably high and progressiveGenerally the desired zone is narrow and a deviationon either side might lead to complaints [28] Progressivebrake pads ie traditional composite pads [15] su erfrom high sensitivity to increases in the DTV level seereference [5 ] A linear pad compression characteristicwould not require as high safety margins for increasesfrom the initial DTV (thermal DTV and long-time wearDTV etc) as the progressive pad does In other wordslinear pads are likely to accept higher disc thickness tol-erances than the 10 iacutem DTV The new lsquobrake-by-wirersquotechnique o ers other ways of achieving lsquoa good brakefeelrsquo than a high and progressive pad compressionsti ness

32 Disc

The thermal stability of the disc shape is in uenced bythe quality of the material and the heat treatment beforemachining as well as the basic design of the disc rotorDisc design variants that are more or less stable toconing have been discussed in references [2 3 22 29]Thermal stability problems can be minimized by choos-ing high carbon disc materials and introducing thermalstress relief treatment into the machining cycle [13]

Some of the thermally most important properties ofdisc brakes are as follows [3 30]

1 Thermal capacitance (ie density and speci c heat) isthe ability to store heat Initially on braking a sig-ni cant amount of frictional heat is stored [3 ] andconsequently during short brakings the thermalcapacitance dominates

2 Heat dissipation becomes important at long brakingtimes (above 2ndash3 min [3 ]) ie drag braking or moun-tain descent braking However it also a ects thediscrsquos ability to recover thermally between stops [31]Convection accounts for more than 90 per cent of allheat dissipation for most braking conditions [3 ]whereby radiation is almost negligible The heat

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

transfer coe cient due to convection varies as thevehiclersquos velocity to the power 08 [3 ]

3 Thermal conductivity is the ability to redistributethermal energy During long low intensity brakingsthe peak temperature depends largely on the discmaterialrsquos conductivity [32] During short brakingshowever the thermal conductivity has little e ect

4 Thermal expansion coe cient (ie related to localiz-ation of friction contact due to the thermal defor-mation) a ects the tendency towards hot spotting andthermal DTV generation Temperature gradients of abrake disc cause temporary DTV owing to uneventhermal expansion of the material

Ventilated brake discs are widely used for their weightsavings and additional convective heat transferHowever they may increase judder problems byinducing an uneven temperature eld around the discOver short ( less than a few minutes) and high speedstops thermal capacity is the most important thermalproperty which is why a solid disc (with its higher mass)runs cooler than the vented design [3 31] In mountaindescent braking the disc brake temperatures mayincrease considerably when the vents are removed [31]

Aluminium especially SiC-reinforced Al metal matrixcomposite materials requires a lower operating tempera-ture than grey cast iron (around 450 degC) [32 ] Becausethe material su ers from low thermal capacity it canonly be used for relatively light passenger cars say below1000 kg The introduction of aluminium composite discsor pure aluminium covered by a composite layer willprobably increase judder problems because of the highcoe cient of thermal expansion and the low heatcapacity [22] The high thermal conductivity has there-fore relatively little in uence on the hot spot and thermalDTV generation

However there are composite materials that mighthave the ability to reduce judder namely ceramic mate-rials An example is a short bre reinforced SiC material(CSiC ) which has recently been introduced in sportscars and high speed trains [33] Judder is avoidedbecause of the low coe cient of thermal expansion andlow wear Also the low elastic modulus should promoteuniform contact and reduce thermal DTV and hot spotsThe excellent resistance to thermal damage of the mate-rial makes it suitable for disc brakes of heavy vehicleswhere cracking of the normally used cast-iron disc is aproblem However the high cost of the material excludesapplications in the ordinary family car segment

33 Vehicle structure

The front suspension is designed to admit largevibrations in the vertical direction However there is avibration in the forendashaft direction [24 27] which isrelated to brake judder as well as a proportional angularvibration [24] Brake judder is strongly related to the

425ASPECTS OF DISC BRAKE JUDDER

suspension design and the forendashaft exibility is a domi-nating parameter [27] Stringham et al [12] stated thatthe sti ness of the lower arm bushing is the most in u-ential parameter It was found to a ect signi cantly theeigenfrequency of the suspension system in the forendashaftdirection Bosworth [34] studied the suspension struc-ture in more detail and found the following factorscontrolling the judder

(a) tie rod bushmdashradial and forendashaft sti ness(b) lower arm bushmdashforendashaft sti ness(c) anti-roll barmdashvertical sti ness

In particular the sti ness of the lower arm bushing isimportant since it signi cantly a ects the eigenfre-quency of the suspension system in the forendashaft direction[12 34 35] Higher eigenfrequencies which will reducejudder problems such as steering wheel vibrations maybe achieved either by higher sti ness of the rubber bush-ings or by a reduced value of the modal mass and inertiaof the wheel suspension see Jacobsson [5 ]

However modern suspensions have become more andmore exible in the forendashaft direction because of theintroduction of radial tyres [27] This is necessary inorder to absorb the longitudinal vibrations from the sti belt of the tyres

Note that it is essential to measure the eigenfrequencyand damping in the brake-on mode When the brakeswere not applied the experimental vehicle was found tohave a signi cantly higher eigenfrequency (18 Hz com-pared with 138 Hz) and a lower equivalent viscousdamping factor (007 compared with 009) than meas-ured under the same braking conditions see reference[24] Also the instantaneous centre of motion of the strutchanges with the brake pressure level [5 ] It movedgradually towards the wheel axle as the brake pressureincreased

4 TIME-SCALES

Brake judder depends strongly on the braking historyon the short as well as on the long time-scale There arethree di erent time-scales involved in brake judder

(a) revolution time of the wheel(b) brake application time or the time between two

brakings(c) lifetime of brake components

Traditionally in brake design only the long-time changesare considered In recent years changes during brakinghave also been focused on The generation of localizedcontact area pressure and temperature gradients suchas hot banding has been studied It is found that DTVis a dynamic property that may change considerablyduring a brake application [7 11]

Changes within the time of a wheel revolution arenormally not included primarily because of di culties

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

in making numerical and signal analysis when using con-ventional techniques However the amplitude functiontechnique [23] handles sinusoidal variations of the braketorque with wheel revolution

5 APPROACH

The way of looking at and describing a problem is herecalled the problem approach It is a theoretical abstrac-tion lsquoa conception of the worldrsquo including a model andits system limits The problem approach determineswhich physical e ects can be studied and also states thetime and space scale The chosen problem approach willhave consequences for how to analyse the problem aswell as for the type of solution that will be found It alsodetermines which type of analytical and experimentaltool is the most appropriate

When studying the literature on brake judder it isclear that two fundamentally di erent approaches are inuse namely the cause and e ect approaches While thee ect approach focuses on the source of the vibrationsin the form of amplitude and vibrational order of theBTV andor BPV the cause approach deals with anumber of physical e ects such as wear and heatingsee Fig 3

The e ect approach can be further split into di erentapproaches [4 ]

1 The system approach examines how a model of thevehicle or the wheel suspension together withBTVBPV generates judder The braking process isusually represented by a constant frequency whichcan be parametrically changed It is used mostly inexperimental analysis [13 25 36 ] Also some quasi-static analyses may be found in literature Kim et al[35] used multibody system (MBS) analysis of amodel with 12 degrees of freedom (DOF ) of aMcPherson-type suspension exposed to rst-orderjudder

2 The frequency sweep approach examines how thebraking process itself (including a frequency sweep)together with the BTVBPV generates judder Thevehicle structure can be represented by a resonancecorresponding to the actual critical speed [23]

3 The human response approach studies the e ects ofjudder on one speci c test driver or on an average

Fig 3 Problem approaches

426 H JACOBSSON

person placed in a speci c vehicle Alternatively thehuman response to judder could be thought of as athird level where the judder level and frequencytogether with the weight size and place of the personin the vehicle etc are the input

Some approaches are listed in Table 1 together withrelated analytical and experimental methods and toolsfound in the literature [4 ] For instance FE analysis isthe natural choice when studying BTV generation bymeans of for instance the TEI process For the e ectapproach where the BTV can be represented by a sinus-oidal brake torque disturbance it is instead the vehicleor relevant parts thereof that should be modelled ThenMBS analysis (commercial programs are ADAMSDADS etc) is more relevant especially for lowfrequency judder (say below 50 Hz)

In experimental brake judder studies bench testing aswell as road testing are used Advantages of bench test-ing [11] are good reproducibility of the testing con-ditions more accurate measurements higher sensitivityof measurements lower cost and less time consumption[37] Disadvantages are that cooling conditions are nottaken into account as well as the in uence of othermachine elements and systems which will a ect thetransmission of BTV in the vehicle (tyres wheel sus-pension steering) [11] In road testing the speci cproblem occurs that the level of BTVBPV cannot becontrolled during a brake application This problemmay be handled by measuring BTVBPV instead oftrying to control it by constant conditions such as speedtemperature pressure etc see references [9 23]

51 Causes of BTVBPV

Traditionally the source of the BTVBPV has beenfocused on It is a ected by a combination of the di er-ent physical e ects discussed in section 2 Disc run-outand DTV which are geometrical irregularities of thedisc directly cause normal force variations and henceBTVBPV see Fig 4 Furthermore the TEI process gen-erates hot spots and sometimes remaining discolouredareas with locally di erent speci c volume and wearproperties which may aggravate the vibrations Finally

Table 1 Approaches and corresponding methods

Approach Methods and tools

Cause approach (FE) analysis nite di erence dynamometertribometer drag braking thermal imagingX-rays

System approach MBS analysis Fourier methods modal analysisTaguchi methodology road testsspectrograms

Frequency sweep Time plane analysis road tests involvingapproach deceleration waterfall analysis order

tracking ABS and capacitive transducersHuman response Subjective rating deceleration tests

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

Fig 4 BTV causes for a disc brake

there is a contribution from the dynamic de ection ofthe disc due to external forces such as tyre forces andunbalances

One of the problems with brake analysis is that it isnecessary to solve coupled de ection and temperature eld problems with combined de ection and thermalload Commercially available FE programs can handlepure mechanical or pure thermal problems Brooks et al[8 ] introduced a two-dimensional (ie axisymmetrical )combined thermal and mechanical method of hot band-ing simulation of a disc brake The basic idea is to switchbetween de ection and temperature eld calculationseach of which can be made in commercial FE programssuch as ABAQUS The FE model takes into account thetime-dependent change in the contact area A similarconcept was developed by Kao et al [7 ] Both three-dimensional (necessary to be able to model buckling)and axisymmetric models have been used to study thein uence of pad design parameters on thermal padcracking as well as to simulate thermoelastic bucklingand its coupling to TEI and thermal DTV

Thermoelastic simulation of brake components underrealistic conditions involves massive central processingunit computational e ort and data storage [7 ] This isespecially the case when simulating slow decelerations(ie sti problems) with long duration timesUnfortunately it is this type of braking that generatesthe most pronounced hot spots There are various waysto make the simulation more e ective

1 Circumferential variations of the instantaneous discsurface conditions and geometry can be neglectedHowever when studying brake judder problems thecircumferential variations are essential

2 A specially dedicated contact element can be used toderive the frictional force and heat generated at theinterface [3 37]

3 Solving the coupled eld problems simultaneously(see reference [14]) is more accurate and e ectiveHowever since it relies on a Newton-type methodfrom the 1990s the algorithms are not yet included incommercial FE programs

4 A three-dimensional hybrid method which combinesfast Fourier transform (FFT) techniques withFE methods has been developed by Floquet and

427ASPECTS OF DISC BRAKE JUDDER

Dubourg [38] The application of the Fourier trans-form (on a space variable) has the e ect of reducingthe dimension of the problem The variable is trans-formed into a discrete parameter the frequency andthe corresponding partial derivatives are removedThe method can handle geometrically periodic butnon-axisymmetric solids such as ventilated discbrakes

5 The FE method can be applied directly to a pertur-bation method [39] The basic idea is not to solve thetransient problem but to consider the conditionsunder which a small perturbation in the temperature eld can grow exponentially in time The method isapplicable to transient processes as long as the contactarea does not change with time However the contactarea does change considerably with time duringbraking

6 A pad model composed of springndashdamper elementscan be used [22]

For vented discs and aluminium discs in particularwhere the air ow is important computational uiddynamics (CFD) is a useful tool CFD is used by somerotor manufacturers to increase air ow [26 40] In amarket survey [26 ] many companies saw the potentialof combining FE analysis and CFD to gain more accu-rate temperature predictions However this wouldrequire enormous computational e orts

As an alternative to CFD the convective cooling maybe estimated by approximative methods On a ventedrotor there are two di erent types of convective coolingair cross- ow over the rotor surface and air pumped owthrough the vents [3 ] Brake rotor vane ow relationsto estimate the heat convective transfer coe cient havelong been used in brake system thermal modellingCurrently two relations are recognized for ventilateddisc air ow those of Sisson and Limpert [30] Analternative is to approximate the convective heat transfercoe cient from the Nusselt modulus [31 32] and tocorrect it with empirically determined factors

52 E ects of BTVBPV

A few research projects have focused on the e ect ofbrake vibrations in the vehicle despite the fact that ithas been qualitatively described in the literature Crollaand Lang [41] Haigh et al [17] and many others havedescribed how brake judder rises to a maximum whenpassing through more or less distinct speeds So far theevaluation of brake judder has been done with a subjec-tive method using a scale from 1 to 10 but hardly anysimulations of brake judder in a vehicle have been car-ried out Brake judder problems have traditionally beensolved by use of trial and error rather than systematicmethods

In the literature there are a few sensitivity studies butin practice no lsquotruersquo simulations The di erence in that

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

lsquotruersquo simulations needs to be evaluated in the time planeThis involves not only a model of the vibration source(BTVBPV) and the vehicle structure and linkage (reson-ances and transfer) but also modelling of the brakingevent (frequency sweep braking conditions) see Fig 5

Straightforward integration of di erential equationswithout intelligent variable transformations or assump-tions using an ordinary equation-solving algorithmdesigned for non-sti problems (eg RungendashKutta) isnot an e cient way of dealing with this type of problemThe simulation will take an unnecessarily long time(hours or days) fail or crash Also the algorithms usedby commercial mechanics programs such as ADAMSare slow and ine cient if one wishes to follow a wholebraking event Hence the maximal vibration levels willbecome largely overestimated at nite braking timesHowever these types of programs are useful for quasi-static sensitivity analysis

521 Sensitivity analysis

Applying the system approach the solution to the judderproblem will be to build robustness into the vehicle andthereby to make it less sensitive to BTVBPV The systemof Engel et al [25] consists of ve di erent steps namelythe brake disc caliper and pad tyre and hubndashbearingunit wheel knuckle and nally the steering system Thereis also feedback between some steps in the outlinedmodel

An attempt to model numerically the vehicle responseto BTV was made by Kim et al [35] using MBS analysisof a similar vehicle structure The modelling of the sus-pension system used in the calculations was howevernot described Similar analyses are often carried out inthe automotive industry but seldom is the modellingdescribed in the literature However the model ofAugsburg et al [11] was described in detail

(a) calliper as two masses connected by a spring (rep-resenting the calliper sti ness in the forendashaftdirection)

(b) brake pads as springs(c) brake piston by a mass(d) hydraulic system as volume accumulating elements

The transfer path from the vibration source to thedriverrsquos contact points can be qualitatively investigatedby simultaneous measurements of accelerations atvarious position such as wheel carrier steering tie rod

Fig 5 The frequency sweep approach

428 H JACOBSSON

steering wheel etc [13] The sampled signals can be usedto generate the transfer functions between di erentpoints [9 36 ] The technique can be used to describeboth the brake excitation and the transfer functions thatcharacterize vehicle sensibility

The amplitude functions [23] can be seen as gen-eralized transfer functions They can be used to classifythe braking event as well as the corresponding vibrationsin the vehicle An advantage of the amplitude functionover the transfer function technique is that it works formuch higher decelerations since it does not rely on theFFT The method also determines the eigenfrequencieswith higher accuracy since it takes into account thetime delay of the maximal ampli cation caused by the nite deceleration and the inertias of the system If thistime delay is not considered the eigenfrequencies willbe systematically underestimated especially at highdecelerations

The analysis can be made in the frequency plane pro-vided that the braking starts above a certain limit often10ndash30 per cent above the critical speed [5 ] The deceler-ation clearly lsquocutsrsquo the maximal vibration amplitudeespecially at low damping Already at relative dampinglevels of the order of 1 per cent the transient analysis(including the frequency sweep) is needed for the rst-order judder except for in nitesimally smalldeclerations

Aviles et al [42] studied a braking event with slowlydecreasing speed and frequency However the con-clusion was drawn that the peak of the vibration ampli-tude at a certain vehicle speed was altogether an e ectof the negative frictionndashvelocity slope introduced in themodel The e ect of the frequency sweep was neveranalysed separately The calculations were made in thefrequency domain

522 Judder vibration simulation

Most of the analyses and measurements of judder aremade for braking with constant speed ie constant rev-olution frequency of the wheel as well as constant press-ure and temperature An argument is that it is easier tomeasure and analyse vibrations on the basis of this pre-scription Another bene t of measuring at constantspeed is e cient data analysis in the frequency domainHowever in a real braking situation the frequency isnot constant

There is a dynamic ampli cation of the brake torqueand pressure variations when passing through orcoming close to a critical speed of a vehicle Thevibration starts when the braking force is applied andreaches a maximal amplitude at a certain speed It iscontinued until low speed if the braking force is continu-ously applied This is the typical behaviour of a forcedvibration with relatively constant source amplitude butwith a sweeping frequency Fig 6

A two-DOF rotorndashstator model [24] with a linearly

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

decreasing disc speed possesses the main characteristicsof judder as shown in Fig 6 Before analysis the de ec-tion angles of rotordisc and statorcaliper respectivelywere split into vibration-free parts W and WC (rotationstatic de ection) and the superimposed vibrations QD andQ

C respectively The shape of the amplitude function Edescribes the relative vibration level QC (second timederivative of QC) almost exactly All parameters of therotorndashstator model can be experimentally generated

A full-vehicle model [5 ] shows the same lsquojudder behav-iourrsquo but can also explain some other e ects It is morecomplicated since it demands information about thewind speed slip etc

It is generally accepted that the front wheel suspensionof passenger cars has a rigid body forendashaft vibrationmode resonance in the frequency range 10ndash20 Hz andthat this resonance is responsible for lower-order judderat corresponding velocities This corresponds to a maxi-mal amplitude of the vibrations at a critical vehicle speedof between 60 and 140 kmh for the rst-order judderThe second-order judder will have a corresponding criti-cal speed (because of the same resonance) of between 30and 70 kmh The present vehicle had a resonance near14 Hz corresponding to a rst-order critical speed of95 kmh

The following possibilities for reducing judder werefound [5 ]

(a) decreased BTV andor BPV which will lead backto the cause approach

(b) increased relative stator mass and inertia momentcompared with the rotor

(c) increased damping(d) lighter braking(e) higher eigenfrequency

A lighter vehicle and a smaller wheel radius decrease thejudder problems [5 ] A reduction of the vehicle mass willalso decrease the thermal DTV and hotspots and reducethe risk of thermal cracking provided that the thermalcapacity of the disc remains the same A lighter stator(ie strut and eventually disc) will tend to increase thejudder problems since the ampli cation of BTV willbecome larger

6 FUTURE

The eld of low frequency braking induced vibrations isstill characterized by confusion Much research is neededin this area before a fairly clear picture becomes appar-ent The author nds the following areas especiallyinteresting

(a) simulation of BTV generation combining wear andTEI (wear especially hot and high pressure weartends to counteract the TEI process)

(b) the groan phenomenon(c) friction lms

429ASPECTS OF DISC BRAKE JUDDER

Fig 6 Model and corresponding brake judder simulation versus measurement

(d) the TEI process and its connection to thermoelasticbuckling

(e) studying wheel suspension vibration modes duringbrake-on conditions

(f ) the relation between BTV and simultaneous vari-ations in geometry (DTV run-out equivalent brakeradius) and friction coe cient

(g) prediction of BTV level and order for speci eddesign parameters and braking conditions

(h) developing models for simulation of vibration levelsin a vehicle at speci ed BTV

Generally in brake judder analysis it is recommendedto split the investigations into two parts

1 Analysis of sources of irregularities such as DTV etcThis involves thermomechanical FE analysis of thebrake components or dynamometer tests These typesof calculations are extremely time demanding

2 Analysis of the e ect of the irregularities in the vehicleIf the disturbances (which may be output from FEanalysis or dynamometer measurements) are given asfunctions of time very fast simulation can be carriedout by means of the amplitude function techniquedescribed in this work

The amplitude function technique is still at an earlystage but there are no di culties in principle involvedin using it to analyse multiple mass system models ofa whole vehicle Such models would be useful in deter-mining design criteria of brake components andsuspensions etc

REFERENCES

1 Hulten J Drum brake squeal PhD thesis Machine andVehicle Design Chalmers University of TechnologyGoteborg 1998

2 Inoue H Analysis of brake judder caused by thermal defor-mation of brake disc rotors In Proceedings 21st FISITACongress Belgrade 1986 pp 213ndash219 paper 865131

3 Kao T K Richmond J W and Moore M W The appli-

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

cation of predictive techniques to study thermo-elasticinstability of brakes In Proceedings of the Twelfth AnnualBrake Colloquium and Engineering Display AtlantaGeorgia 1984 SAE paper 942087

4 Jacobsson H Frequency sweep approach to brake judderpart A the brake judder phenomenon Classi cation andproblem approach Licentiate thesis Chalmers Universityof Technology Goteborg 1998

5 Jacobbson H Brake judder Thesis Chalmers Universityof Technology Goteborg 2001

6 Abdelhamid M K Creep groan of disc brakes InProceedings Noise and Vibration Conference TraverseCity Michigan 1995 pp 396ndash400 SAE paper 951282

7 Kao T K Richmond J W and Douarre A Brake dischot spotting and thermal judder an experimental and niteelement study Int J Veh Des 2000 23(34) 276ndash296

8 Brooks P C Barton D Crolla D A Lang A M andSchafer D R A study of disc brake judder using a fullycoupled thermo-mechanical nite element model InProceedings 25th FISITA Congress Beijing 1994pp 340ndash349 SAE paper 945042

9 Abdelhamid M K Brake judder analysis case studies SAEpaper 972027 1997

10 Kreitlow W Schrodter F and Matthai H Vibration andlsquohumrsquo of disc brakes under load SAE paper 850079 SAETrans Sect 1 1985 431ndash437

11 Augsburg K Brunner H and Grochowicz JUntersuchungen zum Rubbelverhalten von Pkw-Schwimmsattelbremser Automobiltechnische Zeitschrift1999 101

12 Stringham W Jank P Pfeifer J and Wang A Brakeroughnessmdashdisc brake torque variation rotor distortionand vehicle response SAE paper 930803 SAE TransSect 6 1993 1235ndash1247

13 Engel H G Bachman Th Eichhorn U and Saame ChDynamical behavior of brake-disc geometry as cause ofbrake judder In Proceedings EAEC Fourth InternationalConference on Vehicle and Tra c System TechnologyStrasbourg France 1993 Vol 1 pp 456ndash481

14 Thuresson D Thermomechanical analysis of frictionbrakes In Proceedings of the Eighteenth Annual BrakeColloquium and Engineering Display 2000 Vol P-358pp 149ndash159 SAE paper 2000-01-2775

15 Richmond J W Kao T K and Moore M W The devel-opment of computationalanalysis techniques for disc brake

430 H JACOBSSON

pad design In Proceedings Advances in AutomotiveBraking Technology Design Analysis and MaterialDevelopments 1996 (Institution of Mechanical Engineers)

16 Abendroth H Ste en T Falter W and Heidt RInvestigation of CV rotor cracking test procedures InBrakes 2000 International Conference on AutomotiveBrakingmdashTechnologies for the 21st Century 2000pp 149ndash162 (Professional Engineering PublishingLondon)

17 Haigh M J Smales H and Abe M Vehicle judder underdynamic braking caused by disc thickness variation InProceedings Braking of Road Vehicles London 1993pp 247ndash258 IMechE paper C44402293

18 Borjesson M Eriksson P Kuylenstierna C NilssonP H and Hermansson T The role of friction lms inautomotive brakes subjected to low contact forces InProceedings Braking of Road Vehicles London 1993pp 259ndash267 IMechE paper C444026

19 Wirth A and Whitaker R Developments in cast iron tech-nology In Proceedings Advances in Automotive BrakingTechnology Design Analysis and Material DevelopmentsLeeds UK 1996 (Institution of Mechanical Engineers)

20 Thoms E Disc brakes for heavy vehicles In ProceedingsBraking of Road Vehicles London 1988 pp 133ndash137IMechE paper C46488

21 Aviles R Hennequet G Hernandez A and Llorente L ILow frequency vibrations in disc brakes at high car speedPart I experimental approach Int J Veh Des 199516(6) 542ndash555

22 Ste en T and Bruns R Hotspotsbildung bei Pkw-Bremsscheiben Automobiltechnische Zeitschrift 1998100 408ndash413

23 Jacobsson H Analysis of brake judder by use of amplitudefunctions In Proceedings of SAE Noise and VibrationConference 1999 SAE paper 1999-01-1779

24 Jacobsson H Wheel suspension related disc brake judderIn Proceedings ASME Design Engineering TechnicalConferences Sacramento California 1997 VIB-4165

25 Engel H G Hassiotis V and Tiemann R Systemapproach to brake judder In Proceedings 25th FISITACongress Beijing 1994 Vol 1 pp 332ndash339 paper 945041

26 Martin R H and Bowron S Composite materials in trans-port friction applications In Brakes 2000 InternationalConference on Automotive BrakingmdashTechnologies for the21st Century 2000 pp 207ndash216 (Professional EngineeringPublishing London)

27 de Vries A and Wagner M The brake judder phenom-enon SAE Trans Sect 6 1992 101 652ndash660

28 Palmer B B and Weintraub M H The role of engineeredcashew particles on performance In Brakes 2000International Conference on Automotive BrakingmdashTechnologies for the 21st Century 2000 pp 185ndash195(Professional Engineering Publishing London)

29 Koetniyom S Brooks P C and Barton D C Finite

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

element prediction of inelastic strain accumulation in cast-iron brake rotors In Brakes 2000 InternationalConferenceon Automotive BrakingmdashTechnologies for the 21st Century2000 pp 139ndash148 (Professional Engineering PublishingLondon)

30 Hudson M D and Ruhl R L Ventilated brake rotor air ow investigation SAE paper 971033 1997

31 Grieve D G Barton D A Crolla D A Chapman J Land Buckingham J T Alternative brake disc materials InProceedingsAdvances in Automotive Braking TechnologyDesign Analysis and Material Developments Leeds UK1996 (Institution of Mechanical Engineers)

32 Grieve D G Barton D C Crolla D A and BuckinghamJ K Design of a lightweight automotive brake disc using nite element and Taguchi techniques Proc Instn MechEngrs Part D J Automobile Engineering 1998 212245ndash254

33 Krupka R and Kienzle A Fiber reinforced ceramic com-posite for brake discs In Proceeding of the EighteenthAnnual Brake Colloquium and Engineering Display 2000Vol P-358 pp 67ndash69 SAE paper 2000-01-2761

34 Bosworth R Investigations of secondary ride aspects ofsteering wheel vibration (shimmy and judder) using Taguchimethodology In Proceedings AUTOTECH 89 London1989 IMechE paper C3999

35 Kim M-G Jeong H-I and Yoo W-S Sensitivity analy-sis of chassis system to improve shimmy and brake juddervibration on steering wheel SAE Special Publication 11361996 pp 59ndash70

36 Abdelhamid M K Brake judder analysis using transferfunctions In Proceedings SAE Brake Colloquium TempeArizona 1997 pp 5ndash9 SAE paper 973018

37 Kao T K Richmond J W and Moore M WComputational analysis of pad performance InProceedings Braking of Road Vehicles 1993 paperC44402793 (Institution of Mechanical Engineers)

38 Floquet A and Dubourg M-C Realistic braking operationsimulation of ventilated disc brakes Trans ASMEJ Tribology July 1996 118 466ndash472

39 Du S Zagrodzki P Barber J R and Hulbert G MFinite element analysis of frictionally excited thermoelasticinstability J Thermal Stresses 1997 20 185ndash201

40 Daudi A R Dickerson W E and Narain M Hayesrsquoincreased air ow rotor design In Proceedings SecondInternational Seminar on Automotive Braking RecentDevelopments and Future Trends Leeds UK 1998pp 127ndash143 (Institution of Mechanical Engineers)

41 Crolla D A and Lang A M Brake noise and vibrationmdashthe state of the art Vehicle Tribology Tribology SeriesVol 18 1991 (Elsevier) pp 165ndash174

42 Aviles R Hennequet G Amezua E and Vallejo J Lowfrequency vibrations in disc brakes at high car speedPart II mathematical model and simulation Int J VehDes 1995 16(6) 556ndash569

Page 2: Aspects of disc brake judder - Universiti Teknologi Malaysiaarahim/jacobsson.pdf · 419 Aspects of disc brake judder HJacobsson* Machine and Vehicle Systems, Chalmers University of

420 H JACOBSSON

11 Traditional classi cation

Traditionally brake noise and vibrations are classi edaccording to their dominant frequencies with thosebelow a certain limit (100 500 or 1000 Hz) being calledjudder or hum Above this limit the vibrations areregarded as high frequency noise including squeal Themain disadvantage with this classi cation is that onephysical phenomenon can be split into two di erentclasses and at the same time fundamentally di erentphenomena will be included in the same term Howeverthe classi cation is related to the way in which the phen-omena are experienced by the driver and passengers

Thermal or hot judder is caused by the following

(a) thermal deformation for example coning andwaving of a disc

(b) uneven thermal expansion(c) phase transformation of disc material

Cold judder is caused by geometrical irregularities dueto machining mounting uneven wear uneven corrosionor uneven friction lm generation Normally judderconsists of a combination of cold and hot judder andhence the terms lsquohotrsquo and lsquocoldrsquo are somewhat mis-leading For example a high disc thickness variation(DTV) level may indeed induce friction level variationssince a locally thicker area of the disc will be exposed toa locally higher contact pressure and become hotterFurthermore such areas will become hotter and expandmore [2 3 ]

12 Phenomenological classi cation

The classi cation of braking-induced noise andvibrations suggested by the author is as follows [4 5 ]

1 Forced vibrations These include brake juddervibration and its associated brake noise called hum

2 Vibrations primarily caused by friction characteristicsThe group includes creep groan and dynamic groanvibration and their associated moan noise Creepgroan which is related to stickndashslip motion is causedby a static coe cient of friction that is higher thanthe dynamic one Dynamic groan on the other handis an instability phenomenon occurring as a result ofa speci c type of frictionndashvelocity characteristic usu-ally known as lsquonegative dampingrsquo Groan is discussedin more detail in references [4 ] and [5 ]

3 Vibrations primarily caused by resonances of the brakecomponents Noises in this class are squeal and wirebrush noises etc The corresponding vibrationspropagate through the air rather than through thevehicle structure

This is similar to the classi cation by Abdelhamid [6 ]One of the bene ts of the classi cation is that it iscoupled to the way of modelling the vibrations Anotherbene t is the connection to appropriate experimental

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

tools In addition the classi cation separates the twofundamentally di erent brake vibrations judder andgroan from each other

The vibration frequency of brake judder is directlyproportional to the wheel speed and therefore also tothe velocity of the vehicle Hence it is common to relatethe judder frequencies to the wheel speed for examplefrequencies at twice the number of wheel rotationsper second are called second-order judder Two maingroups of judder are identi ed [4 ] according to theirvibration order

1 Normally there are some more or less static(ie lsquocoldrsquo) pronounced deviations from the idealgeometry of the lower order (LO) type with avibration order from 1 to 5 The disturbed geometrywill result in uneven contact pressure and temperature elds as well as uneven thermal expansion especiallyat long or repeated brake applications [7 ] Hence thestatic deviations will be reinforced during braking

2 Superimposed on the LO variations of for instancea brake disc there are higher-order geometricalandor frictional deviations with low static ampli-tudes However especially for long low intensitybrakings the temperature and pressure eld willgradually become more and more localized as thebraking continues Hot bands are generated on thepad and disc leading to a number (usually 6ndash20 [8 ] )of hot spots on the disc The dominant judder orderand the actual number of hot spots normally coincide[9 10] As for LO judder an uneven heating of thedisc will cause a temporary DTV and also often shapedeformation (eg coning and buckling) At su c-iently high local temperatures remaining discolouredareas [10] with locally di erent speci c volume wearand friction characteristics will occur

When de ning brake judder as braking-induced forcedvibrations the upper limit of its frequency is determinedby the maximal vehicle speed the wheel radius andjudder order For instance let a passenger car brakefrom 170 kmh down to zero Then the 20th-order juddervibrations will sweep from 500 Hz while the upper limitof the rst-order vibration will be only 25 Hz owingto the maximum revolution speed of the wheelsConsequently resonances above 100 Hz will not inpractice be excited by the rst-order disturbances

2 PHYSICAL EFFECTS CAUSING BRAKETORQUE VARIATION AND BRAKE PRESSUREVARIATION

There are several physical e ects causing brake torquevariation (BTV) and brake pressure variation (BPV )and hence judder The ones discussed in this work (seeFig 1) are geometrical irregularities uneven wear of thebrake rotor uneven friction lm between rotor and

421ASPECTS OF DISC BRAKE JUDDER

Fig 1 Physical e ects causing BTVBPV

lining uneven heating of the rotor uneven pressure dis-tribution the friction characteristic and friction leveland external forces The di erent e ects or sources aregenerally not independent of each other There arestrong couplings between geometrical irregularitiesuneven wear and uneven heating

21 Geometrical irregularities

For disc brake judder the most important geometricalproperties are DTV and run-out of the disc In additionto geometrical irregularities of a static or remainingnature there can be a dynamic and reversible variationof disc geometry (thermal DTV etc)

Because of the oating calliper normally used inmodern disc brakes an increase of the pad normal forceon one side is compensated (at least partly) by a decreaseon the opposite side Hence de ections from idealshapes such as run-out etc do not contribute to BTVand BPV (and judder) except at the extreme values wherenon-linearities inertia forces and unbalances becomeimportant [11] However run-out can indirectly causevibrations by the increase of DTV due to uneven wear[8 ]

The magnitude of the run-out is determined by discmachining and mounting tolerances bearing clearancesand disc distortion during braking In addition externalforces such as tyre forces and unbalances a ect therun-out

A DTV of 15 iacutem (measured in cold conditions) isobservable as brake judder to an experienced driver ina sensitive car under certain braking conditionsConsequently to achieve safety margins the initial DTVlevel varies between 6 and 10 iacutem for most manufacturers[11 12] On a long time scale DTV is known to growasymptotically from its initial value to a maximumbecause of wear [13] the higher the initial disc run-outthe faster the DTV growth [13] DTV can also be causedby uneven corrosion of the rotor when parked since thepads partly lsquoprotectrsquo the disc surface

Kao et al [7 ] found a considerable thermal coningand thermal growth of DTV ( rst and second order)when measuring the instantaneous disc surface de ectionduring a brake stop using capacitive transducers TheDTV level (and hence BTV ) increased linearly with timeduring braking The brake application time [7 11] and

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

how often the braking is repeated [2 ] are also importantfactors for brake judder to develop

Experimental investigations [11 12] have shown thatthe instantaneous DTV is the primary contributor todisc brake judder on passenger cars DTV is a verycomplex phenomenon consisting of the following

1 Initial DTV arises from manufacturing andmounting

2 Wear and cleaning processes produce DTV3 There are more or less permanent areas with locally

di erent speci c volume friction and wear propertiescaused by phase transformations when locallyoverheating the disc This DTV remains after coolingof the disc

4 Temporary thermal growth of DTV takes placeduring each brake application owing to unevenheating and localized contact area and pressureie thermoelastic instability (TEI) processes [7 11]Thermal expansion due to a local temperature di er-ence of 200ndash300 degC directly causes a di erence ofDTV amplitude of the order of 10 iacutem ConsequentlyDTV increases with braking time especially forlsquohardrsquo pads

5 Uneven friction lm thickness may contribute sev-eral iacutem

6 Uneven corrosion and deposition of heated padmaterial on the disc could occur

22 Uneven wear

O -brake wear sometimes called lsquocold erosionrsquo iscoupled to DTV and can lead to lsquocold judderrsquo Brakediscs can develop DTV because the brake pads in theo -brake mode lightly touch the rotors in some sectorsbut not at all in others resulting in non-uniform wearThe o -brake wear may be caused by disc run-out andcan be reduced by increasing the distance that the cal-liper piston is retarded after application of the brakethe so-called rollback [8 ]

The DTV created by pad contact has two phases gen-eration and cleaning The ratio between generation andcleaning is in uenced by the selection of the frictionmaterial Friction materials which generate DTV in theo -brake mode will usually have the ability to eliminateDTV by a higher disc wear in the on-brake mode Inparticular an increase of the high temperature and press-ure pad wear could be used to reduce hot spot develop-ment by counteracting localization of the contactpressure on the friction surface [3 14] Howeverincreased wear will also speed up the motion of the hotbands [3 14 15] which is believed to be a cause ofthermal fatigue of the disc [16 ]

Careful drivers may experience brake judder morequickly than sporty drivers since slow application of thebrakes at low brake pad pressures prevents lsquocleaningrsquoof the disc Discs causing BTV and hence judder can

422 H JACOBSSON

sometimes be cured by making several hard stopsHowever the relative amount of motorway driving is amuch more important factor for DTV generation thanthe driving style [17]

During long brake applications wear especially padwear becomes substantial Generally wear results in amore even temperature distribution and lower tempera-ture maxima [14] However the high wear will move thecontact surface (ie moving hot spotsbands) whichmight contribute to thermal fatigue of discs Simulations[3 14] and measurements [18] show that an increase ofthe hot pad wear could be used to reduce hot spot devel-opment by counteracting localization of the contactpressure on the friction surface

23 Uneven friction lms

The third-body layer friction lm or transfer lm is a lm a few iacutem thick consisting of material produced byattrition [19] The ferrous particles produced by the wearof the cast-iron disc are transformed and oxidized by theatmospheric oxygen and deposited as a greyndashblack layeron the braking surface of the disc This layer togetherwith the corresponding layers on the pads determinesthe frictional behaviour of the brake

When hot brakes are applied on a stationary vehiclesticking of the pad to the rotor can occur At veryhigh temperatures perhaps 500 degC the melted frictionmaterial can be lsquoburntrsquo into the disc

24 Uneven heating

Thermal deformation of a disc consists of the following

1 Waving or warping of the disc2 Coning of the disc This can lead to high run-out

Inoue [2 ] found that thermal run-out can be avoidedby a disc design that is stable to coning

3 Uneven thermal expansion A temperature di erenceof 250 degC which is not unusual causes a DTV ampli-tude of 10 iacutem [2 ] Even if no visible hot spots (orblue areas caused by phase transformations) occurduring braking this phenomenon is still importantfor brake judder occurrence by causing temporarygrowth of geometrical disturbances

4 Phase transformation5 Deposition of heated pad material on the disc

In disc brakes the rubbing speed and the frictional heatgenerated increase with the radius Hence the tempera-ture and pressure elds tend to be localized into band(s)near the outer radius even if the pad and disc are initiallyperfectly at and parallel with evenly distributedcoe cient of friction [3 ] The hot bands or rings maydevelop into hot spots as the rotor buckles [7 20] Themaximum disc temperature of the spots increases withpad sti ness [15] Measurements show that a local hot

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

spot can have a temperature of over 700ndash800 degC and thatthere can be a temperature di erence of over 300ndash600 degCbetween the hottest and the coldest local areas of thesame disc [2 3 21] Hot spots are usually more or lessbut not fully uniformly distributed [2 21]

The thicker areas of a brake disc become hotter thanthe thinner ones which causes thermal deformation ofthe brake disc (thermal coning and buckling [2 7 ] ) andalso uneven thermal expansion ie thermal DTV Theprocess can become unstable and is then de ned as aTEI TEI leads to a more and more localized brake press-ure and temperature eld as the braking continues Inthe extreme case especially at higher order (6ndash20) discdisturbances the disc will crack

Studies by Ste en and Bruns [22] have led to theexpected result that small dimensions (ie disc and padthickness and diameter of friction ring) increase the tend-ency towards hot spotting Also a higher revolutionspeed (ie higher energy level ) of the disc was found toincrease the hot spot generation

It is the temperature gradients and not the increase inabsolute temperature level that cause the increasingjudder level during long or repeated braking see refer-ence [23] The temperature gradients cause temporaryDTV owing to uneven thermal expansion of the discmaterial [2 ] The DTV level (and hence BTV ) increasesoften more or less linearly with time while braking [7 ]especially for lsquohardrsquo pads and at the outer radius Hencethe brake application time [7 11] and how often thebraking is repeated [23] are important factors for brakejudder development Hot spotting and thermal DTVbecome worse for low torque long duration applicationsthan for high torque ones [15] A light long applicationtime (20ndash45 s) gives substantially higher temperatureand pressure gradients than heavy shorter ones (3ndash4 s)[7 15 16 ]

Also a higher revolution speed (ie higher energylevel ) of the disc was found to increase the hot spotgeneration [11 22] In addition the localization process(and the correlated thermal DTV ) is particularly pro-nounced at high speed above 100 kmh [11] This mightbe explained by the fact that the TEI process demandsa minimal lsquocriticalrsquo speed to develop As a consequenceof this it is essential to test friction material at speedsabove the limit 100 kmh (60 milesh) which is usuallystandard

25 Uneven pressure

In a conventional disc brake analysis the interfacepressure is assumed to be either constant (ie constantpressure assumption) or inversely proportional to theradius (ie constant wear assumption) However underdynamic braking conditions the contact area and brakepressure distribution varies continuously with timebecause of

423ASPECTS OF DISC BRAKE JUDDER

(a) thermal distortion arising from the friction heatgeneration

(b) mechanical distortion due to the applied actuationforce

(c) wear of the friction pair material and formation offriction lm

(d) initial DTV and run-out

Conventional brake analysis gives an even temperatureand pressure distribution as well as maximal tempera-ture pressure and stress levels which are much lowerthan their actual peak values [3 ]

26 Friction characteristics and level

The variation of friction with velocity has historicallybeen regarded as the source of all kinds of braking-induced vibrations including brake judder Jacobsson[24] analytically showed that even a constant coe cientof friction may generate judder No speci c frictioncharacteristics are needed for the phenomenon to occurHowever a negative brake fade or a friction coe cientthat increases with brake pressure may increase the prob-lems To achieve a given brake torque a pad materialwith a lower friction coe cient needs a higher brakepressure level This induces more evenly distributedpressure and temperature elds on the contact surface[16 ] Consequently a reduction of the friction coe cientlevel decreases the judder problems and at the same timereduces the crack probability Also the relation betweenBTV and BPV is a ected by the absolute friction levelThis is because BTV is proportional to the coe cient offriction [11] while BPV is independent of friction

27 External forces

Unbalances and tyre force variations may induce a tum-bling rigid body motion of the disc as a result of elas-ticities of the wheel hub and bearing unit [13] Suchdynamic de ections cause the same type of vibrations(with a frequency that is an integer multiple of the instan-taneous brake rotor frequency) as geometrical irregu-larities Hence they may contribute to judder The wheelhubndashbearing design and sti ness contribute to themagnitude of the disc deviation [11] When the judderis due to the tyre force variation or imbalance the termbrake judder is misleading because it suggests that theexcitation force originates from the brakes

3 VEHICLE COMPONENTS

BTV and BPV are usually produced by geometrical orother irregularities of the brake components and furthertransmitted to and ampli ed in the wheel suspension andhydraulic system as outlined in Fig 2

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

Fig 2 Brake vibrations are transmitted to di erent vehiclecomponents

Theoretically a spatial friction coe cient variationaround the disc may occur without corresponding vari-ation of the hydraulic pressure (ie BPV) Howeverphysical e ects that generate friction variation such asphase transformation uneven transfer lm generationcorrosion etc will also generate geometrical irregularit-ies (DTV etc) with normal force variation and BPVHence it is often meaningful to consider BTV and BPVas an entity However their relative magnitudes arefunctions of the actual friction coe cient

Independently of how and where the disturbance isproduced it is transmitted and ampli ed in the sameway The wheel suspension ampli es the vibrationsespecially the frequencies near its eigenfrequenciesUsually there is a second ampli cation of the vibrationin for instance the steering system

An obvious way of reducing the judder is to reducethe BTVBPV which is the source of the vibrations Thistraditional approach will place the focus on the brakecomponents ie pad and disc

An alternative strategy especially with severe steeringwheel vibrations is to reduce the ampli cation eitherthe primary ampli cation in the wheel suspension ora relevant secondary ampli cation at the steeringsystem This can e ectively be achieved by introductionof the brake-by-wire and steering-by-wire techniquesSimulations and measurements by Jacobsson [23] dem-onstrate that the ampli cation is relatively low in thesubcritical region as indicated in Fig 6 Hence thevibration is reduced if the eigenfrequencies of the compo-nents in the transfer path are shifted above the frequencyrange of the rst wheel order excitation (above 25ndash30 Hzor vehicle speeds above 170ndash200 kmh) which was sug-gested by Engel et al [25] Also modal separation ofeigenfrequencies in the transfer path should be ensured

31 Pads

When developing or choosing a pad material more than20 properties are considered [26 ] Everything from den-sity melting point strength (tensile compressive ex-ural and shear) machinability environmental impactsqueal probability etc should be considered Withrespect to judder properties of interest are sti ness

424 H JACOBSSON

coe cient of friction coe cient of thermal expansionthermal conductivity corrosion and porosity

The most important pad property for judder reductionis the compressive sti ness [11] The BTV level can varyby a factor of 2ndash3 (with the same DTV ) depending onthe pad composition [21 27] The pad compressivesti ness should also be as low as possible to promoteuniform contact pressure [3 8 ] and to avoid TEI pro-cesses such as hot banding and thermal DTV This will atthe same time reduce eventual brake squeal problems [1 ]

The relation between the BTVBPV level and the padsti ness of modern passenger cars is non-linear [11] Inparticular during compression the material becomesprogressively sti er as the load is applied [15] For theseprogressive materials the same DTV level will result ina higher BTV level for hard than for light brakings

To achieve a good lsquopedal feelrsquo and positive retractionthe sti ness should be reasonably high and progressiveGenerally the desired zone is narrow and a deviationon either side might lead to complaints [28] Progressivebrake pads ie traditional composite pads [15] su erfrom high sensitivity to increases in the DTV level seereference [5 ] A linear pad compression characteristicwould not require as high safety margins for increasesfrom the initial DTV (thermal DTV and long-time wearDTV etc) as the progressive pad does In other wordslinear pads are likely to accept higher disc thickness tol-erances than the 10 iacutem DTV The new lsquobrake-by-wirersquotechnique o ers other ways of achieving lsquoa good brakefeelrsquo than a high and progressive pad compressionsti ness

32 Disc

The thermal stability of the disc shape is in uenced bythe quality of the material and the heat treatment beforemachining as well as the basic design of the disc rotorDisc design variants that are more or less stable toconing have been discussed in references [2 3 22 29]Thermal stability problems can be minimized by choos-ing high carbon disc materials and introducing thermalstress relief treatment into the machining cycle [13]

Some of the thermally most important properties ofdisc brakes are as follows [3 30]

1 Thermal capacitance (ie density and speci c heat) isthe ability to store heat Initially on braking a sig-ni cant amount of frictional heat is stored [3 ] andconsequently during short brakings the thermalcapacitance dominates

2 Heat dissipation becomes important at long brakingtimes (above 2ndash3 min [3 ]) ie drag braking or moun-tain descent braking However it also a ects thediscrsquos ability to recover thermally between stops [31]Convection accounts for more than 90 per cent of allheat dissipation for most braking conditions [3 ]whereby radiation is almost negligible The heat

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

transfer coe cient due to convection varies as thevehiclersquos velocity to the power 08 [3 ]

3 Thermal conductivity is the ability to redistributethermal energy During long low intensity brakingsthe peak temperature depends largely on the discmaterialrsquos conductivity [32] During short brakingshowever the thermal conductivity has little e ect

4 Thermal expansion coe cient (ie related to localiz-ation of friction contact due to the thermal defor-mation) a ects the tendency towards hot spotting andthermal DTV generation Temperature gradients of abrake disc cause temporary DTV owing to uneventhermal expansion of the material

Ventilated brake discs are widely used for their weightsavings and additional convective heat transferHowever they may increase judder problems byinducing an uneven temperature eld around the discOver short ( less than a few minutes) and high speedstops thermal capacity is the most important thermalproperty which is why a solid disc (with its higher mass)runs cooler than the vented design [3 31] In mountaindescent braking the disc brake temperatures mayincrease considerably when the vents are removed [31]

Aluminium especially SiC-reinforced Al metal matrixcomposite materials requires a lower operating tempera-ture than grey cast iron (around 450 degC) [32 ] Becausethe material su ers from low thermal capacity it canonly be used for relatively light passenger cars say below1000 kg The introduction of aluminium composite discsor pure aluminium covered by a composite layer willprobably increase judder problems because of the highcoe cient of thermal expansion and the low heatcapacity [22] The high thermal conductivity has there-fore relatively little in uence on the hot spot and thermalDTV generation

However there are composite materials that mighthave the ability to reduce judder namely ceramic mate-rials An example is a short bre reinforced SiC material(CSiC ) which has recently been introduced in sportscars and high speed trains [33] Judder is avoidedbecause of the low coe cient of thermal expansion andlow wear Also the low elastic modulus should promoteuniform contact and reduce thermal DTV and hot spotsThe excellent resistance to thermal damage of the mate-rial makes it suitable for disc brakes of heavy vehicleswhere cracking of the normally used cast-iron disc is aproblem However the high cost of the material excludesapplications in the ordinary family car segment

33 Vehicle structure

The front suspension is designed to admit largevibrations in the vertical direction However there is avibration in the forendashaft direction [24 27] which isrelated to brake judder as well as a proportional angularvibration [24] Brake judder is strongly related to the

425ASPECTS OF DISC BRAKE JUDDER

suspension design and the forendashaft exibility is a domi-nating parameter [27] Stringham et al [12] stated thatthe sti ness of the lower arm bushing is the most in u-ential parameter It was found to a ect signi cantly theeigenfrequency of the suspension system in the forendashaftdirection Bosworth [34] studied the suspension struc-ture in more detail and found the following factorscontrolling the judder

(a) tie rod bushmdashradial and forendashaft sti ness(b) lower arm bushmdashforendashaft sti ness(c) anti-roll barmdashvertical sti ness

In particular the sti ness of the lower arm bushing isimportant since it signi cantly a ects the eigenfre-quency of the suspension system in the forendashaft direction[12 34 35] Higher eigenfrequencies which will reducejudder problems such as steering wheel vibrations maybe achieved either by higher sti ness of the rubber bush-ings or by a reduced value of the modal mass and inertiaof the wheel suspension see Jacobsson [5 ]

However modern suspensions have become more andmore exible in the forendashaft direction because of theintroduction of radial tyres [27] This is necessary inorder to absorb the longitudinal vibrations from the sti belt of the tyres

Note that it is essential to measure the eigenfrequencyand damping in the brake-on mode When the brakeswere not applied the experimental vehicle was found tohave a signi cantly higher eigenfrequency (18 Hz com-pared with 138 Hz) and a lower equivalent viscousdamping factor (007 compared with 009) than meas-ured under the same braking conditions see reference[24] Also the instantaneous centre of motion of the strutchanges with the brake pressure level [5 ] It movedgradually towards the wheel axle as the brake pressureincreased

4 TIME-SCALES

Brake judder depends strongly on the braking historyon the short as well as on the long time-scale There arethree di erent time-scales involved in brake judder

(a) revolution time of the wheel(b) brake application time or the time between two

brakings(c) lifetime of brake components

Traditionally in brake design only the long-time changesare considered In recent years changes during brakinghave also been focused on The generation of localizedcontact area pressure and temperature gradients suchas hot banding has been studied It is found that DTVis a dynamic property that may change considerablyduring a brake application [7 11]

Changes within the time of a wheel revolution arenormally not included primarily because of di culties

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

in making numerical and signal analysis when using con-ventional techniques However the amplitude functiontechnique [23] handles sinusoidal variations of the braketorque with wheel revolution

5 APPROACH

The way of looking at and describing a problem is herecalled the problem approach It is a theoretical abstrac-tion lsquoa conception of the worldrsquo including a model andits system limits The problem approach determineswhich physical e ects can be studied and also states thetime and space scale The chosen problem approach willhave consequences for how to analyse the problem aswell as for the type of solution that will be found It alsodetermines which type of analytical and experimentaltool is the most appropriate

When studying the literature on brake judder it isclear that two fundamentally di erent approaches are inuse namely the cause and e ect approaches While thee ect approach focuses on the source of the vibrationsin the form of amplitude and vibrational order of theBTV andor BPV the cause approach deals with anumber of physical e ects such as wear and heatingsee Fig 3

The e ect approach can be further split into di erentapproaches [4 ]

1 The system approach examines how a model of thevehicle or the wheel suspension together withBTVBPV generates judder The braking process isusually represented by a constant frequency whichcan be parametrically changed It is used mostly inexperimental analysis [13 25 36 ] Also some quasi-static analyses may be found in literature Kim et al[35] used multibody system (MBS) analysis of amodel with 12 degrees of freedom (DOF ) of aMcPherson-type suspension exposed to rst-orderjudder

2 The frequency sweep approach examines how thebraking process itself (including a frequency sweep)together with the BTVBPV generates judder Thevehicle structure can be represented by a resonancecorresponding to the actual critical speed [23]

3 The human response approach studies the e ects ofjudder on one speci c test driver or on an average

Fig 3 Problem approaches

426 H JACOBSSON

person placed in a speci c vehicle Alternatively thehuman response to judder could be thought of as athird level where the judder level and frequencytogether with the weight size and place of the personin the vehicle etc are the input

Some approaches are listed in Table 1 together withrelated analytical and experimental methods and toolsfound in the literature [4 ] For instance FE analysis isthe natural choice when studying BTV generation bymeans of for instance the TEI process For the e ectapproach where the BTV can be represented by a sinus-oidal brake torque disturbance it is instead the vehicleor relevant parts thereof that should be modelled ThenMBS analysis (commercial programs are ADAMSDADS etc) is more relevant especially for lowfrequency judder (say below 50 Hz)

In experimental brake judder studies bench testing aswell as road testing are used Advantages of bench test-ing [11] are good reproducibility of the testing con-ditions more accurate measurements higher sensitivityof measurements lower cost and less time consumption[37] Disadvantages are that cooling conditions are nottaken into account as well as the in uence of othermachine elements and systems which will a ect thetransmission of BTV in the vehicle (tyres wheel sus-pension steering) [11] In road testing the speci cproblem occurs that the level of BTVBPV cannot becontrolled during a brake application This problemmay be handled by measuring BTVBPV instead oftrying to control it by constant conditions such as speedtemperature pressure etc see references [9 23]

51 Causes of BTVBPV

Traditionally the source of the BTVBPV has beenfocused on It is a ected by a combination of the di er-ent physical e ects discussed in section 2 Disc run-outand DTV which are geometrical irregularities of thedisc directly cause normal force variations and henceBTVBPV see Fig 4 Furthermore the TEI process gen-erates hot spots and sometimes remaining discolouredareas with locally di erent speci c volume and wearproperties which may aggravate the vibrations Finally

Table 1 Approaches and corresponding methods

Approach Methods and tools

Cause approach (FE) analysis nite di erence dynamometertribometer drag braking thermal imagingX-rays

System approach MBS analysis Fourier methods modal analysisTaguchi methodology road testsspectrograms

Frequency sweep Time plane analysis road tests involvingapproach deceleration waterfall analysis order

tracking ABS and capacitive transducersHuman response Subjective rating deceleration tests

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

Fig 4 BTV causes for a disc brake

there is a contribution from the dynamic de ection ofthe disc due to external forces such as tyre forces andunbalances

One of the problems with brake analysis is that it isnecessary to solve coupled de ection and temperature eld problems with combined de ection and thermalload Commercially available FE programs can handlepure mechanical or pure thermal problems Brooks et al[8 ] introduced a two-dimensional (ie axisymmetrical )combined thermal and mechanical method of hot band-ing simulation of a disc brake The basic idea is to switchbetween de ection and temperature eld calculationseach of which can be made in commercial FE programssuch as ABAQUS The FE model takes into account thetime-dependent change in the contact area A similarconcept was developed by Kao et al [7 ] Both three-dimensional (necessary to be able to model buckling)and axisymmetric models have been used to study thein uence of pad design parameters on thermal padcracking as well as to simulate thermoelastic bucklingand its coupling to TEI and thermal DTV

Thermoelastic simulation of brake components underrealistic conditions involves massive central processingunit computational e ort and data storage [7 ] This isespecially the case when simulating slow decelerations(ie sti problems) with long duration timesUnfortunately it is this type of braking that generatesthe most pronounced hot spots There are various waysto make the simulation more e ective

1 Circumferential variations of the instantaneous discsurface conditions and geometry can be neglectedHowever when studying brake judder problems thecircumferential variations are essential

2 A specially dedicated contact element can be used toderive the frictional force and heat generated at theinterface [3 37]

3 Solving the coupled eld problems simultaneously(see reference [14]) is more accurate and e ectiveHowever since it relies on a Newton-type methodfrom the 1990s the algorithms are not yet included incommercial FE programs

4 A three-dimensional hybrid method which combinesfast Fourier transform (FFT) techniques withFE methods has been developed by Floquet and

427ASPECTS OF DISC BRAKE JUDDER

Dubourg [38] The application of the Fourier trans-form (on a space variable) has the e ect of reducingthe dimension of the problem The variable is trans-formed into a discrete parameter the frequency andthe corresponding partial derivatives are removedThe method can handle geometrically periodic butnon-axisymmetric solids such as ventilated discbrakes

5 The FE method can be applied directly to a pertur-bation method [39] The basic idea is not to solve thetransient problem but to consider the conditionsunder which a small perturbation in the temperature eld can grow exponentially in time The method isapplicable to transient processes as long as the contactarea does not change with time However the contactarea does change considerably with time duringbraking

6 A pad model composed of springndashdamper elementscan be used [22]

For vented discs and aluminium discs in particularwhere the air ow is important computational uiddynamics (CFD) is a useful tool CFD is used by somerotor manufacturers to increase air ow [26 40] In amarket survey [26 ] many companies saw the potentialof combining FE analysis and CFD to gain more accu-rate temperature predictions However this wouldrequire enormous computational e orts

As an alternative to CFD the convective cooling maybe estimated by approximative methods On a ventedrotor there are two di erent types of convective coolingair cross- ow over the rotor surface and air pumped owthrough the vents [3 ] Brake rotor vane ow relationsto estimate the heat convective transfer coe cient havelong been used in brake system thermal modellingCurrently two relations are recognized for ventilateddisc air ow those of Sisson and Limpert [30] Analternative is to approximate the convective heat transfercoe cient from the Nusselt modulus [31 32] and tocorrect it with empirically determined factors

52 E ects of BTVBPV

A few research projects have focused on the e ect ofbrake vibrations in the vehicle despite the fact that ithas been qualitatively described in the literature Crollaand Lang [41] Haigh et al [17] and many others havedescribed how brake judder rises to a maximum whenpassing through more or less distinct speeds So far theevaluation of brake judder has been done with a subjec-tive method using a scale from 1 to 10 but hardly anysimulations of brake judder in a vehicle have been car-ried out Brake judder problems have traditionally beensolved by use of trial and error rather than systematicmethods

In the literature there are a few sensitivity studies butin practice no lsquotruersquo simulations The di erence in that

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

lsquotruersquo simulations needs to be evaluated in the time planeThis involves not only a model of the vibration source(BTVBPV) and the vehicle structure and linkage (reson-ances and transfer) but also modelling of the brakingevent (frequency sweep braking conditions) see Fig 5

Straightforward integration of di erential equationswithout intelligent variable transformations or assump-tions using an ordinary equation-solving algorithmdesigned for non-sti problems (eg RungendashKutta) isnot an e cient way of dealing with this type of problemThe simulation will take an unnecessarily long time(hours or days) fail or crash Also the algorithms usedby commercial mechanics programs such as ADAMSare slow and ine cient if one wishes to follow a wholebraking event Hence the maximal vibration levels willbecome largely overestimated at nite braking timesHowever these types of programs are useful for quasi-static sensitivity analysis

521 Sensitivity analysis

Applying the system approach the solution to the judderproblem will be to build robustness into the vehicle andthereby to make it less sensitive to BTVBPV The systemof Engel et al [25] consists of ve di erent steps namelythe brake disc caliper and pad tyre and hubndashbearingunit wheel knuckle and nally the steering system Thereis also feedback between some steps in the outlinedmodel

An attempt to model numerically the vehicle responseto BTV was made by Kim et al [35] using MBS analysisof a similar vehicle structure The modelling of the sus-pension system used in the calculations was howevernot described Similar analyses are often carried out inthe automotive industry but seldom is the modellingdescribed in the literature However the model ofAugsburg et al [11] was described in detail

(a) calliper as two masses connected by a spring (rep-resenting the calliper sti ness in the forendashaftdirection)

(b) brake pads as springs(c) brake piston by a mass(d) hydraulic system as volume accumulating elements

The transfer path from the vibration source to thedriverrsquos contact points can be qualitatively investigatedby simultaneous measurements of accelerations atvarious position such as wheel carrier steering tie rod

Fig 5 The frequency sweep approach

428 H JACOBSSON

steering wheel etc [13] The sampled signals can be usedto generate the transfer functions between di erentpoints [9 36 ] The technique can be used to describeboth the brake excitation and the transfer functions thatcharacterize vehicle sensibility

The amplitude functions [23] can be seen as gen-eralized transfer functions They can be used to classifythe braking event as well as the corresponding vibrationsin the vehicle An advantage of the amplitude functionover the transfer function technique is that it works formuch higher decelerations since it does not rely on theFFT The method also determines the eigenfrequencieswith higher accuracy since it takes into account thetime delay of the maximal ampli cation caused by the nite deceleration and the inertias of the system If thistime delay is not considered the eigenfrequencies willbe systematically underestimated especially at highdecelerations

The analysis can be made in the frequency plane pro-vided that the braking starts above a certain limit often10ndash30 per cent above the critical speed [5 ] The deceler-ation clearly lsquocutsrsquo the maximal vibration amplitudeespecially at low damping Already at relative dampinglevels of the order of 1 per cent the transient analysis(including the frequency sweep) is needed for the rst-order judder except for in nitesimally smalldeclerations

Aviles et al [42] studied a braking event with slowlydecreasing speed and frequency However the con-clusion was drawn that the peak of the vibration ampli-tude at a certain vehicle speed was altogether an e ectof the negative frictionndashvelocity slope introduced in themodel The e ect of the frequency sweep was neveranalysed separately The calculations were made in thefrequency domain

522 Judder vibration simulation

Most of the analyses and measurements of judder aremade for braking with constant speed ie constant rev-olution frequency of the wheel as well as constant press-ure and temperature An argument is that it is easier tomeasure and analyse vibrations on the basis of this pre-scription Another bene t of measuring at constantspeed is e cient data analysis in the frequency domainHowever in a real braking situation the frequency isnot constant

There is a dynamic ampli cation of the brake torqueand pressure variations when passing through orcoming close to a critical speed of a vehicle Thevibration starts when the braking force is applied andreaches a maximal amplitude at a certain speed It iscontinued until low speed if the braking force is continu-ously applied This is the typical behaviour of a forcedvibration with relatively constant source amplitude butwith a sweeping frequency Fig 6

A two-DOF rotorndashstator model [24] with a linearly

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

decreasing disc speed possesses the main characteristicsof judder as shown in Fig 6 Before analysis the de ec-tion angles of rotordisc and statorcaliper respectivelywere split into vibration-free parts W and WC (rotationstatic de ection) and the superimposed vibrations QD andQ

C respectively The shape of the amplitude function Edescribes the relative vibration level QC (second timederivative of QC) almost exactly All parameters of therotorndashstator model can be experimentally generated

A full-vehicle model [5 ] shows the same lsquojudder behav-iourrsquo but can also explain some other e ects It is morecomplicated since it demands information about thewind speed slip etc

It is generally accepted that the front wheel suspensionof passenger cars has a rigid body forendashaft vibrationmode resonance in the frequency range 10ndash20 Hz andthat this resonance is responsible for lower-order judderat corresponding velocities This corresponds to a maxi-mal amplitude of the vibrations at a critical vehicle speedof between 60 and 140 kmh for the rst-order judderThe second-order judder will have a corresponding criti-cal speed (because of the same resonance) of between 30and 70 kmh The present vehicle had a resonance near14 Hz corresponding to a rst-order critical speed of95 kmh

The following possibilities for reducing judder werefound [5 ]

(a) decreased BTV andor BPV which will lead backto the cause approach

(b) increased relative stator mass and inertia momentcompared with the rotor

(c) increased damping(d) lighter braking(e) higher eigenfrequency

A lighter vehicle and a smaller wheel radius decrease thejudder problems [5 ] A reduction of the vehicle mass willalso decrease the thermal DTV and hotspots and reducethe risk of thermal cracking provided that the thermalcapacity of the disc remains the same A lighter stator(ie strut and eventually disc) will tend to increase thejudder problems since the ampli cation of BTV willbecome larger

6 FUTURE

The eld of low frequency braking induced vibrations isstill characterized by confusion Much research is neededin this area before a fairly clear picture becomes appar-ent The author nds the following areas especiallyinteresting

(a) simulation of BTV generation combining wear andTEI (wear especially hot and high pressure weartends to counteract the TEI process)

(b) the groan phenomenon(c) friction lms

429ASPECTS OF DISC BRAKE JUDDER

Fig 6 Model and corresponding brake judder simulation versus measurement

(d) the TEI process and its connection to thermoelasticbuckling

(e) studying wheel suspension vibration modes duringbrake-on conditions

(f ) the relation between BTV and simultaneous vari-ations in geometry (DTV run-out equivalent brakeradius) and friction coe cient

(g) prediction of BTV level and order for speci eddesign parameters and braking conditions

(h) developing models for simulation of vibration levelsin a vehicle at speci ed BTV

Generally in brake judder analysis it is recommendedto split the investigations into two parts

1 Analysis of sources of irregularities such as DTV etcThis involves thermomechanical FE analysis of thebrake components or dynamometer tests These typesof calculations are extremely time demanding

2 Analysis of the e ect of the irregularities in the vehicleIf the disturbances (which may be output from FEanalysis or dynamometer measurements) are given asfunctions of time very fast simulation can be carriedout by means of the amplitude function techniquedescribed in this work

The amplitude function technique is still at an earlystage but there are no di culties in principle involvedin using it to analyse multiple mass system models ofa whole vehicle Such models would be useful in deter-mining design criteria of brake components andsuspensions etc

REFERENCES

1 Hulten J Drum brake squeal PhD thesis Machine andVehicle Design Chalmers University of TechnologyGoteborg 1998

2 Inoue H Analysis of brake judder caused by thermal defor-mation of brake disc rotors In Proceedings 21st FISITACongress Belgrade 1986 pp 213ndash219 paper 865131

3 Kao T K Richmond J W and Moore M W The appli-

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

cation of predictive techniques to study thermo-elasticinstability of brakes In Proceedings of the Twelfth AnnualBrake Colloquium and Engineering Display AtlantaGeorgia 1984 SAE paper 942087

4 Jacobsson H Frequency sweep approach to brake judderpart A the brake judder phenomenon Classi cation andproblem approach Licentiate thesis Chalmers Universityof Technology Goteborg 1998

5 Jacobbson H Brake judder Thesis Chalmers Universityof Technology Goteborg 2001

6 Abdelhamid M K Creep groan of disc brakes InProceedings Noise and Vibration Conference TraverseCity Michigan 1995 pp 396ndash400 SAE paper 951282

7 Kao T K Richmond J W and Douarre A Brake dischot spotting and thermal judder an experimental and niteelement study Int J Veh Des 2000 23(34) 276ndash296

8 Brooks P C Barton D Crolla D A Lang A M andSchafer D R A study of disc brake judder using a fullycoupled thermo-mechanical nite element model InProceedings 25th FISITA Congress Beijing 1994pp 340ndash349 SAE paper 945042

9 Abdelhamid M K Brake judder analysis case studies SAEpaper 972027 1997

10 Kreitlow W Schrodter F and Matthai H Vibration andlsquohumrsquo of disc brakes under load SAE paper 850079 SAETrans Sect 1 1985 431ndash437

11 Augsburg K Brunner H and Grochowicz JUntersuchungen zum Rubbelverhalten von Pkw-Schwimmsattelbremser Automobiltechnische Zeitschrift1999 101

12 Stringham W Jank P Pfeifer J and Wang A Brakeroughnessmdashdisc brake torque variation rotor distortionand vehicle response SAE paper 930803 SAE TransSect 6 1993 1235ndash1247

13 Engel H G Bachman Th Eichhorn U and Saame ChDynamical behavior of brake-disc geometry as cause ofbrake judder In Proceedings EAEC Fourth InternationalConference on Vehicle and Tra c System TechnologyStrasbourg France 1993 Vol 1 pp 456ndash481

14 Thuresson D Thermomechanical analysis of frictionbrakes In Proceedings of the Eighteenth Annual BrakeColloquium and Engineering Display 2000 Vol P-358pp 149ndash159 SAE paper 2000-01-2775

15 Richmond J W Kao T K and Moore M W The devel-opment of computationalanalysis techniques for disc brake

430 H JACOBSSON

pad design In Proceedings Advances in AutomotiveBraking Technology Design Analysis and MaterialDevelopments 1996 (Institution of Mechanical Engineers)

16 Abendroth H Ste en T Falter W and Heidt RInvestigation of CV rotor cracking test procedures InBrakes 2000 International Conference on AutomotiveBrakingmdashTechnologies for the 21st Century 2000pp 149ndash162 (Professional Engineering PublishingLondon)

17 Haigh M J Smales H and Abe M Vehicle judder underdynamic braking caused by disc thickness variation InProceedings Braking of Road Vehicles London 1993pp 247ndash258 IMechE paper C44402293

18 Borjesson M Eriksson P Kuylenstierna C NilssonP H and Hermansson T The role of friction lms inautomotive brakes subjected to low contact forces InProceedings Braking of Road Vehicles London 1993pp 259ndash267 IMechE paper C444026

19 Wirth A and Whitaker R Developments in cast iron tech-nology In Proceedings Advances in Automotive BrakingTechnology Design Analysis and Material DevelopmentsLeeds UK 1996 (Institution of Mechanical Engineers)

20 Thoms E Disc brakes for heavy vehicles In ProceedingsBraking of Road Vehicles London 1988 pp 133ndash137IMechE paper C46488

21 Aviles R Hennequet G Hernandez A and Llorente L ILow frequency vibrations in disc brakes at high car speedPart I experimental approach Int J Veh Des 199516(6) 542ndash555

22 Ste en T and Bruns R Hotspotsbildung bei Pkw-Bremsscheiben Automobiltechnische Zeitschrift 1998100 408ndash413

23 Jacobsson H Analysis of brake judder by use of amplitudefunctions In Proceedings of SAE Noise and VibrationConference 1999 SAE paper 1999-01-1779

24 Jacobsson H Wheel suspension related disc brake judderIn Proceedings ASME Design Engineering TechnicalConferences Sacramento California 1997 VIB-4165

25 Engel H G Hassiotis V and Tiemann R Systemapproach to brake judder In Proceedings 25th FISITACongress Beijing 1994 Vol 1 pp 332ndash339 paper 945041

26 Martin R H and Bowron S Composite materials in trans-port friction applications In Brakes 2000 InternationalConference on Automotive BrakingmdashTechnologies for the21st Century 2000 pp 207ndash216 (Professional EngineeringPublishing London)

27 de Vries A and Wagner M The brake judder phenom-enon SAE Trans Sect 6 1992 101 652ndash660

28 Palmer B B and Weintraub M H The role of engineeredcashew particles on performance In Brakes 2000International Conference on Automotive BrakingmdashTechnologies for the 21st Century 2000 pp 185ndash195(Professional Engineering Publishing London)

29 Koetniyom S Brooks P C and Barton D C Finite

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

element prediction of inelastic strain accumulation in cast-iron brake rotors In Brakes 2000 InternationalConferenceon Automotive BrakingmdashTechnologies for the 21st Century2000 pp 139ndash148 (Professional Engineering PublishingLondon)

30 Hudson M D and Ruhl R L Ventilated brake rotor air ow investigation SAE paper 971033 1997

31 Grieve D G Barton D A Crolla D A Chapman J Land Buckingham J T Alternative brake disc materials InProceedingsAdvances in Automotive Braking TechnologyDesign Analysis and Material Developments Leeds UK1996 (Institution of Mechanical Engineers)

32 Grieve D G Barton D C Crolla D A and BuckinghamJ K Design of a lightweight automotive brake disc using nite element and Taguchi techniques Proc Instn MechEngrs Part D J Automobile Engineering 1998 212245ndash254

33 Krupka R and Kienzle A Fiber reinforced ceramic com-posite for brake discs In Proceeding of the EighteenthAnnual Brake Colloquium and Engineering Display 2000Vol P-358 pp 67ndash69 SAE paper 2000-01-2761

34 Bosworth R Investigations of secondary ride aspects ofsteering wheel vibration (shimmy and judder) using Taguchimethodology In Proceedings AUTOTECH 89 London1989 IMechE paper C3999

35 Kim M-G Jeong H-I and Yoo W-S Sensitivity analy-sis of chassis system to improve shimmy and brake juddervibration on steering wheel SAE Special Publication 11361996 pp 59ndash70

36 Abdelhamid M K Brake judder analysis using transferfunctions In Proceedings SAE Brake Colloquium TempeArizona 1997 pp 5ndash9 SAE paper 973018

37 Kao T K Richmond J W and Moore M WComputational analysis of pad performance InProceedings Braking of Road Vehicles 1993 paperC44402793 (Institution of Mechanical Engineers)

38 Floquet A and Dubourg M-C Realistic braking operationsimulation of ventilated disc brakes Trans ASMEJ Tribology July 1996 118 466ndash472

39 Du S Zagrodzki P Barber J R and Hulbert G MFinite element analysis of frictionally excited thermoelasticinstability J Thermal Stresses 1997 20 185ndash201

40 Daudi A R Dickerson W E and Narain M Hayesrsquoincreased air ow rotor design In Proceedings SecondInternational Seminar on Automotive Braking RecentDevelopments and Future Trends Leeds UK 1998pp 127ndash143 (Institution of Mechanical Engineers)

41 Crolla D A and Lang A M Brake noise and vibrationmdashthe state of the art Vehicle Tribology Tribology SeriesVol 18 1991 (Elsevier) pp 165ndash174

42 Aviles R Hennequet G Amezua E and Vallejo J Lowfrequency vibrations in disc brakes at high car speedPart II mathematical model and simulation Int J VehDes 1995 16(6) 556ndash569

Page 3: Aspects of disc brake judder - Universiti Teknologi Malaysiaarahim/jacobsson.pdf · 419 Aspects of disc brake judder HJacobsson* Machine and Vehicle Systems, Chalmers University of

421ASPECTS OF DISC BRAKE JUDDER

Fig 1 Physical e ects causing BTVBPV

lining uneven heating of the rotor uneven pressure dis-tribution the friction characteristic and friction leveland external forces The di erent e ects or sources aregenerally not independent of each other There arestrong couplings between geometrical irregularitiesuneven wear and uneven heating

21 Geometrical irregularities

For disc brake judder the most important geometricalproperties are DTV and run-out of the disc In additionto geometrical irregularities of a static or remainingnature there can be a dynamic and reversible variationof disc geometry (thermal DTV etc)

Because of the oating calliper normally used inmodern disc brakes an increase of the pad normal forceon one side is compensated (at least partly) by a decreaseon the opposite side Hence de ections from idealshapes such as run-out etc do not contribute to BTVand BPV (and judder) except at the extreme values wherenon-linearities inertia forces and unbalances becomeimportant [11] However run-out can indirectly causevibrations by the increase of DTV due to uneven wear[8 ]

The magnitude of the run-out is determined by discmachining and mounting tolerances bearing clearancesand disc distortion during braking In addition externalforces such as tyre forces and unbalances a ect therun-out

A DTV of 15 iacutem (measured in cold conditions) isobservable as brake judder to an experienced driver ina sensitive car under certain braking conditionsConsequently to achieve safety margins the initial DTVlevel varies between 6 and 10 iacutem for most manufacturers[11 12] On a long time scale DTV is known to growasymptotically from its initial value to a maximumbecause of wear [13] the higher the initial disc run-outthe faster the DTV growth [13] DTV can also be causedby uneven corrosion of the rotor when parked since thepads partly lsquoprotectrsquo the disc surface

Kao et al [7 ] found a considerable thermal coningand thermal growth of DTV ( rst and second order)when measuring the instantaneous disc surface de ectionduring a brake stop using capacitive transducers TheDTV level (and hence BTV ) increased linearly with timeduring braking The brake application time [7 11] and

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

how often the braking is repeated [2 ] are also importantfactors for brake judder to develop

Experimental investigations [11 12] have shown thatthe instantaneous DTV is the primary contributor todisc brake judder on passenger cars DTV is a verycomplex phenomenon consisting of the following

1 Initial DTV arises from manufacturing andmounting

2 Wear and cleaning processes produce DTV3 There are more or less permanent areas with locally

di erent speci c volume friction and wear propertiescaused by phase transformations when locallyoverheating the disc This DTV remains after coolingof the disc

4 Temporary thermal growth of DTV takes placeduring each brake application owing to unevenheating and localized contact area and pressureie thermoelastic instability (TEI) processes [7 11]Thermal expansion due to a local temperature di er-ence of 200ndash300 degC directly causes a di erence ofDTV amplitude of the order of 10 iacutem ConsequentlyDTV increases with braking time especially forlsquohardrsquo pads

5 Uneven friction lm thickness may contribute sev-eral iacutem

6 Uneven corrosion and deposition of heated padmaterial on the disc could occur

22 Uneven wear

O -brake wear sometimes called lsquocold erosionrsquo iscoupled to DTV and can lead to lsquocold judderrsquo Brakediscs can develop DTV because the brake pads in theo -brake mode lightly touch the rotors in some sectorsbut not at all in others resulting in non-uniform wearThe o -brake wear may be caused by disc run-out andcan be reduced by increasing the distance that the cal-liper piston is retarded after application of the brakethe so-called rollback [8 ]

The DTV created by pad contact has two phases gen-eration and cleaning The ratio between generation andcleaning is in uenced by the selection of the frictionmaterial Friction materials which generate DTV in theo -brake mode will usually have the ability to eliminateDTV by a higher disc wear in the on-brake mode Inparticular an increase of the high temperature and press-ure pad wear could be used to reduce hot spot develop-ment by counteracting localization of the contactpressure on the friction surface [3 14] Howeverincreased wear will also speed up the motion of the hotbands [3 14 15] which is believed to be a cause ofthermal fatigue of the disc [16 ]

Careful drivers may experience brake judder morequickly than sporty drivers since slow application of thebrakes at low brake pad pressures prevents lsquocleaningrsquoof the disc Discs causing BTV and hence judder can

422 H JACOBSSON

sometimes be cured by making several hard stopsHowever the relative amount of motorway driving is amuch more important factor for DTV generation thanthe driving style [17]

During long brake applications wear especially padwear becomes substantial Generally wear results in amore even temperature distribution and lower tempera-ture maxima [14] However the high wear will move thecontact surface (ie moving hot spotsbands) whichmight contribute to thermal fatigue of discs Simulations[3 14] and measurements [18] show that an increase ofthe hot pad wear could be used to reduce hot spot devel-opment by counteracting localization of the contactpressure on the friction surface

23 Uneven friction lms

The third-body layer friction lm or transfer lm is a lm a few iacutem thick consisting of material produced byattrition [19] The ferrous particles produced by the wearof the cast-iron disc are transformed and oxidized by theatmospheric oxygen and deposited as a greyndashblack layeron the braking surface of the disc This layer togetherwith the corresponding layers on the pads determinesthe frictional behaviour of the brake

When hot brakes are applied on a stationary vehiclesticking of the pad to the rotor can occur At veryhigh temperatures perhaps 500 degC the melted frictionmaterial can be lsquoburntrsquo into the disc

24 Uneven heating

Thermal deformation of a disc consists of the following

1 Waving or warping of the disc2 Coning of the disc This can lead to high run-out

Inoue [2 ] found that thermal run-out can be avoidedby a disc design that is stable to coning

3 Uneven thermal expansion A temperature di erenceof 250 degC which is not unusual causes a DTV ampli-tude of 10 iacutem [2 ] Even if no visible hot spots (orblue areas caused by phase transformations) occurduring braking this phenomenon is still importantfor brake judder occurrence by causing temporarygrowth of geometrical disturbances

4 Phase transformation5 Deposition of heated pad material on the disc

In disc brakes the rubbing speed and the frictional heatgenerated increase with the radius Hence the tempera-ture and pressure elds tend to be localized into band(s)near the outer radius even if the pad and disc are initiallyperfectly at and parallel with evenly distributedcoe cient of friction [3 ] The hot bands or rings maydevelop into hot spots as the rotor buckles [7 20] Themaximum disc temperature of the spots increases withpad sti ness [15] Measurements show that a local hot

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

spot can have a temperature of over 700ndash800 degC and thatthere can be a temperature di erence of over 300ndash600 degCbetween the hottest and the coldest local areas of thesame disc [2 3 21] Hot spots are usually more or lessbut not fully uniformly distributed [2 21]

The thicker areas of a brake disc become hotter thanthe thinner ones which causes thermal deformation ofthe brake disc (thermal coning and buckling [2 7 ] ) andalso uneven thermal expansion ie thermal DTV Theprocess can become unstable and is then de ned as aTEI TEI leads to a more and more localized brake press-ure and temperature eld as the braking continues Inthe extreme case especially at higher order (6ndash20) discdisturbances the disc will crack

Studies by Ste en and Bruns [22] have led to theexpected result that small dimensions (ie disc and padthickness and diameter of friction ring) increase the tend-ency towards hot spotting Also a higher revolutionspeed (ie higher energy level ) of the disc was found toincrease the hot spot generation

It is the temperature gradients and not the increase inabsolute temperature level that cause the increasingjudder level during long or repeated braking see refer-ence [23] The temperature gradients cause temporaryDTV owing to uneven thermal expansion of the discmaterial [2 ] The DTV level (and hence BTV ) increasesoften more or less linearly with time while braking [7 ]especially for lsquohardrsquo pads and at the outer radius Hencethe brake application time [7 11] and how often thebraking is repeated [23] are important factors for brakejudder development Hot spotting and thermal DTVbecome worse for low torque long duration applicationsthan for high torque ones [15] A light long applicationtime (20ndash45 s) gives substantially higher temperatureand pressure gradients than heavy shorter ones (3ndash4 s)[7 15 16 ]

Also a higher revolution speed (ie higher energylevel ) of the disc was found to increase the hot spotgeneration [11 22] In addition the localization process(and the correlated thermal DTV ) is particularly pro-nounced at high speed above 100 kmh [11] This mightbe explained by the fact that the TEI process demandsa minimal lsquocriticalrsquo speed to develop As a consequenceof this it is essential to test friction material at speedsabove the limit 100 kmh (60 milesh) which is usuallystandard

25 Uneven pressure

In a conventional disc brake analysis the interfacepressure is assumed to be either constant (ie constantpressure assumption) or inversely proportional to theradius (ie constant wear assumption) However underdynamic braking conditions the contact area and brakepressure distribution varies continuously with timebecause of

423ASPECTS OF DISC BRAKE JUDDER

(a) thermal distortion arising from the friction heatgeneration

(b) mechanical distortion due to the applied actuationforce

(c) wear of the friction pair material and formation offriction lm

(d) initial DTV and run-out

Conventional brake analysis gives an even temperatureand pressure distribution as well as maximal tempera-ture pressure and stress levels which are much lowerthan their actual peak values [3 ]

26 Friction characteristics and level

The variation of friction with velocity has historicallybeen regarded as the source of all kinds of braking-induced vibrations including brake judder Jacobsson[24] analytically showed that even a constant coe cientof friction may generate judder No speci c frictioncharacteristics are needed for the phenomenon to occurHowever a negative brake fade or a friction coe cientthat increases with brake pressure may increase the prob-lems To achieve a given brake torque a pad materialwith a lower friction coe cient needs a higher brakepressure level This induces more evenly distributedpressure and temperature elds on the contact surface[16 ] Consequently a reduction of the friction coe cientlevel decreases the judder problems and at the same timereduces the crack probability Also the relation betweenBTV and BPV is a ected by the absolute friction levelThis is because BTV is proportional to the coe cient offriction [11] while BPV is independent of friction

27 External forces

Unbalances and tyre force variations may induce a tum-bling rigid body motion of the disc as a result of elas-ticities of the wheel hub and bearing unit [13] Suchdynamic de ections cause the same type of vibrations(with a frequency that is an integer multiple of the instan-taneous brake rotor frequency) as geometrical irregu-larities Hence they may contribute to judder The wheelhubndashbearing design and sti ness contribute to themagnitude of the disc deviation [11] When the judderis due to the tyre force variation or imbalance the termbrake judder is misleading because it suggests that theexcitation force originates from the brakes

3 VEHICLE COMPONENTS

BTV and BPV are usually produced by geometrical orother irregularities of the brake components and furthertransmitted to and ampli ed in the wheel suspension andhydraulic system as outlined in Fig 2

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

Fig 2 Brake vibrations are transmitted to di erent vehiclecomponents

Theoretically a spatial friction coe cient variationaround the disc may occur without corresponding vari-ation of the hydraulic pressure (ie BPV) Howeverphysical e ects that generate friction variation such asphase transformation uneven transfer lm generationcorrosion etc will also generate geometrical irregularit-ies (DTV etc) with normal force variation and BPVHence it is often meaningful to consider BTV and BPVas an entity However their relative magnitudes arefunctions of the actual friction coe cient

Independently of how and where the disturbance isproduced it is transmitted and ampli ed in the sameway The wheel suspension ampli es the vibrationsespecially the frequencies near its eigenfrequenciesUsually there is a second ampli cation of the vibrationin for instance the steering system

An obvious way of reducing the judder is to reducethe BTVBPV which is the source of the vibrations Thistraditional approach will place the focus on the brakecomponents ie pad and disc

An alternative strategy especially with severe steeringwheel vibrations is to reduce the ampli cation eitherthe primary ampli cation in the wheel suspension ora relevant secondary ampli cation at the steeringsystem This can e ectively be achieved by introductionof the brake-by-wire and steering-by-wire techniquesSimulations and measurements by Jacobsson [23] dem-onstrate that the ampli cation is relatively low in thesubcritical region as indicated in Fig 6 Hence thevibration is reduced if the eigenfrequencies of the compo-nents in the transfer path are shifted above the frequencyrange of the rst wheel order excitation (above 25ndash30 Hzor vehicle speeds above 170ndash200 kmh) which was sug-gested by Engel et al [25] Also modal separation ofeigenfrequencies in the transfer path should be ensured

31 Pads

When developing or choosing a pad material more than20 properties are considered [26 ] Everything from den-sity melting point strength (tensile compressive ex-ural and shear) machinability environmental impactsqueal probability etc should be considered Withrespect to judder properties of interest are sti ness

424 H JACOBSSON

coe cient of friction coe cient of thermal expansionthermal conductivity corrosion and porosity

The most important pad property for judder reductionis the compressive sti ness [11] The BTV level can varyby a factor of 2ndash3 (with the same DTV ) depending onthe pad composition [21 27] The pad compressivesti ness should also be as low as possible to promoteuniform contact pressure [3 8 ] and to avoid TEI pro-cesses such as hot banding and thermal DTV This will atthe same time reduce eventual brake squeal problems [1 ]

The relation between the BTVBPV level and the padsti ness of modern passenger cars is non-linear [11] Inparticular during compression the material becomesprogressively sti er as the load is applied [15] For theseprogressive materials the same DTV level will result ina higher BTV level for hard than for light brakings

To achieve a good lsquopedal feelrsquo and positive retractionthe sti ness should be reasonably high and progressiveGenerally the desired zone is narrow and a deviationon either side might lead to complaints [28] Progressivebrake pads ie traditional composite pads [15] su erfrom high sensitivity to increases in the DTV level seereference [5 ] A linear pad compression characteristicwould not require as high safety margins for increasesfrom the initial DTV (thermal DTV and long-time wearDTV etc) as the progressive pad does In other wordslinear pads are likely to accept higher disc thickness tol-erances than the 10 iacutem DTV The new lsquobrake-by-wirersquotechnique o ers other ways of achieving lsquoa good brakefeelrsquo than a high and progressive pad compressionsti ness

32 Disc

The thermal stability of the disc shape is in uenced bythe quality of the material and the heat treatment beforemachining as well as the basic design of the disc rotorDisc design variants that are more or less stable toconing have been discussed in references [2 3 22 29]Thermal stability problems can be minimized by choos-ing high carbon disc materials and introducing thermalstress relief treatment into the machining cycle [13]

Some of the thermally most important properties ofdisc brakes are as follows [3 30]

1 Thermal capacitance (ie density and speci c heat) isthe ability to store heat Initially on braking a sig-ni cant amount of frictional heat is stored [3 ] andconsequently during short brakings the thermalcapacitance dominates

2 Heat dissipation becomes important at long brakingtimes (above 2ndash3 min [3 ]) ie drag braking or moun-tain descent braking However it also a ects thediscrsquos ability to recover thermally between stops [31]Convection accounts for more than 90 per cent of allheat dissipation for most braking conditions [3 ]whereby radiation is almost negligible The heat

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

transfer coe cient due to convection varies as thevehiclersquos velocity to the power 08 [3 ]

3 Thermal conductivity is the ability to redistributethermal energy During long low intensity brakingsthe peak temperature depends largely on the discmaterialrsquos conductivity [32] During short brakingshowever the thermal conductivity has little e ect

4 Thermal expansion coe cient (ie related to localiz-ation of friction contact due to the thermal defor-mation) a ects the tendency towards hot spotting andthermal DTV generation Temperature gradients of abrake disc cause temporary DTV owing to uneventhermal expansion of the material

Ventilated brake discs are widely used for their weightsavings and additional convective heat transferHowever they may increase judder problems byinducing an uneven temperature eld around the discOver short ( less than a few minutes) and high speedstops thermal capacity is the most important thermalproperty which is why a solid disc (with its higher mass)runs cooler than the vented design [3 31] In mountaindescent braking the disc brake temperatures mayincrease considerably when the vents are removed [31]

Aluminium especially SiC-reinforced Al metal matrixcomposite materials requires a lower operating tempera-ture than grey cast iron (around 450 degC) [32 ] Becausethe material su ers from low thermal capacity it canonly be used for relatively light passenger cars say below1000 kg The introduction of aluminium composite discsor pure aluminium covered by a composite layer willprobably increase judder problems because of the highcoe cient of thermal expansion and the low heatcapacity [22] The high thermal conductivity has there-fore relatively little in uence on the hot spot and thermalDTV generation

However there are composite materials that mighthave the ability to reduce judder namely ceramic mate-rials An example is a short bre reinforced SiC material(CSiC ) which has recently been introduced in sportscars and high speed trains [33] Judder is avoidedbecause of the low coe cient of thermal expansion andlow wear Also the low elastic modulus should promoteuniform contact and reduce thermal DTV and hot spotsThe excellent resistance to thermal damage of the mate-rial makes it suitable for disc brakes of heavy vehicleswhere cracking of the normally used cast-iron disc is aproblem However the high cost of the material excludesapplications in the ordinary family car segment

33 Vehicle structure

The front suspension is designed to admit largevibrations in the vertical direction However there is avibration in the forendashaft direction [24 27] which isrelated to brake judder as well as a proportional angularvibration [24] Brake judder is strongly related to the

425ASPECTS OF DISC BRAKE JUDDER

suspension design and the forendashaft exibility is a domi-nating parameter [27] Stringham et al [12] stated thatthe sti ness of the lower arm bushing is the most in u-ential parameter It was found to a ect signi cantly theeigenfrequency of the suspension system in the forendashaftdirection Bosworth [34] studied the suspension struc-ture in more detail and found the following factorscontrolling the judder

(a) tie rod bushmdashradial and forendashaft sti ness(b) lower arm bushmdashforendashaft sti ness(c) anti-roll barmdashvertical sti ness

In particular the sti ness of the lower arm bushing isimportant since it signi cantly a ects the eigenfre-quency of the suspension system in the forendashaft direction[12 34 35] Higher eigenfrequencies which will reducejudder problems such as steering wheel vibrations maybe achieved either by higher sti ness of the rubber bush-ings or by a reduced value of the modal mass and inertiaof the wheel suspension see Jacobsson [5 ]

However modern suspensions have become more andmore exible in the forendashaft direction because of theintroduction of radial tyres [27] This is necessary inorder to absorb the longitudinal vibrations from the sti belt of the tyres

Note that it is essential to measure the eigenfrequencyand damping in the brake-on mode When the brakeswere not applied the experimental vehicle was found tohave a signi cantly higher eigenfrequency (18 Hz com-pared with 138 Hz) and a lower equivalent viscousdamping factor (007 compared with 009) than meas-ured under the same braking conditions see reference[24] Also the instantaneous centre of motion of the strutchanges with the brake pressure level [5 ] It movedgradually towards the wheel axle as the brake pressureincreased

4 TIME-SCALES

Brake judder depends strongly on the braking historyon the short as well as on the long time-scale There arethree di erent time-scales involved in brake judder

(a) revolution time of the wheel(b) brake application time or the time between two

brakings(c) lifetime of brake components

Traditionally in brake design only the long-time changesare considered In recent years changes during brakinghave also been focused on The generation of localizedcontact area pressure and temperature gradients suchas hot banding has been studied It is found that DTVis a dynamic property that may change considerablyduring a brake application [7 11]

Changes within the time of a wheel revolution arenormally not included primarily because of di culties

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

in making numerical and signal analysis when using con-ventional techniques However the amplitude functiontechnique [23] handles sinusoidal variations of the braketorque with wheel revolution

5 APPROACH

The way of looking at and describing a problem is herecalled the problem approach It is a theoretical abstrac-tion lsquoa conception of the worldrsquo including a model andits system limits The problem approach determineswhich physical e ects can be studied and also states thetime and space scale The chosen problem approach willhave consequences for how to analyse the problem aswell as for the type of solution that will be found It alsodetermines which type of analytical and experimentaltool is the most appropriate

When studying the literature on brake judder it isclear that two fundamentally di erent approaches are inuse namely the cause and e ect approaches While thee ect approach focuses on the source of the vibrationsin the form of amplitude and vibrational order of theBTV andor BPV the cause approach deals with anumber of physical e ects such as wear and heatingsee Fig 3

The e ect approach can be further split into di erentapproaches [4 ]

1 The system approach examines how a model of thevehicle or the wheel suspension together withBTVBPV generates judder The braking process isusually represented by a constant frequency whichcan be parametrically changed It is used mostly inexperimental analysis [13 25 36 ] Also some quasi-static analyses may be found in literature Kim et al[35] used multibody system (MBS) analysis of amodel with 12 degrees of freedom (DOF ) of aMcPherson-type suspension exposed to rst-orderjudder

2 The frequency sweep approach examines how thebraking process itself (including a frequency sweep)together with the BTVBPV generates judder Thevehicle structure can be represented by a resonancecorresponding to the actual critical speed [23]

3 The human response approach studies the e ects ofjudder on one speci c test driver or on an average

Fig 3 Problem approaches

426 H JACOBSSON

person placed in a speci c vehicle Alternatively thehuman response to judder could be thought of as athird level where the judder level and frequencytogether with the weight size and place of the personin the vehicle etc are the input

Some approaches are listed in Table 1 together withrelated analytical and experimental methods and toolsfound in the literature [4 ] For instance FE analysis isthe natural choice when studying BTV generation bymeans of for instance the TEI process For the e ectapproach where the BTV can be represented by a sinus-oidal brake torque disturbance it is instead the vehicleor relevant parts thereof that should be modelled ThenMBS analysis (commercial programs are ADAMSDADS etc) is more relevant especially for lowfrequency judder (say below 50 Hz)

In experimental brake judder studies bench testing aswell as road testing are used Advantages of bench test-ing [11] are good reproducibility of the testing con-ditions more accurate measurements higher sensitivityof measurements lower cost and less time consumption[37] Disadvantages are that cooling conditions are nottaken into account as well as the in uence of othermachine elements and systems which will a ect thetransmission of BTV in the vehicle (tyres wheel sus-pension steering) [11] In road testing the speci cproblem occurs that the level of BTVBPV cannot becontrolled during a brake application This problemmay be handled by measuring BTVBPV instead oftrying to control it by constant conditions such as speedtemperature pressure etc see references [9 23]

51 Causes of BTVBPV

Traditionally the source of the BTVBPV has beenfocused on It is a ected by a combination of the di er-ent physical e ects discussed in section 2 Disc run-outand DTV which are geometrical irregularities of thedisc directly cause normal force variations and henceBTVBPV see Fig 4 Furthermore the TEI process gen-erates hot spots and sometimes remaining discolouredareas with locally di erent speci c volume and wearproperties which may aggravate the vibrations Finally

Table 1 Approaches and corresponding methods

Approach Methods and tools

Cause approach (FE) analysis nite di erence dynamometertribometer drag braking thermal imagingX-rays

System approach MBS analysis Fourier methods modal analysisTaguchi methodology road testsspectrograms

Frequency sweep Time plane analysis road tests involvingapproach deceleration waterfall analysis order

tracking ABS and capacitive transducersHuman response Subjective rating deceleration tests

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

Fig 4 BTV causes for a disc brake

there is a contribution from the dynamic de ection ofthe disc due to external forces such as tyre forces andunbalances

One of the problems with brake analysis is that it isnecessary to solve coupled de ection and temperature eld problems with combined de ection and thermalload Commercially available FE programs can handlepure mechanical or pure thermal problems Brooks et al[8 ] introduced a two-dimensional (ie axisymmetrical )combined thermal and mechanical method of hot band-ing simulation of a disc brake The basic idea is to switchbetween de ection and temperature eld calculationseach of which can be made in commercial FE programssuch as ABAQUS The FE model takes into account thetime-dependent change in the contact area A similarconcept was developed by Kao et al [7 ] Both three-dimensional (necessary to be able to model buckling)and axisymmetric models have been used to study thein uence of pad design parameters on thermal padcracking as well as to simulate thermoelastic bucklingand its coupling to TEI and thermal DTV

Thermoelastic simulation of brake components underrealistic conditions involves massive central processingunit computational e ort and data storage [7 ] This isespecially the case when simulating slow decelerations(ie sti problems) with long duration timesUnfortunately it is this type of braking that generatesthe most pronounced hot spots There are various waysto make the simulation more e ective

1 Circumferential variations of the instantaneous discsurface conditions and geometry can be neglectedHowever when studying brake judder problems thecircumferential variations are essential

2 A specially dedicated contact element can be used toderive the frictional force and heat generated at theinterface [3 37]

3 Solving the coupled eld problems simultaneously(see reference [14]) is more accurate and e ectiveHowever since it relies on a Newton-type methodfrom the 1990s the algorithms are not yet included incommercial FE programs

4 A three-dimensional hybrid method which combinesfast Fourier transform (FFT) techniques withFE methods has been developed by Floquet and

427ASPECTS OF DISC BRAKE JUDDER

Dubourg [38] The application of the Fourier trans-form (on a space variable) has the e ect of reducingthe dimension of the problem The variable is trans-formed into a discrete parameter the frequency andthe corresponding partial derivatives are removedThe method can handle geometrically periodic butnon-axisymmetric solids such as ventilated discbrakes

5 The FE method can be applied directly to a pertur-bation method [39] The basic idea is not to solve thetransient problem but to consider the conditionsunder which a small perturbation in the temperature eld can grow exponentially in time The method isapplicable to transient processes as long as the contactarea does not change with time However the contactarea does change considerably with time duringbraking

6 A pad model composed of springndashdamper elementscan be used [22]

For vented discs and aluminium discs in particularwhere the air ow is important computational uiddynamics (CFD) is a useful tool CFD is used by somerotor manufacturers to increase air ow [26 40] In amarket survey [26 ] many companies saw the potentialof combining FE analysis and CFD to gain more accu-rate temperature predictions However this wouldrequire enormous computational e orts

As an alternative to CFD the convective cooling maybe estimated by approximative methods On a ventedrotor there are two di erent types of convective coolingair cross- ow over the rotor surface and air pumped owthrough the vents [3 ] Brake rotor vane ow relationsto estimate the heat convective transfer coe cient havelong been used in brake system thermal modellingCurrently two relations are recognized for ventilateddisc air ow those of Sisson and Limpert [30] Analternative is to approximate the convective heat transfercoe cient from the Nusselt modulus [31 32] and tocorrect it with empirically determined factors

52 E ects of BTVBPV

A few research projects have focused on the e ect ofbrake vibrations in the vehicle despite the fact that ithas been qualitatively described in the literature Crollaand Lang [41] Haigh et al [17] and many others havedescribed how brake judder rises to a maximum whenpassing through more or less distinct speeds So far theevaluation of brake judder has been done with a subjec-tive method using a scale from 1 to 10 but hardly anysimulations of brake judder in a vehicle have been car-ried out Brake judder problems have traditionally beensolved by use of trial and error rather than systematicmethods

In the literature there are a few sensitivity studies butin practice no lsquotruersquo simulations The di erence in that

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

lsquotruersquo simulations needs to be evaluated in the time planeThis involves not only a model of the vibration source(BTVBPV) and the vehicle structure and linkage (reson-ances and transfer) but also modelling of the brakingevent (frequency sweep braking conditions) see Fig 5

Straightforward integration of di erential equationswithout intelligent variable transformations or assump-tions using an ordinary equation-solving algorithmdesigned for non-sti problems (eg RungendashKutta) isnot an e cient way of dealing with this type of problemThe simulation will take an unnecessarily long time(hours or days) fail or crash Also the algorithms usedby commercial mechanics programs such as ADAMSare slow and ine cient if one wishes to follow a wholebraking event Hence the maximal vibration levels willbecome largely overestimated at nite braking timesHowever these types of programs are useful for quasi-static sensitivity analysis

521 Sensitivity analysis

Applying the system approach the solution to the judderproblem will be to build robustness into the vehicle andthereby to make it less sensitive to BTVBPV The systemof Engel et al [25] consists of ve di erent steps namelythe brake disc caliper and pad tyre and hubndashbearingunit wheel knuckle and nally the steering system Thereis also feedback between some steps in the outlinedmodel

An attempt to model numerically the vehicle responseto BTV was made by Kim et al [35] using MBS analysisof a similar vehicle structure The modelling of the sus-pension system used in the calculations was howevernot described Similar analyses are often carried out inthe automotive industry but seldom is the modellingdescribed in the literature However the model ofAugsburg et al [11] was described in detail

(a) calliper as two masses connected by a spring (rep-resenting the calliper sti ness in the forendashaftdirection)

(b) brake pads as springs(c) brake piston by a mass(d) hydraulic system as volume accumulating elements

The transfer path from the vibration source to thedriverrsquos contact points can be qualitatively investigatedby simultaneous measurements of accelerations atvarious position such as wheel carrier steering tie rod

Fig 5 The frequency sweep approach

428 H JACOBSSON

steering wheel etc [13] The sampled signals can be usedto generate the transfer functions between di erentpoints [9 36 ] The technique can be used to describeboth the brake excitation and the transfer functions thatcharacterize vehicle sensibility

The amplitude functions [23] can be seen as gen-eralized transfer functions They can be used to classifythe braking event as well as the corresponding vibrationsin the vehicle An advantage of the amplitude functionover the transfer function technique is that it works formuch higher decelerations since it does not rely on theFFT The method also determines the eigenfrequencieswith higher accuracy since it takes into account thetime delay of the maximal ampli cation caused by the nite deceleration and the inertias of the system If thistime delay is not considered the eigenfrequencies willbe systematically underestimated especially at highdecelerations

The analysis can be made in the frequency plane pro-vided that the braking starts above a certain limit often10ndash30 per cent above the critical speed [5 ] The deceler-ation clearly lsquocutsrsquo the maximal vibration amplitudeespecially at low damping Already at relative dampinglevels of the order of 1 per cent the transient analysis(including the frequency sweep) is needed for the rst-order judder except for in nitesimally smalldeclerations

Aviles et al [42] studied a braking event with slowlydecreasing speed and frequency However the con-clusion was drawn that the peak of the vibration ampli-tude at a certain vehicle speed was altogether an e ectof the negative frictionndashvelocity slope introduced in themodel The e ect of the frequency sweep was neveranalysed separately The calculations were made in thefrequency domain

522 Judder vibration simulation

Most of the analyses and measurements of judder aremade for braking with constant speed ie constant rev-olution frequency of the wheel as well as constant press-ure and temperature An argument is that it is easier tomeasure and analyse vibrations on the basis of this pre-scription Another bene t of measuring at constantspeed is e cient data analysis in the frequency domainHowever in a real braking situation the frequency isnot constant

There is a dynamic ampli cation of the brake torqueand pressure variations when passing through orcoming close to a critical speed of a vehicle Thevibration starts when the braking force is applied andreaches a maximal amplitude at a certain speed It iscontinued until low speed if the braking force is continu-ously applied This is the typical behaviour of a forcedvibration with relatively constant source amplitude butwith a sweeping frequency Fig 6

A two-DOF rotorndashstator model [24] with a linearly

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

decreasing disc speed possesses the main characteristicsof judder as shown in Fig 6 Before analysis the de ec-tion angles of rotordisc and statorcaliper respectivelywere split into vibration-free parts W and WC (rotationstatic de ection) and the superimposed vibrations QD andQ

C respectively The shape of the amplitude function Edescribes the relative vibration level QC (second timederivative of QC) almost exactly All parameters of therotorndashstator model can be experimentally generated

A full-vehicle model [5 ] shows the same lsquojudder behav-iourrsquo but can also explain some other e ects It is morecomplicated since it demands information about thewind speed slip etc

It is generally accepted that the front wheel suspensionof passenger cars has a rigid body forendashaft vibrationmode resonance in the frequency range 10ndash20 Hz andthat this resonance is responsible for lower-order judderat corresponding velocities This corresponds to a maxi-mal amplitude of the vibrations at a critical vehicle speedof between 60 and 140 kmh for the rst-order judderThe second-order judder will have a corresponding criti-cal speed (because of the same resonance) of between 30and 70 kmh The present vehicle had a resonance near14 Hz corresponding to a rst-order critical speed of95 kmh

The following possibilities for reducing judder werefound [5 ]

(a) decreased BTV andor BPV which will lead backto the cause approach

(b) increased relative stator mass and inertia momentcompared with the rotor

(c) increased damping(d) lighter braking(e) higher eigenfrequency

A lighter vehicle and a smaller wheel radius decrease thejudder problems [5 ] A reduction of the vehicle mass willalso decrease the thermal DTV and hotspots and reducethe risk of thermal cracking provided that the thermalcapacity of the disc remains the same A lighter stator(ie strut and eventually disc) will tend to increase thejudder problems since the ampli cation of BTV willbecome larger

6 FUTURE

The eld of low frequency braking induced vibrations isstill characterized by confusion Much research is neededin this area before a fairly clear picture becomes appar-ent The author nds the following areas especiallyinteresting

(a) simulation of BTV generation combining wear andTEI (wear especially hot and high pressure weartends to counteract the TEI process)

(b) the groan phenomenon(c) friction lms

429ASPECTS OF DISC BRAKE JUDDER

Fig 6 Model and corresponding brake judder simulation versus measurement

(d) the TEI process and its connection to thermoelasticbuckling

(e) studying wheel suspension vibration modes duringbrake-on conditions

(f ) the relation between BTV and simultaneous vari-ations in geometry (DTV run-out equivalent brakeradius) and friction coe cient

(g) prediction of BTV level and order for speci eddesign parameters and braking conditions

(h) developing models for simulation of vibration levelsin a vehicle at speci ed BTV

Generally in brake judder analysis it is recommendedto split the investigations into two parts

1 Analysis of sources of irregularities such as DTV etcThis involves thermomechanical FE analysis of thebrake components or dynamometer tests These typesof calculations are extremely time demanding

2 Analysis of the e ect of the irregularities in the vehicleIf the disturbances (which may be output from FEanalysis or dynamometer measurements) are given asfunctions of time very fast simulation can be carriedout by means of the amplitude function techniquedescribed in this work

The amplitude function technique is still at an earlystage but there are no di culties in principle involvedin using it to analyse multiple mass system models ofa whole vehicle Such models would be useful in deter-mining design criteria of brake components andsuspensions etc

REFERENCES

1 Hulten J Drum brake squeal PhD thesis Machine andVehicle Design Chalmers University of TechnologyGoteborg 1998

2 Inoue H Analysis of brake judder caused by thermal defor-mation of brake disc rotors In Proceedings 21st FISITACongress Belgrade 1986 pp 213ndash219 paper 865131

3 Kao T K Richmond J W and Moore M W The appli-

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

cation of predictive techniques to study thermo-elasticinstability of brakes In Proceedings of the Twelfth AnnualBrake Colloquium and Engineering Display AtlantaGeorgia 1984 SAE paper 942087

4 Jacobsson H Frequency sweep approach to brake judderpart A the brake judder phenomenon Classi cation andproblem approach Licentiate thesis Chalmers Universityof Technology Goteborg 1998

5 Jacobbson H Brake judder Thesis Chalmers Universityof Technology Goteborg 2001

6 Abdelhamid M K Creep groan of disc brakes InProceedings Noise and Vibration Conference TraverseCity Michigan 1995 pp 396ndash400 SAE paper 951282

7 Kao T K Richmond J W and Douarre A Brake dischot spotting and thermal judder an experimental and niteelement study Int J Veh Des 2000 23(34) 276ndash296

8 Brooks P C Barton D Crolla D A Lang A M andSchafer D R A study of disc brake judder using a fullycoupled thermo-mechanical nite element model InProceedings 25th FISITA Congress Beijing 1994pp 340ndash349 SAE paper 945042

9 Abdelhamid M K Brake judder analysis case studies SAEpaper 972027 1997

10 Kreitlow W Schrodter F and Matthai H Vibration andlsquohumrsquo of disc brakes under load SAE paper 850079 SAETrans Sect 1 1985 431ndash437

11 Augsburg K Brunner H and Grochowicz JUntersuchungen zum Rubbelverhalten von Pkw-Schwimmsattelbremser Automobiltechnische Zeitschrift1999 101

12 Stringham W Jank P Pfeifer J and Wang A Brakeroughnessmdashdisc brake torque variation rotor distortionand vehicle response SAE paper 930803 SAE TransSect 6 1993 1235ndash1247

13 Engel H G Bachman Th Eichhorn U and Saame ChDynamical behavior of brake-disc geometry as cause ofbrake judder In Proceedings EAEC Fourth InternationalConference on Vehicle and Tra c System TechnologyStrasbourg France 1993 Vol 1 pp 456ndash481

14 Thuresson D Thermomechanical analysis of frictionbrakes In Proceedings of the Eighteenth Annual BrakeColloquium and Engineering Display 2000 Vol P-358pp 149ndash159 SAE paper 2000-01-2775

15 Richmond J W Kao T K and Moore M W The devel-opment of computationalanalysis techniques for disc brake

430 H JACOBSSON

pad design In Proceedings Advances in AutomotiveBraking Technology Design Analysis and MaterialDevelopments 1996 (Institution of Mechanical Engineers)

16 Abendroth H Ste en T Falter W and Heidt RInvestigation of CV rotor cracking test procedures InBrakes 2000 International Conference on AutomotiveBrakingmdashTechnologies for the 21st Century 2000pp 149ndash162 (Professional Engineering PublishingLondon)

17 Haigh M J Smales H and Abe M Vehicle judder underdynamic braking caused by disc thickness variation InProceedings Braking of Road Vehicles London 1993pp 247ndash258 IMechE paper C44402293

18 Borjesson M Eriksson P Kuylenstierna C NilssonP H and Hermansson T The role of friction lms inautomotive brakes subjected to low contact forces InProceedings Braking of Road Vehicles London 1993pp 259ndash267 IMechE paper C444026

19 Wirth A and Whitaker R Developments in cast iron tech-nology In Proceedings Advances in Automotive BrakingTechnology Design Analysis and Material DevelopmentsLeeds UK 1996 (Institution of Mechanical Engineers)

20 Thoms E Disc brakes for heavy vehicles In ProceedingsBraking of Road Vehicles London 1988 pp 133ndash137IMechE paper C46488

21 Aviles R Hennequet G Hernandez A and Llorente L ILow frequency vibrations in disc brakes at high car speedPart I experimental approach Int J Veh Des 199516(6) 542ndash555

22 Ste en T and Bruns R Hotspotsbildung bei Pkw-Bremsscheiben Automobiltechnische Zeitschrift 1998100 408ndash413

23 Jacobsson H Analysis of brake judder by use of amplitudefunctions In Proceedings of SAE Noise and VibrationConference 1999 SAE paper 1999-01-1779

24 Jacobsson H Wheel suspension related disc brake judderIn Proceedings ASME Design Engineering TechnicalConferences Sacramento California 1997 VIB-4165

25 Engel H G Hassiotis V and Tiemann R Systemapproach to brake judder In Proceedings 25th FISITACongress Beijing 1994 Vol 1 pp 332ndash339 paper 945041

26 Martin R H and Bowron S Composite materials in trans-port friction applications In Brakes 2000 InternationalConference on Automotive BrakingmdashTechnologies for the21st Century 2000 pp 207ndash216 (Professional EngineeringPublishing London)

27 de Vries A and Wagner M The brake judder phenom-enon SAE Trans Sect 6 1992 101 652ndash660

28 Palmer B B and Weintraub M H The role of engineeredcashew particles on performance In Brakes 2000International Conference on Automotive BrakingmdashTechnologies for the 21st Century 2000 pp 185ndash195(Professional Engineering Publishing London)

29 Koetniyom S Brooks P C and Barton D C Finite

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

element prediction of inelastic strain accumulation in cast-iron brake rotors In Brakes 2000 InternationalConferenceon Automotive BrakingmdashTechnologies for the 21st Century2000 pp 139ndash148 (Professional Engineering PublishingLondon)

30 Hudson M D and Ruhl R L Ventilated brake rotor air ow investigation SAE paper 971033 1997

31 Grieve D G Barton D A Crolla D A Chapman J Land Buckingham J T Alternative brake disc materials InProceedingsAdvances in Automotive Braking TechnologyDesign Analysis and Material Developments Leeds UK1996 (Institution of Mechanical Engineers)

32 Grieve D G Barton D C Crolla D A and BuckinghamJ K Design of a lightweight automotive brake disc using nite element and Taguchi techniques Proc Instn MechEngrs Part D J Automobile Engineering 1998 212245ndash254

33 Krupka R and Kienzle A Fiber reinforced ceramic com-posite for brake discs In Proceeding of the EighteenthAnnual Brake Colloquium and Engineering Display 2000Vol P-358 pp 67ndash69 SAE paper 2000-01-2761

34 Bosworth R Investigations of secondary ride aspects ofsteering wheel vibration (shimmy and judder) using Taguchimethodology In Proceedings AUTOTECH 89 London1989 IMechE paper C3999

35 Kim M-G Jeong H-I and Yoo W-S Sensitivity analy-sis of chassis system to improve shimmy and brake juddervibration on steering wheel SAE Special Publication 11361996 pp 59ndash70

36 Abdelhamid M K Brake judder analysis using transferfunctions In Proceedings SAE Brake Colloquium TempeArizona 1997 pp 5ndash9 SAE paper 973018

37 Kao T K Richmond J W and Moore M WComputational analysis of pad performance InProceedings Braking of Road Vehicles 1993 paperC44402793 (Institution of Mechanical Engineers)

38 Floquet A and Dubourg M-C Realistic braking operationsimulation of ventilated disc brakes Trans ASMEJ Tribology July 1996 118 466ndash472

39 Du S Zagrodzki P Barber J R and Hulbert G MFinite element analysis of frictionally excited thermoelasticinstability J Thermal Stresses 1997 20 185ndash201

40 Daudi A R Dickerson W E and Narain M Hayesrsquoincreased air ow rotor design In Proceedings SecondInternational Seminar on Automotive Braking RecentDevelopments and Future Trends Leeds UK 1998pp 127ndash143 (Institution of Mechanical Engineers)

41 Crolla D A and Lang A M Brake noise and vibrationmdashthe state of the art Vehicle Tribology Tribology SeriesVol 18 1991 (Elsevier) pp 165ndash174

42 Aviles R Hennequet G Amezua E and Vallejo J Lowfrequency vibrations in disc brakes at high car speedPart II mathematical model and simulation Int J VehDes 1995 16(6) 556ndash569

Page 4: Aspects of disc brake judder - Universiti Teknologi Malaysiaarahim/jacobsson.pdf · 419 Aspects of disc brake judder HJacobsson* Machine and Vehicle Systems, Chalmers University of

422 H JACOBSSON

sometimes be cured by making several hard stopsHowever the relative amount of motorway driving is amuch more important factor for DTV generation thanthe driving style [17]

During long brake applications wear especially padwear becomes substantial Generally wear results in amore even temperature distribution and lower tempera-ture maxima [14] However the high wear will move thecontact surface (ie moving hot spotsbands) whichmight contribute to thermal fatigue of discs Simulations[3 14] and measurements [18] show that an increase ofthe hot pad wear could be used to reduce hot spot devel-opment by counteracting localization of the contactpressure on the friction surface

23 Uneven friction lms

The third-body layer friction lm or transfer lm is a lm a few iacutem thick consisting of material produced byattrition [19] The ferrous particles produced by the wearof the cast-iron disc are transformed and oxidized by theatmospheric oxygen and deposited as a greyndashblack layeron the braking surface of the disc This layer togetherwith the corresponding layers on the pads determinesthe frictional behaviour of the brake

When hot brakes are applied on a stationary vehiclesticking of the pad to the rotor can occur At veryhigh temperatures perhaps 500 degC the melted frictionmaterial can be lsquoburntrsquo into the disc

24 Uneven heating

Thermal deformation of a disc consists of the following

1 Waving or warping of the disc2 Coning of the disc This can lead to high run-out

Inoue [2 ] found that thermal run-out can be avoidedby a disc design that is stable to coning

3 Uneven thermal expansion A temperature di erenceof 250 degC which is not unusual causes a DTV ampli-tude of 10 iacutem [2 ] Even if no visible hot spots (orblue areas caused by phase transformations) occurduring braking this phenomenon is still importantfor brake judder occurrence by causing temporarygrowth of geometrical disturbances

4 Phase transformation5 Deposition of heated pad material on the disc

In disc brakes the rubbing speed and the frictional heatgenerated increase with the radius Hence the tempera-ture and pressure elds tend to be localized into band(s)near the outer radius even if the pad and disc are initiallyperfectly at and parallel with evenly distributedcoe cient of friction [3 ] The hot bands or rings maydevelop into hot spots as the rotor buckles [7 20] Themaximum disc temperature of the spots increases withpad sti ness [15] Measurements show that a local hot

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

spot can have a temperature of over 700ndash800 degC and thatthere can be a temperature di erence of over 300ndash600 degCbetween the hottest and the coldest local areas of thesame disc [2 3 21] Hot spots are usually more or lessbut not fully uniformly distributed [2 21]

The thicker areas of a brake disc become hotter thanthe thinner ones which causes thermal deformation ofthe brake disc (thermal coning and buckling [2 7 ] ) andalso uneven thermal expansion ie thermal DTV Theprocess can become unstable and is then de ned as aTEI TEI leads to a more and more localized brake press-ure and temperature eld as the braking continues Inthe extreme case especially at higher order (6ndash20) discdisturbances the disc will crack

Studies by Ste en and Bruns [22] have led to theexpected result that small dimensions (ie disc and padthickness and diameter of friction ring) increase the tend-ency towards hot spotting Also a higher revolutionspeed (ie higher energy level ) of the disc was found toincrease the hot spot generation

It is the temperature gradients and not the increase inabsolute temperature level that cause the increasingjudder level during long or repeated braking see refer-ence [23] The temperature gradients cause temporaryDTV owing to uneven thermal expansion of the discmaterial [2 ] The DTV level (and hence BTV ) increasesoften more or less linearly with time while braking [7 ]especially for lsquohardrsquo pads and at the outer radius Hencethe brake application time [7 11] and how often thebraking is repeated [23] are important factors for brakejudder development Hot spotting and thermal DTVbecome worse for low torque long duration applicationsthan for high torque ones [15] A light long applicationtime (20ndash45 s) gives substantially higher temperatureand pressure gradients than heavy shorter ones (3ndash4 s)[7 15 16 ]

Also a higher revolution speed (ie higher energylevel ) of the disc was found to increase the hot spotgeneration [11 22] In addition the localization process(and the correlated thermal DTV ) is particularly pro-nounced at high speed above 100 kmh [11] This mightbe explained by the fact that the TEI process demandsa minimal lsquocriticalrsquo speed to develop As a consequenceof this it is essential to test friction material at speedsabove the limit 100 kmh (60 milesh) which is usuallystandard

25 Uneven pressure

In a conventional disc brake analysis the interfacepressure is assumed to be either constant (ie constantpressure assumption) or inversely proportional to theradius (ie constant wear assumption) However underdynamic braking conditions the contact area and brakepressure distribution varies continuously with timebecause of

423ASPECTS OF DISC BRAKE JUDDER

(a) thermal distortion arising from the friction heatgeneration

(b) mechanical distortion due to the applied actuationforce

(c) wear of the friction pair material and formation offriction lm

(d) initial DTV and run-out

Conventional brake analysis gives an even temperatureand pressure distribution as well as maximal tempera-ture pressure and stress levels which are much lowerthan their actual peak values [3 ]

26 Friction characteristics and level

The variation of friction with velocity has historicallybeen regarded as the source of all kinds of braking-induced vibrations including brake judder Jacobsson[24] analytically showed that even a constant coe cientof friction may generate judder No speci c frictioncharacteristics are needed for the phenomenon to occurHowever a negative brake fade or a friction coe cientthat increases with brake pressure may increase the prob-lems To achieve a given brake torque a pad materialwith a lower friction coe cient needs a higher brakepressure level This induces more evenly distributedpressure and temperature elds on the contact surface[16 ] Consequently a reduction of the friction coe cientlevel decreases the judder problems and at the same timereduces the crack probability Also the relation betweenBTV and BPV is a ected by the absolute friction levelThis is because BTV is proportional to the coe cient offriction [11] while BPV is independent of friction

27 External forces

Unbalances and tyre force variations may induce a tum-bling rigid body motion of the disc as a result of elas-ticities of the wheel hub and bearing unit [13] Suchdynamic de ections cause the same type of vibrations(with a frequency that is an integer multiple of the instan-taneous brake rotor frequency) as geometrical irregu-larities Hence they may contribute to judder The wheelhubndashbearing design and sti ness contribute to themagnitude of the disc deviation [11] When the judderis due to the tyre force variation or imbalance the termbrake judder is misleading because it suggests that theexcitation force originates from the brakes

3 VEHICLE COMPONENTS

BTV and BPV are usually produced by geometrical orother irregularities of the brake components and furthertransmitted to and ampli ed in the wheel suspension andhydraulic system as outlined in Fig 2

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

Fig 2 Brake vibrations are transmitted to di erent vehiclecomponents

Theoretically a spatial friction coe cient variationaround the disc may occur without corresponding vari-ation of the hydraulic pressure (ie BPV) Howeverphysical e ects that generate friction variation such asphase transformation uneven transfer lm generationcorrosion etc will also generate geometrical irregularit-ies (DTV etc) with normal force variation and BPVHence it is often meaningful to consider BTV and BPVas an entity However their relative magnitudes arefunctions of the actual friction coe cient

Independently of how and where the disturbance isproduced it is transmitted and ampli ed in the sameway The wheel suspension ampli es the vibrationsespecially the frequencies near its eigenfrequenciesUsually there is a second ampli cation of the vibrationin for instance the steering system

An obvious way of reducing the judder is to reducethe BTVBPV which is the source of the vibrations Thistraditional approach will place the focus on the brakecomponents ie pad and disc

An alternative strategy especially with severe steeringwheel vibrations is to reduce the ampli cation eitherthe primary ampli cation in the wheel suspension ora relevant secondary ampli cation at the steeringsystem This can e ectively be achieved by introductionof the brake-by-wire and steering-by-wire techniquesSimulations and measurements by Jacobsson [23] dem-onstrate that the ampli cation is relatively low in thesubcritical region as indicated in Fig 6 Hence thevibration is reduced if the eigenfrequencies of the compo-nents in the transfer path are shifted above the frequencyrange of the rst wheel order excitation (above 25ndash30 Hzor vehicle speeds above 170ndash200 kmh) which was sug-gested by Engel et al [25] Also modal separation ofeigenfrequencies in the transfer path should be ensured

31 Pads

When developing or choosing a pad material more than20 properties are considered [26 ] Everything from den-sity melting point strength (tensile compressive ex-ural and shear) machinability environmental impactsqueal probability etc should be considered Withrespect to judder properties of interest are sti ness

424 H JACOBSSON

coe cient of friction coe cient of thermal expansionthermal conductivity corrosion and porosity

The most important pad property for judder reductionis the compressive sti ness [11] The BTV level can varyby a factor of 2ndash3 (with the same DTV ) depending onthe pad composition [21 27] The pad compressivesti ness should also be as low as possible to promoteuniform contact pressure [3 8 ] and to avoid TEI pro-cesses such as hot banding and thermal DTV This will atthe same time reduce eventual brake squeal problems [1 ]

The relation between the BTVBPV level and the padsti ness of modern passenger cars is non-linear [11] Inparticular during compression the material becomesprogressively sti er as the load is applied [15] For theseprogressive materials the same DTV level will result ina higher BTV level for hard than for light brakings

To achieve a good lsquopedal feelrsquo and positive retractionthe sti ness should be reasonably high and progressiveGenerally the desired zone is narrow and a deviationon either side might lead to complaints [28] Progressivebrake pads ie traditional composite pads [15] su erfrom high sensitivity to increases in the DTV level seereference [5 ] A linear pad compression characteristicwould not require as high safety margins for increasesfrom the initial DTV (thermal DTV and long-time wearDTV etc) as the progressive pad does In other wordslinear pads are likely to accept higher disc thickness tol-erances than the 10 iacutem DTV The new lsquobrake-by-wirersquotechnique o ers other ways of achieving lsquoa good brakefeelrsquo than a high and progressive pad compressionsti ness

32 Disc

The thermal stability of the disc shape is in uenced bythe quality of the material and the heat treatment beforemachining as well as the basic design of the disc rotorDisc design variants that are more or less stable toconing have been discussed in references [2 3 22 29]Thermal stability problems can be minimized by choos-ing high carbon disc materials and introducing thermalstress relief treatment into the machining cycle [13]

Some of the thermally most important properties ofdisc brakes are as follows [3 30]

1 Thermal capacitance (ie density and speci c heat) isthe ability to store heat Initially on braking a sig-ni cant amount of frictional heat is stored [3 ] andconsequently during short brakings the thermalcapacitance dominates

2 Heat dissipation becomes important at long brakingtimes (above 2ndash3 min [3 ]) ie drag braking or moun-tain descent braking However it also a ects thediscrsquos ability to recover thermally between stops [31]Convection accounts for more than 90 per cent of allheat dissipation for most braking conditions [3 ]whereby radiation is almost negligible The heat

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

transfer coe cient due to convection varies as thevehiclersquos velocity to the power 08 [3 ]

3 Thermal conductivity is the ability to redistributethermal energy During long low intensity brakingsthe peak temperature depends largely on the discmaterialrsquos conductivity [32] During short brakingshowever the thermal conductivity has little e ect

4 Thermal expansion coe cient (ie related to localiz-ation of friction contact due to the thermal defor-mation) a ects the tendency towards hot spotting andthermal DTV generation Temperature gradients of abrake disc cause temporary DTV owing to uneventhermal expansion of the material

Ventilated brake discs are widely used for their weightsavings and additional convective heat transferHowever they may increase judder problems byinducing an uneven temperature eld around the discOver short ( less than a few minutes) and high speedstops thermal capacity is the most important thermalproperty which is why a solid disc (with its higher mass)runs cooler than the vented design [3 31] In mountaindescent braking the disc brake temperatures mayincrease considerably when the vents are removed [31]

Aluminium especially SiC-reinforced Al metal matrixcomposite materials requires a lower operating tempera-ture than grey cast iron (around 450 degC) [32 ] Becausethe material su ers from low thermal capacity it canonly be used for relatively light passenger cars say below1000 kg The introduction of aluminium composite discsor pure aluminium covered by a composite layer willprobably increase judder problems because of the highcoe cient of thermal expansion and the low heatcapacity [22] The high thermal conductivity has there-fore relatively little in uence on the hot spot and thermalDTV generation

However there are composite materials that mighthave the ability to reduce judder namely ceramic mate-rials An example is a short bre reinforced SiC material(CSiC ) which has recently been introduced in sportscars and high speed trains [33] Judder is avoidedbecause of the low coe cient of thermal expansion andlow wear Also the low elastic modulus should promoteuniform contact and reduce thermal DTV and hot spotsThe excellent resistance to thermal damage of the mate-rial makes it suitable for disc brakes of heavy vehicleswhere cracking of the normally used cast-iron disc is aproblem However the high cost of the material excludesapplications in the ordinary family car segment

33 Vehicle structure

The front suspension is designed to admit largevibrations in the vertical direction However there is avibration in the forendashaft direction [24 27] which isrelated to brake judder as well as a proportional angularvibration [24] Brake judder is strongly related to the

425ASPECTS OF DISC BRAKE JUDDER

suspension design and the forendashaft exibility is a domi-nating parameter [27] Stringham et al [12] stated thatthe sti ness of the lower arm bushing is the most in u-ential parameter It was found to a ect signi cantly theeigenfrequency of the suspension system in the forendashaftdirection Bosworth [34] studied the suspension struc-ture in more detail and found the following factorscontrolling the judder

(a) tie rod bushmdashradial and forendashaft sti ness(b) lower arm bushmdashforendashaft sti ness(c) anti-roll barmdashvertical sti ness

In particular the sti ness of the lower arm bushing isimportant since it signi cantly a ects the eigenfre-quency of the suspension system in the forendashaft direction[12 34 35] Higher eigenfrequencies which will reducejudder problems such as steering wheel vibrations maybe achieved either by higher sti ness of the rubber bush-ings or by a reduced value of the modal mass and inertiaof the wheel suspension see Jacobsson [5 ]

However modern suspensions have become more andmore exible in the forendashaft direction because of theintroduction of radial tyres [27] This is necessary inorder to absorb the longitudinal vibrations from the sti belt of the tyres

Note that it is essential to measure the eigenfrequencyand damping in the brake-on mode When the brakeswere not applied the experimental vehicle was found tohave a signi cantly higher eigenfrequency (18 Hz com-pared with 138 Hz) and a lower equivalent viscousdamping factor (007 compared with 009) than meas-ured under the same braking conditions see reference[24] Also the instantaneous centre of motion of the strutchanges with the brake pressure level [5 ] It movedgradually towards the wheel axle as the brake pressureincreased

4 TIME-SCALES

Brake judder depends strongly on the braking historyon the short as well as on the long time-scale There arethree di erent time-scales involved in brake judder

(a) revolution time of the wheel(b) brake application time or the time between two

brakings(c) lifetime of brake components

Traditionally in brake design only the long-time changesare considered In recent years changes during brakinghave also been focused on The generation of localizedcontact area pressure and temperature gradients suchas hot banding has been studied It is found that DTVis a dynamic property that may change considerablyduring a brake application [7 11]

Changes within the time of a wheel revolution arenormally not included primarily because of di culties

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

in making numerical and signal analysis when using con-ventional techniques However the amplitude functiontechnique [23] handles sinusoidal variations of the braketorque with wheel revolution

5 APPROACH

The way of looking at and describing a problem is herecalled the problem approach It is a theoretical abstrac-tion lsquoa conception of the worldrsquo including a model andits system limits The problem approach determineswhich physical e ects can be studied and also states thetime and space scale The chosen problem approach willhave consequences for how to analyse the problem aswell as for the type of solution that will be found It alsodetermines which type of analytical and experimentaltool is the most appropriate

When studying the literature on brake judder it isclear that two fundamentally di erent approaches are inuse namely the cause and e ect approaches While thee ect approach focuses on the source of the vibrationsin the form of amplitude and vibrational order of theBTV andor BPV the cause approach deals with anumber of physical e ects such as wear and heatingsee Fig 3

The e ect approach can be further split into di erentapproaches [4 ]

1 The system approach examines how a model of thevehicle or the wheel suspension together withBTVBPV generates judder The braking process isusually represented by a constant frequency whichcan be parametrically changed It is used mostly inexperimental analysis [13 25 36 ] Also some quasi-static analyses may be found in literature Kim et al[35] used multibody system (MBS) analysis of amodel with 12 degrees of freedom (DOF ) of aMcPherson-type suspension exposed to rst-orderjudder

2 The frequency sweep approach examines how thebraking process itself (including a frequency sweep)together with the BTVBPV generates judder Thevehicle structure can be represented by a resonancecorresponding to the actual critical speed [23]

3 The human response approach studies the e ects ofjudder on one speci c test driver or on an average

Fig 3 Problem approaches

426 H JACOBSSON

person placed in a speci c vehicle Alternatively thehuman response to judder could be thought of as athird level where the judder level and frequencytogether with the weight size and place of the personin the vehicle etc are the input

Some approaches are listed in Table 1 together withrelated analytical and experimental methods and toolsfound in the literature [4 ] For instance FE analysis isthe natural choice when studying BTV generation bymeans of for instance the TEI process For the e ectapproach where the BTV can be represented by a sinus-oidal brake torque disturbance it is instead the vehicleor relevant parts thereof that should be modelled ThenMBS analysis (commercial programs are ADAMSDADS etc) is more relevant especially for lowfrequency judder (say below 50 Hz)

In experimental brake judder studies bench testing aswell as road testing are used Advantages of bench test-ing [11] are good reproducibility of the testing con-ditions more accurate measurements higher sensitivityof measurements lower cost and less time consumption[37] Disadvantages are that cooling conditions are nottaken into account as well as the in uence of othermachine elements and systems which will a ect thetransmission of BTV in the vehicle (tyres wheel sus-pension steering) [11] In road testing the speci cproblem occurs that the level of BTVBPV cannot becontrolled during a brake application This problemmay be handled by measuring BTVBPV instead oftrying to control it by constant conditions such as speedtemperature pressure etc see references [9 23]

51 Causes of BTVBPV

Traditionally the source of the BTVBPV has beenfocused on It is a ected by a combination of the di er-ent physical e ects discussed in section 2 Disc run-outand DTV which are geometrical irregularities of thedisc directly cause normal force variations and henceBTVBPV see Fig 4 Furthermore the TEI process gen-erates hot spots and sometimes remaining discolouredareas with locally di erent speci c volume and wearproperties which may aggravate the vibrations Finally

Table 1 Approaches and corresponding methods

Approach Methods and tools

Cause approach (FE) analysis nite di erence dynamometertribometer drag braking thermal imagingX-rays

System approach MBS analysis Fourier methods modal analysisTaguchi methodology road testsspectrograms

Frequency sweep Time plane analysis road tests involvingapproach deceleration waterfall analysis order

tracking ABS and capacitive transducersHuman response Subjective rating deceleration tests

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

Fig 4 BTV causes for a disc brake

there is a contribution from the dynamic de ection ofthe disc due to external forces such as tyre forces andunbalances

One of the problems with brake analysis is that it isnecessary to solve coupled de ection and temperature eld problems with combined de ection and thermalload Commercially available FE programs can handlepure mechanical or pure thermal problems Brooks et al[8 ] introduced a two-dimensional (ie axisymmetrical )combined thermal and mechanical method of hot band-ing simulation of a disc brake The basic idea is to switchbetween de ection and temperature eld calculationseach of which can be made in commercial FE programssuch as ABAQUS The FE model takes into account thetime-dependent change in the contact area A similarconcept was developed by Kao et al [7 ] Both three-dimensional (necessary to be able to model buckling)and axisymmetric models have been used to study thein uence of pad design parameters on thermal padcracking as well as to simulate thermoelastic bucklingand its coupling to TEI and thermal DTV

Thermoelastic simulation of brake components underrealistic conditions involves massive central processingunit computational e ort and data storage [7 ] This isespecially the case when simulating slow decelerations(ie sti problems) with long duration timesUnfortunately it is this type of braking that generatesthe most pronounced hot spots There are various waysto make the simulation more e ective

1 Circumferential variations of the instantaneous discsurface conditions and geometry can be neglectedHowever when studying brake judder problems thecircumferential variations are essential

2 A specially dedicated contact element can be used toderive the frictional force and heat generated at theinterface [3 37]

3 Solving the coupled eld problems simultaneously(see reference [14]) is more accurate and e ectiveHowever since it relies on a Newton-type methodfrom the 1990s the algorithms are not yet included incommercial FE programs

4 A three-dimensional hybrid method which combinesfast Fourier transform (FFT) techniques withFE methods has been developed by Floquet and

427ASPECTS OF DISC BRAKE JUDDER

Dubourg [38] The application of the Fourier trans-form (on a space variable) has the e ect of reducingthe dimension of the problem The variable is trans-formed into a discrete parameter the frequency andthe corresponding partial derivatives are removedThe method can handle geometrically periodic butnon-axisymmetric solids such as ventilated discbrakes

5 The FE method can be applied directly to a pertur-bation method [39] The basic idea is not to solve thetransient problem but to consider the conditionsunder which a small perturbation in the temperature eld can grow exponentially in time The method isapplicable to transient processes as long as the contactarea does not change with time However the contactarea does change considerably with time duringbraking

6 A pad model composed of springndashdamper elementscan be used [22]

For vented discs and aluminium discs in particularwhere the air ow is important computational uiddynamics (CFD) is a useful tool CFD is used by somerotor manufacturers to increase air ow [26 40] In amarket survey [26 ] many companies saw the potentialof combining FE analysis and CFD to gain more accu-rate temperature predictions However this wouldrequire enormous computational e orts

As an alternative to CFD the convective cooling maybe estimated by approximative methods On a ventedrotor there are two di erent types of convective coolingair cross- ow over the rotor surface and air pumped owthrough the vents [3 ] Brake rotor vane ow relationsto estimate the heat convective transfer coe cient havelong been used in brake system thermal modellingCurrently two relations are recognized for ventilateddisc air ow those of Sisson and Limpert [30] Analternative is to approximate the convective heat transfercoe cient from the Nusselt modulus [31 32] and tocorrect it with empirically determined factors

52 E ects of BTVBPV

A few research projects have focused on the e ect ofbrake vibrations in the vehicle despite the fact that ithas been qualitatively described in the literature Crollaand Lang [41] Haigh et al [17] and many others havedescribed how brake judder rises to a maximum whenpassing through more or less distinct speeds So far theevaluation of brake judder has been done with a subjec-tive method using a scale from 1 to 10 but hardly anysimulations of brake judder in a vehicle have been car-ried out Brake judder problems have traditionally beensolved by use of trial and error rather than systematicmethods

In the literature there are a few sensitivity studies butin practice no lsquotruersquo simulations The di erence in that

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

lsquotruersquo simulations needs to be evaluated in the time planeThis involves not only a model of the vibration source(BTVBPV) and the vehicle structure and linkage (reson-ances and transfer) but also modelling of the brakingevent (frequency sweep braking conditions) see Fig 5

Straightforward integration of di erential equationswithout intelligent variable transformations or assump-tions using an ordinary equation-solving algorithmdesigned for non-sti problems (eg RungendashKutta) isnot an e cient way of dealing with this type of problemThe simulation will take an unnecessarily long time(hours or days) fail or crash Also the algorithms usedby commercial mechanics programs such as ADAMSare slow and ine cient if one wishes to follow a wholebraking event Hence the maximal vibration levels willbecome largely overestimated at nite braking timesHowever these types of programs are useful for quasi-static sensitivity analysis

521 Sensitivity analysis

Applying the system approach the solution to the judderproblem will be to build robustness into the vehicle andthereby to make it less sensitive to BTVBPV The systemof Engel et al [25] consists of ve di erent steps namelythe brake disc caliper and pad tyre and hubndashbearingunit wheel knuckle and nally the steering system Thereis also feedback between some steps in the outlinedmodel

An attempt to model numerically the vehicle responseto BTV was made by Kim et al [35] using MBS analysisof a similar vehicle structure The modelling of the sus-pension system used in the calculations was howevernot described Similar analyses are often carried out inthe automotive industry but seldom is the modellingdescribed in the literature However the model ofAugsburg et al [11] was described in detail

(a) calliper as two masses connected by a spring (rep-resenting the calliper sti ness in the forendashaftdirection)

(b) brake pads as springs(c) brake piston by a mass(d) hydraulic system as volume accumulating elements

The transfer path from the vibration source to thedriverrsquos contact points can be qualitatively investigatedby simultaneous measurements of accelerations atvarious position such as wheel carrier steering tie rod

Fig 5 The frequency sweep approach

428 H JACOBSSON

steering wheel etc [13] The sampled signals can be usedto generate the transfer functions between di erentpoints [9 36 ] The technique can be used to describeboth the brake excitation and the transfer functions thatcharacterize vehicle sensibility

The amplitude functions [23] can be seen as gen-eralized transfer functions They can be used to classifythe braking event as well as the corresponding vibrationsin the vehicle An advantage of the amplitude functionover the transfer function technique is that it works formuch higher decelerations since it does not rely on theFFT The method also determines the eigenfrequencieswith higher accuracy since it takes into account thetime delay of the maximal ampli cation caused by the nite deceleration and the inertias of the system If thistime delay is not considered the eigenfrequencies willbe systematically underestimated especially at highdecelerations

The analysis can be made in the frequency plane pro-vided that the braking starts above a certain limit often10ndash30 per cent above the critical speed [5 ] The deceler-ation clearly lsquocutsrsquo the maximal vibration amplitudeespecially at low damping Already at relative dampinglevels of the order of 1 per cent the transient analysis(including the frequency sweep) is needed for the rst-order judder except for in nitesimally smalldeclerations

Aviles et al [42] studied a braking event with slowlydecreasing speed and frequency However the con-clusion was drawn that the peak of the vibration ampli-tude at a certain vehicle speed was altogether an e ectof the negative frictionndashvelocity slope introduced in themodel The e ect of the frequency sweep was neveranalysed separately The calculations were made in thefrequency domain

522 Judder vibration simulation

Most of the analyses and measurements of judder aremade for braking with constant speed ie constant rev-olution frequency of the wheel as well as constant press-ure and temperature An argument is that it is easier tomeasure and analyse vibrations on the basis of this pre-scription Another bene t of measuring at constantspeed is e cient data analysis in the frequency domainHowever in a real braking situation the frequency isnot constant

There is a dynamic ampli cation of the brake torqueand pressure variations when passing through orcoming close to a critical speed of a vehicle Thevibration starts when the braking force is applied andreaches a maximal amplitude at a certain speed It iscontinued until low speed if the braking force is continu-ously applied This is the typical behaviour of a forcedvibration with relatively constant source amplitude butwith a sweeping frequency Fig 6

A two-DOF rotorndashstator model [24] with a linearly

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

decreasing disc speed possesses the main characteristicsof judder as shown in Fig 6 Before analysis the de ec-tion angles of rotordisc and statorcaliper respectivelywere split into vibration-free parts W and WC (rotationstatic de ection) and the superimposed vibrations QD andQ

C respectively The shape of the amplitude function Edescribes the relative vibration level QC (second timederivative of QC) almost exactly All parameters of therotorndashstator model can be experimentally generated

A full-vehicle model [5 ] shows the same lsquojudder behav-iourrsquo but can also explain some other e ects It is morecomplicated since it demands information about thewind speed slip etc

It is generally accepted that the front wheel suspensionof passenger cars has a rigid body forendashaft vibrationmode resonance in the frequency range 10ndash20 Hz andthat this resonance is responsible for lower-order judderat corresponding velocities This corresponds to a maxi-mal amplitude of the vibrations at a critical vehicle speedof between 60 and 140 kmh for the rst-order judderThe second-order judder will have a corresponding criti-cal speed (because of the same resonance) of between 30and 70 kmh The present vehicle had a resonance near14 Hz corresponding to a rst-order critical speed of95 kmh

The following possibilities for reducing judder werefound [5 ]

(a) decreased BTV andor BPV which will lead backto the cause approach

(b) increased relative stator mass and inertia momentcompared with the rotor

(c) increased damping(d) lighter braking(e) higher eigenfrequency

A lighter vehicle and a smaller wheel radius decrease thejudder problems [5 ] A reduction of the vehicle mass willalso decrease the thermal DTV and hotspots and reducethe risk of thermal cracking provided that the thermalcapacity of the disc remains the same A lighter stator(ie strut and eventually disc) will tend to increase thejudder problems since the ampli cation of BTV willbecome larger

6 FUTURE

The eld of low frequency braking induced vibrations isstill characterized by confusion Much research is neededin this area before a fairly clear picture becomes appar-ent The author nds the following areas especiallyinteresting

(a) simulation of BTV generation combining wear andTEI (wear especially hot and high pressure weartends to counteract the TEI process)

(b) the groan phenomenon(c) friction lms

429ASPECTS OF DISC BRAKE JUDDER

Fig 6 Model and corresponding brake judder simulation versus measurement

(d) the TEI process and its connection to thermoelasticbuckling

(e) studying wheel suspension vibration modes duringbrake-on conditions

(f ) the relation between BTV and simultaneous vari-ations in geometry (DTV run-out equivalent brakeradius) and friction coe cient

(g) prediction of BTV level and order for speci eddesign parameters and braking conditions

(h) developing models for simulation of vibration levelsin a vehicle at speci ed BTV

Generally in brake judder analysis it is recommendedto split the investigations into two parts

1 Analysis of sources of irregularities such as DTV etcThis involves thermomechanical FE analysis of thebrake components or dynamometer tests These typesof calculations are extremely time demanding

2 Analysis of the e ect of the irregularities in the vehicleIf the disturbances (which may be output from FEanalysis or dynamometer measurements) are given asfunctions of time very fast simulation can be carriedout by means of the amplitude function techniquedescribed in this work

The amplitude function technique is still at an earlystage but there are no di culties in principle involvedin using it to analyse multiple mass system models ofa whole vehicle Such models would be useful in deter-mining design criteria of brake components andsuspensions etc

REFERENCES

1 Hulten J Drum brake squeal PhD thesis Machine andVehicle Design Chalmers University of TechnologyGoteborg 1998

2 Inoue H Analysis of brake judder caused by thermal defor-mation of brake disc rotors In Proceedings 21st FISITACongress Belgrade 1986 pp 213ndash219 paper 865131

3 Kao T K Richmond J W and Moore M W The appli-

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

cation of predictive techniques to study thermo-elasticinstability of brakes In Proceedings of the Twelfth AnnualBrake Colloquium and Engineering Display AtlantaGeorgia 1984 SAE paper 942087

4 Jacobsson H Frequency sweep approach to brake judderpart A the brake judder phenomenon Classi cation andproblem approach Licentiate thesis Chalmers Universityof Technology Goteborg 1998

5 Jacobbson H Brake judder Thesis Chalmers Universityof Technology Goteborg 2001

6 Abdelhamid M K Creep groan of disc brakes InProceedings Noise and Vibration Conference TraverseCity Michigan 1995 pp 396ndash400 SAE paper 951282

7 Kao T K Richmond J W and Douarre A Brake dischot spotting and thermal judder an experimental and niteelement study Int J Veh Des 2000 23(34) 276ndash296

8 Brooks P C Barton D Crolla D A Lang A M andSchafer D R A study of disc brake judder using a fullycoupled thermo-mechanical nite element model InProceedings 25th FISITA Congress Beijing 1994pp 340ndash349 SAE paper 945042

9 Abdelhamid M K Brake judder analysis case studies SAEpaper 972027 1997

10 Kreitlow W Schrodter F and Matthai H Vibration andlsquohumrsquo of disc brakes under load SAE paper 850079 SAETrans Sect 1 1985 431ndash437

11 Augsburg K Brunner H and Grochowicz JUntersuchungen zum Rubbelverhalten von Pkw-Schwimmsattelbremser Automobiltechnische Zeitschrift1999 101

12 Stringham W Jank P Pfeifer J and Wang A Brakeroughnessmdashdisc brake torque variation rotor distortionand vehicle response SAE paper 930803 SAE TransSect 6 1993 1235ndash1247

13 Engel H G Bachman Th Eichhorn U and Saame ChDynamical behavior of brake-disc geometry as cause ofbrake judder In Proceedings EAEC Fourth InternationalConference on Vehicle and Tra c System TechnologyStrasbourg France 1993 Vol 1 pp 456ndash481

14 Thuresson D Thermomechanical analysis of frictionbrakes In Proceedings of the Eighteenth Annual BrakeColloquium and Engineering Display 2000 Vol P-358pp 149ndash159 SAE paper 2000-01-2775

15 Richmond J W Kao T K and Moore M W The devel-opment of computationalanalysis techniques for disc brake

430 H JACOBSSON

pad design In Proceedings Advances in AutomotiveBraking Technology Design Analysis and MaterialDevelopments 1996 (Institution of Mechanical Engineers)

16 Abendroth H Ste en T Falter W and Heidt RInvestigation of CV rotor cracking test procedures InBrakes 2000 International Conference on AutomotiveBrakingmdashTechnologies for the 21st Century 2000pp 149ndash162 (Professional Engineering PublishingLondon)

17 Haigh M J Smales H and Abe M Vehicle judder underdynamic braking caused by disc thickness variation InProceedings Braking of Road Vehicles London 1993pp 247ndash258 IMechE paper C44402293

18 Borjesson M Eriksson P Kuylenstierna C NilssonP H and Hermansson T The role of friction lms inautomotive brakes subjected to low contact forces InProceedings Braking of Road Vehicles London 1993pp 259ndash267 IMechE paper C444026

19 Wirth A and Whitaker R Developments in cast iron tech-nology In Proceedings Advances in Automotive BrakingTechnology Design Analysis and Material DevelopmentsLeeds UK 1996 (Institution of Mechanical Engineers)

20 Thoms E Disc brakes for heavy vehicles In ProceedingsBraking of Road Vehicles London 1988 pp 133ndash137IMechE paper C46488

21 Aviles R Hennequet G Hernandez A and Llorente L ILow frequency vibrations in disc brakes at high car speedPart I experimental approach Int J Veh Des 199516(6) 542ndash555

22 Ste en T and Bruns R Hotspotsbildung bei Pkw-Bremsscheiben Automobiltechnische Zeitschrift 1998100 408ndash413

23 Jacobsson H Analysis of brake judder by use of amplitudefunctions In Proceedings of SAE Noise and VibrationConference 1999 SAE paper 1999-01-1779

24 Jacobsson H Wheel suspension related disc brake judderIn Proceedings ASME Design Engineering TechnicalConferences Sacramento California 1997 VIB-4165

25 Engel H G Hassiotis V and Tiemann R Systemapproach to brake judder In Proceedings 25th FISITACongress Beijing 1994 Vol 1 pp 332ndash339 paper 945041

26 Martin R H and Bowron S Composite materials in trans-port friction applications In Brakes 2000 InternationalConference on Automotive BrakingmdashTechnologies for the21st Century 2000 pp 207ndash216 (Professional EngineeringPublishing London)

27 de Vries A and Wagner M The brake judder phenom-enon SAE Trans Sect 6 1992 101 652ndash660

28 Palmer B B and Weintraub M H The role of engineeredcashew particles on performance In Brakes 2000International Conference on Automotive BrakingmdashTechnologies for the 21st Century 2000 pp 185ndash195(Professional Engineering Publishing London)

29 Koetniyom S Brooks P C and Barton D C Finite

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

element prediction of inelastic strain accumulation in cast-iron brake rotors In Brakes 2000 InternationalConferenceon Automotive BrakingmdashTechnologies for the 21st Century2000 pp 139ndash148 (Professional Engineering PublishingLondon)

30 Hudson M D and Ruhl R L Ventilated brake rotor air ow investigation SAE paper 971033 1997

31 Grieve D G Barton D A Crolla D A Chapman J Land Buckingham J T Alternative brake disc materials InProceedingsAdvances in Automotive Braking TechnologyDesign Analysis and Material Developments Leeds UK1996 (Institution of Mechanical Engineers)

32 Grieve D G Barton D C Crolla D A and BuckinghamJ K Design of a lightweight automotive brake disc using nite element and Taguchi techniques Proc Instn MechEngrs Part D J Automobile Engineering 1998 212245ndash254

33 Krupka R and Kienzle A Fiber reinforced ceramic com-posite for brake discs In Proceeding of the EighteenthAnnual Brake Colloquium and Engineering Display 2000Vol P-358 pp 67ndash69 SAE paper 2000-01-2761

34 Bosworth R Investigations of secondary ride aspects ofsteering wheel vibration (shimmy and judder) using Taguchimethodology In Proceedings AUTOTECH 89 London1989 IMechE paper C3999

35 Kim M-G Jeong H-I and Yoo W-S Sensitivity analy-sis of chassis system to improve shimmy and brake juddervibration on steering wheel SAE Special Publication 11361996 pp 59ndash70

36 Abdelhamid M K Brake judder analysis using transferfunctions In Proceedings SAE Brake Colloquium TempeArizona 1997 pp 5ndash9 SAE paper 973018

37 Kao T K Richmond J W and Moore M WComputational analysis of pad performance InProceedings Braking of Road Vehicles 1993 paperC44402793 (Institution of Mechanical Engineers)

38 Floquet A and Dubourg M-C Realistic braking operationsimulation of ventilated disc brakes Trans ASMEJ Tribology July 1996 118 466ndash472

39 Du S Zagrodzki P Barber J R and Hulbert G MFinite element analysis of frictionally excited thermoelasticinstability J Thermal Stresses 1997 20 185ndash201

40 Daudi A R Dickerson W E and Narain M Hayesrsquoincreased air ow rotor design In Proceedings SecondInternational Seminar on Automotive Braking RecentDevelopments and Future Trends Leeds UK 1998pp 127ndash143 (Institution of Mechanical Engineers)

41 Crolla D A and Lang A M Brake noise and vibrationmdashthe state of the art Vehicle Tribology Tribology SeriesVol 18 1991 (Elsevier) pp 165ndash174

42 Aviles R Hennequet G Amezua E and Vallejo J Lowfrequency vibrations in disc brakes at high car speedPart II mathematical model and simulation Int J VehDes 1995 16(6) 556ndash569

Page 5: Aspects of disc brake judder - Universiti Teknologi Malaysiaarahim/jacobsson.pdf · 419 Aspects of disc brake judder HJacobsson* Machine and Vehicle Systems, Chalmers University of

423ASPECTS OF DISC BRAKE JUDDER

(a) thermal distortion arising from the friction heatgeneration

(b) mechanical distortion due to the applied actuationforce

(c) wear of the friction pair material and formation offriction lm

(d) initial DTV and run-out

Conventional brake analysis gives an even temperatureand pressure distribution as well as maximal tempera-ture pressure and stress levels which are much lowerthan their actual peak values [3 ]

26 Friction characteristics and level

The variation of friction with velocity has historicallybeen regarded as the source of all kinds of braking-induced vibrations including brake judder Jacobsson[24] analytically showed that even a constant coe cientof friction may generate judder No speci c frictioncharacteristics are needed for the phenomenon to occurHowever a negative brake fade or a friction coe cientthat increases with brake pressure may increase the prob-lems To achieve a given brake torque a pad materialwith a lower friction coe cient needs a higher brakepressure level This induces more evenly distributedpressure and temperature elds on the contact surface[16 ] Consequently a reduction of the friction coe cientlevel decreases the judder problems and at the same timereduces the crack probability Also the relation betweenBTV and BPV is a ected by the absolute friction levelThis is because BTV is proportional to the coe cient offriction [11] while BPV is independent of friction

27 External forces

Unbalances and tyre force variations may induce a tum-bling rigid body motion of the disc as a result of elas-ticities of the wheel hub and bearing unit [13] Suchdynamic de ections cause the same type of vibrations(with a frequency that is an integer multiple of the instan-taneous brake rotor frequency) as geometrical irregu-larities Hence they may contribute to judder The wheelhubndashbearing design and sti ness contribute to themagnitude of the disc deviation [11] When the judderis due to the tyre force variation or imbalance the termbrake judder is misleading because it suggests that theexcitation force originates from the brakes

3 VEHICLE COMPONENTS

BTV and BPV are usually produced by geometrical orother irregularities of the brake components and furthertransmitted to and ampli ed in the wheel suspension andhydraulic system as outlined in Fig 2

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

Fig 2 Brake vibrations are transmitted to di erent vehiclecomponents

Theoretically a spatial friction coe cient variationaround the disc may occur without corresponding vari-ation of the hydraulic pressure (ie BPV) Howeverphysical e ects that generate friction variation such asphase transformation uneven transfer lm generationcorrosion etc will also generate geometrical irregularit-ies (DTV etc) with normal force variation and BPVHence it is often meaningful to consider BTV and BPVas an entity However their relative magnitudes arefunctions of the actual friction coe cient

Independently of how and where the disturbance isproduced it is transmitted and ampli ed in the sameway The wheel suspension ampli es the vibrationsespecially the frequencies near its eigenfrequenciesUsually there is a second ampli cation of the vibrationin for instance the steering system

An obvious way of reducing the judder is to reducethe BTVBPV which is the source of the vibrations Thistraditional approach will place the focus on the brakecomponents ie pad and disc

An alternative strategy especially with severe steeringwheel vibrations is to reduce the ampli cation eitherthe primary ampli cation in the wheel suspension ora relevant secondary ampli cation at the steeringsystem This can e ectively be achieved by introductionof the brake-by-wire and steering-by-wire techniquesSimulations and measurements by Jacobsson [23] dem-onstrate that the ampli cation is relatively low in thesubcritical region as indicated in Fig 6 Hence thevibration is reduced if the eigenfrequencies of the compo-nents in the transfer path are shifted above the frequencyrange of the rst wheel order excitation (above 25ndash30 Hzor vehicle speeds above 170ndash200 kmh) which was sug-gested by Engel et al [25] Also modal separation ofeigenfrequencies in the transfer path should be ensured

31 Pads

When developing or choosing a pad material more than20 properties are considered [26 ] Everything from den-sity melting point strength (tensile compressive ex-ural and shear) machinability environmental impactsqueal probability etc should be considered Withrespect to judder properties of interest are sti ness

424 H JACOBSSON

coe cient of friction coe cient of thermal expansionthermal conductivity corrosion and porosity

The most important pad property for judder reductionis the compressive sti ness [11] The BTV level can varyby a factor of 2ndash3 (with the same DTV ) depending onthe pad composition [21 27] The pad compressivesti ness should also be as low as possible to promoteuniform contact pressure [3 8 ] and to avoid TEI pro-cesses such as hot banding and thermal DTV This will atthe same time reduce eventual brake squeal problems [1 ]

The relation between the BTVBPV level and the padsti ness of modern passenger cars is non-linear [11] Inparticular during compression the material becomesprogressively sti er as the load is applied [15] For theseprogressive materials the same DTV level will result ina higher BTV level for hard than for light brakings

To achieve a good lsquopedal feelrsquo and positive retractionthe sti ness should be reasonably high and progressiveGenerally the desired zone is narrow and a deviationon either side might lead to complaints [28] Progressivebrake pads ie traditional composite pads [15] su erfrom high sensitivity to increases in the DTV level seereference [5 ] A linear pad compression characteristicwould not require as high safety margins for increasesfrom the initial DTV (thermal DTV and long-time wearDTV etc) as the progressive pad does In other wordslinear pads are likely to accept higher disc thickness tol-erances than the 10 iacutem DTV The new lsquobrake-by-wirersquotechnique o ers other ways of achieving lsquoa good brakefeelrsquo than a high and progressive pad compressionsti ness

32 Disc

The thermal stability of the disc shape is in uenced bythe quality of the material and the heat treatment beforemachining as well as the basic design of the disc rotorDisc design variants that are more or less stable toconing have been discussed in references [2 3 22 29]Thermal stability problems can be minimized by choos-ing high carbon disc materials and introducing thermalstress relief treatment into the machining cycle [13]

Some of the thermally most important properties ofdisc brakes are as follows [3 30]

1 Thermal capacitance (ie density and speci c heat) isthe ability to store heat Initially on braking a sig-ni cant amount of frictional heat is stored [3 ] andconsequently during short brakings the thermalcapacitance dominates

2 Heat dissipation becomes important at long brakingtimes (above 2ndash3 min [3 ]) ie drag braking or moun-tain descent braking However it also a ects thediscrsquos ability to recover thermally between stops [31]Convection accounts for more than 90 per cent of allheat dissipation for most braking conditions [3 ]whereby radiation is almost negligible The heat

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

transfer coe cient due to convection varies as thevehiclersquos velocity to the power 08 [3 ]

3 Thermal conductivity is the ability to redistributethermal energy During long low intensity brakingsthe peak temperature depends largely on the discmaterialrsquos conductivity [32] During short brakingshowever the thermal conductivity has little e ect

4 Thermal expansion coe cient (ie related to localiz-ation of friction contact due to the thermal defor-mation) a ects the tendency towards hot spotting andthermal DTV generation Temperature gradients of abrake disc cause temporary DTV owing to uneventhermal expansion of the material

Ventilated brake discs are widely used for their weightsavings and additional convective heat transferHowever they may increase judder problems byinducing an uneven temperature eld around the discOver short ( less than a few minutes) and high speedstops thermal capacity is the most important thermalproperty which is why a solid disc (with its higher mass)runs cooler than the vented design [3 31] In mountaindescent braking the disc brake temperatures mayincrease considerably when the vents are removed [31]

Aluminium especially SiC-reinforced Al metal matrixcomposite materials requires a lower operating tempera-ture than grey cast iron (around 450 degC) [32 ] Becausethe material su ers from low thermal capacity it canonly be used for relatively light passenger cars say below1000 kg The introduction of aluminium composite discsor pure aluminium covered by a composite layer willprobably increase judder problems because of the highcoe cient of thermal expansion and the low heatcapacity [22] The high thermal conductivity has there-fore relatively little in uence on the hot spot and thermalDTV generation

However there are composite materials that mighthave the ability to reduce judder namely ceramic mate-rials An example is a short bre reinforced SiC material(CSiC ) which has recently been introduced in sportscars and high speed trains [33] Judder is avoidedbecause of the low coe cient of thermal expansion andlow wear Also the low elastic modulus should promoteuniform contact and reduce thermal DTV and hot spotsThe excellent resistance to thermal damage of the mate-rial makes it suitable for disc brakes of heavy vehicleswhere cracking of the normally used cast-iron disc is aproblem However the high cost of the material excludesapplications in the ordinary family car segment

33 Vehicle structure

The front suspension is designed to admit largevibrations in the vertical direction However there is avibration in the forendashaft direction [24 27] which isrelated to brake judder as well as a proportional angularvibration [24] Brake judder is strongly related to the

425ASPECTS OF DISC BRAKE JUDDER

suspension design and the forendashaft exibility is a domi-nating parameter [27] Stringham et al [12] stated thatthe sti ness of the lower arm bushing is the most in u-ential parameter It was found to a ect signi cantly theeigenfrequency of the suspension system in the forendashaftdirection Bosworth [34] studied the suspension struc-ture in more detail and found the following factorscontrolling the judder

(a) tie rod bushmdashradial and forendashaft sti ness(b) lower arm bushmdashforendashaft sti ness(c) anti-roll barmdashvertical sti ness

In particular the sti ness of the lower arm bushing isimportant since it signi cantly a ects the eigenfre-quency of the suspension system in the forendashaft direction[12 34 35] Higher eigenfrequencies which will reducejudder problems such as steering wheel vibrations maybe achieved either by higher sti ness of the rubber bush-ings or by a reduced value of the modal mass and inertiaof the wheel suspension see Jacobsson [5 ]

However modern suspensions have become more andmore exible in the forendashaft direction because of theintroduction of radial tyres [27] This is necessary inorder to absorb the longitudinal vibrations from the sti belt of the tyres

Note that it is essential to measure the eigenfrequencyand damping in the brake-on mode When the brakeswere not applied the experimental vehicle was found tohave a signi cantly higher eigenfrequency (18 Hz com-pared with 138 Hz) and a lower equivalent viscousdamping factor (007 compared with 009) than meas-ured under the same braking conditions see reference[24] Also the instantaneous centre of motion of the strutchanges with the brake pressure level [5 ] It movedgradually towards the wheel axle as the brake pressureincreased

4 TIME-SCALES

Brake judder depends strongly on the braking historyon the short as well as on the long time-scale There arethree di erent time-scales involved in brake judder

(a) revolution time of the wheel(b) brake application time or the time between two

brakings(c) lifetime of brake components

Traditionally in brake design only the long-time changesare considered In recent years changes during brakinghave also been focused on The generation of localizedcontact area pressure and temperature gradients suchas hot banding has been studied It is found that DTVis a dynamic property that may change considerablyduring a brake application [7 11]

Changes within the time of a wheel revolution arenormally not included primarily because of di culties

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

in making numerical and signal analysis when using con-ventional techniques However the amplitude functiontechnique [23] handles sinusoidal variations of the braketorque with wheel revolution

5 APPROACH

The way of looking at and describing a problem is herecalled the problem approach It is a theoretical abstrac-tion lsquoa conception of the worldrsquo including a model andits system limits The problem approach determineswhich physical e ects can be studied and also states thetime and space scale The chosen problem approach willhave consequences for how to analyse the problem aswell as for the type of solution that will be found It alsodetermines which type of analytical and experimentaltool is the most appropriate

When studying the literature on brake judder it isclear that two fundamentally di erent approaches are inuse namely the cause and e ect approaches While thee ect approach focuses on the source of the vibrationsin the form of amplitude and vibrational order of theBTV andor BPV the cause approach deals with anumber of physical e ects such as wear and heatingsee Fig 3

The e ect approach can be further split into di erentapproaches [4 ]

1 The system approach examines how a model of thevehicle or the wheel suspension together withBTVBPV generates judder The braking process isusually represented by a constant frequency whichcan be parametrically changed It is used mostly inexperimental analysis [13 25 36 ] Also some quasi-static analyses may be found in literature Kim et al[35] used multibody system (MBS) analysis of amodel with 12 degrees of freedom (DOF ) of aMcPherson-type suspension exposed to rst-orderjudder

2 The frequency sweep approach examines how thebraking process itself (including a frequency sweep)together with the BTVBPV generates judder Thevehicle structure can be represented by a resonancecorresponding to the actual critical speed [23]

3 The human response approach studies the e ects ofjudder on one speci c test driver or on an average

Fig 3 Problem approaches

426 H JACOBSSON

person placed in a speci c vehicle Alternatively thehuman response to judder could be thought of as athird level where the judder level and frequencytogether with the weight size and place of the personin the vehicle etc are the input

Some approaches are listed in Table 1 together withrelated analytical and experimental methods and toolsfound in the literature [4 ] For instance FE analysis isthe natural choice when studying BTV generation bymeans of for instance the TEI process For the e ectapproach where the BTV can be represented by a sinus-oidal brake torque disturbance it is instead the vehicleor relevant parts thereof that should be modelled ThenMBS analysis (commercial programs are ADAMSDADS etc) is more relevant especially for lowfrequency judder (say below 50 Hz)

In experimental brake judder studies bench testing aswell as road testing are used Advantages of bench test-ing [11] are good reproducibility of the testing con-ditions more accurate measurements higher sensitivityof measurements lower cost and less time consumption[37] Disadvantages are that cooling conditions are nottaken into account as well as the in uence of othermachine elements and systems which will a ect thetransmission of BTV in the vehicle (tyres wheel sus-pension steering) [11] In road testing the speci cproblem occurs that the level of BTVBPV cannot becontrolled during a brake application This problemmay be handled by measuring BTVBPV instead oftrying to control it by constant conditions such as speedtemperature pressure etc see references [9 23]

51 Causes of BTVBPV

Traditionally the source of the BTVBPV has beenfocused on It is a ected by a combination of the di er-ent physical e ects discussed in section 2 Disc run-outand DTV which are geometrical irregularities of thedisc directly cause normal force variations and henceBTVBPV see Fig 4 Furthermore the TEI process gen-erates hot spots and sometimes remaining discolouredareas with locally di erent speci c volume and wearproperties which may aggravate the vibrations Finally

Table 1 Approaches and corresponding methods

Approach Methods and tools

Cause approach (FE) analysis nite di erence dynamometertribometer drag braking thermal imagingX-rays

System approach MBS analysis Fourier methods modal analysisTaguchi methodology road testsspectrograms

Frequency sweep Time plane analysis road tests involvingapproach deceleration waterfall analysis order

tracking ABS and capacitive transducersHuman response Subjective rating deceleration tests

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

Fig 4 BTV causes for a disc brake

there is a contribution from the dynamic de ection ofthe disc due to external forces such as tyre forces andunbalances

One of the problems with brake analysis is that it isnecessary to solve coupled de ection and temperature eld problems with combined de ection and thermalload Commercially available FE programs can handlepure mechanical or pure thermal problems Brooks et al[8 ] introduced a two-dimensional (ie axisymmetrical )combined thermal and mechanical method of hot band-ing simulation of a disc brake The basic idea is to switchbetween de ection and temperature eld calculationseach of which can be made in commercial FE programssuch as ABAQUS The FE model takes into account thetime-dependent change in the contact area A similarconcept was developed by Kao et al [7 ] Both three-dimensional (necessary to be able to model buckling)and axisymmetric models have been used to study thein uence of pad design parameters on thermal padcracking as well as to simulate thermoelastic bucklingand its coupling to TEI and thermal DTV

Thermoelastic simulation of brake components underrealistic conditions involves massive central processingunit computational e ort and data storage [7 ] This isespecially the case when simulating slow decelerations(ie sti problems) with long duration timesUnfortunately it is this type of braking that generatesthe most pronounced hot spots There are various waysto make the simulation more e ective

1 Circumferential variations of the instantaneous discsurface conditions and geometry can be neglectedHowever when studying brake judder problems thecircumferential variations are essential

2 A specially dedicated contact element can be used toderive the frictional force and heat generated at theinterface [3 37]

3 Solving the coupled eld problems simultaneously(see reference [14]) is more accurate and e ectiveHowever since it relies on a Newton-type methodfrom the 1990s the algorithms are not yet included incommercial FE programs

4 A three-dimensional hybrid method which combinesfast Fourier transform (FFT) techniques withFE methods has been developed by Floquet and

427ASPECTS OF DISC BRAKE JUDDER

Dubourg [38] The application of the Fourier trans-form (on a space variable) has the e ect of reducingthe dimension of the problem The variable is trans-formed into a discrete parameter the frequency andthe corresponding partial derivatives are removedThe method can handle geometrically periodic butnon-axisymmetric solids such as ventilated discbrakes

5 The FE method can be applied directly to a pertur-bation method [39] The basic idea is not to solve thetransient problem but to consider the conditionsunder which a small perturbation in the temperature eld can grow exponentially in time The method isapplicable to transient processes as long as the contactarea does not change with time However the contactarea does change considerably with time duringbraking

6 A pad model composed of springndashdamper elementscan be used [22]

For vented discs and aluminium discs in particularwhere the air ow is important computational uiddynamics (CFD) is a useful tool CFD is used by somerotor manufacturers to increase air ow [26 40] In amarket survey [26 ] many companies saw the potentialof combining FE analysis and CFD to gain more accu-rate temperature predictions However this wouldrequire enormous computational e orts

As an alternative to CFD the convective cooling maybe estimated by approximative methods On a ventedrotor there are two di erent types of convective coolingair cross- ow over the rotor surface and air pumped owthrough the vents [3 ] Brake rotor vane ow relationsto estimate the heat convective transfer coe cient havelong been used in brake system thermal modellingCurrently two relations are recognized for ventilateddisc air ow those of Sisson and Limpert [30] Analternative is to approximate the convective heat transfercoe cient from the Nusselt modulus [31 32] and tocorrect it with empirically determined factors

52 E ects of BTVBPV

A few research projects have focused on the e ect ofbrake vibrations in the vehicle despite the fact that ithas been qualitatively described in the literature Crollaand Lang [41] Haigh et al [17] and many others havedescribed how brake judder rises to a maximum whenpassing through more or less distinct speeds So far theevaluation of brake judder has been done with a subjec-tive method using a scale from 1 to 10 but hardly anysimulations of brake judder in a vehicle have been car-ried out Brake judder problems have traditionally beensolved by use of trial and error rather than systematicmethods

In the literature there are a few sensitivity studies butin practice no lsquotruersquo simulations The di erence in that

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

lsquotruersquo simulations needs to be evaluated in the time planeThis involves not only a model of the vibration source(BTVBPV) and the vehicle structure and linkage (reson-ances and transfer) but also modelling of the brakingevent (frequency sweep braking conditions) see Fig 5

Straightforward integration of di erential equationswithout intelligent variable transformations or assump-tions using an ordinary equation-solving algorithmdesigned for non-sti problems (eg RungendashKutta) isnot an e cient way of dealing with this type of problemThe simulation will take an unnecessarily long time(hours or days) fail or crash Also the algorithms usedby commercial mechanics programs such as ADAMSare slow and ine cient if one wishes to follow a wholebraking event Hence the maximal vibration levels willbecome largely overestimated at nite braking timesHowever these types of programs are useful for quasi-static sensitivity analysis

521 Sensitivity analysis

Applying the system approach the solution to the judderproblem will be to build robustness into the vehicle andthereby to make it less sensitive to BTVBPV The systemof Engel et al [25] consists of ve di erent steps namelythe brake disc caliper and pad tyre and hubndashbearingunit wheel knuckle and nally the steering system Thereis also feedback between some steps in the outlinedmodel

An attempt to model numerically the vehicle responseto BTV was made by Kim et al [35] using MBS analysisof a similar vehicle structure The modelling of the sus-pension system used in the calculations was howevernot described Similar analyses are often carried out inthe automotive industry but seldom is the modellingdescribed in the literature However the model ofAugsburg et al [11] was described in detail

(a) calliper as two masses connected by a spring (rep-resenting the calliper sti ness in the forendashaftdirection)

(b) brake pads as springs(c) brake piston by a mass(d) hydraulic system as volume accumulating elements

The transfer path from the vibration source to thedriverrsquos contact points can be qualitatively investigatedby simultaneous measurements of accelerations atvarious position such as wheel carrier steering tie rod

Fig 5 The frequency sweep approach

428 H JACOBSSON

steering wheel etc [13] The sampled signals can be usedto generate the transfer functions between di erentpoints [9 36 ] The technique can be used to describeboth the brake excitation and the transfer functions thatcharacterize vehicle sensibility

The amplitude functions [23] can be seen as gen-eralized transfer functions They can be used to classifythe braking event as well as the corresponding vibrationsin the vehicle An advantage of the amplitude functionover the transfer function technique is that it works formuch higher decelerations since it does not rely on theFFT The method also determines the eigenfrequencieswith higher accuracy since it takes into account thetime delay of the maximal ampli cation caused by the nite deceleration and the inertias of the system If thistime delay is not considered the eigenfrequencies willbe systematically underestimated especially at highdecelerations

The analysis can be made in the frequency plane pro-vided that the braking starts above a certain limit often10ndash30 per cent above the critical speed [5 ] The deceler-ation clearly lsquocutsrsquo the maximal vibration amplitudeespecially at low damping Already at relative dampinglevels of the order of 1 per cent the transient analysis(including the frequency sweep) is needed for the rst-order judder except for in nitesimally smalldeclerations

Aviles et al [42] studied a braking event with slowlydecreasing speed and frequency However the con-clusion was drawn that the peak of the vibration ampli-tude at a certain vehicle speed was altogether an e ectof the negative frictionndashvelocity slope introduced in themodel The e ect of the frequency sweep was neveranalysed separately The calculations were made in thefrequency domain

522 Judder vibration simulation

Most of the analyses and measurements of judder aremade for braking with constant speed ie constant rev-olution frequency of the wheel as well as constant press-ure and temperature An argument is that it is easier tomeasure and analyse vibrations on the basis of this pre-scription Another bene t of measuring at constantspeed is e cient data analysis in the frequency domainHowever in a real braking situation the frequency isnot constant

There is a dynamic ampli cation of the brake torqueand pressure variations when passing through orcoming close to a critical speed of a vehicle Thevibration starts when the braking force is applied andreaches a maximal amplitude at a certain speed It iscontinued until low speed if the braking force is continu-ously applied This is the typical behaviour of a forcedvibration with relatively constant source amplitude butwith a sweeping frequency Fig 6

A two-DOF rotorndashstator model [24] with a linearly

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

decreasing disc speed possesses the main characteristicsof judder as shown in Fig 6 Before analysis the de ec-tion angles of rotordisc and statorcaliper respectivelywere split into vibration-free parts W and WC (rotationstatic de ection) and the superimposed vibrations QD andQ

C respectively The shape of the amplitude function Edescribes the relative vibration level QC (second timederivative of QC) almost exactly All parameters of therotorndashstator model can be experimentally generated

A full-vehicle model [5 ] shows the same lsquojudder behav-iourrsquo but can also explain some other e ects It is morecomplicated since it demands information about thewind speed slip etc

It is generally accepted that the front wheel suspensionof passenger cars has a rigid body forendashaft vibrationmode resonance in the frequency range 10ndash20 Hz andthat this resonance is responsible for lower-order judderat corresponding velocities This corresponds to a maxi-mal amplitude of the vibrations at a critical vehicle speedof between 60 and 140 kmh for the rst-order judderThe second-order judder will have a corresponding criti-cal speed (because of the same resonance) of between 30and 70 kmh The present vehicle had a resonance near14 Hz corresponding to a rst-order critical speed of95 kmh

The following possibilities for reducing judder werefound [5 ]

(a) decreased BTV andor BPV which will lead backto the cause approach

(b) increased relative stator mass and inertia momentcompared with the rotor

(c) increased damping(d) lighter braking(e) higher eigenfrequency

A lighter vehicle and a smaller wheel radius decrease thejudder problems [5 ] A reduction of the vehicle mass willalso decrease the thermal DTV and hotspots and reducethe risk of thermal cracking provided that the thermalcapacity of the disc remains the same A lighter stator(ie strut and eventually disc) will tend to increase thejudder problems since the ampli cation of BTV willbecome larger

6 FUTURE

The eld of low frequency braking induced vibrations isstill characterized by confusion Much research is neededin this area before a fairly clear picture becomes appar-ent The author nds the following areas especiallyinteresting

(a) simulation of BTV generation combining wear andTEI (wear especially hot and high pressure weartends to counteract the TEI process)

(b) the groan phenomenon(c) friction lms

429ASPECTS OF DISC BRAKE JUDDER

Fig 6 Model and corresponding brake judder simulation versus measurement

(d) the TEI process and its connection to thermoelasticbuckling

(e) studying wheel suspension vibration modes duringbrake-on conditions

(f ) the relation between BTV and simultaneous vari-ations in geometry (DTV run-out equivalent brakeradius) and friction coe cient

(g) prediction of BTV level and order for speci eddesign parameters and braking conditions

(h) developing models for simulation of vibration levelsin a vehicle at speci ed BTV

Generally in brake judder analysis it is recommendedto split the investigations into two parts

1 Analysis of sources of irregularities such as DTV etcThis involves thermomechanical FE analysis of thebrake components or dynamometer tests These typesof calculations are extremely time demanding

2 Analysis of the e ect of the irregularities in the vehicleIf the disturbances (which may be output from FEanalysis or dynamometer measurements) are given asfunctions of time very fast simulation can be carriedout by means of the amplitude function techniquedescribed in this work

The amplitude function technique is still at an earlystage but there are no di culties in principle involvedin using it to analyse multiple mass system models ofa whole vehicle Such models would be useful in deter-mining design criteria of brake components andsuspensions etc

REFERENCES

1 Hulten J Drum brake squeal PhD thesis Machine andVehicle Design Chalmers University of TechnologyGoteborg 1998

2 Inoue H Analysis of brake judder caused by thermal defor-mation of brake disc rotors In Proceedings 21st FISITACongress Belgrade 1986 pp 213ndash219 paper 865131

3 Kao T K Richmond J W and Moore M W The appli-

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

cation of predictive techniques to study thermo-elasticinstability of brakes In Proceedings of the Twelfth AnnualBrake Colloquium and Engineering Display AtlantaGeorgia 1984 SAE paper 942087

4 Jacobsson H Frequency sweep approach to brake judderpart A the brake judder phenomenon Classi cation andproblem approach Licentiate thesis Chalmers Universityof Technology Goteborg 1998

5 Jacobbson H Brake judder Thesis Chalmers Universityof Technology Goteborg 2001

6 Abdelhamid M K Creep groan of disc brakes InProceedings Noise and Vibration Conference TraverseCity Michigan 1995 pp 396ndash400 SAE paper 951282

7 Kao T K Richmond J W and Douarre A Brake dischot spotting and thermal judder an experimental and niteelement study Int J Veh Des 2000 23(34) 276ndash296

8 Brooks P C Barton D Crolla D A Lang A M andSchafer D R A study of disc brake judder using a fullycoupled thermo-mechanical nite element model InProceedings 25th FISITA Congress Beijing 1994pp 340ndash349 SAE paper 945042

9 Abdelhamid M K Brake judder analysis case studies SAEpaper 972027 1997

10 Kreitlow W Schrodter F and Matthai H Vibration andlsquohumrsquo of disc brakes under load SAE paper 850079 SAETrans Sect 1 1985 431ndash437

11 Augsburg K Brunner H and Grochowicz JUntersuchungen zum Rubbelverhalten von Pkw-Schwimmsattelbremser Automobiltechnische Zeitschrift1999 101

12 Stringham W Jank P Pfeifer J and Wang A Brakeroughnessmdashdisc brake torque variation rotor distortionand vehicle response SAE paper 930803 SAE TransSect 6 1993 1235ndash1247

13 Engel H G Bachman Th Eichhorn U and Saame ChDynamical behavior of brake-disc geometry as cause ofbrake judder In Proceedings EAEC Fourth InternationalConference on Vehicle and Tra c System TechnologyStrasbourg France 1993 Vol 1 pp 456ndash481

14 Thuresson D Thermomechanical analysis of frictionbrakes In Proceedings of the Eighteenth Annual BrakeColloquium and Engineering Display 2000 Vol P-358pp 149ndash159 SAE paper 2000-01-2775

15 Richmond J W Kao T K and Moore M W The devel-opment of computationalanalysis techniques for disc brake

430 H JACOBSSON

pad design In Proceedings Advances in AutomotiveBraking Technology Design Analysis and MaterialDevelopments 1996 (Institution of Mechanical Engineers)

16 Abendroth H Ste en T Falter W and Heidt RInvestigation of CV rotor cracking test procedures InBrakes 2000 International Conference on AutomotiveBrakingmdashTechnologies for the 21st Century 2000pp 149ndash162 (Professional Engineering PublishingLondon)

17 Haigh M J Smales H and Abe M Vehicle judder underdynamic braking caused by disc thickness variation InProceedings Braking of Road Vehicles London 1993pp 247ndash258 IMechE paper C44402293

18 Borjesson M Eriksson P Kuylenstierna C NilssonP H and Hermansson T The role of friction lms inautomotive brakes subjected to low contact forces InProceedings Braking of Road Vehicles London 1993pp 259ndash267 IMechE paper C444026

19 Wirth A and Whitaker R Developments in cast iron tech-nology In Proceedings Advances in Automotive BrakingTechnology Design Analysis and Material DevelopmentsLeeds UK 1996 (Institution of Mechanical Engineers)

20 Thoms E Disc brakes for heavy vehicles In ProceedingsBraking of Road Vehicles London 1988 pp 133ndash137IMechE paper C46488

21 Aviles R Hennequet G Hernandez A and Llorente L ILow frequency vibrations in disc brakes at high car speedPart I experimental approach Int J Veh Des 199516(6) 542ndash555

22 Ste en T and Bruns R Hotspotsbildung bei Pkw-Bremsscheiben Automobiltechnische Zeitschrift 1998100 408ndash413

23 Jacobsson H Analysis of brake judder by use of amplitudefunctions In Proceedings of SAE Noise and VibrationConference 1999 SAE paper 1999-01-1779

24 Jacobsson H Wheel suspension related disc brake judderIn Proceedings ASME Design Engineering TechnicalConferences Sacramento California 1997 VIB-4165

25 Engel H G Hassiotis V and Tiemann R Systemapproach to brake judder In Proceedings 25th FISITACongress Beijing 1994 Vol 1 pp 332ndash339 paper 945041

26 Martin R H and Bowron S Composite materials in trans-port friction applications In Brakes 2000 InternationalConference on Automotive BrakingmdashTechnologies for the21st Century 2000 pp 207ndash216 (Professional EngineeringPublishing London)

27 de Vries A and Wagner M The brake judder phenom-enon SAE Trans Sect 6 1992 101 652ndash660

28 Palmer B B and Weintraub M H The role of engineeredcashew particles on performance In Brakes 2000International Conference on Automotive BrakingmdashTechnologies for the 21st Century 2000 pp 185ndash195(Professional Engineering Publishing London)

29 Koetniyom S Brooks P C and Barton D C Finite

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

element prediction of inelastic strain accumulation in cast-iron brake rotors In Brakes 2000 InternationalConferenceon Automotive BrakingmdashTechnologies for the 21st Century2000 pp 139ndash148 (Professional Engineering PublishingLondon)

30 Hudson M D and Ruhl R L Ventilated brake rotor air ow investigation SAE paper 971033 1997

31 Grieve D G Barton D A Crolla D A Chapman J Land Buckingham J T Alternative brake disc materials InProceedingsAdvances in Automotive Braking TechnologyDesign Analysis and Material Developments Leeds UK1996 (Institution of Mechanical Engineers)

32 Grieve D G Barton D C Crolla D A and BuckinghamJ K Design of a lightweight automotive brake disc using nite element and Taguchi techniques Proc Instn MechEngrs Part D J Automobile Engineering 1998 212245ndash254

33 Krupka R and Kienzle A Fiber reinforced ceramic com-posite for brake discs In Proceeding of the EighteenthAnnual Brake Colloquium and Engineering Display 2000Vol P-358 pp 67ndash69 SAE paper 2000-01-2761

34 Bosworth R Investigations of secondary ride aspects ofsteering wheel vibration (shimmy and judder) using Taguchimethodology In Proceedings AUTOTECH 89 London1989 IMechE paper C3999

35 Kim M-G Jeong H-I and Yoo W-S Sensitivity analy-sis of chassis system to improve shimmy and brake juddervibration on steering wheel SAE Special Publication 11361996 pp 59ndash70

36 Abdelhamid M K Brake judder analysis using transferfunctions In Proceedings SAE Brake Colloquium TempeArizona 1997 pp 5ndash9 SAE paper 973018

37 Kao T K Richmond J W and Moore M WComputational analysis of pad performance InProceedings Braking of Road Vehicles 1993 paperC44402793 (Institution of Mechanical Engineers)

38 Floquet A and Dubourg M-C Realistic braking operationsimulation of ventilated disc brakes Trans ASMEJ Tribology July 1996 118 466ndash472

39 Du S Zagrodzki P Barber J R and Hulbert G MFinite element analysis of frictionally excited thermoelasticinstability J Thermal Stresses 1997 20 185ndash201

40 Daudi A R Dickerson W E and Narain M Hayesrsquoincreased air ow rotor design In Proceedings SecondInternational Seminar on Automotive Braking RecentDevelopments and Future Trends Leeds UK 1998pp 127ndash143 (Institution of Mechanical Engineers)

41 Crolla D A and Lang A M Brake noise and vibrationmdashthe state of the art Vehicle Tribology Tribology SeriesVol 18 1991 (Elsevier) pp 165ndash174

42 Aviles R Hennequet G Amezua E and Vallejo J Lowfrequency vibrations in disc brakes at high car speedPart II mathematical model and simulation Int J VehDes 1995 16(6) 556ndash569

Page 6: Aspects of disc brake judder - Universiti Teknologi Malaysiaarahim/jacobsson.pdf · 419 Aspects of disc brake judder HJacobsson* Machine and Vehicle Systems, Chalmers University of

424 H JACOBSSON

coe cient of friction coe cient of thermal expansionthermal conductivity corrosion and porosity

The most important pad property for judder reductionis the compressive sti ness [11] The BTV level can varyby a factor of 2ndash3 (with the same DTV ) depending onthe pad composition [21 27] The pad compressivesti ness should also be as low as possible to promoteuniform contact pressure [3 8 ] and to avoid TEI pro-cesses such as hot banding and thermal DTV This will atthe same time reduce eventual brake squeal problems [1 ]

The relation between the BTVBPV level and the padsti ness of modern passenger cars is non-linear [11] Inparticular during compression the material becomesprogressively sti er as the load is applied [15] For theseprogressive materials the same DTV level will result ina higher BTV level for hard than for light brakings

To achieve a good lsquopedal feelrsquo and positive retractionthe sti ness should be reasonably high and progressiveGenerally the desired zone is narrow and a deviationon either side might lead to complaints [28] Progressivebrake pads ie traditional composite pads [15] su erfrom high sensitivity to increases in the DTV level seereference [5 ] A linear pad compression characteristicwould not require as high safety margins for increasesfrom the initial DTV (thermal DTV and long-time wearDTV etc) as the progressive pad does In other wordslinear pads are likely to accept higher disc thickness tol-erances than the 10 iacutem DTV The new lsquobrake-by-wirersquotechnique o ers other ways of achieving lsquoa good brakefeelrsquo than a high and progressive pad compressionsti ness

32 Disc

The thermal stability of the disc shape is in uenced bythe quality of the material and the heat treatment beforemachining as well as the basic design of the disc rotorDisc design variants that are more or less stable toconing have been discussed in references [2 3 22 29]Thermal stability problems can be minimized by choos-ing high carbon disc materials and introducing thermalstress relief treatment into the machining cycle [13]

Some of the thermally most important properties ofdisc brakes are as follows [3 30]

1 Thermal capacitance (ie density and speci c heat) isthe ability to store heat Initially on braking a sig-ni cant amount of frictional heat is stored [3 ] andconsequently during short brakings the thermalcapacitance dominates

2 Heat dissipation becomes important at long brakingtimes (above 2ndash3 min [3 ]) ie drag braking or moun-tain descent braking However it also a ects thediscrsquos ability to recover thermally between stops [31]Convection accounts for more than 90 per cent of allheat dissipation for most braking conditions [3 ]whereby radiation is almost negligible The heat

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

transfer coe cient due to convection varies as thevehiclersquos velocity to the power 08 [3 ]

3 Thermal conductivity is the ability to redistributethermal energy During long low intensity brakingsthe peak temperature depends largely on the discmaterialrsquos conductivity [32] During short brakingshowever the thermal conductivity has little e ect

4 Thermal expansion coe cient (ie related to localiz-ation of friction contact due to the thermal defor-mation) a ects the tendency towards hot spotting andthermal DTV generation Temperature gradients of abrake disc cause temporary DTV owing to uneventhermal expansion of the material

Ventilated brake discs are widely used for their weightsavings and additional convective heat transferHowever they may increase judder problems byinducing an uneven temperature eld around the discOver short ( less than a few minutes) and high speedstops thermal capacity is the most important thermalproperty which is why a solid disc (with its higher mass)runs cooler than the vented design [3 31] In mountaindescent braking the disc brake temperatures mayincrease considerably when the vents are removed [31]

Aluminium especially SiC-reinforced Al metal matrixcomposite materials requires a lower operating tempera-ture than grey cast iron (around 450 degC) [32 ] Becausethe material su ers from low thermal capacity it canonly be used for relatively light passenger cars say below1000 kg The introduction of aluminium composite discsor pure aluminium covered by a composite layer willprobably increase judder problems because of the highcoe cient of thermal expansion and the low heatcapacity [22] The high thermal conductivity has there-fore relatively little in uence on the hot spot and thermalDTV generation

However there are composite materials that mighthave the ability to reduce judder namely ceramic mate-rials An example is a short bre reinforced SiC material(CSiC ) which has recently been introduced in sportscars and high speed trains [33] Judder is avoidedbecause of the low coe cient of thermal expansion andlow wear Also the low elastic modulus should promoteuniform contact and reduce thermal DTV and hot spotsThe excellent resistance to thermal damage of the mate-rial makes it suitable for disc brakes of heavy vehicleswhere cracking of the normally used cast-iron disc is aproblem However the high cost of the material excludesapplications in the ordinary family car segment

33 Vehicle structure

The front suspension is designed to admit largevibrations in the vertical direction However there is avibration in the forendashaft direction [24 27] which isrelated to brake judder as well as a proportional angularvibration [24] Brake judder is strongly related to the

425ASPECTS OF DISC BRAKE JUDDER

suspension design and the forendashaft exibility is a domi-nating parameter [27] Stringham et al [12] stated thatthe sti ness of the lower arm bushing is the most in u-ential parameter It was found to a ect signi cantly theeigenfrequency of the suspension system in the forendashaftdirection Bosworth [34] studied the suspension struc-ture in more detail and found the following factorscontrolling the judder

(a) tie rod bushmdashradial and forendashaft sti ness(b) lower arm bushmdashforendashaft sti ness(c) anti-roll barmdashvertical sti ness

In particular the sti ness of the lower arm bushing isimportant since it signi cantly a ects the eigenfre-quency of the suspension system in the forendashaft direction[12 34 35] Higher eigenfrequencies which will reducejudder problems such as steering wheel vibrations maybe achieved either by higher sti ness of the rubber bush-ings or by a reduced value of the modal mass and inertiaof the wheel suspension see Jacobsson [5 ]

However modern suspensions have become more andmore exible in the forendashaft direction because of theintroduction of radial tyres [27] This is necessary inorder to absorb the longitudinal vibrations from the sti belt of the tyres

Note that it is essential to measure the eigenfrequencyand damping in the brake-on mode When the brakeswere not applied the experimental vehicle was found tohave a signi cantly higher eigenfrequency (18 Hz com-pared with 138 Hz) and a lower equivalent viscousdamping factor (007 compared with 009) than meas-ured under the same braking conditions see reference[24] Also the instantaneous centre of motion of the strutchanges with the brake pressure level [5 ] It movedgradually towards the wheel axle as the brake pressureincreased

4 TIME-SCALES

Brake judder depends strongly on the braking historyon the short as well as on the long time-scale There arethree di erent time-scales involved in brake judder

(a) revolution time of the wheel(b) brake application time or the time between two

brakings(c) lifetime of brake components

Traditionally in brake design only the long-time changesare considered In recent years changes during brakinghave also been focused on The generation of localizedcontact area pressure and temperature gradients suchas hot banding has been studied It is found that DTVis a dynamic property that may change considerablyduring a brake application [7 11]

Changes within the time of a wheel revolution arenormally not included primarily because of di culties

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

in making numerical and signal analysis when using con-ventional techniques However the amplitude functiontechnique [23] handles sinusoidal variations of the braketorque with wheel revolution

5 APPROACH

The way of looking at and describing a problem is herecalled the problem approach It is a theoretical abstrac-tion lsquoa conception of the worldrsquo including a model andits system limits The problem approach determineswhich physical e ects can be studied and also states thetime and space scale The chosen problem approach willhave consequences for how to analyse the problem aswell as for the type of solution that will be found It alsodetermines which type of analytical and experimentaltool is the most appropriate

When studying the literature on brake judder it isclear that two fundamentally di erent approaches are inuse namely the cause and e ect approaches While thee ect approach focuses on the source of the vibrationsin the form of amplitude and vibrational order of theBTV andor BPV the cause approach deals with anumber of physical e ects such as wear and heatingsee Fig 3

The e ect approach can be further split into di erentapproaches [4 ]

1 The system approach examines how a model of thevehicle or the wheel suspension together withBTVBPV generates judder The braking process isusually represented by a constant frequency whichcan be parametrically changed It is used mostly inexperimental analysis [13 25 36 ] Also some quasi-static analyses may be found in literature Kim et al[35] used multibody system (MBS) analysis of amodel with 12 degrees of freedom (DOF ) of aMcPherson-type suspension exposed to rst-orderjudder

2 The frequency sweep approach examines how thebraking process itself (including a frequency sweep)together with the BTVBPV generates judder Thevehicle structure can be represented by a resonancecorresponding to the actual critical speed [23]

3 The human response approach studies the e ects ofjudder on one speci c test driver or on an average

Fig 3 Problem approaches

426 H JACOBSSON

person placed in a speci c vehicle Alternatively thehuman response to judder could be thought of as athird level where the judder level and frequencytogether with the weight size and place of the personin the vehicle etc are the input

Some approaches are listed in Table 1 together withrelated analytical and experimental methods and toolsfound in the literature [4 ] For instance FE analysis isthe natural choice when studying BTV generation bymeans of for instance the TEI process For the e ectapproach where the BTV can be represented by a sinus-oidal brake torque disturbance it is instead the vehicleor relevant parts thereof that should be modelled ThenMBS analysis (commercial programs are ADAMSDADS etc) is more relevant especially for lowfrequency judder (say below 50 Hz)

In experimental brake judder studies bench testing aswell as road testing are used Advantages of bench test-ing [11] are good reproducibility of the testing con-ditions more accurate measurements higher sensitivityof measurements lower cost and less time consumption[37] Disadvantages are that cooling conditions are nottaken into account as well as the in uence of othermachine elements and systems which will a ect thetransmission of BTV in the vehicle (tyres wheel sus-pension steering) [11] In road testing the speci cproblem occurs that the level of BTVBPV cannot becontrolled during a brake application This problemmay be handled by measuring BTVBPV instead oftrying to control it by constant conditions such as speedtemperature pressure etc see references [9 23]

51 Causes of BTVBPV

Traditionally the source of the BTVBPV has beenfocused on It is a ected by a combination of the di er-ent physical e ects discussed in section 2 Disc run-outand DTV which are geometrical irregularities of thedisc directly cause normal force variations and henceBTVBPV see Fig 4 Furthermore the TEI process gen-erates hot spots and sometimes remaining discolouredareas with locally di erent speci c volume and wearproperties which may aggravate the vibrations Finally

Table 1 Approaches and corresponding methods

Approach Methods and tools

Cause approach (FE) analysis nite di erence dynamometertribometer drag braking thermal imagingX-rays

System approach MBS analysis Fourier methods modal analysisTaguchi methodology road testsspectrograms

Frequency sweep Time plane analysis road tests involvingapproach deceleration waterfall analysis order

tracking ABS and capacitive transducersHuman response Subjective rating deceleration tests

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

Fig 4 BTV causes for a disc brake

there is a contribution from the dynamic de ection ofthe disc due to external forces such as tyre forces andunbalances

One of the problems with brake analysis is that it isnecessary to solve coupled de ection and temperature eld problems with combined de ection and thermalload Commercially available FE programs can handlepure mechanical or pure thermal problems Brooks et al[8 ] introduced a two-dimensional (ie axisymmetrical )combined thermal and mechanical method of hot band-ing simulation of a disc brake The basic idea is to switchbetween de ection and temperature eld calculationseach of which can be made in commercial FE programssuch as ABAQUS The FE model takes into account thetime-dependent change in the contact area A similarconcept was developed by Kao et al [7 ] Both three-dimensional (necessary to be able to model buckling)and axisymmetric models have been used to study thein uence of pad design parameters on thermal padcracking as well as to simulate thermoelastic bucklingand its coupling to TEI and thermal DTV

Thermoelastic simulation of brake components underrealistic conditions involves massive central processingunit computational e ort and data storage [7 ] This isespecially the case when simulating slow decelerations(ie sti problems) with long duration timesUnfortunately it is this type of braking that generatesthe most pronounced hot spots There are various waysto make the simulation more e ective

1 Circumferential variations of the instantaneous discsurface conditions and geometry can be neglectedHowever when studying brake judder problems thecircumferential variations are essential

2 A specially dedicated contact element can be used toderive the frictional force and heat generated at theinterface [3 37]

3 Solving the coupled eld problems simultaneously(see reference [14]) is more accurate and e ectiveHowever since it relies on a Newton-type methodfrom the 1990s the algorithms are not yet included incommercial FE programs

4 A three-dimensional hybrid method which combinesfast Fourier transform (FFT) techniques withFE methods has been developed by Floquet and

427ASPECTS OF DISC BRAKE JUDDER

Dubourg [38] The application of the Fourier trans-form (on a space variable) has the e ect of reducingthe dimension of the problem The variable is trans-formed into a discrete parameter the frequency andthe corresponding partial derivatives are removedThe method can handle geometrically periodic butnon-axisymmetric solids such as ventilated discbrakes

5 The FE method can be applied directly to a pertur-bation method [39] The basic idea is not to solve thetransient problem but to consider the conditionsunder which a small perturbation in the temperature eld can grow exponentially in time The method isapplicable to transient processes as long as the contactarea does not change with time However the contactarea does change considerably with time duringbraking

6 A pad model composed of springndashdamper elementscan be used [22]

For vented discs and aluminium discs in particularwhere the air ow is important computational uiddynamics (CFD) is a useful tool CFD is used by somerotor manufacturers to increase air ow [26 40] In amarket survey [26 ] many companies saw the potentialof combining FE analysis and CFD to gain more accu-rate temperature predictions However this wouldrequire enormous computational e orts

As an alternative to CFD the convective cooling maybe estimated by approximative methods On a ventedrotor there are two di erent types of convective coolingair cross- ow over the rotor surface and air pumped owthrough the vents [3 ] Brake rotor vane ow relationsto estimate the heat convective transfer coe cient havelong been used in brake system thermal modellingCurrently two relations are recognized for ventilateddisc air ow those of Sisson and Limpert [30] Analternative is to approximate the convective heat transfercoe cient from the Nusselt modulus [31 32] and tocorrect it with empirically determined factors

52 E ects of BTVBPV

A few research projects have focused on the e ect ofbrake vibrations in the vehicle despite the fact that ithas been qualitatively described in the literature Crollaand Lang [41] Haigh et al [17] and many others havedescribed how brake judder rises to a maximum whenpassing through more or less distinct speeds So far theevaluation of brake judder has been done with a subjec-tive method using a scale from 1 to 10 but hardly anysimulations of brake judder in a vehicle have been car-ried out Brake judder problems have traditionally beensolved by use of trial and error rather than systematicmethods

In the literature there are a few sensitivity studies butin practice no lsquotruersquo simulations The di erence in that

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

lsquotruersquo simulations needs to be evaluated in the time planeThis involves not only a model of the vibration source(BTVBPV) and the vehicle structure and linkage (reson-ances and transfer) but also modelling of the brakingevent (frequency sweep braking conditions) see Fig 5

Straightforward integration of di erential equationswithout intelligent variable transformations or assump-tions using an ordinary equation-solving algorithmdesigned for non-sti problems (eg RungendashKutta) isnot an e cient way of dealing with this type of problemThe simulation will take an unnecessarily long time(hours or days) fail or crash Also the algorithms usedby commercial mechanics programs such as ADAMSare slow and ine cient if one wishes to follow a wholebraking event Hence the maximal vibration levels willbecome largely overestimated at nite braking timesHowever these types of programs are useful for quasi-static sensitivity analysis

521 Sensitivity analysis

Applying the system approach the solution to the judderproblem will be to build robustness into the vehicle andthereby to make it less sensitive to BTVBPV The systemof Engel et al [25] consists of ve di erent steps namelythe brake disc caliper and pad tyre and hubndashbearingunit wheel knuckle and nally the steering system Thereis also feedback between some steps in the outlinedmodel

An attempt to model numerically the vehicle responseto BTV was made by Kim et al [35] using MBS analysisof a similar vehicle structure The modelling of the sus-pension system used in the calculations was howevernot described Similar analyses are often carried out inthe automotive industry but seldom is the modellingdescribed in the literature However the model ofAugsburg et al [11] was described in detail

(a) calliper as two masses connected by a spring (rep-resenting the calliper sti ness in the forendashaftdirection)

(b) brake pads as springs(c) brake piston by a mass(d) hydraulic system as volume accumulating elements

The transfer path from the vibration source to thedriverrsquos contact points can be qualitatively investigatedby simultaneous measurements of accelerations atvarious position such as wheel carrier steering tie rod

Fig 5 The frequency sweep approach

428 H JACOBSSON

steering wheel etc [13] The sampled signals can be usedto generate the transfer functions between di erentpoints [9 36 ] The technique can be used to describeboth the brake excitation and the transfer functions thatcharacterize vehicle sensibility

The amplitude functions [23] can be seen as gen-eralized transfer functions They can be used to classifythe braking event as well as the corresponding vibrationsin the vehicle An advantage of the amplitude functionover the transfer function technique is that it works formuch higher decelerations since it does not rely on theFFT The method also determines the eigenfrequencieswith higher accuracy since it takes into account thetime delay of the maximal ampli cation caused by the nite deceleration and the inertias of the system If thistime delay is not considered the eigenfrequencies willbe systematically underestimated especially at highdecelerations

The analysis can be made in the frequency plane pro-vided that the braking starts above a certain limit often10ndash30 per cent above the critical speed [5 ] The deceler-ation clearly lsquocutsrsquo the maximal vibration amplitudeespecially at low damping Already at relative dampinglevels of the order of 1 per cent the transient analysis(including the frequency sweep) is needed for the rst-order judder except for in nitesimally smalldeclerations

Aviles et al [42] studied a braking event with slowlydecreasing speed and frequency However the con-clusion was drawn that the peak of the vibration ampli-tude at a certain vehicle speed was altogether an e ectof the negative frictionndashvelocity slope introduced in themodel The e ect of the frequency sweep was neveranalysed separately The calculations were made in thefrequency domain

522 Judder vibration simulation

Most of the analyses and measurements of judder aremade for braking with constant speed ie constant rev-olution frequency of the wheel as well as constant press-ure and temperature An argument is that it is easier tomeasure and analyse vibrations on the basis of this pre-scription Another bene t of measuring at constantspeed is e cient data analysis in the frequency domainHowever in a real braking situation the frequency isnot constant

There is a dynamic ampli cation of the brake torqueand pressure variations when passing through orcoming close to a critical speed of a vehicle Thevibration starts when the braking force is applied andreaches a maximal amplitude at a certain speed It iscontinued until low speed if the braking force is continu-ously applied This is the typical behaviour of a forcedvibration with relatively constant source amplitude butwith a sweeping frequency Fig 6

A two-DOF rotorndashstator model [24] with a linearly

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

decreasing disc speed possesses the main characteristicsof judder as shown in Fig 6 Before analysis the de ec-tion angles of rotordisc and statorcaliper respectivelywere split into vibration-free parts W and WC (rotationstatic de ection) and the superimposed vibrations QD andQ

C respectively The shape of the amplitude function Edescribes the relative vibration level QC (second timederivative of QC) almost exactly All parameters of therotorndashstator model can be experimentally generated

A full-vehicle model [5 ] shows the same lsquojudder behav-iourrsquo but can also explain some other e ects It is morecomplicated since it demands information about thewind speed slip etc

It is generally accepted that the front wheel suspensionof passenger cars has a rigid body forendashaft vibrationmode resonance in the frequency range 10ndash20 Hz andthat this resonance is responsible for lower-order judderat corresponding velocities This corresponds to a maxi-mal amplitude of the vibrations at a critical vehicle speedof between 60 and 140 kmh for the rst-order judderThe second-order judder will have a corresponding criti-cal speed (because of the same resonance) of between 30and 70 kmh The present vehicle had a resonance near14 Hz corresponding to a rst-order critical speed of95 kmh

The following possibilities for reducing judder werefound [5 ]

(a) decreased BTV andor BPV which will lead backto the cause approach

(b) increased relative stator mass and inertia momentcompared with the rotor

(c) increased damping(d) lighter braking(e) higher eigenfrequency

A lighter vehicle and a smaller wheel radius decrease thejudder problems [5 ] A reduction of the vehicle mass willalso decrease the thermal DTV and hotspots and reducethe risk of thermal cracking provided that the thermalcapacity of the disc remains the same A lighter stator(ie strut and eventually disc) will tend to increase thejudder problems since the ampli cation of BTV willbecome larger

6 FUTURE

The eld of low frequency braking induced vibrations isstill characterized by confusion Much research is neededin this area before a fairly clear picture becomes appar-ent The author nds the following areas especiallyinteresting

(a) simulation of BTV generation combining wear andTEI (wear especially hot and high pressure weartends to counteract the TEI process)

(b) the groan phenomenon(c) friction lms

429ASPECTS OF DISC BRAKE JUDDER

Fig 6 Model and corresponding brake judder simulation versus measurement

(d) the TEI process and its connection to thermoelasticbuckling

(e) studying wheel suspension vibration modes duringbrake-on conditions

(f ) the relation between BTV and simultaneous vari-ations in geometry (DTV run-out equivalent brakeradius) and friction coe cient

(g) prediction of BTV level and order for speci eddesign parameters and braking conditions

(h) developing models for simulation of vibration levelsin a vehicle at speci ed BTV

Generally in brake judder analysis it is recommendedto split the investigations into two parts

1 Analysis of sources of irregularities such as DTV etcThis involves thermomechanical FE analysis of thebrake components or dynamometer tests These typesof calculations are extremely time demanding

2 Analysis of the e ect of the irregularities in the vehicleIf the disturbances (which may be output from FEanalysis or dynamometer measurements) are given asfunctions of time very fast simulation can be carriedout by means of the amplitude function techniquedescribed in this work

The amplitude function technique is still at an earlystage but there are no di culties in principle involvedin using it to analyse multiple mass system models ofa whole vehicle Such models would be useful in deter-mining design criteria of brake components andsuspensions etc

REFERENCES

1 Hulten J Drum brake squeal PhD thesis Machine andVehicle Design Chalmers University of TechnologyGoteborg 1998

2 Inoue H Analysis of brake judder caused by thermal defor-mation of brake disc rotors In Proceedings 21st FISITACongress Belgrade 1986 pp 213ndash219 paper 865131

3 Kao T K Richmond J W and Moore M W The appli-

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

cation of predictive techniques to study thermo-elasticinstability of brakes In Proceedings of the Twelfth AnnualBrake Colloquium and Engineering Display AtlantaGeorgia 1984 SAE paper 942087

4 Jacobsson H Frequency sweep approach to brake judderpart A the brake judder phenomenon Classi cation andproblem approach Licentiate thesis Chalmers Universityof Technology Goteborg 1998

5 Jacobbson H Brake judder Thesis Chalmers Universityof Technology Goteborg 2001

6 Abdelhamid M K Creep groan of disc brakes InProceedings Noise and Vibration Conference TraverseCity Michigan 1995 pp 396ndash400 SAE paper 951282

7 Kao T K Richmond J W and Douarre A Brake dischot spotting and thermal judder an experimental and niteelement study Int J Veh Des 2000 23(34) 276ndash296

8 Brooks P C Barton D Crolla D A Lang A M andSchafer D R A study of disc brake judder using a fullycoupled thermo-mechanical nite element model InProceedings 25th FISITA Congress Beijing 1994pp 340ndash349 SAE paper 945042

9 Abdelhamid M K Brake judder analysis case studies SAEpaper 972027 1997

10 Kreitlow W Schrodter F and Matthai H Vibration andlsquohumrsquo of disc brakes under load SAE paper 850079 SAETrans Sect 1 1985 431ndash437

11 Augsburg K Brunner H and Grochowicz JUntersuchungen zum Rubbelverhalten von Pkw-Schwimmsattelbremser Automobiltechnische Zeitschrift1999 101

12 Stringham W Jank P Pfeifer J and Wang A Brakeroughnessmdashdisc brake torque variation rotor distortionand vehicle response SAE paper 930803 SAE TransSect 6 1993 1235ndash1247

13 Engel H G Bachman Th Eichhorn U and Saame ChDynamical behavior of brake-disc geometry as cause ofbrake judder In Proceedings EAEC Fourth InternationalConference on Vehicle and Tra c System TechnologyStrasbourg France 1993 Vol 1 pp 456ndash481

14 Thuresson D Thermomechanical analysis of frictionbrakes In Proceedings of the Eighteenth Annual BrakeColloquium and Engineering Display 2000 Vol P-358pp 149ndash159 SAE paper 2000-01-2775

15 Richmond J W Kao T K and Moore M W The devel-opment of computationalanalysis techniques for disc brake

430 H JACOBSSON

pad design In Proceedings Advances in AutomotiveBraking Technology Design Analysis and MaterialDevelopments 1996 (Institution of Mechanical Engineers)

16 Abendroth H Ste en T Falter W and Heidt RInvestigation of CV rotor cracking test procedures InBrakes 2000 International Conference on AutomotiveBrakingmdashTechnologies for the 21st Century 2000pp 149ndash162 (Professional Engineering PublishingLondon)

17 Haigh M J Smales H and Abe M Vehicle judder underdynamic braking caused by disc thickness variation InProceedings Braking of Road Vehicles London 1993pp 247ndash258 IMechE paper C44402293

18 Borjesson M Eriksson P Kuylenstierna C NilssonP H and Hermansson T The role of friction lms inautomotive brakes subjected to low contact forces InProceedings Braking of Road Vehicles London 1993pp 259ndash267 IMechE paper C444026

19 Wirth A and Whitaker R Developments in cast iron tech-nology In Proceedings Advances in Automotive BrakingTechnology Design Analysis and Material DevelopmentsLeeds UK 1996 (Institution of Mechanical Engineers)

20 Thoms E Disc brakes for heavy vehicles In ProceedingsBraking of Road Vehicles London 1988 pp 133ndash137IMechE paper C46488

21 Aviles R Hennequet G Hernandez A and Llorente L ILow frequency vibrations in disc brakes at high car speedPart I experimental approach Int J Veh Des 199516(6) 542ndash555

22 Ste en T and Bruns R Hotspotsbildung bei Pkw-Bremsscheiben Automobiltechnische Zeitschrift 1998100 408ndash413

23 Jacobsson H Analysis of brake judder by use of amplitudefunctions In Proceedings of SAE Noise and VibrationConference 1999 SAE paper 1999-01-1779

24 Jacobsson H Wheel suspension related disc brake judderIn Proceedings ASME Design Engineering TechnicalConferences Sacramento California 1997 VIB-4165

25 Engel H G Hassiotis V and Tiemann R Systemapproach to brake judder In Proceedings 25th FISITACongress Beijing 1994 Vol 1 pp 332ndash339 paper 945041

26 Martin R H and Bowron S Composite materials in trans-port friction applications In Brakes 2000 InternationalConference on Automotive BrakingmdashTechnologies for the21st Century 2000 pp 207ndash216 (Professional EngineeringPublishing London)

27 de Vries A and Wagner M The brake judder phenom-enon SAE Trans Sect 6 1992 101 652ndash660

28 Palmer B B and Weintraub M H The role of engineeredcashew particles on performance In Brakes 2000International Conference on Automotive BrakingmdashTechnologies for the 21st Century 2000 pp 185ndash195(Professional Engineering Publishing London)

29 Koetniyom S Brooks P C and Barton D C Finite

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

element prediction of inelastic strain accumulation in cast-iron brake rotors In Brakes 2000 InternationalConferenceon Automotive BrakingmdashTechnologies for the 21st Century2000 pp 139ndash148 (Professional Engineering PublishingLondon)

30 Hudson M D and Ruhl R L Ventilated brake rotor air ow investigation SAE paper 971033 1997

31 Grieve D G Barton D A Crolla D A Chapman J Land Buckingham J T Alternative brake disc materials InProceedingsAdvances in Automotive Braking TechnologyDesign Analysis and Material Developments Leeds UK1996 (Institution of Mechanical Engineers)

32 Grieve D G Barton D C Crolla D A and BuckinghamJ K Design of a lightweight automotive brake disc using nite element and Taguchi techniques Proc Instn MechEngrs Part D J Automobile Engineering 1998 212245ndash254

33 Krupka R and Kienzle A Fiber reinforced ceramic com-posite for brake discs In Proceeding of the EighteenthAnnual Brake Colloquium and Engineering Display 2000Vol P-358 pp 67ndash69 SAE paper 2000-01-2761

34 Bosworth R Investigations of secondary ride aspects ofsteering wheel vibration (shimmy and judder) using Taguchimethodology In Proceedings AUTOTECH 89 London1989 IMechE paper C3999

35 Kim M-G Jeong H-I and Yoo W-S Sensitivity analy-sis of chassis system to improve shimmy and brake juddervibration on steering wheel SAE Special Publication 11361996 pp 59ndash70

36 Abdelhamid M K Brake judder analysis using transferfunctions In Proceedings SAE Brake Colloquium TempeArizona 1997 pp 5ndash9 SAE paper 973018

37 Kao T K Richmond J W and Moore M WComputational analysis of pad performance InProceedings Braking of Road Vehicles 1993 paperC44402793 (Institution of Mechanical Engineers)

38 Floquet A and Dubourg M-C Realistic braking operationsimulation of ventilated disc brakes Trans ASMEJ Tribology July 1996 118 466ndash472

39 Du S Zagrodzki P Barber J R and Hulbert G MFinite element analysis of frictionally excited thermoelasticinstability J Thermal Stresses 1997 20 185ndash201

40 Daudi A R Dickerson W E and Narain M Hayesrsquoincreased air ow rotor design In Proceedings SecondInternational Seminar on Automotive Braking RecentDevelopments and Future Trends Leeds UK 1998pp 127ndash143 (Institution of Mechanical Engineers)

41 Crolla D A and Lang A M Brake noise and vibrationmdashthe state of the art Vehicle Tribology Tribology SeriesVol 18 1991 (Elsevier) pp 165ndash174

42 Aviles R Hennequet G Amezua E and Vallejo J Lowfrequency vibrations in disc brakes at high car speedPart II mathematical model and simulation Int J VehDes 1995 16(6) 556ndash569

Page 7: Aspects of disc brake judder - Universiti Teknologi Malaysiaarahim/jacobsson.pdf · 419 Aspects of disc brake judder HJacobsson* Machine and Vehicle Systems, Chalmers University of

425ASPECTS OF DISC BRAKE JUDDER

suspension design and the forendashaft exibility is a domi-nating parameter [27] Stringham et al [12] stated thatthe sti ness of the lower arm bushing is the most in u-ential parameter It was found to a ect signi cantly theeigenfrequency of the suspension system in the forendashaftdirection Bosworth [34] studied the suspension struc-ture in more detail and found the following factorscontrolling the judder

(a) tie rod bushmdashradial and forendashaft sti ness(b) lower arm bushmdashforendashaft sti ness(c) anti-roll barmdashvertical sti ness

In particular the sti ness of the lower arm bushing isimportant since it signi cantly a ects the eigenfre-quency of the suspension system in the forendashaft direction[12 34 35] Higher eigenfrequencies which will reducejudder problems such as steering wheel vibrations maybe achieved either by higher sti ness of the rubber bush-ings or by a reduced value of the modal mass and inertiaof the wheel suspension see Jacobsson [5 ]

However modern suspensions have become more andmore exible in the forendashaft direction because of theintroduction of radial tyres [27] This is necessary inorder to absorb the longitudinal vibrations from the sti belt of the tyres

Note that it is essential to measure the eigenfrequencyand damping in the brake-on mode When the brakeswere not applied the experimental vehicle was found tohave a signi cantly higher eigenfrequency (18 Hz com-pared with 138 Hz) and a lower equivalent viscousdamping factor (007 compared with 009) than meas-ured under the same braking conditions see reference[24] Also the instantaneous centre of motion of the strutchanges with the brake pressure level [5 ] It movedgradually towards the wheel axle as the brake pressureincreased

4 TIME-SCALES

Brake judder depends strongly on the braking historyon the short as well as on the long time-scale There arethree di erent time-scales involved in brake judder

(a) revolution time of the wheel(b) brake application time or the time between two

brakings(c) lifetime of brake components

Traditionally in brake design only the long-time changesare considered In recent years changes during brakinghave also been focused on The generation of localizedcontact area pressure and temperature gradients suchas hot banding has been studied It is found that DTVis a dynamic property that may change considerablyduring a brake application [7 11]

Changes within the time of a wheel revolution arenormally not included primarily because of di culties

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

in making numerical and signal analysis when using con-ventional techniques However the amplitude functiontechnique [23] handles sinusoidal variations of the braketorque with wheel revolution

5 APPROACH

The way of looking at and describing a problem is herecalled the problem approach It is a theoretical abstrac-tion lsquoa conception of the worldrsquo including a model andits system limits The problem approach determineswhich physical e ects can be studied and also states thetime and space scale The chosen problem approach willhave consequences for how to analyse the problem aswell as for the type of solution that will be found It alsodetermines which type of analytical and experimentaltool is the most appropriate

When studying the literature on brake judder it isclear that two fundamentally di erent approaches are inuse namely the cause and e ect approaches While thee ect approach focuses on the source of the vibrationsin the form of amplitude and vibrational order of theBTV andor BPV the cause approach deals with anumber of physical e ects such as wear and heatingsee Fig 3

The e ect approach can be further split into di erentapproaches [4 ]

1 The system approach examines how a model of thevehicle or the wheel suspension together withBTVBPV generates judder The braking process isusually represented by a constant frequency whichcan be parametrically changed It is used mostly inexperimental analysis [13 25 36 ] Also some quasi-static analyses may be found in literature Kim et al[35] used multibody system (MBS) analysis of amodel with 12 degrees of freedom (DOF ) of aMcPherson-type suspension exposed to rst-orderjudder

2 The frequency sweep approach examines how thebraking process itself (including a frequency sweep)together with the BTVBPV generates judder Thevehicle structure can be represented by a resonancecorresponding to the actual critical speed [23]

3 The human response approach studies the e ects ofjudder on one speci c test driver or on an average

Fig 3 Problem approaches

426 H JACOBSSON

person placed in a speci c vehicle Alternatively thehuman response to judder could be thought of as athird level where the judder level and frequencytogether with the weight size and place of the personin the vehicle etc are the input

Some approaches are listed in Table 1 together withrelated analytical and experimental methods and toolsfound in the literature [4 ] For instance FE analysis isthe natural choice when studying BTV generation bymeans of for instance the TEI process For the e ectapproach where the BTV can be represented by a sinus-oidal brake torque disturbance it is instead the vehicleor relevant parts thereof that should be modelled ThenMBS analysis (commercial programs are ADAMSDADS etc) is more relevant especially for lowfrequency judder (say below 50 Hz)

In experimental brake judder studies bench testing aswell as road testing are used Advantages of bench test-ing [11] are good reproducibility of the testing con-ditions more accurate measurements higher sensitivityof measurements lower cost and less time consumption[37] Disadvantages are that cooling conditions are nottaken into account as well as the in uence of othermachine elements and systems which will a ect thetransmission of BTV in the vehicle (tyres wheel sus-pension steering) [11] In road testing the speci cproblem occurs that the level of BTVBPV cannot becontrolled during a brake application This problemmay be handled by measuring BTVBPV instead oftrying to control it by constant conditions such as speedtemperature pressure etc see references [9 23]

51 Causes of BTVBPV

Traditionally the source of the BTVBPV has beenfocused on It is a ected by a combination of the di er-ent physical e ects discussed in section 2 Disc run-outand DTV which are geometrical irregularities of thedisc directly cause normal force variations and henceBTVBPV see Fig 4 Furthermore the TEI process gen-erates hot spots and sometimes remaining discolouredareas with locally di erent speci c volume and wearproperties which may aggravate the vibrations Finally

Table 1 Approaches and corresponding methods

Approach Methods and tools

Cause approach (FE) analysis nite di erence dynamometertribometer drag braking thermal imagingX-rays

System approach MBS analysis Fourier methods modal analysisTaguchi methodology road testsspectrograms

Frequency sweep Time plane analysis road tests involvingapproach deceleration waterfall analysis order

tracking ABS and capacitive transducersHuman response Subjective rating deceleration tests

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

Fig 4 BTV causes for a disc brake

there is a contribution from the dynamic de ection ofthe disc due to external forces such as tyre forces andunbalances

One of the problems with brake analysis is that it isnecessary to solve coupled de ection and temperature eld problems with combined de ection and thermalload Commercially available FE programs can handlepure mechanical or pure thermal problems Brooks et al[8 ] introduced a two-dimensional (ie axisymmetrical )combined thermal and mechanical method of hot band-ing simulation of a disc brake The basic idea is to switchbetween de ection and temperature eld calculationseach of which can be made in commercial FE programssuch as ABAQUS The FE model takes into account thetime-dependent change in the contact area A similarconcept was developed by Kao et al [7 ] Both three-dimensional (necessary to be able to model buckling)and axisymmetric models have been used to study thein uence of pad design parameters on thermal padcracking as well as to simulate thermoelastic bucklingand its coupling to TEI and thermal DTV

Thermoelastic simulation of brake components underrealistic conditions involves massive central processingunit computational e ort and data storage [7 ] This isespecially the case when simulating slow decelerations(ie sti problems) with long duration timesUnfortunately it is this type of braking that generatesthe most pronounced hot spots There are various waysto make the simulation more e ective

1 Circumferential variations of the instantaneous discsurface conditions and geometry can be neglectedHowever when studying brake judder problems thecircumferential variations are essential

2 A specially dedicated contact element can be used toderive the frictional force and heat generated at theinterface [3 37]

3 Solving the coupled eld problems simultaneously(see reference [14]) is more accurate and e ectiveHowever since it relies on a Newton-type methodfrom the 1990s the algorithms are not yet included incommercial FE programs

4 A three-dimensional hybrid method which combinesfast Fourier transform (FFT) techniques withFE methods has been developed by Floquet and

427ASPECTS OF DISC BRAKE JUDDER

Dubourg [38] The application of the Fourier trans-form (on a space variable) has the e ect of reducingthe dimension of the problem The variable is trans-formed into a discrete parameter the frequency andthe corresponding partial derivatives are removedThe method can handle geometrically periodic butnon-axisymmetric solids such as ventilated discbrakes

5 The FE method can be applied directly to a pertur-bation method [39] The basic idea is not to solve thetransient problem but to consider the conditionsunder which a small perturbation in the temperature eld can grow exponentially in time The method isapplicable to transient processes as long as the contactarea does not change with time However the contactarea does change considerably with time duringbraking

6 A pad model composed of springndashdamper elementscan be used [22]

For vented discs and aluminium discs in particularwhere the air ow is important computational uiddynamics (CFD) is a useful tool CFD is used by somerotor manufacturers to increase air ow [26 40] In amarket survey [26 ] many companies saw the potentialof combining FE analysis and CFD to gain more accu-rate temperature predictions However this wouldrequire enormous computational e orts

As an alternative to CFD the convective cooling maybe estimated by approximative methods On a ventedrotor there are two di erent types of convective coolingair cross- ow over the rotor surface and air pumped owthrough the vents [3 ] Brake rotor vane ow relationsto estimate the heat convective transfer coe cient havelong been used in brake system thermal modellingCurrently two relations are recognized for ventilateddisc air ow those of Sisson and Limpert [30] Analternative is to approximate the convective heat transfercoe cient from the Nusselt modulus [31 32] and tocorrect it with empirically determined factors

52 E ects of BTVBPV

A few research projects have focused on the e ect ofbrake vibrations in the vehicle despite the fact that ithas been qualitatively described in the literature Crollaand Lang [41] Haigh et al [17] and many others havedescribed how brake judder rises to a maximum whenpassing through more or less distinct speeds So far theevaluation of brake judder has been done with a subjec-tive method using a scale from 1 to 10 but hardly anysimulations of brake judder in a vehicle have been car-ried out Brake judder problems have traditionally beensolved by use of trial and error rather than systematicmethods

In the literature there are a few sensitivity studies butin practice no lsquotruersquo simulations The di erence in that

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

lsquotruersquo simulations needs to be evaluated in the time planeThis involves not only a model of the vibration source(BTVBPV) and the vehicle structure and linkage (reson-ances and transfer) but also modelling of the brakingevent (frequency sweep braking conditions) see Fig 5

Straightforward integration of di erential equationswithout intelligent variable transformations or assump-tions using an ordinary equation-solving algorithmdesigned for non-sti problems (eg RungendashKutta) isnot an e cient way of dealing with this type of problemThe simulation will take an unnecessarily long time(hours or days) fail or crash Also the algorithms usedby commercial mechanics programs such as ADAMSare slow and ine cient if one wishes to follow a wholebraking event Hence the maximal vibration levels willbecome largely overestimated at nite braking timesHowever these types of programs are useful for quasi-static sensitivity analysis

521 Sensitivity analysis

Applying the system approach the solution to the judderproblem will be to build robustness into the vehicle andthereby to make it less sensitive to BTVBPV The systemof Engel et al [25] consists of ve di erent steps namelythe brake disc caliper and pad tyre and hubndashbearingunit wheel knuckle and nally the steering system Thereis also feedback between some steps in the outlinedmodel

An attempt to model numerically the vehicle responseto BTV was made by Kim et al [35] using MBS analysisof a similar vehicle structure The modelling of the sus-pension system used in the calculations was howevernot described Similar analyses are often carried out inthe automotive industry but seldom is the modellingdescribed in the literature However the model ofAugsburg et al [11] was described in detail

(a) calliper as two masses connected by a spring (rep-resenting the calliper sti ness in the forendashaftdirection)

(b) brake pads as springs(c) brake piston by a mass(d) hydraulic system as volume accumulating elements

The transfer path from the vibration source to thedriverrsquos contact points can be qualitatively investigatedby simultaneous measurements of accelerations atvarious position such as wheel carrier steering tie rod

Fig 5 The frequency sweep approach

428 H JACOBSSON

steering wheel etc [13] The sampled signals can be usedto generate the transfer functions between di erentpoints [9 36 ] The technique can be used to describeboth the brake excitation and the transfer functions thatcharacterize vehicle sensibility

The amplitude functions [23] can be seen as gen-eralized transfer functions They can be used to classifythe braking event as well as the corresponding vibrationsin the vehicle An advantage of the amplitude functionover the transfer function technique is that it works formuch higher decelerations since it does not rely on theFFT The method also determines the eigenfrequencieswith higher accuracy since it takes into account thetime delay of the maximal ampli cation caused by the nite deceleration and the inertias of the system If thistime delay is not considered the eigenfrequencies willbe systematically underestimated especially at highdecelerations

The analysis can be made in the frequency plane pro-vided that the braking starts above a certain limit often10ndash30 per cent above the critical speed [5 ] The deceler-ation clearly lsquocutsrsquo the maximal vibration amplitudeespecially at low damping Already at relative dampinglevels of the order of 1 per cent the transient analysis(including the frequency sweep) is needed for the rst-order judder except for in nitesimally smalldeclerations

Aviles et al [42] studied a braking event with slowlydecreasing speed and frequency However the con-clusion was drawn that the peak of the vibration ampli-tude at a certain vehicle speed was altogether an e ectof the negative frictionndashvelocity slope introduced in themodel The e ect of the frequency sweep was neveranalysed separately The calculations were made in thefrequency domain

522 Judder vibration simulation

Most of the analyses and measurements of judder aremade for braking with constant speed ie constant rev-olution frequency of the wheel as well as constant press-ure and temperature An argument is that it is easier tomeasure and analyse vibrations on the basis of this pre-scription Another bene t of measuring at constantspeed is e cient data analysis in the frequency domainHowever in a real braking situation the frequency isnot constant

There is a dynamic ampli cation of the brake torqueand pressure variations when passing through orcoming close to a critical speed of a vehicle Thevibration starts when the braking force is applied andreaches a maximal amplitude at a certain speed It iscontinued until low speed if the braking force is continu-ously applied This is the typical behaviour of a forcedvibration with relatively constant source amplitude butwith a sweeping frequency Fig 6

A two-DOF rotorndashstator model [24] with a linearly

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

decreasing disc speed possesses the main characteristicsof judder as shown in Fig 6 Before analysis the de ec-tion angles of rotordisc and statorcaliper respectivelywere split into vibration-free parts W and WC (rotationstatic de ection) and the superimposed vibrations QD andQ

C respectively The shape of the amplitude function Edescribes the relative vibration level QC (second timederivative of QC) almost exactly All parameters of therotorndashstator model can be experimentally generated

A full-vehicle model [5 ] shows the same lsquojudder behav-iourrsquo but can also explain some other e ects It is morecomplicated since it demands information about thewind speed slip etc

It is generally accepted that the front wheel suspensionof passenger cars has a rigid body forendashaft vibrationmode resonance in the frequency range 10ndash20 Hz andthat this resonance is responsible for lower-order judderat corresponding velocities This corresponds to a maxi-mal amplitude of the vibrations at a critical vehicle speedof between 60 and 140 kmh for the rst-order judderThe second-order judder will have a corresponding criti-cal speed (because of the same resonance) of between 30and 70 kmh The present vehicle had a resonance near14 Hz corresponding to a rst-order critical speed of95 kmh

The following possibilities for reducing judder werefound [5 ]

(a) decreased BTV andor BPV which will lead backto the cause approach

(b) increased relative stator mass and inertia momentcompared with the rotor

(c) increased damping(d) lighter braking(e) higher eigenfrequency

A lighter vehicle and a smaller wheel radius decrease thejudder problems [5 ] A reduction of the vehicle mass willalso decrease the thermal DTV and hotspots and reducethe risk of thermal cracking provided that the thermalcapacity of the disc remains the same A lighter stator(ie strut and eventually disc) will tend to increase thejudder problems since the ampli cation of BTV willbecome larger

6 FUTURE

The eld of low frequency braking induced vibrations isstill characterized by confusion Much research is neededin this area before a fairly clear picture becomes appar-ent The author nds the following areas especiallyinteresting

(a) simulation of BTV generation combining wear andTEI (wear especially hot and high pressure weartends to counteract the TEI process)

(b) the groan phenomenon(c) friction lms

429ASPECTS OF DISC BRAKE JUDDER

Fig 6 Model and corresponding brake judder simulation versus measurement

(d) the TEI process and its connection to thermoelasticbuckling

(e) studying wheel suspension vibration modes duringbrake-on conditions

(f ) the relation between BTV and simultaneous vari-ations in geometry (DTV run-out equivalent brakeradius) and friction coe cient

(g) prediction of BTV level and order for speci eddesign parameters and braking conditions

(h) developing models for simulation of vibration levelsin a vehicle at speci ed BTV

Generally in brake judder analysis it is recommendedto split the investigations into two parts

1 Analysis of sources of irregularities such as DTV etcThis involves thermomechanical FE analysis of thebrake components or dynamometer tests These typesof calculations are extremely time demanding

2 Analysis of the e ect of the irregularities in the vehicleIf the disturbances (which may be output from FEanalysis or dynamometer measurements) are given asfunctions of time very fast simulation can be carriedout by means of the amplitude function techniquedescribed in this work

The amplitude function technique is still at an earlystage but there are no di culties in principle involvedin using it to analyse multiple mass system models ofa whole vehicle Such models would be useful in deter-mining design criteria of brake components andsuspensions etc

REFERENCES

1 Hulten J Drum brake squeal PhD thesis Machine andVehicle Design Chalmers University of TechnologyGoteborg 1998

2 Inoue H Analysis of brake judder caused by thermal defor-mation of brake disc rotors In Proceedings 21st FISITACongress Belgrade 1986 pp 213ndash219 paper 865131

3 Kao T K Richmond J W and Moore M W The appli-

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

cation of predictive techniques to study thermo-elasticinstability of brakes In Proceedings of the Twelfth AnnualBrake Colloquium and Engineering Display AtlantaGeorgia 1984 SAE paper 942087

4 Jacobsson H Frequency sweep approach to brake judderpart A the brake judder phenomenon Classi cation andproblem approach Licentiate thesis Chalmers Universityof Technology Goteborg 1998

5 Jacobbson H Brake judder Thesis Chalmers Universityof Technology Goteborg 2001

6 Abdelhamid M K Creep groan of disc brakes InProceedings Noise and Vibration Conference TraverseCity Michigan 1995 pp 396ndash400 SAE paper 951282

7 Kao T K Richmond J W and Douarre A Brake dischot spotting and thermal judder an experimental and niteelement study Int J Veh Des 2000 23(34) 276ndash296

8 Brooks P C Barton D Crolla D A Lang A M andSchafer D R A study of disc brake judder using a fullycoupled thermo-mechanical nite element model InProceedings 25th FISITA Congress Beijing 1994pp 340ndash349 SAE paper 945042

9 Abdelhamid M K Brake judder analysis case studies SAEpaper 972027 1997

10 Kreitlow W Schrodter F and Matthai H Vibration andlsquohumrsquo of disc brakes under load SAE paper 850079 SAETrans Sect 1 1985 431ndash437

11 Augsburg K Brunner H and Grochowicz JUntersuchungen zum Rubbelverhalten von Pkw-Schwimmsattelbremser Automobiltechnische Zeitschrift1999 101

12 Stringham W Jank P Pfeifer J and Wang A Brakeroughnessmdashdisc brake torque variation rotor distortionand vehicle response SAE paper 930803 SAE TransSect 6 1993 1235ndash1247

13 Engel H G Bachman Th Eichhorn U and Saame ChDynamical behavior of brake-disc geometry as cause ofbrake judder In Proceedings EAEC Fourth InternationalConference on Vehicle and Tra c System TechnologyStrasbourg France 1993 Vol 1 pp 456ndash481

14 Thuresson D Thermomechanical analysis of frictionbrakes In Proceedings of the Eighteenth Annual BrakeColloquium and Engineering Display 2000 Vol P-358pp 149ndash159 SAE paper 2000-01-2775

15 Richmond J W Kao T K and Moore M W The devel-opment of computationalanalysis techniques for disc brake

430 H JACOBSSON

pad design In Proceedings Advances in AutomotiveBraking Technology Design Analysis and MaterialDevelopments 1996 (Institution of Mechanical Engineers)

16 Abendroth H Ste en T Falter W and Heidt RInvestigation of CV rotor cracking test procedures InBrakes 2000 International Conference on AutomotiveBrakingmdashTechnologies for the 21st Century 2000pp 149ndash162 (Professional Engineering PublishingLondon)

17 Haigh M J Smales H and Abe M Vehicle judder underdynamic braking caused by disc thickness variation InProceedings Braking of Road Vehicles London 1993pp 247ndash258 IMechE paper C44402293

18 Borjesson M Eriksson P Kuylenstierna C NilssonP H and Hermansson T The role of friction lms inautomotive brakes subjected to low contact forces InProceedings Braking of Road Vehicles London 1993pp 259ndash267 IMechE paper C444026

19 Wirth A and Whitaker R Developments in cast iron tech-nology In Proceedings Advances in Automotive BrakingTechnology Design Analysis and Material DevelopmentsLeeds UK 1996 (Institution of Mechanical Engineers)

20 Thoms E Disc brakes for heavy vehicles In ProceedingsBraking of Road Vehicles London 1988 pp 133ndash137IMechE paper C46488

21 Aviles R Hennequet G Hernandez A and Llorente L ILow frequency vibrations in disc brakes at high car speedPart I experimental approach Int J Veh Des 199516(6) 542ndash555

22 Ste en T and Bruns R Hotspotsbildung bei Pkw-Bremsscheiben Automobiltechnische Zeitschrift 1998100 408ndash413

23 Jacobsson H Analysis of brake judder by use of amplitudefunctions In Proceedings of SAE Noise and VibrationConference 1999 SAE paper 1999-01-1779

24 Jacobsson H Wheel suspension related disc brake judderIn Proceedings ASME Design Engineering TechnicalConferences Sacramento California 1997 VIB-4165

25 Engel H G Hassiotis V and Tiemann R Systemapproach to brake judder In Proceedings 25th FISITACongress Beijing 1994 Vol 1 pp 332ndash339 paper 945041

26 Martin R H and Bowron S Composite materials in trans-port friction applications In Brakes 2000 InternationalConference on Automotive BrakingmdashTechnologies for the21st Century 2000 pp 207ndash216 (Professional EngineeringPublishing London)

27 de Vries A and Wagner M The brake judder phenom-enon SAE Trans Sect 6 1992 101 652ndash660

28 Palmer B B and Weintraub M H The role of engineeredcashew particles on performance In Brakes 2000International Conference on Automotive BrakingmdashTechnologies for the 21st Century 2000 pp 185ndash195(Professional Engineering Publishing London)

29 Koetniyom S Brooks P C and Barton D C Finite

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

element prediction of inelastic strain accumulation in cast-iron brake rotors In Brakes 2000 InternationalConferenceon Automotive BrakingmdashTechnologies for the 21st Century2000 pp 139ndash148 (Professional Engineering PublishingLondon)

30 Hudson M D and Ruhl R L Ventilated brake rotor air ow investigation SAE paper 971033 1997

31 Grieve D G Barton D A Crolla D A Chapman J Land Buckingham J T Alternative brake disc materials InProceedingsAdvances in Automotive Braking TechnologyDesign Analysis and Material Developments Leeds UK1996 (Institution of Mechanical Engineers)

32 Grieve D G Barton D C Crolla D A and BuckinghamJ K Design of a lightweight automotive brake disc using nite element and Taguchi techniques Proc Instn MechEngrs Part D J Automobile Engineering 1998 212245ndash254

33 Krupka R and Kienzle A Fiber reinforced ceramic com-posite for brake discs In Proceeding of the EighteenthAnnual Brake Colloquium and Engineering Display 2000Vol P-358 pp 67ndash69 SAE paper 2000-01-2761

34 Bosworth R Investigations of secondary ride aspects ofsteering wheel vibration (shimmy and judder) using Taguchimethodology In Proceedings AUTOTECH 89 London1989 IMechE paper C3999

35 Kim M-G Jeong H-I and Yoo W-S Sensitivity analy-sis of chassis system to improve shimmy and brake juddervibration on steering wheel SAE Special Publication 11361996 pp 59ndash70

36 Abdelhamid M K Brake judder analysis using transferfunctions In Proceedings SAE Brake Colloquium TempeArizona 1997 pp 5ndash9 SAE paper 973018

37 Kao T K Richmond J W and Moore M WComputational analysis of pad performance InProceedings Braking of Road Vehicles 1993 paperC44402793 (Institution of Mechanical Engineers)

38 Floquet A and Dubourg M-C Realistic braking operationsimulation of ventilated disc brakes Trans ASMEJ Tribology July 1996 118 466ndash472

39 Du S Zagrodzki P Barber J R and Hulbert G MFinite element analysis of frictionally excited thermoelasticinstability J Thermal Stresses 1997 20 185ndash201

40 Daudi A R Dickerson W E and Narain M Hayesrsquoincreased air ow rotor design In Proceedings SecondInternational Seminar on Automotive Braking RecentDevelopments and Future Trends Leeds UK 1998pp 127ndash143 (Institution of Mechanical Engineers)

41 Crolla D A and Lang A M Brake noise and vibrationmdashthe state of the art Vehicle Tribology Tribology SeriesVol 18 1991 (Elsevier) pp 165ndash174

42 Aviles R Hennequet G Amezua E and Vallejo J Lowfrequency vibrations in disc brakes at high car speedPart II mathematical model and simulation Int J VehDes 1995 16(6) 556ndash569

Page 8: Aspects of disc brake judder - Universiti Teknologi Malaysiaarahim/jacobsson.pdf · 419 Aspects of disc brake judder HJacobsson* Machine and Vehicle Systems, Chalmers University of

426 H JACOBSSON

person placed in a speci c vehicle Alternatively thehuman response to judder could be thought of as athird level where the judder level and frequencytogether with the weight size and place of the personin the vehicle etc are the input

Some approaches are listed in Table 1 together withrelated analytical and experimental methods and toolsfound in the literature [4 ] For instance FE analysis isthe natural choice when studying BTV generation bymeans of for instance the TEI process For the e ectapproach where the BTV can be represented by a sinus-oidal brake torque disturbance it is instead the vehicleor relevant parts thereof that should be modelled ThenMBS analysis (commercial programs are ADAMSDADS etc) is more relevant especially for lowfrequency judder (say below 50 Hz)

In experimental brake judder studies bench testing aswell as road testing are used Advantages of bench test-ing [11] are good reproducibility of the testing con-ditions more accurate measurements higher sensitivityof measurements lower cost and less time consumption[37] Disadvantages are that cooling conditions are nottaken into account as well as the in uence of othermachine elements and systems which will a ect thetransmission of BTV in the vehicle (tyres wheel sus-pension steering) [11] In road testing the speci cproblem occurs that the level of BTVBPV cannot becontrolled during a brake application This problemmay be handled by measuring BTVBPV instead oftrying to control it by constant conditions such as speedtemperature pressure etc see references [9 23]

51 Causes of BTVBPV

Traditionally the source of the BTVBPV has beenfocused on It is a ected by a combination of the di er-ent physical e ects discussed in section 2 Disc run-outand DTV which are geometrical irregularities of thedisc directly cause normal force variations and henceBTVBPV see Fig 4 Furthermore the TEI process gen-erates hot spots and sometimes remaining discolouredareas with locally di erent speci c volume and wearproperties which may aggravate the vibrations Finally

Table 1 Approaches and corresponding methods

Approach Methods and tools

Cause approach (FE) analysis nite di erence dynamometertribometer drag braking thermal imagingX-rays

System approach MBS analysis Fourier methods modal analysisTaguchi methodology road testsspectrograms

Frequency sweep Time plane analysis road tests involvingapproach deceleration waterfall analysis order

tracking ABS and capacitive transducersHuman response Subjective rating deceleration tests

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

Fig 4 BTV causes for a disc brake

there is a contribution from the dynamic de ection ofthe disc due to external forces such as tyre forces andunbalances

One of the problems with brake analysis is that it isnecessary to solve coupled de ection and temperature eld problems with combined de ection and thermalload Commercially available FE programs can handlepure mechanical or pure thermal problems Brooks et al[8 ] introduced a two-dimensional (ie axisymmetrical )combined thermal and mechanical method of hot band-ing simulation of a disc brake The basic idea is to switchbetween de ection and temperature eld calculationseach of which can be made in commercial FE programssuch as ABAQUS The FE model takes into account thetime-dependent change in the contact area A similarconcept was developed by Kao et al [7 ] Both three-dimensional (necessary to be able to model buckling)and axisymmetric models have been used to study thein uence of pad design parameters on thermal padcracking as well as to simulate thermoelastic bucklingand its coupling to TEI and thermal DTV

Thermoelastic simulation of brake components underrealistic conditions involves massive central processingunit computational e ort and data storage [7 ] This isespecially the case when simulating slow decelerations(ie sti problems) with long duration timesUnfortunately it is this type of braking that generatesthe most pronounced hot spots There are various waysto make the simulation more e ective

1 Circumferential variations of the instantaneous discsurface conditions and geometry can be neglectedHowever when studying brake judder problems thecircumferential variations are essential

2 A specially dedicated contact element can be used toderive the frictional force and heat generated at theinterface [3 37]

3 Solving the coupled eld problems simultaneously(see reference [14]) is more accurate and e ectiveHowever since it relies on a Newton-type methodfrom the 1990s the algorithms are not yet included incommercial FE programs

4 A three-dimensional hybrid method which combinesfast Fourier transform (FFT) techniques withFE methods has been developed by Floquet and

427ASPECTS OF DISC BRAKE JUDDER

Dubourg [38] The application of the Fourier trans-form (on a space variable) has the e ect of reducingthe dimension of the problem The variable is trans-formed into a discrete parameter the frequency andthe corresponding partial derivatives are removedThe method can handle geometrically periodic butnon-axisymmetric solids such as ventilated discbrakes

5 The FE method can be applied directly to a pertur-bation method [39] The basic idea is not to solve thetransient problem but to consider the conditionsunder which a small perturbation in the temperature eld can grow exponentially in time The method isapplicable to transient processes as long as the contactarea does not change with time However the contactarea does change considerably with time duringbraking

6 A pad model composed of springndashdamper elementscan be used [22]

For vented discs and aluminium discs in particularwhere the air ow is important computational uiddynamics (CFD) is a useful tool CFD is used by somerotor manufacturers to increase air ow [26 40] In amarket survey [26 ] many companies saw the potentialof combining FE analysis and CFD to gain more accu-rate temperature predictions However this wouldrequire enormous computational e orts

As an alternative to CFD the convective cooling maybe estimated by approximative methods On a ventedrotor there are two di erent types of convective coolingair cross- ow over the rotor surface and air pumped owthrough the vents [3 ] Brake rotor vane ow relationsto estimate the heat convective transfer coe cient havelong been used in brake system thermal modellingCurrently two relations are recognized for ventilateddisc air ow those of Sisson and Limpert [30] Analternative is to approximate the convective heat transfercoe cient from the Nusselt modulus [31 32] and tocorrect it with empirically determined factors

52 E ects of BTVBPV

A few research projects have focused on the e ect ofbrake vibrations in the vehicle despite the fact that ithas been qualitatively described in the literature Crollaand Lang [41] Haigh et al [17] and many others havedescribed how brake judder rises to a maximum whenpassing through more or less distinct speeds So far theevaluation of brake judder has been done with a subjec-tive method using a scale from 1 to 10 but hardly anysimulations of brake judder in a vehicle have been car-ried out Brake judder problems have traditionally beensolved by use of trial and error rather than systematicmethods

In the literature there are a few sensitivity studies butin practice no lsquotruersquo simulations The di erence in that

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

lsquotruersquo simulations needs to be evaluated in the time planeThis involves not only a model of the vibration source(BTVBPV) and the vehicle structure and linkage (reson-ances and transfer) but also modelling of the brakingevent (frequency sweep braking conditions) see Fig 5

Straightforward integration of di erential equationswithout intelligent variable transformations or assump-tions using an ordinary equation-solving algorithmdesigned for non-sti problems (eg RungendashKutta) isnot an e cient way of dealing with this type of problemThe simulation will take an unnecessarily long time(hours or days) fail or crash Also the algorithms usedby commercial mechanics programs such as ADAMSare slow and ine cient if one wishes to follow a wholebraking event Hence the maximal vibration levels willbecome largely overestimated at nite braking timesHowever these types of programs are useful for quasi-static sensitivity analysis

521 Sensitivity analysis

Applying the system approach the solution to the judderproblem will be to build robustness into the vehicle andthereby to make it less sensitive to BTVBPV The systemof Engel et al [25] consists of ve di erent steps namelythe brake disc caliper and pad tyre and hubndashbearingunit wheel knuckle and nally the steering system Thereis also feedback between some steps in the outlinedmodel

An attempt to model numerically the vehicle responseto BTV was made by Kim et al [35] using MBS analysisof a similar vehicle structure The modelling of the sus-pension system used in the calculations was howevernot described Similar analyses are often carried out inthe automotive industry but seldom is the modellingdescribed in the literature However the model ofAugsburg et al [11] was described in detail

(a) calliper as two masses connected by a spring (rep-resenting the calliper sti ness in the forendashaftdirection)

(b) brake pads as springs(c) brake piston by a mass(d) hydraulic system as volume accumulating elements

The transfer path from the vibration source to thedriverrsquos contact points can be qualitatively investigatedby simultaneous measurements of accelerations atvarious position such as wheel carrier steering tie rod

Fig 5 The frequency sweep approach

428 H JACOBSSON

steering wheel etc [13] The sampled signals can be usedto generate the transfer functions between di erentpoints [9 36 ] The technique can be used to describeboth the brake excitation and the transfer functions thatcharacterize vehicle sensibility

The amplitude functions [23] can be seen as gen-eralized transfer functions They can be used to classifythe braking event as well as the corresponding vibrationsin the vehicle An advantage of the amplitude functionover the transfer function technique is that it works formuch higher decelerations since it does not rely on theFFT The method also determines the eigenfrequencieswith higher accuracy since it takes into account thetime delay of the maximal ampli cation caused by the nite deceleration and the inertias of the system If thistime delay is not considered the eigenfrequencies willbe systematically underestimated especially at highdecelerations

The analysis can be made in the frequency plane pro-vided that the braking starts above a certain limit often10ndash30 per cent above the critical speed [5 ] The deceler-ation clearly lsquocutsrsquo the maximal vibration amplitudeespecially at low damping Already at relative dampinglevels of the order of 1 per cent the transient analysis(including the frequency sweep) is needed for the rst-order judder except for in nitesimally smalldeclerations

Aviles et al [42] studied a braking event with slowlydecreasing speed and frequency However the con-clusion was drawn that the peak of the vibration ampli-tude at a certain vehicle speed was altogether an e ectof the negative frictionndashvelocity slope introduced in themodel The e ect of the frequency sweep was neveranalysed separately The calculations were made in thefrequency domain

522 Judder vibration simulation

Most of the analyses and measurements of judder aremade for braking with constant speed ie constant rev-olution frequency of the wheel as well as constant press-ure and temperature An argument is that it is easier tomeasure and analyse vibrations on the basis of this pre-scription Another bene t of measuring at constantspeed is e cient data analysis in the frequency domainHowever in a real braking situation the frequency isnot constant

There is a dynamic ampli cation of the brake torqueand pressure variations when passing through orcoming close to a critical speed of a vehicle Thevibration starts when the braking force is applied andreaches a maximal amplitude at a certain speed It iscontinued until low speed if the braking force is continu-ously applied This is the typical behaviour of a forcedvibration with relatively constant source amplitude butwith a sweeping frequency Fig 6

A two-DOF rotorndashstator model [24] with a linearly

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

decreasing disc speed possesses the main characteristicsof judder as shown in Fig 6 Before analysis the de ec-tion angles of rotordisc and statorcaliper respectivelywere split into vibration-free parts W and WC (rotationstatic de ection) and the superimposed vibrations QD andQ

C respectively The shape of the amplitude function Edescribes the relative vibration level QC (second timederivative of QC) almost exactly All parameters of therotorndashstator model can be experimentally generated

A full-vehicle model [5 ] shows the same lsquojudder behav-iourrsquo but can also explain some other e ects It is morecomplicated since it demands information about thewind speed slip etc

It is generally accepted that the front wheel suspensionof passenger cars has a rigid body forendashaft vibrationmode resonance in the frequency range 10ndash20 Hz andthat this resonance is responsible for lower-order judderat corresponding velocities This corresponds to a maxi-mal amplitude of the vibrations at a critical vehicle speedof between 60 and 140 kmh for the rst-order judderThe second-order judder will have a corresponding criti-cal speed (because of the same resonance) of between 30and 70 kmh The present vehicle had a resonance near14 Hz corresponding to a rst-order critical speed of95 kmh

The following possibilities for reducing judder werefound [5 ]

(a) decreased BTV andor BPV which will lead backto the cause approach

(b) increased relative stator mass and inertia momentcompared with the rotor

(c) increased damping(d) lighter braking(e) higher eigenfrequency

A lighter vehicle and a smaller wheel radius decrease thejudder problems [5 ] A reduction of the vehicle mass willalso decrease the thermal DTV and hotspots and reducethe risk of thermal cracking provided that the thermalcapacity of the disc remains the same A lighter stator(ie strut and eventually disc) will tend to increase thejudder problems since the ampli cation of BTV willbecome larger

6 FUTURE

The eld of low frequency braking induced vibrations isstill characterized by confusion Much research is neededin this area before a fairly clear picture becomes appar-ent The author nds the following areas especiallyinteresting

(a) simulation of BTV generation combining wear andTEI (wear especially hot and high pressure weartends to counteract the TEI process)

(b) the groan phenomenon(c) friction lms

429ASPECTS OF DISC BRAKE JUDDER

Fig 6 Model and corresponding brake judder simulation versus measurement

(d) the TEI process and its connection to thermoelasticbuckling

(e) studying wheel suspension vibration modes duringbrake-on conditions

(f ) the relation between BTV and simultaneous vari-ations in geometry (DTV run-out equivalent brakeradius) and friction coe cient

(g) prediction of BTV level and order for speci eddesign parameters and braking conditions

(h) developing models for simulation of vibration levelsin a vehicle at speci ed BTV

Generally in brake judder analysis it is recommendedto split the investigations into two parts

1 Analysis of sources of irregularities such as DTV etcThis involves thermomechanical FE analysis of thebrake components or dynamometer tests These typesof calculations are extremely time demanding

2 Analysis of the e ect of the irregularities in the vehicleIf the disturbances (which may be output from FEanalysis or dynamometer measurements) are given asfunctions of time very fast simulation can be carriedout by means of the amplitude function techniquedescribed in this work

The amplitude function technique is still at an earlystage but there are no di culties in principle involvedin using it to analyse multiple mass system models ofa whole vehicle Such models would be useful in deter-mining design criteria of brake components andsuspensions etc

REFERENCES

1 Hulten J Drum brake squeal PhD thesis Machine andVehicle Design Chalmers University of TechnologyGoteborg 1998

2 Inoue H Analysis of brake judder caused by thermal defor-mation of brake disc rotors In Proceedings 21st FISITACongress Belgrade 1986 pp 213ndash219 paper 865131

3 Kao T K Richmond J W and Moore M W The appli-

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

cation of predictive techniques to study thermo-elasticinstability of brakes In Proceedings of the Twelfth AnnualBrake Colloquium and Engineering Display AtlantaGeorgia 1984 SAE paper 942087

4 Jacobsson H Frequency sweep approach to brake judderpart A the brake judder phenomenon Classi cation andproblem approach Licentiate thesis Chalmers Universityof Technology Goteborg 1998

5 Jacobbson H Brake judder Thesis Chalmers Universityof Technology Goteborg 2001

6 Abdelhamid M K Creep groan of disc brakes InProceedings Noise and Vibration Conference TraverseCity Michigan 1995 pp 396ndash400 SAE paper 951282

7 Kao T K Richmond J W and Douarre A Brake dischot spotting and thermal judder an experimental and niteelement study Int J Veh Des 2000 23(34) 276ndash296

8 Brooks P C Barton D Crolla D A Lang A M andSchafer D R A study of disc brake judder using a fullycoupled thermo-mechanical nite element model InProceedings 25th FISITA Congress Beijing 1994pp 340ndash349 SAE paper 945042

9 Abdelhamid M K Brake judder analysis case studies SAEpaper 972027 1997

10 Kreitlow W Schrodter F and Matthai H Vibration andlsquohumrsquo of disc brakes under load SAE paper 850079 SAETrans Sect 1 1985 431ndash437

11 Augsburg K Brunner H and Grochowicz JUntersuchungen zum Rubbelverhalten von Pkw-Schwimmsattelbremser Automobiltechnische Zeitschrift1999 101

12 Stringham W Jank P Pfeifer J and Wang A Brakeroughnessmdashdisc brake torque variation rotor distortionand vehicle response SAE paper 930803 SAE TransSect 6 1993 1235ndash1247

13 Engel H G Bachman Th Eichhorn U and Saame ChDynamical behavior of brake-disc geometry as cause ofbrake judder In Proceedings EAEC Fourth InternationalConference on Vehicle and Tra c System TechnologyStrasbourg France 1993 Vol 1 pp 456ndash481

14 Thuresson D Thermomechanical analysis of frictionbrakes In Proceedings of the Eighteenth Annual BrakeColloquium and Engineering Display 2000 Vol P-358pp 149ndash159 SAE paper 2000-01-2775

15 Richmond J W Kao T K and Moore M W The devel-opment of computationalanalysis techniques for disc brake

430 H JACOBSSON

pad design In Proceedings Advances in AutomotiveBraking Technology Design Analysis and MaterialDevelopments 1996 (Institution of Mechanical Engineers)

16 Abendroth H Ste en T Falter W and Heidt RInvestigation of CV rotor cracking test procedures InBrakes 2000 International Conference on AutomotiveBrakingmdashTechnologies for the 21st Century 2000pp 149ndash162 (Professional Engineering PublishingLondon)

17 Haigh M J Smales H and Abe M Vehicle judder underdynamic braking caused by disc thickness variation InProceedings Braking of Road Vehicles London 1993pp 247ndash258 IMechE paper C44402293

18 Borjesson M Eriksson P Kuylenstierna C NilssonP H and Hermansson T The role of friction lms inautomotive brakes subjected to low contact forces InProceedings Braking of Road Vehicles London 1993pp 259ndash267 IMechE paper C444026

19 Wirth A and Whitaker R Developments in cast iron tech-nology In Proceedings Advances in Automotive BrakingTechnology Design Analysis and Material DevelopmentsLeeds UK 1996 (Institution of Mechanical Engineers)

20 Thoms E Disc brakes for heavy vehicles In ProceedingsBraking of Road Vehicles London 1988 pp 133ndash137IMechE paper C46488

21 Aviles R Hennequet G Hernandez A and Llorente L ILow frequency vibrations in disc brakes at high car speedPart I experimental approach Int J Veh Des 199516(6) 542ndash555

22 Ste en T and Bruns R Hotspotsbildung bei Pkw-Bremsscheiben Automobiltechnische Zeitschrift 1998100 408ndash413

23 Jacobsson H Analysis of brake judder by use of amplitudefunctions In Proceedings of SAE Noise and VibrationConference 1999 SAE paper 1999-01-1779

24 Jacobsson H Wheel suspension related disc brake judderIn Proceedings ASME Design Engineering TechnicalConferences Sacramento California 1997 VIB-4165

25 Engel H G Hassiotis V and Tiemann R Systemapproach to brake judder In Proceedings 25th FISITACongress Beijing 1994 Vol 1 pp 332ndash339 paper 945041

26 Martin R H and Bowron S Composite materials in trans-port friction applications In Brakes 2000 InternationalConference on Automotive BrakingmdashTechnologies for the21st Century 2000 pp 207ndash216 (Professional EngineeringPublishing London)

27 de Vries A and Wagner M The brake judder phenom-enon SAE Trans Sect 6 1992 101 652ndash660

28 Palmer B B and Weintraub M H The role of engineeredcashew particles on performance In Brakes 2000International Conference on Automotive BrakingmdashTechnologies for the 21st Century 2000 pp 185ndash195(Professional Engineering Publishing London)

29 Koetniyom S Brooks P C and Barton D C Finite

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

element prediction of inelastic strain accumulation in cast-iron brake rotors In Brakes 2000 InternationalConferenceon Automotive BrakingmdashTechnologies for the 21st Century2000 pp 139ndash148 (Professional Engineering PublishingLondon)

30 Hudson M D and Ruhl R L Ventilated brake rotor air ow investigation SAE paper 971033 1997

31 Grieve D G Barton D A Crolla D A Chapman J Land Buckingham J T Alternative brake disc materials InProceedingsAdvances in Automotive Braking TechnologyDesign Analysis and Material Developments Leeds UK1996 (Institution of Mechanical Engineers)

32 Grieve D G Barton D C Crolla D A and BuckinghamJ K Design of a lightweight automotive brake disc using nite element and Taguchi techniques Proc Instn MechEngrs Part D J Automobile Engineering 1998 212245ndash254

33 Krupka R and Kienzle A Fiber reinforced ceramic com-posite for brake discs In Proceeding of the EighteenthAnnual Brake Colloquium and Engineering Display 2000Vol P-358 pp 67ndash69 SAE paper 2000-01-2761

34 Bosworth R Investigations of secondary ride aspects ofsteering wheel vibration (shimmy and judder) using Taguchimethodology In Proceedings AUTOTECH 89 London1989 IMechE paper C3999

35 Kim M-G Jeong H-I and Yoo W-S Sensitivity analy-sis of chassis system to improve shimmy and brake juddervibration on steering wheel SAE Special Publication 11361996 pp 59ndash70

36 Abdelhamid M K Brake judder analysis using transferfunctions In Proceedings SAE Brake Colloquium TempeArizona 1997 pp 5ndash9 SAE paper 973018

37 Kao T K Richmond J W and Moore M WComputational analysis of pad performance InProceedings Braking of Road Vehicles 1993 paperC44402793 (Institution of Mechanical Engineers)

38 Floquet A and Dubourg M-C Realistic braking operationsimulation of ventilated disc brakes Trans ASMEJ Tribology July 1996 118 466ndash472

39 Du S Zagrodzki P Barber J R and Hulbert G MFinite element analysis of frictionally excited thermoelasticinstability J Thermal Stresses 1997 20 185ndash201

40 Daudi A R Dickerson W E and Narain M Hayesrsquoincreased air ow rotor design In Proceedings SecondInternational Seminar on Automotive Braking RecentDevelopments and Future Trends Leeds UK 1998pp 127ndash143 (Institution of Mechanical Engineers)

41 Crolla D A and Lang A M Brake noise and vibrationmdashthe state of the art Vehicle Tribology Tribology SeriesVol 18 1991 (Elsevier) pp 165ndash174

42 Aviles R Hennequet G Amezua E and Vallejo J Lowfrequency vibrations in disc brakes at high car speedPart II mathematical model and simulation Int J VehDes 1995 16(6) 556ndash569

Page 9: Aspects of disc brake judder - Universiti Teknologi Malaysiaarahim/jacobsson.pdf · 419 Aspects of disc brake judder HJacobsson* Machine and Vehicle Systems, Chalmers University of

427ASPECTS OF DISC BRAKE JUDDER

Dubourg [38] The application of the Fourier trans-form (on a space variable) has the e ect of reducingthe dimension of the problem The variable is trans-formed into a discrete parameter the frequency andthe corresponding partial derivatives are removedThe method can handle geometrically periodic butnon-axisymmetric solids such as ventilated discbrakes

5 The FE method can be applied directly to a pertur-bation method [39] The basic idea is not to solve thetransient problem but to consider the conditionsunder which a small perturbation in the temperature eld can grow exponentially in time The method isapplicable to transient processes as long as the contactarea does not change with time However the contactarea does change considerably with time duringbraking

6 A pad model composed of springndashdamper elementscan be used [22]

For vented discs and aluminium discs in particularwhere the air ow is important computational uiddynamics (CFD) is a useful tool CFD is used by somerotor manufacturers to increase air ow [26 40] In amarket survey [26 ] many companies saw the potentialof combining FE analysis and CFD to gain more accu-rate temperature predictions However this wouldrequire enormous computational e orts

As an alternative to CFD the convective cooling maybe estimated by approximative methods On a ventedrotor there are two di erent types of convective coolingair cross- ow over the rotor surface and air pumped owthrough the vents [3 ] Brake rotor vane ow relationsto estimate the heat convective transfer coe cient havelong been used in brake system thermal modellingCurrently two relations are recognized for ventilateddisc air ow those of Sisson and Limpert [30] Analternative is to approximate the convective heat transfercoe cient from the Nusselt modulus [31 32] and tocorrect it with empirically determined factors

52 E ects of BTVBPV

A few research projects have focused on the e ect ofbrake vibrations in the vehicle despite the fact that ithas been qualitatively described in the literature Crollaand Lang [41] Haigh et al [17] and many others havedescribed how brake judder rises to a maximum whenpassing through more or less distinct speeds So far theevaluation of brake judder has been done with a subjec-tive method using a scale from 1 to 10 but hardly anysimulations of brake judder in a vehicle have been car-ried out Brake judder problems have traditionally beensolved by use of trial and error rather than systematicmethods

In the literature there are a few sensitivity studies butin practice no lsquotruersquo simulations The di erence in that

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

lsquotruersquo simulations needs to be evaluated in the time planeThis involves not only a model of the vibration source(BTVBPV) and the vehicle structure and linkage (reson-ances and transfer) but also modelling of the brakingevent (frequency sweep braking conditions) see Fig 5

Straightforward integration of di erential equationswithout intelligent variable transformations or assump-tions using an ordinary equation-solving algorithmdesigned for non-sti problems (eg RungendashKutta) isnot an e cient way of dealing with this type of problemThe simulation will take an unnecessarily long time(hours or days) fail or crash Also the algorithms usedby commercial mechanics programs such as ADAMSare slow and ine cient if one wishes to follow a wholebraking event Hence the maximal vibration levels willbecome largely overestimated at nite braking timesHowever these types of programs are useful for quasi-static sensitivity analysis

521 Sensitivity analysis

Applying the system approach the solution to the judderproblem will be to build robustness into the vehicle andthereby to make it less sensitive to BTVBPV The systemof Engel et al [25] consists of ve di erent steps namelythe brake disc caliper and pad tyre and hubndashbearingunit wheel knuckle and nally the steering system Thereis also feedback between some steps in the outlinedmodel

An attempt to model numerically the vehicle responseto BTV was made by Kim et al [35] using MBS analysisof a similar vehicle structure The modelling of the sus-pension system used in the calculations was howevernot described Similar analyses are often carried out inthe automotive industry but seldom is the modellingdescribed in the literature However the model ofAugsburg et al [11] was described in detail

(a) calliper as two masses connected by a spring (rep-resenting the calliper sti ness in the forendashaftdirection)

(b) brake pads as springs(c) brake piston by a mass(d) hydraulic system as volume accumulating elements

The transfer path from the vibration source to thedriverrsquos contact points can be qualitatively investigatedby simultaneous measurements of accelerations atvarious position such as wheel carrier steering tie rod

Fig 5 The frequency sweep approach

428 H JACOBSSON

steering wheel etc [13] The sampled signals can be usedto generate the transfer functions between di erentpoints [9 36 ] The technique can be used to describeboth the brake excitation and the transfer functions thatcharacterize vehicle sensibility

The amplitude functions [23] can be seen as gen-eralized transfer functions They can be used to classifythe braking event as well as the corresponding vibrationsin the vehicle An advantage of the amplitude functionover the transfer function technique is that it works formuch higher decelerations since it does not rely on theFFT The method also determines the eigenfrequencieswith higher accuracy since it takes into account thetime delay of the maximal ampli cation caused by the nite deceleration and the inertias of the system If thistime delay is not considered the eigenfrequencies willbe systematically underestimated especially at highdecelerations

The analysis can be made in the frequency plane pro-vided that the braking starts above a certain limit often10ndash30 per cent above the critical speed [5 ] The deceler-ation clearly lsquocutsrsquo the maximal vibration amplitudeespecially at low damping Already at relative dampinglevels of the order of 1 per cent the transient analysis(including the frequency sweep) is needed for the rst-order judder except for in nitesimally smalldeclerations

Aviles et al [42] studied a braking event with slowlydecreasing speed and frequency However the con-clusion was drawn that the peak of the vibration ampli-tude at a certain vehicle speed was altogether an e ectof the negative frictionndashvelocity slope introduced in themodel The e ect of the frequency sweep was neveranalysed separately The calculations were made in thefrequency domain

522 Judder vibration simulation

Most of the analyses and measurements of judder aremade for braking with constant speed ie constant rev-olution frequency of the wheel as well as constant press-ure and temperature An argument is that it is easier tomeasure and analyse vibrations on the basis of this pre-scription Another bene t of measuring at constantspeed is e cient data analysis in the frequency domainHowever in a real braking situation the frequency isnot constant

There is a dynamic ampli cation of the brake torqueand pressure variations when passing through orcoming close to a critical speed of a vehicle Thevibration starts when the braking force is applied andreaches a maximal amplitude at a certain speed It iscontinued until low speed if the braking force is continu-ously applied This is the typical behaviour of a forcedvibration with relatively constant source amplitude butwith a sweeping frequency Fig 6

A two-DOF rotorndashstator model [24] with a linearly

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

decreasing disc speed possesses the main characteristicsof judder as shown in Fig 6 Before analysis the de ec-tion angles of rotordisc and statorcaliper respectivelywere split into vibration-free parts W and WC (rotationstatic de ection) and the superimposed vibrations QD andQ

C respectively The shape of the amplitude function Edescribes the relative vibration level QC (second timederivative of QC) almost exactly All parameters of therotorndashstator model can be experimentally generated

A full-vehicle model [5 ] shows the same lsquojudder behav-iourrsquo but can also explain some other e ects It is morecomplicated since it demands information about thewind speed slip etc

It is generally accepted that the front wheel suspensionof passenger cars has a rigid body forendashaft vibrationmode resonance in the frequency range 10ndash20 Hz andthat this resonance is responsible for lower-order judderat corresponding velocities This corresponds to a maxi-mal amplitude of the vibrations at a critical vehicle speedof between 60 and 140 kmh for the rst-order judderThe second-order judder will have a corresponding criti-cal speed (because of the same resonance) of between 30and 70 kmh The present vehicle had a resonance near14 Hz corresponding to a rst-order critical speed of95 kmh

The following possibilities for reducing judder werefound [5 ]

(a) decreased BTV andor BPV which will lead backto the cause approach

(b) increased relative stator mass and inertia momentcompared with the rotor

(c) increased damping(d) lighter braking(e) higher eigenfrequency

A lighter vehicle and a smaller wheel radius decrease thejudder problems [5 ] A reduction of the vehicle mass willalso decrease the thermal DTV and hotspots and reducethe risk of thermal cracking provided that the thermalcapacity of the disc remains the same A lighter stator(ie strut and eventually disc) will tend to increase thejudder problems since the ampli cation of BTV willbecome larger

6 FUTURE

The eld of low frequency braking induced vibrations isstill characterized by confusion Much research is neededin this area before a fairly clear picture becomes appar-ent The author nds the following areas especiallyinteresting

(a) simulation of BTV generation combining wear andTEI (wear especially hot and high pressure weartends to counteract the TEI process)

(b) the groan phenomenon(c) friction lms

429ASPECTS OF DISC BRAKE JUDDER

Fig 6 Model and corresponding brake judder simulation versus measurement

(d) the TEI process and its connection to thermoelasticbuckling

(e) studying wheel suspension vibration modes duringbrake-on conditions

(f ) the relation between BTV and simultaneous vari-ations in geometry (DTV run-out equivalent brakeradius) and friction coe cient

(g) prediction of BTV level and order for speci eddesign parameters and braking conditions

(h) developing models for simulation of vibration levelsin a vehicle at speci ed BTV

Generally in brake judder analysis it is recommendedto split the investigations into two parts

1 Analysis of sources of irregularities such as DTV etcThis involves thermomechanical FE analysis of thebrake components or dynamometer tests These typesof calculations are extremely time demanding

2 Analysis of the e ect of the irregularities in the vehicleIf the disturbances (which may be output from FEanalysis or dynamometer measurements) are given asfunctions of time very fast simulation can be carriedout by means of the amplitude function techniquedescribed in this work

The amplitude function technique is still at an earlystage but there are no di culties in principle involvedin using it to analyse multiple mass system models ofa whole vehicle Such models would be useful in deter-mining design criteria of brake components andsuspensions etc

REFERENCES

1 Hulten J Drum brake squeal PhD thesis Machine andVehicle Design Chalmers University of TechnologyGoteborg 1998

2 Inoue H Analysis of brake judder caused by thermal defor-mation of brake disc rotors In Proceedings 21st FISITACongress Belgrade 1986 pp 213ndash219 paper 865131

3 Kao T K Richmond J W and Moore M W The appli-

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

cation of predictive techniques to study thermo-elasticinstability of brakes In Proceedings of the Twelfth AnnualBrake Colloquium and Engineering Display AtlantaGeorgia 1984 SAE paper 942087

4 Jacobsson H Frequency sweep approach to brake judderpart A the brake judder phenomenon Classi cation andproblem approach Licentiate thesis Chalmers Universityof Technology Goteborg 1998

5 Jacobbson H Brake judder Thesis Chalmers Universityof Technology Goteborg 2001

6 Abdelhamid M K Creep groan of disc brakes InProceedings Noise and Vibration Conference TraverseCity Michigan 1995 pp 396ndash400 SAE paper 951282

7 Kao T K Richmond J W and Douarre A Brake dischot spotting and thermal judder an experimental and niteelement study Int J Veh Des 2000 23(34) 276ndash296

8 Brooks P C Barton D Crolla D A Lang A M andSchafer D R A study of disc brake judder using a fullycoupled thermo-mechanical nite element model InProceedings 25th FISITA Congress Beijing 1994pp 340ndash349 SAE paper 945042

9 Abdelhamid M K Brake judder analysis case studies SAEpaper 972027 1997

10 Kreitlow W Schrodter F and Matthai H Vibration andlsquohumrsquo of disc brakes under load SAE paper 850079 SAETrans Sect 1 1985 431ndash437

11 Augsburg K Brunner H and Grochowicz JUntersuchungen zum Rubbelverhalten von Pkw-Schwimmsattelbremser Automobiltechnische Zeitschrift1999 101

12 Stringham W Jank P Pfeifer J and Wang A Brakeroughnessmdashdisc brake torque variation rotor distortionand vehicle response SAE paper 930803 SAE TransSect 6 1993 1235ndash1247

13 Engel H G Bachman Th Eichhorn U and Saame ChDynamical behavior of brake-disc geometry as cause ofbrake judder In Proceedings EAEC Fourth InternationalConference on Vehicle and Tra c System TechnologyStrasbourg France 1993 Vol 1 pp 456ndash481

14 Thuresson D Thermomechanical analysis of frictionbrakes In Proceedings of the Eighteenth Annual BrakeColloquium and Engineering Display 2000 Vol P-358pp 149ndash159 SAE paper 2000-01-2775

15 Richmond J W Kao T K and Moore M W The devel-opment of computationalanalysis techniques for disc brake

430 H JACOBSSON

pad design In Proceedings Advances in AutomotiveBraking Technology Design Analysis and MaterialDevelopments 1996 (Institution of Mechanical Engineers)

16 Abendroth H Ste en T Falter W and Heidt RInvestigation of CV rotor cracking test procedures InBrakes 2000 International Conference on AutomotiveBrakingmdashTechnologies for the 21st Century 2000pp 149ndash162 (Professional Engineering PublishingLondon)

17 Haigh M J Smales H and Abe M Vehicle judder underdynamic braking caused by disc thickness variation InProceedings Braking of Road Vehicles London 1993pp 247ndash258 IMechE paper C44402293

18 Borjesson M Eriksson P Kuylenstierna C NilssonP H and Hermansson T The role of friction lms inautomotive brakes subjected to low contact forces InProceedings Braking of Road Vehicles London 1993pp 259ndash267 IMechE paper C444026

19 Wirth A and Whitaker R Developments in cast iron tech-nology In Proceedings Advances in Automotive BrakingTechnology Design Analysis and Material DevelopmentsLeeds UK 1996 (Institution of Mechanical Engineers)

20 Thoms E Disc brakes for heavy vehicles In ProceedingsBraking of Road Vehicles London 1988 pp 133ndash137IMechE paper C46488

21 Aviles R Hennequet G Hernandez A and Llorente L ILow frequency vibrations in disc brakes at high car speedPart I experimental approach Int J Veh Des 199516(6) 542ndash555

22 Ste en T and Bruns R Hotspotsbildung bei Pkw-Bremsscheiben Automobiltechnische Zeitschrift 1998100 408ndash413

23 Jacobsson H Analysis of brake judder by use of amplitudefunctions In Proceedings of SAE Noise and VibrationConference 1999 SAE paper 1999-01-1779

24 Jacobsson H Wheel suspension related disc brake judderIn Proceedings ASME Design Engineering TechnicalConferences Sacramento California 1997 VIB-4165

25 Engel H G Hassiotis V and Tiemann R Systemapproach to brake judder In Proceedings 25th FISITACongress Beijing 1994 Vol 1 pp 332ndash339 paper 945041

26 Martin R H and Bowron S Composite materials in trans-port friction applications In Brakes 2000 InternationalConference on Automotive BrakingmdashTechnologies for the21st Century 2000 pp 207ndash216 (Professional EngineeringPublishing London)

27 de Vries A and Wagner M The brake judder phenom-enon SAE Trans Sect 6 1992 101 652ndash660

28 Palmer B B and Weintraub M H The role of engineeredcashew particles on performance In Brakes 2000International Conference on Automotive BrakingmdashTechnologies for the 21st Century 2000 pp 185ndash195(Professional Engineering Publishing London)

29 Koetniyom S Brooks P C and Barton D C Finite

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

element prediction of inelastic strain accumulation in cast-iron brake rotors In Brakes 2000 InternationalConferenceon Automotive BrakingmdashTechnologies for the 21st Century2000 pp 139ndash148 (Professional Engineering PublishingLondon)

30 Hudson M D and Ruhl R L Ventilated brake rotor air ow investigation SAE paper 971033 1997

31 Grieve D G Barton D A Crolla D A Chapman J Land Buckingham J T Alternative brake disc materials InProceedingsAdvances in Automotive Braking TechnologyDesign Analysis and Material Developments Leeds UK1996 (Institution of Mechanical Engineers)

32 Grieve D G Barton D C Crolla D A and BuckinghamJ K Design of a lightweight automotive brake disc using nite element and Taguchi techniques Proc Instn MechEngrs Part D J Automobile Engineering 1998 212245ndash254

33 Krupka R and Kienzle A Fiber reinforced ceramic com-posite for brake discs In Proceeding of the EighteenthAnnual Brake Colloquium and Engineering Display 2000Vol P-358 pp 67ndash69 SAE paper 2000-01-2761

34 Bosworth R Investigations of secondary ride aspects ofsteering wheel vibration (shimmy and judder) using Taguchimethodology In Proceedings AUTOTECH 89 London1989 IMechE paper C3999

35 Kim M-G Jeong H-I and Yoo W-S Sensitivity analy-sis of chassis system to improve shimmy and brake juddervibration on steering wheel SAE Special Publication 11361996 pp 59ndash70

36 Abdelhamid M K Brake judder analysis using transferfunctions In Proceedings SAE Brake Colloquium TempeArizona 1997 pp 5ndash9 SAE paper 973018

37 Kao T K Richmond J W and Moore M WComputational analysis of pad performance InProceedings Braking of Road Vehicles 1993 paperC44402793 (Institution of Mechanical Engineers)

38 Floquet A and Dubourg M-C Realistic braking operationsimulation of ventilated disc brakes Trans ASMEJ Tribology July 1996 118 466ndash472

39 Du S Zagrodzki P Barber J R and Hulbert G MFinite element analysis of frictionally excited thermoelasticinstability J Thermal Stresses 1997 20 185ndash201

40 Daudi A R Dickerson W E and Narain M Hayesrsquoincreased air ow rotor design In Proceedings SecondInternational Seminar on Automotive Braking RecentDevelopments and Future Trends Leeds UK 1998pp 127ndash143 (Institution of Mechanical Engineers)

41 Crolla D A and Lang A M Brake noise and vibrationmdashthe state of the art Vehicle Tribology Tribology SeriesVol 18 1991 (Elsevier) pp 165ndash174

42 Aviles R Hennequet G Amezua E and Vallejo J Lowfrequency vibrations in disc brakes at high car speedPart II mathematical model and simulation Int J VehDes 1995 16(6) 556ndash569

Page 10: Aspects of disc brake judder - Universiti Teknologi Malaysiaarahim/jacobsson.pdf · 419 Aspects of disc brake judder HJacobsson* Machine and Vehicle Systems, Chalmers University of

428 H JACOBSSON

steering wheel etc [13] The sampled signals can be usedto generate the transfer functions between di erentpoints [9 36 ] The technique can be used to describeboth the brake excitation and the transfer functions thatcharacterize vehicle sensibility

The amplitude functions [23] can be seen as gen-eralized transfer functions They can be used to classifythe braking event as well as the corresponding vibrationsin the vehicle An advantage of the amplitude functionover the transfer function technique is that it works formuch higher decelerations since it does not rely on theFFT The method also determines the eigenfrequencieswith higher accuracy since it takes into account thetime delay of the maximal ampli cation caused by the nite deceleration and the inertias of the system If thistime delay is not considered the eigenfrequencies willbe systematically underestimated especially at highdecelerations

The analysis can be made in the frequency plane pro-vided that the braking starts above a certain limit often10ndash30 per cent above the critical speed [5 ] The deceler-ation clearly lsquocutsrsquo the maximal vibration amplitudeespecially at low damping Already at relative dampinglevels of the order of 1 per cent the transient analysis(including the frequency sweep) is needed for the rst-order judder except for in nitesimally smalldeclerations

Aviles et al [42] studied a braking event with slowlydecreasing speed and frequency However the con-clusion was drawn that the peak of the vibration ampli-tude at a certain vehicle speed was altogether an e ectof the negative frictionndashvelocity slope introduced in themodel The e ect of the frequency sweep was neveranalysed separately The calculations were made in thefrequency domain

522 Judder vibration simulation

Most of the analyses and measurements of judder aremade for braking with constant speed ie constant rev-olution frequency of the wheel as well as constant press-ure and temperature An argument is that it is easier tomeasure and analyse vibrations on the basis of this pre-scription Another bene t of measuring at constantspeed is e cient data analysis in the frequency domainHowever in a real braking situation the frequency isnot constant

There is a dynamic ampli cation of the brake torqueand pressure variations when passing through orcoming close to a critical speed of a vehicle Thevibration starts when the braking force is applied andreaches a maximal amplitude at a certain speed It iscontinued until low speed if the braking force is continu-ously applied This is the typical behaviour of a forcedvibration with relatively constant source amplitude butwith a sweeping frequency Fig 6

A two-DOF rotorndashstator model [24] with a linearly

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

decreasing disc speed possesses the main characteristicsof judder as shown in Fig 6 Before analysis the de ec-tion angles of rotordisc and statorcaliper respectivelywere split into vibration-free parts W and WC (rotationstatic de ection) and the superimposed vibrations QD andQ

C respectively The shape of the amplitude function Edescribes the relative vibration level QC (second timederivative of QC) almost exactly All parameters of therotorndashstator model can be experimentally generated

A full-vehicle model [5 ] shows the same lsquojudder behav-iourrsquo but can also explain some other e ects It is morecomplicated since it demands information about thewind speed slip etc

It is generally accepted that the front wheel suspensionof passenger cars has a rigid body forendashaft vibrationmode resonance in the frequency range 10ndash20 Hz andthat this resonance is responsible for lower-order judderat corresponding velocities This corresponds to a maxi-mal amplitude of the vibrations at a critical vehicle speedof between 60 and 140 kmh for the rst-order judderThe second-order judder will have a corresponding criti-cal speed (because of the same resonance) of between 30and 70 kmh The present vehicle had a resonance near14 Hz corresponding to a rst-order critical speed of95 kmh

The following possibilities for reducing judder werefound [5 ]

(a) decreased BTV andor BPV which will lead backto the cause approach

(b) increased relative stator mass and inertia momentcompared with the rotor

(c) increased damping(d) lighter braking(e) higher eigenfrequency

A lighter vehicle and a smaller wheel radius decrease thejudder problems [5 ] A reduction of the vehicle mass willalso decrease the thermal DTV and hotspots and reducethe risk of thermal cracking provided that the thermalcapacity of the disc remains the same A lighter stator(ie strut and eventually disc) will tend to increase thejudder problems since the ampli cation of BTV willbecome larger

6 FUTURE

The eld of low frequency braking induced vibrations isstill characterized by confusion Much research is neededin this area before a fairly clear picture becomes appar-ent The author nds the following areas especiallyinteresting

(a) simulation of BTV generation combining wear andTEI (wear especially hot and high pressure weartends to counteract the TEI process)

(b) the groan phenomenon(c) friction lms

429ASPECTS OF DISC BRAKE JUDDER

Fig 6 Model and corresponding brake judder simulation versus measurement

(d) the TEI process and its connection to thermoelasticbuckling

(e) studying wheel suspension vibration modes duringbrake-on conditions

(f ) the relation between BTV and simultaneous vari-ations in geometry (DTV run-out equivalent brakeradius) and friction coe cient

(g) prediction of BTV level and order for speci eddesign parameters and braking conditions

(h) developing models for simulation of vibration levelsin a vehicle at speci ed BTV

Generally in brake judder analysis it is recommendedto split the investigations into two parts

1 Analysis of sources of irregularities such as DTV etcThis involves thermomechanical FE analysis of thebrake components or dynamometer tests These typesof calculations are extremely time demanding

2 Analysis of the e ect of the irregularities in the vehicleIf the disturbances (which may be output from FEanalysis or dynamometer measurements) are given asfunctions of time very fast simulation can be carriedout by means of the amplitude function techniquedescribed in this work

The amplitude function technique is still at an earlystage but there are no di culties in principle involvedin using it to analyse multiple mass system models ofa whole vehicle Such models would be useful in deter-mining design criteria of brake components andsuspensions etc

REFERENCES

1 Hulten J Drum brake squeal PhD thesis Machine andVehicle Design Chalmers University of TechnologyGoteborg 1998

2 Inoue H Analysis of brake judder caused by thermal defor-mation of brake disc rotors In Proceedings 21st FISITACongress Belgrade 1986 pp 213ndash219 paper 865131

3 Kao T K Richmond J W and Moore M W The appli-

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

cation of predictive techniques to study thermo-elasticinstability of brakes In Proceedings of the Twelfth AnnualBrake Colloquium and Engineering Display AtlantaGeorgia 1984 SAE paper 942087

4 Jacobsson H Frequency sweep approach to brake judderpart A the brake judder phenomenon Classi cation andproblem approach Licentiate thesis Chalmers Universityof Technology Goteborg 1998

5 Jacobbson H Brake judder Thesis Chalmers Universityof Technology Goteborg 2001

6 Abdelhamid M K Creep groan of disc brakes InProceedings Noise and Vibration Conference TraverseCity Michigan 1995 pp 396ndash400 SAE paper 951282

7 Kao T K Richmond J W and Douarre A Brake dischot spotting and thermal judder an experimental and niteelement study Int J Veh Des 2000 23(34) 276ndash296

8 Brooks P C Barton D Crolla D A Lang A M andSchafer D R A study of disc brake judder using a fullycoupled thermo-mechanical nite element model InProceedings 25th FISITA Congress Beijing 1994pp 340ndash349 SAE paper 945042

9 Abdelhamid M K Brake judder analysis case studies SAEpaper 972027 1997

10 Kreitlow W Schrodter F and Matthai H Vibration andlsquohumrsquo of disc brakes under load SAE paper 850079 SAETrans Sect 1 1985 431ndash437

11 Augsburg K Brunner H and Grochowicz JUntersuchungen zum Rubbelverhalten von Pkw-Schwimmsattelbremser Automobiltechnische Zeitschrift1999 101

12 Stringham W Jank P Pfeifer J and Wang A Brakeroughnessmdashdisc brake torque variation rotor distortionand vehicle response SAE paper 930803 SAE TransSect 6 1993 1235ndash1247

13 Engel H G Bachman Th Eichhorn U and Saame ChDynamical behavior of brake-disc geometry as cause ofbrake judder In Proceedings EAEC Fourth InternationalConference on Vehicle and Tra c System TechnologyStrasbourg France 1993 Vol 1 pp 456ndash481

14 Thuresson D Thermomechanical analysis of frictionbrakes In Proceedings of the Eighteenth Annual BrakeColloquium and Engineering Display 2000 Vol P-358pp 149ndash159 SAE paper 2000-01-2775

15 Richmond J W Kao T K and Moore M W The devel-opment of computationalanalysis techniques for disc brake

430 H JACOBSSON

pad design In Proceedings Advances in AutomotiveBraking Technology Design Analysis and MaterialDevelopments 1996 (Institution of Mechanical Engineers)

16 Abendroth H Ste en T Falter W and Heidt RInvestigation of CV rotor cracking test procedures InBrakes 2000 International Conference on AutomotiveBrakingmdashTechnologies for the 21st Century 2000pp 149ndash162 (Professional Engineering PublishingLondon)

17 Haigh M J Smales H and Abe M Vehicle judder underdynamic braking caused by disc thickness variation InProceedings Braking of Road Vehicles London 1993pp 247ndash258 IMechE paper C44402293

18 Borjesson M Eriksson P Kuylenstierna C NilssonP H and Hermansson T The role of friction lms inautomotive brakes subjected to low contact forces InProceedings Braking of Road Vehicles London 1993pp 259ndash267 IMechE paper C444026

19 Wirth A and Whitaker R Developments in cast iron tech-nology In Proceedings Advances in Automotive BrakingTechnology Design Analysis and Material DevelopmentsLeeds UK 1996 (Institution of Mechanical Engineers)

20 Thoms E Disc brakes for heavy vehicles In ProceedingsBraking of Road Vehicles London 1988 pp 133ndash137IMechE paper C46488

21 Aviles R Hennequet G Hernandez A and Llorente L ILow frequency vibrations in disc brakes at high car speedPart I experimental approach Int J Veh Des 199516(6) 542ndash555

22 Ste en T and Bruns R Hotspotsbildung bei Pkw-Bremsscheiben Automobiltechnische Zeitschrift 1998100 408ndash413

23 Jacobsson H Analysis of brake judder by use of amplitudefunctions In Proceedings of SAE Noise and VibrationConference 1999 SAE paper 1999-01-1779

24 Jacobsson H Wheel suspension related disc brake judderIn Proceedings ASME Design Engineering TechnicalConferences Sacramento California 1997 VIB-4165

25 Engel H G Hassiotis V and Tiemann R Systemapproach to brake judder In Proceedings 25th FISITACongress Beijing 1994 Vol 1 pp 332ndash339 paper 945041

26 Martin R H and Bowron S Composite materials in trans-port friction applications In Brakes 2000 InternationalConference on Automotive BrakingmdashTechnologies for the21st Century 2000 pp 207ndash216 (Professional EngineeringPublishing London)

27 de Vries A and Wagner M The brake judder phenom-enon SAE Trans Sect 6 1992 101 652ndash660

28 Palmer B B and Weintraub M H The role of engineeredcashew particles on performance In Brakes 2000International Conference on Automotive BrakingmdashTechnologies for the 21st Century 2000 pp 185ndash195(Professional Engineering Publishing London)

29 Koetniyom S Brooks P C and Barton D C Finite

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

element prediction of inelastic strain accumulation in cast-iron brake rotors In Brakes 2000 InternationalConferenceon Automotive BrakingmdashTechnologies for the 21st Century2000 pp 139ndash148 (Professional Engineering PublishingLondon)

30 Hudson M D and Ruhl R L Ventilated brake rotor air ow investigation SAE paper 971033 1997

31 Grieve D G Barton D A Crolla D A Chapman J Land Buckingham J T Alternative brake disc materials InProceedingsAdvances in Automotive Braking TechnologyDesign Analysis and Material Developments Leeds UK1996 (Institution of Mechanical Engineers)

32 Grieve D G Barton D C Crolla D A and BuckinghamJ K Design of a lightweight automotive brake disc using nite element and Taguchi techniques Proc Instn MechEngrs Part D J Automobile Engineering 1998 212245ndash254

33 Krupka R and Kienzle A Fiber reinforced ceramic com-posite for brake discs In Proceeding of the EighteenthAnnual Brake Colloquium and Engineering Display 2000Vol P-358 pp 67ndash69 SAE paper 2000-01-2761

34 Bosworth R Investigations of secondary ride aspects ofsteering wheel vibration (shimmy and judder) using Taguchimethodology In Proceedings AUTOTECH 89 London1989 IMechE paper C3999

35 Kim M-G Jeong H-I and Yoo W-S Sensitivity analy-sis of chassis system to improve shimmy and brake juddervibration on steering wheel SAE Special Publication 11361996 pp 59ndash70

36 Abdelhamid M K Brake judder analysis using transferfunctions In Proceedings SAE Brake Colloquium TempeArizona 1997 pp 5ndash9 SAE paper 973018

37 Kao T K Richmond J W and Moore M WComputational analysis of pad performance InProceedings Braking of Road Vehicles 1993 paperC44402793 (Institution of Mechanical Engineers)

38 Floquet A and Dubourg M-C Realistic braking operationsimulation of ventilated disc brakes Trans ASMEJ Tribology July 1996 118 466ndash472

39 Du S Zagrodzki P Barber J R and Hulbert G MFinite element analysis of frictionally excited thermoelasticinstability J Thermal Stresses 1997 20 185ndash201

40 Daudi A R Dickerson W E and Narain M Hayesrsquoincreased air ow rotor design In Proceedings SecondInternational Seminar on Automotive Braking RecentDevelopments and Future Trends Leeds UK 1998pp 127ndash143 (Institution of Mechanical Engineers)

41 Crolla D A and Lang A M Brake noise and vibrationmdashthe state of the art Vehicle Tribology Tribology SeriesVol 18 1991 (Elsevier) pp 165ndash174

42 Aviles R Hennequet G Amezua E and Vallejo J Lowfrequency vibrations in disc brakes at high car speedPart II mathematical model and simulation Int J VehDes 1995 16(6) 556ndash569

Page 11: Aspects of disc brake judder - Universiti Teknologi Malaysiaarahim/jacobsson.pdf · 419 Aspects of disc brake judder HJacobsson* Machine and Vehicle Systems, Chalmers University of

429ASPECTS OF DISC BRAKE JUDDER

Fig 6 Model and corresponding brake judder simulation versus measurement

(d) the TEI process and its connection to thermoelasticbuckling

(e) studying wheel suspension vibration modes duringbrake-on conditions

(f ) the relation between BTV and simultaneous vari-ations in geometry (DTV run-out equivalent brakeradius) and friction coe cient

(g) prediction of BTV level and order for speci eddesign parameters and braking conditions

(h) developing models for simulation of vibration levelsin a vehicle at speci ed BTV

Generally in brake judder analysis it is recommendedto split the investigations into two parts

1 Analysis of sources of irregularities such as DTV etcThis involves thermomechanical FE analysis of thebrake components or dynamometer tests These typesof calculations are extremely time demanding

2 Analysis of the e ect of the irregularities in the vehicleIf the disturbances (which may be output from FEanalysis or dynamometer measurements) are given asfunctions of time very fast simulation can be carriedout by means of the amplitude function techniquedescribed in this work

The amplitude function technique is still at an earlystage but there are no di culties in principle involvedin using it to analyse multiple mass system models ofa whole vehicle Such models would be useful in deter-mining design criteria of brake components andsuspensions etc

REFERENCES

1 Hulten J Drum brake squeal PhD thesis Machine andVehicle Design Chalmers University of TechnologyGoteborg 1998

2 Inoue H Analysis of brake judder caused by thermal defor-mation of brake disc rotors In Proceedings 21st FISITACongress Belgrade 1986 pp 213ndash219 paper 865131

3 Kao T K Richmond J W and Moore M W The appli-

D12302 copy IMechE 2003 Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

cation of predictive techniques to study thermo-elasticinstability of brakes In Proceedings of the Twelfth AnnualBrake Colloquium and Engineering Display AtlantaGeorgia 1984 SAE paper 942087

4 Jacobsson H Frequency sweep approach to brake judderpart A the brake judder phenomenon Classi cation andproblem approach Licentiate thesis Chalmers Universityof Technology Goteborg 1998

5 Jacobbson H Brake judder Thesis Chalmers Universityof Technology Goteborg 2001

6 Abdelhamid M K Creep groan of disc brakes InProceedings Noise and Vibration Conference TraverseCity Michigan 1995 pp 396ndash400 SAE paper 951282

7 Kao T K Richmond J W and Douarre A Brake dischot spotting and thermal judder an experimental and niteelement study Int J Veh Des 2000 23(34) 276ndash296

8 Brooks P C Barton D Crolla D A Lang A M andSchafer D R A study of disc brake judder using a fullycoupled thermo-mechanical nite element model InProceedings 25th FISITA Congress Beijing 1994pp 340ndash349 SAE paper 945042

9 Abdelhamid M K Brake judder analysis case studies SAEpaper 972027 1997

10 Kreitlow W Schrodter F and Matthai H Vibration andlsquohumrsquo of disc brakes under load SAE paper 850079 SAETrans Sect 1 1985 431ndash437

11 Augsburg K Brunner H and Grochowicz JUntersuchungen zum Rubbelverhalten von Pkw-Schwimmsattelbremser Automobiltechnische Zeitschrift1999 101

12 Stringham W Jank P Pfeifer J and Wang A Brakeroughnessmdashdisc brake torque variation rotor distortionand vehicle response SAE paper 930803 SAE TransSect 6 1993 1235ndash1247

13 Engel H G Bachman Th Eichhorn U and Saame ChDynamical behavior of brake-disc geometry as cause ofbrake judder In Proceedings EAEC Fourth InternationalConference on Vehicle and Tra c System TechnologyStrasbourg France 1993 Vol 1 pp 456ndash481

14 Thuresson D Thermomechanical analysis of frictionbrakes In Proceedings of the Eighteenth Annual BrakeColloquium and Engineering Display 2000 Vol P-358pp 149ndash159 SAE paper 2000-01-2775

15 Richmond J W Kao T K and Moore M W The devel-opment of computationalanalysis techniques for disc brake

430 H JACOBSSON

pad design In Proceedings Advances in AutomotiveBraking Technology Design Analysis and MaterialDevelopments 1996 (Institution of Mechanical Engineers)

16 Abendroth H Ste en T Falter W and Heidt RInvestigation of CV rotor cracking test procedures InBrakes 2000 International Conference on AutomotiveBrakingmdashTechnologies for the 21st Century 2000pp 149ndash162 (Professional Engineering PublishingLondon)

17 Haigh M J Smales H and Abe M Vehicle judder underdynamic braking caused by disc thickness variation InProceedings Braking of Road Vehicles London 1993pp 247ndash258 IMechE paper C44402293

18 Borjesson M Eriksson P Kuylenstierna C NilssonP H and Hermansson T The role of friction lms inautomotive brakes subjected to low contact forces InProceedings Braking of Road Vehicles London 1993pp 259ndash267 IMechE paper C444026

19 Wirth A and Whitaker R Developments in cast iron tech-nology In Proceedings Advances in Automotive BrakingTechnology Design Analysis and Material DevelopmentsLeeds UK 1996 (Institution of Mechanical Engineers)

20 Thoms E Disc brakes for heavy vehicles In ProceedingsBraking of Road Vehicles London 1988 pp 133ndash137IMechE paper C46488

21 Aviles R Hennequet G Hernandez A and Llorente L ILow frequency vibrations in disc brakes at high car speedPart I experimental approach Int J Veh Des 199516(6) 542ndash555

22 Ste en T and Bruns R Hotspotsbildung bei Pkw-Bremsscheiben Automobiltechnische Zeitschrift 1998100 408ndash413

23 Jacobsson H Analysis of brake judder by use of amplitudefunctions In Proceedings of SAE Noise and VibrationConference 1999 SAE paper 1999-01-1779

24 Jacobsson H Wheel suspension related disc brake judderIn Proceedings ASME Design Engineering TechnicalConferences Sacramento California 1997 VIB-4165

25 Engel H G Hassiotis V and Tiemann R Systemapproach to brake judder In Proceedings 25th FISITACongress Beijing 1994 Vol 1 pp 332ndash339 paper 945041

26 Martin R H and Bowron S Composite materials in trans-port friction applications In Brakes 2000 InternationalConference on Automotive BrakingmdashTechnologies for the21st Century 2000 pp 207ndash216 (Professional EngineeringPublishing London)

27 de Vries A and Wagner M The brake judder phenom-enon SAE Trans Sect 6 1992 101 652ndash660

28 Palmer B B and Weintraub M H The role of engineeredcashew particles on performance In Brakes 2000International Conference on Automotive BrakingmdashTechnologies for the 21st Century 2000 pp 185ndash195(Professional Engineering Publishing London)

29 Koetniyom S Brooks P C and Barton D C Finite

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

element prediction of inelastic strain accumulation in cast-iron brake rotors In Brakes 2000 InternationalConferenceon Automotive BrakingmdashTechnologies for the 21st Century2000 pp 139ndash148 (Professional Engineering PublishingLondon)

30 Hudson M D and Ruhl R L Ventilated brake rotor air ow investigation SAE paper 971033 1997

31 Grieve D G Barton D A Crolla D A Chapman J Land Buckingham J T Alternative brake disc materials InProceedingsAdvances in Automotive Braking TechnologyDesign Analysis and Material Developments Leeds UK1996 (Institution of Mechanical Engineers)

32 Grieve D G Barton D C Crolla D A and BuckinghamJ K Design of a lightweight automotive brake disc using nite element and Taguchi techniques Proc Instn MechEngrs Part D J Automobile Engineering 1998 212245ndash254

33 Krupka R and Kienzle A Fiber reinforced ceramic com-posite for brake discs In Proceeding of the EighteenthAnnual Brake Colloquium and Engineering Display 2000Vol P-358 pp 67ndash69 SAE paper 2000-01-2761

34 Bosworth R Investigations of secondary ride aspects ofsteering wheel vibration (shimmy and judder) using Taguchimethodology In Proceedings AUTOTECH 89 London1989 IMechE paper C3999

35 Kim M-G Jeong H-I and Yoo W-S Sensitivity analy-sis of chassis system to improve shimmy and brake juddervibration on steering wheel SAE Special Publication 11361996 pp 59ndash70

36 Abdelhamid M K Brake judder analysis using transferfunctions In Proceedings SAE Brake Colloquium TempeArizona 1997 pp 5ndash9 SAE paper 973018

37 Kao T K Richmond J W and Moore M WComputational analysis of pad performance InProceedings Braking of Road Vehicles 1993 paperC44402793 (Institution of Mechanical Engineers)

38 Floquet A and Dubourg M-C Realistic braking operationsimulation of ventilated disc brakes Trans ASMEJ Tribology July 1996 118 466ndash472

39 Du S Zagrodzki P Barber J R and Hulbert G MFinite element analysis of frictionally excited thermoelasticinstability J Thermal Stresses 1997 20 185ndash201

40 Daudi A R Dickerson W E and Narain M Hayesrsquoincreased air ow rotor design In Proceedings SecondInternational Seminar on Automotive Braking RecentDevelopments and Future Trends Leeds UK 1998pp 127ndash143 (Institution of Mechanical Engineers)

41 Crolla D A and Lang A M Brake noise and vibrationmdashthe state of the art Vehicle Tribology Tribology SeriesVol 18 1991 (Elsevier) pp 165ndash174

42 Aviles R Hennequet G Amezua E and Vallejo J Lowfrequency vibrations in disc brakes at high car speedPart II mathematical model and simulation Int J VehDes 1995 16(6) 556ndash569

Page 12: Aspects of disc brake judder - Universiti Teknologi Malaysiaarahim/jacobsson.pdf · 419 Aspects of disc brake judder HJacobsson* Machine and Vehicle Systems, Chalmers University of

430 H JACOBSSON

pad design In Proceedings Advances in AutomotiveBraking Technology Design Analysis and MaterialDevelopments 1996 (Institution of Mechanical Engineers)

16 Abendroth H Ste en T Falter W and Heidt RInvestigation of CV rotor cracking test procedures InBrakes 2000 International Conference on AutomotiveBrakingmdashTechnologies for the 21st Century 2000pp 149ndash162 (Professional Engineering PublishingLondon)

17 Haigh M J Smales H and Abe M Vehicle judder underdynamic braking caused by disc thickness variation InProceedings Braking of Road Vehicles London 1993pp 247ndash258 IMechE paper C44402293

18 Borjesson M Eriksson P Kuylenstierna C NilssonP H and Hermansson T The role of friction lms inautomotive brakes subjected to low contact forces InProceedings Braking of Road Vehicles London 1993pp 259ndash267 IMechE paper C444026

19 Wirth A and Whitaker R Developments in cast iron tech-nology In Proceedings Advances in Automotive BrakingTechnology Design Analysis and Material DevelopmentsLeeds UK 1996 (Institution of Mechanical Engineers)

20 Thoms E Disc brakes for heavy vehicles In ProceedingsBraking of Road Vehicles London 1988 pp 133ndash137IMechE paper C46488

21 Aviles R Hennequet G Hernandez A and Llorente L ILow frequency vibrations in disc brakes at high car speedPart I experimental approach Int J Veh Des 199516(6) 542ndash555

22 Ste en T and Bruns R Hotspotsbildung bei Pkw-Bremsscheiben Automobiltechnische Zeitschrift 1998100 408ndash413

23 Jacobsson H Analysis of brake judder by use of amplitudefunctions In Proceedings of SAE Noise and VibrationConference 1999 SAE paper 1999-01-1779

24 Jacobsson H Wheel suspension related disc brake judderIn Proceedings ASME Design Engineering TechnicalConferences Sacramento California 1997 VIB-4165

25 Engel H G Hassiotis V and Tiemann R Systemapproach to brake judder In Proceedings 25th FISITACongress Beijing 1994 Vol 1 pp 332ndash339 paper 945041

26 Martin R H and Bowron S Composite materials in trans-port friction applications In Brakes 2000 InternationalConference on Automotive BrakingmdashTechnologies for the21st Century 2000 pp 207ndash216 (Professional EngineeringPublishing London)

27 de Vries A and Wagner M The brake judder phenom-enon SAE Trans Sect 6 1992 101 652ndash660

28 Palmer B B and Weintraub M H The role of engineeredcashew particles on performance In Brakes 2000International Conference on Automotive BrakingmdashTechnologies for the 21st Century 2000 pp 185ndash195(Professional Engineering Publishing London)

29 Koetniyom S Brooks P C and Barton D C Finite

D12302 copy IMechE 2003Proc Instn Mech Engrs Vol 217 Part D J Automobile Engineering

element prediction of inelastic strain accumulation in cast-iron brake rotors In Brakes 2000 InternationalConferenceon Automotive BrakingmdashTechnologies for the 21st Century2000 pp 139ndash148 (Professional Engineering PublishingLondon)

30 Hudson M D and Ruhl R L Ventilated brake rotor air ow investigation SAE paper 971033 1997

31 Grieve D G Barton D A Crolla D A Chapman J Land Buckingham J T Alternative brake disc materials InProceedingsAdvances in Automotive Braking TechnologyDesign Analysis and Material Developments Leeds UK1996 (Institution of Mechanical Engineers)

32 Grieve D G Barton D C Crolla D A and BuckinghamJ K Design of a lightweight automotive brake disc using nite element and Taguchi techniques Proc Instn MechEngrs Part D J Automobile Engineering 1998 212245ndash254

33 Krupka R and Kienzle A Fiber reinforced ceramic com-posite for brake discs In Proceeding of the EighteenthAnnual Brake Colloquium and Engineering Display 2000Vol P-358 pp 67ndash69 SAE paper 2000-01-2761

34 Bosworth R Investigations of secondary ride aspects ofsteering wheel vibration (shimmy and judder) using Taguchimethodology In Proceedings AUTOTECH 89 London1989 IMechE paper C3999

35 Kim M-G Jeong H-I and Yoo W-S Sensitivity analy-sis of chassis system to improve shimmy and brake juddervibration on steering wheel SAE Special Publication 11361996 pp 59ndash70

36 Abdelhamid M K Brake judder analysis using transferfunctions In Proceedings SAE Brake Colloquium TempeArizona 1997 pp 5ndash9 SAE paper 973018

37 Kao T K Richmond J W and Moore M WComputational analysis of pad performance InProceedings Braking of Road Vehicles 1993 paperC44402793 (Institution of Mechanical Engineers)

38 Floquet A and Dubourg M-C Realistic braking operationsimulation of ventilated disc brakes Trans ASMEJ Tribology July 1996 118 466ndash472

39 Du S Zagrodzki P Barber J R and Hulbert G MFinite element analysis of frictionally excited thermoelasticinstability J Thermal Stresses 1997 20 185ndash201

40 Daudi A R Dickerson W E and Narain M Hayesrsquoincreased air ow rotor design In Proceedings SecondInternational Seminar on Automotive Braking RecentDevelopments and Future Trends Leeds UK 1998pp 127ndash143 (Institution of Mechanical Engineers)

41 Crolla D A and Lang A M Brake noise and vibrationmdashthe state of the art Vehicle Tribology Tribology SeriesVol 18 1991 (Elsevier) pp 165ndash174

42 Aviles R Hennequet G Amezua E and Vallejo J Lowfrequency vibrations in disc brakes at high car speedPart II mathematical model and simulation Int J VehDes 1995 16(6) 556ndash569