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TRANSPORT PROBLEMS 2010

PROBLEMY TRANSPORTU Volume 5 Issue 4

stabilizer bars, calculation, construction

Adam-Markus WITTEK*, Hans-Christian RICHTER

ThyssenKrupp Bilstein Suspension GmbH

Oeger St. 85, 58095 Hagen, Germany

Bogusaw AZARZ

Silesian University of Technology, Faculty of Transport

Krasiskiego St. 8, 40-019 Katowice, Poland

*Corresponding author. E-mail: [email protected]

STABILIZER BARS: Part 1. CALCULATIONS AND CONSTRUCTION

Summary. The article outlines the calculation methods for stabilizer bars. Modern

technological and structural solutions in contemporary cars are reflected also in the

construction and manufacturing of stabilizer bars. A proper construction and the selection

of parameters influence the strength properties, the weight, durability and reliability as

well as the selection of an appropriate production method.

STABILIZATORY SAMOCHODOWE: Cz1. OBLICZENIA I KONSTRUKCJA

Streszczenie. W artykule przedstawiono zarys metod obliczeniowych stabilizatorwsamochodowych. Nowoczesne rozwizania technologiczno-konstrukcyjne we

wspczesnych samochodach znajduj rwnie odzwierciedlenie w konstrukcji i

produkcji stabilizatorw. Prawidowa konstrukcja i dobr parametrw maj wpyw na

cechy wytrzymaociowe, ciar, trwao oraz niezawodno jak i wybr waciwej

metody produkcyjnej.

1. INTRODUCTION

The function of stabilizer bars in motor vehicles is to reduce the body roll during cornering. The

body roll is influenced by the occurring wheel load shift and the change of camber angle. Decisive is

the steering performance which may be purposefully adjusted towards understeer or oversteer whendesigning the stabilization. So the stabilizer bars increases the travelling comfort and to a considerable

extent the driving safety [10].

Stabilizer bars are non-bearing spring elements in vehicles. In contrast to all bearing springs, which

are loaded by the static forces also in resting condition, the stabilizer bars are normally loaded during

the driving phases only [4]. As resilient components of the chassis, stabilizer bars are connectors

between axle and body as well as between the wheels of an axle. The position of stabilizer bars is

selected in such a way that the anti-roll suspension stiffens the rotation of the body about the

vehicles longitudinal axis is made difficult without simultaneously hindering the vertical

suspension, i.e. motion of the body towards the vertical axis. For this purpose, the stabilizer bar is

arranged in the axle in such a way that the back comes to rest approximately at the level of the wheel

centers across the driving direction. The bearings of the stabilizer bar support themselves against the

body; stabilizer bars do not contribute to static support of the weight of the body against the axle and

remain unloaded during synchronistic downward or upward deflection of the spring.


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136 A.-M. Wittek, H.-Ch. Richter, B. azarz

When the body leans due to centrifugal forces acting in the transverse direction of the vehicle, the

so-called reciprocal suspension comes about. This means that at the bend of the road the bend-external

wheel deflects downwards and the bend-internal wheel deflects upwards. As a result of this, the

stabilizer bar arms are deflected in the opposite direction and the back is twisted [9, 10].

The body roll during cornering could be reduced also by the selection of a harder vertical

suspension, but it would have a negative impact on the driving comfort. The stabilizer bars contribute

thus considerably to the improvement of comfort of the motor vehicles.

2. CALCULATION AND CONSTRUCTION

Stabilizer bars for the chassis of motor vehicles are usually U-shaped bars of spring steel with

circular or circular ring cross-section, so they form a bow with the back and the arms. As few as

possible kinks preferably in a single plane should be planned when constructing stabilizer bars.

Fig. 1. Form of stabilizersRys. 1. Ksztaty stabilizatorw

This makes the manufacturing of the parts easier. However, as a rule, the stabilizer bars do not lie

in a single plane, but for the purpose of avoidance of other chassis parts are arranged spatially

bent, angled and cranked in a partly bizarre way (fig. 1, 2). Their U-shape is principally maintained

[1, 3, 4]. Fig. 2 contains examples of different shapes of stabilizer bars.

As large bending radii as possible should be selected. The inner bending radius must have at least

the size of the bar diameter. The arm ends are shaped differently for the purpose of force transmission

and steering. Generally, when constructing stabilizer bars, effort must be made to minimize the

weight, e.g. by shortening the arms while maintaining constant stabilizer bar action (fig. 4) [1, 3, 4].

Most commonly, stabilizer bars are mounted in rubber or plastic (fig. 3), and each shape of bearing

requires an appropriate shape of the bar end. The plastic bearing, the rubber stiffness and the rubber

strain have an influence on all stabilizer bars or the wheel rate, respectively.


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Stabilizer bars: Part 1. Calculation and construction 137

Fig. 2. Shapes of stabilizer bars - examplesRys. 2. Ksztaty stabilizatorw samochodowych przykady

Fig. 3. Plastic bearings for stabilizer bars

Rys. 3. Przykady oysk stabilizatorw samochodowych

Stabilizer bars are manufactured mostly of round stock with rolled, drawn, peeled or ground

surface. Bars that additionally take over the axle location functions are manufactured principally of

ground or peeled primary material. Stabilizer bars are loaded only in turns. In contrast to the load-

bearing spring elements, there are no requirements in respect of the relaxation performance. Therefore,

also considering the notch sensitivity, the heat treatment strength is selected lower than in case ofload-bearing spring elements [1, 3, 4].


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Fig. 4. Optimization of the weight of stabilizer bars by shortening the arm length with unchanged stabilizationeffect

Rys. 4. Redukcja ciaru stabilizatorw poprzez skrcenie ramion przy niezmienionej sztywnoci

The curb weight of a car has been increasing steadily in the course of years due to increased

requirements with regard to safety and convenience equipment. In order to counteract the tendency,components with substantial weight saving potential have been identified. The consideration of the

load of stabilizer bars has shown that the max. load is on the outer edges of the diameter. The load

decreases inwards to the neutral stage to a mean stress of vm = 0. Theoretically, the solid stabilizer bar

could be hollowed out without affecting the function. Therefore, the tubular stabilizer bars come into

question with increasing frequency. In case of a tubular stabilizer bar, the weight may be reduced in

comparison with the solid stabilizer bar of equal shape, with equal stabilization effect and adequate

maximum stress [10].

The concern of the stabilizer bar calculation is to consider the numerous influences and various

requirements based on the strain and stress relations in such a way that the designed stabilizer bar

satisfies the requirements ofthe strength testwithin the scope of which the compliance with the permitted stress, safety, load

capacity or endurance limits are tested

and the requirements of

the function testwithin the scope of which the compliance with the requested stabilizer bar rate,

the forces and stabilizer bar travels within the specified tolerances, the vibration performance and

other requirements are tested [6].

2.1. Strength test

A force applied on the bar ends of a U-shaped bent solid stabilizer bar causes bending stress as well

as torsional stress at the bar. While torsional stresses prevail at the back of the bar, the bending stressesare particularly great in the area of the arms [1, 3, 4, 6].


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The permitted equivalent stress V may be calculated according to the equation

223 V (1)

where: -bending stress, torsional stress.

From the permitted torsional and bending stress values. In most cases, during stress analysis it willbe found that the maximum equivalent stress and consequently the vulnerable cross-section is at the

transition radius from the back to the arm. The position (stress maximum) is determined by the shape

of the arm and the relationship bending radius/arm length [1, 3, 4].

The torsional stresses may be calculated from

p

t

W

M

,

(2)

were:Mt torque moment, Wp modulus of twist.

For bar backs with round profile

3

16

d

Ft

, (3)

where: t lever arm (fig. 5),F- force, d diameter of stabilizer bar.

And the bending stresses from

W

Mb, (4)

where:Mbbending moment, W modulus of section.

For bar backs with round profile

3

32

d

Fb

, (5)

where: b lever arm (fig. 5).

The equivalent stressvmay be calculated according to the equation

22

334

16tb

d

FV

. (6)

The value of strains at the transition radius depends on the distances h1+r and h2 fig. 6 [3] shows

different arm shapes of a stabilizer bar with circular profile.

Depending on the angle wo defined in (fig. 7), the torsional and bending stresses as well as the

equivalent stress resulting from the summing-up may be calculated:

Fig. 5. Exemplary embodiment and transmission of forcesRys. 5. Przykadowy model zastpczy do obliczewytrzymaociowych stabilizatora


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1

2

2

1

21 )1/3arccos(

h

harctg

h

hhrw

o

(7)

2

2

1

21max 31 r

h

hh

W

FV

(8)

The equations describe the place and size of the maximum equivalent stress in the transition area

between the back and the arms [3]is the angle at which the transfer of equivalent stress is zero.

0dw

d V (9)

The equivalent stress reaches its maximum at these points.

Fig. 6. Load , bandvat the transition radius from the shaft to the arm of a stabilizer barRys. 6. Naprenia , bund vw przejciu promienia z czci prostej do ramienia prta stabilizatora

Fig. 7. Change in shape of the arm in the transition areaRys. 7. Zmiany geometrii ramion stabilizatora w strefie promienia

Due to different requirements on stabilizer bars and numerous influences on the strength of

materials, the characteristic value of the planned material is not always used in full value when

dimensioning.

[degree]


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Permitted stresses which result as a quotient from the strength value regarded as ultimate stress

),,,,,( 01.02.0 tFbEppem RRRR and the required safety erfSS are taken into account[6, 7, 8].

Sertrzul / (10)

Sertrzul / (11)

In some cases, characteristic values as shear modulus G and shear-spring limit (torsional elasticity

limit) tE are required for the design of torsionally strained stabilizer bars, but they are usually

missing. Using approximation notations,

12

EG (12)

where: - Poisson ratio,E modulus of elasticity.

bEbE

tE

578,073,1 (13)

a calculation is possible ( 103

set). When the abovementioned material data is missing, the tensilestrength mR is used as a basis for the calculation of permitted stress zul [6, 7, 8].

2.2. Function test

2.2.1. Rough determination of the total spring travel 2s

The rough calculation assumes that a part of the stabilizer bar is stressed only by twisting and the

other only by bending. Participation of the back in the total spring travel:

F

GI

lrhs

p

TT

2

11

22

(14)

where:Ip polar moment of inertia.

Participation of the arm in the total spring travel:

FEI

ls sB

3

22

3

2 (15)

where:I moment of inertia about axis.

The total spring travel results from:

2122 BT sss (16)

FEI

l

GI

lrhs s

p

T

3

)(22

32

1 (17)

The force F is calculable from the equation (17). Generally, the rough calculation yields greater forcesthan the measurements. This can be also traced back to the fact that the straining of rubber bearing is

left out of consideration. Therefore, it is recommended to reduce the calculated force by about 10%. In

case of simple geometries of stabilizer bar arms, the errors are of the order of 5%, however, in case of

arms which, due to their shaping, allows assuming high torsion rates, the error may increase

considerably [3, 4].

2.2.2. Exact determination of the total spring travels 2s

In case of an exact calculation, strains occurring in each profile are taken into consideration. Here, too,

simplifying assumptions are made:

The flexibility of the arms is small in relation to their length, In unloaded condition, the stabilizer bar lies in a single plane, The bearings are rigid,


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The stabilizer bar is symmetrical, As a result, only one side of the stabilizer bar is calculated.

Participation of the back in the total spring travel resulting from torsion:

FGI

lrhsp

TT

2

11

(18)

Resulting from bending:

2

2

202

2

21

21

3 hl

hlhll

EI

hlFs

c

cac

B (19)

Participation of the arm in the total spring travel resulting from torsion:

sl

p

T

p

dltGI

Fsdl

GI

Ftds

0

2

1

2

(20)

Participation of the arm in the total spring travel resulting from bending:

sl

B dlbGI

Fsdl

GI

Fbds

0

2

1

2

(21)

The total spring travel 2s for the entire bar gives then (16)(17)(18)(19):

221122 TBTB sssss (22)

3. CONCLUSIONS

The engineering data for stabilizer bars are specified by car manufacturers. These physical

characteristics must not be altered by the stabilizer bar manufacturers. The described calculation

methods serve thus the purpose of determining the following:

1. Whether the most important physical characteristics such as stabilizer bar rate, geometricaldata (such as bending radii and planes) have been chosen correctly.

2. Whether the stress concentration, in particular in radii areas, remains comparable to the otherstabilizer bar constructions within permitted limits.

3. Whether the chosen, possible method of production guarantees that the stresses in criticalareas remain under the permitted limit.

4. Whether the geometrical requirements of the car manufacturer for bars are feasible in theseries production.

References

1. Von Estorff H.-E.: Technische Daten Fahrzeugfedern Teil:3 Stabilisatoren. StahlwerkeBrninghaus GmbH, Werk Werdohl, Hang Druck KG, Kln 1969.2. Technische Daten Fahrzeugfedern.Stahlwerke Brninghaus GmbH, Werk Werdohl, E.Anding

KG, Herborn 1965.

3. Ulbricht J., Vondracek H., Kindermann S.: Warm geformte Federn Leitfaden frKonstruktionund Fertigung.Hoesch Werke, Hohenlimburg Schwerte AG, W.Stumpf KG, Bochum 1973.

4. Fischer F., H.Vondracek H.: Warm geformte Federn - Konstruktion und Fertigung. HoeschWerke, Hoesch Hohenlimburg AG, W.Stumpf KG, Bochum 1987.

5. Mitschke M.: Teoria samochodu Dynamika samochodu tom 2/ Drgania.Wydanie 2Wydawnictwa Komunikacji i cznoci, Warszawa 1989.

6. Meissner M.,.Schorcht H.-J.: Metallfedern Grundlagen, Werkstoffe, Berechnung, Gestaltungund Rechnereinsatz. 2. Auflage, Springer Verlag, Ilmenau 2007.

7. Muhs D., Wittel H., Jannasch D., Voiek J.:Roloff / Matek Maschinenelemente Normung,Berechnung, Gestaltung.18. Auflage, Viewegs Fachbcher der Technik, Wiesbaden 2007.


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8. Jakubowicz A., OrloZ.: Wytrzymaomateriaw. Wydanie 6, Wydawnictwa Naukowo-Techniczne, Warszawa 1984.

9. Reimpell J., Betzler J.W.:Fahrwerktechnik Grundlagen.5. Auflage, Vogel Verlag, Wrzburg2005.

10. Dziemballa H., Manke L.: Gewichtsreduzierung durch hochbeanspruchte Rohrstabilisatoren.ThyssenKrupp Technoforum 2004, Essen 2004.

11. Topac M., Kuralay N.S.: Computer aided design of an anti-roll bar for a passenger bus.http://www.turkcadcam.net/rapor/otobus-stab-cae/index.html,23.10.2010

12. Tschtsch H., Dietrich J.:Praxis der Umformtechnik. 9. Auflage, Vieweg + Teubner, Wiesbaden2008.

13. Klocke F., W.Knig W.:Fertigungsverfahren 4 Umformen. 5. Auflage, Springer Verlag. Berlin Heidelberg 2006.

14. Krist T.: Handbuch fr Techniker und Ingenieure. 12. Auflage, Hoppenstedt Technik TabellenVerlag, Darmstadt 1991.

15. Klein B.:FEM Grundlagen und Anwendungen der Finite-Element-Methode im Maschinen- undFahrzeugbau. 7. Auflage, Vieweg Studium Technik, Wiesbaden 2007.

16. Meissner M., Fischer F., Wanke K., Plitzko M.: Die Geschichte der Metallfedern undFedertechnikin Deutschland.1. Auflage, Universittsverlag Ilmenau. Ilmenau 2009.

17. Heiing B., Ersoy M.:Fahrwerkhandbuch Grundlagen, Fahrdynamik, Komponenten, Systeme,Mechatronik, Perspektiven.2. Auflage, Vieweg + Teubner, Wiesbaden 2008.

18. Prochowski L.:Mechanika ruchu.Wydanie 2 Wydawnictwa Komunikacji i cznoci, Warszawa2008.

Received 11.10.2009; accepted in revised form 9.12.2010


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138 A.M. Wittek, H.Ch. Richter, B. azarz

2. CALCULATION OF THE STABILIZER BAR RATE

Fig. 1. Arrangement and principle of operation of stabilizer bars in a motor vehicle

Rys. 1.Rozwizania i funkcje stabilizatorw w pojazdach samochodowych

In case of the calculation of cornering ability, the transmission ratios and from wheel to spring or

stabilizer bar are specified [1]. They are understood as quotients from the spring travel of the wheeland from the spring or stabilizer bar end [1, 10]:

and (1)

Whereas the forces are transmitted in the reversed ratio as compared to the travels from wheel to

spring or to stabilizer bar, and are adopted square in the transmission ratio of the spring orstabilizer bar rate which are indeed quotients from force and spring travel:

and (2)

The stresses and in the stabilizer bar can be calculated with the given dimensions as a function of

forces acting on the arm ends:

[N] (3)

Characterizing feature of the typical stabilizer bar (fig. 2) is the double mounting of its back on thevehicle frame or body, or on the axle or the wheel suspension arms, respectively, and fastening of itsarm ends on the axle or the wheel suspension arms, or on the vehicle frame or body, respectively.These stabilizer bars can be designed for all wheel suspensions.


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Stabilizer bars: Part 2. Calculations example 139

Fig. 2. Equivalent system for stabilizer bar calculation

Rys. 2. Model zastpczy obliczeniowy stabilizatora

(4)

(5)

With the given longitudinal dimensions, the bar diameter may be calculated [1, 7, 8, 10]:

(6)

where for Ushaped, fulllength round stabilizer bar (constant diameter)

Calculation of a stabilizer bar with circular crosssection and pure torsional strain [510]:

Fig. 3. Equivalent system for stabilizer bar calculationRys. 3. Model obliczeniowy stabilizatora


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Table 1

stabilizer geometry (points of intersection)

Bar geometry:bar diameter d [mm]: 28.000lenght [mm]: 1711.490

Fig. 4. Stabilizer bar / production drawing / bar geometryRys. 4. Rysunek wykonawczy stabilizatora prtowego, wsprzdne

point [-] X [mm] Y [mm] Z [mm] radius [mm]

1 335,000 -541,000 0,000

2 225,000 -541,000 -51,300 51,000

3 124,800 -400,200 -80,700 51,000

4 0,000 -395,000 0,000 51,000

5 0,000 -228,200 0,000 51,000

6 105,600 -223,400 -85,900 51,000

7 105,600 0,000 -85,900 51,000

8 0,000 265,000 0,000 51,000

9 0,000 410,000 0,000 51,000

10 105,000 410,000 0,000 51,000

11 210,000 541,000 0,000 51,000

12 335,000 541,000 0,000


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4.2. Warehousing, forces and tensions:

Table 2

stabilizer with back bearings:

bearing X [mm] Y [mm] Z [mm] Fx[N] Fy[N] Fz[N]point No.: [-]

1 335,000 -541,000 0,000 0 0 2127 1

2 0,000 -326,147 0,000 0 0 -3528,5 2415

3 0,000 326,093 0,000 0 0 3528,5 6291

4 335,000 541,000 0,000 0 0 -2127 8557

deflection (wanted) 2s [mm]: 77.000tangent force [N]: not defined

Table 3

bearing spacing

bearing X [mm] Y [mm] Z [mm] distance

3-2 0,000 652,240 0,000 632,24

4-1 0,000 1082,000 0,000 1082

2-1 -335,000 214,853 0,000

3-4 -335,000 -214,907 0,000

lenght of leg [mm] : 335.0 3leg distance [mm] : 1082.0 3

bearings distance [mm] : 326.0

Fig. 5. Stabilizer bar spring travel / warehousing

Rys. 5. Droga sprysta stabilizatora, oyskowanie - mocowanie


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maximum equivalent stress at 0 [MPa]: 390 at length 631.9mm

maximum corrected equivalent stress [MPa]: 465 at length 713.1mm Pos. 0

4.3.Results of calculationMaximum bar diameter [mm]: 28.00lenght theor. (for pipe stabilizers) [mm]: 1711.5lenght theor. (for rod stabilizers) [mm]: 1728.2lenght before / after [mm]: 0.00

mass theor. / actual [kg]: 8.27calculated deflection [mm]: 71.30rate [N/mm]: 29.83roll angle [] : 3.77leg angle (bearing 1-4) [] : 12.15

stress / roll angle [MPa/] : 103.42

4.4. End configurationleft right

inner eye diameter [mm]: 12.3 3 12.3 3

outer eye diameter [mm]: 40.0 1 40.0 1

thickness at eye [mm]: 9.0 0.5 9.0 0.5

Fig. 6. Stabilizer bar - end configuration

Rys. 6.Kocwki stabilizatora

4.5. Aterial and production requirements

Table 4


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Fig. 7. Stabilizer bar - stress distribution

Rys. 7. Wykresy napre w stabilizatorze

material: SAE 5160 or DIN 55Cr3

E-modulus, G-modulus [MPa]: 206000, 78500

spec. gravity [MPa]: 7.85 kg/m

surface condition: black bar bar diameter [mm]: 28.000.28

bar lenght (pipe) [mm]: 1711.00 bar lenght (rod) [mm]: 1728.00

temper strength: HB- diameter [mm] 0.00 0.00 hardness (Rockwell) [HR] 45.0 49.0

tensile strength: [MPa] 1444 1625

5. CONCLUSIONS

The described calculation methods should be instrumental in designing the stabilizer bars. If the

calculated stresses in the bearing / bend are too high ( ), thereare two ways to solve it when

constructing the stabilizer bar [11]:

1. Use of a steel of higher strength (possibilities limited).2. Stabilizer bar with variable diameter:


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If the maximum permissible stress is exceeded even using high-strength steel, a transfer ofthe deformation work to less stressed areas must follow. Consequence stabilizer bar with

non-constant diameter / wall thickness (rotary swaging).

Large diameters / wall thicknesses in critical areas (e.g. bends, bearing surfaces).

Thinner diameters / wall thicknesses at the back / arms.The required rate may be achieved only by reducing the diameter/wall thickness in the less

stressed areas may.

Refeferences

1. von Estorff H.-E.:Technische Daten Fahrzeugfedern Teil:3 Stabilisatoren. Stahlwerke BrninghausGmbH, Werk Werdohl, Hang Druck KG, Kln, 1969.

2. Technische Daten Fahrzeugfedern.Stahlwerke Brninghaus GmbH, Werk Werdohl, E.Anding KG,Herborn, 1965.

3. Ulbricht J., Vondracek H., Kindermann S.; Warm geformte Federn Leitfaden frKonstruktionund Fertigung.Hoesch Werke, Hohenlimburg Schwerte AG, W.Stumpf KG, Bochum, 1973.

4. Fischer F., H.Vondracek H.: Warm geformte Federn Konstruktion und Fertigung. HoeschWerke, Hoesch Hohenlimburg AG, W.Stumpf KG, Bochum, 1987.

5. Mitschke M.: Teoria samochodu Dynamika samochodu tom 2/ Drgania. Wydanie 2Wydawnictwa Komunikacji i cznoci, Warszawa, 1989.

6. Meissner M.,.Schorcht H.-J.:Metallfedern Grundlagen, Werkstoffe, Berechnung, Gestaltung undRechnereinsatz. 2. Auflage, Springer Verlag, Ilmenau, 2007.

7. Muhs D., Wittel H., Jannasch D., Voiek J.: Roloff / Matek Maschinenelemente Normung,Berechnung, Gestaltung.18. Auflage, Viewegs Fachbcher der Technik, Wiesbaden, 2007.

8. Jakubowicz A. Orlo Z.: Wytrzymao materiaw. Wydanie 6, Wydawnictwa Naukowo-Techniczne, Warszawa, 1984.

9. Reimpell J., Betzler J.W.: Fahrwerktechnik Grundlagen. 5. Auflage, Vogel Verlag, Wrzburg,2005.

10.Topac M., Kuralay N.S.: Computer aided design of an antiroll bar for a passenger bus.http://www.turkcadcam.net/rapor/otobus-stab-cae/index.html,23.10.2010.

11.Brendecke T., Gtz O., Schneider F., Brust B.: Prsentation Wissenmanagment StabilisatorenThyssenKrupp Bilstein Suspension GmbH, Hagen, Dezember, 2006.

Received 11.10.2009; accepted in revised form 20.03.2011
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