detection of friction-induced instabilities at the origin of...
TRANSCRIPT
Detection of friction-induced instabilities at the origin of the squeal
of wet poly-V belts
Simon GATIGNOL1,2 *; Thierry DEMASSOUGNE2; Alain LE BOT1
1 Laboratoire de Tribologie et de Dynamique des Systèmes (LTDS), France
2 Hutchinson SNC, France
ABSTRACT
Wet belt squeal is an example of the multiple parasite noises that appear in automotive system. Linked
warranty costs and brand images leads the car manufacturers to investigate the phenomenon that cause these
disturbing noise. The wet belt squeal has been reproduced on a laboratory test rig and the mode of vibrations
of the belt that generates noise has been identified. Then the friction-induced instabilities that can appear at
the interface between the pulley and the belt have been investigated. A negative slope on the coefficient of
friction versus sliding velocity curve has been observed. However, the correlation between the slope and the
appearance of noise is insufficient to affirm that this phenomenon triggers the instability. On another side, the
participation of stick-slip in the instability of the system has been observed for a particular type of coating of
the belts but not for all the other. Investigation of the participation of other friction-induced instabilities and
an in-depth study of the role of the coatings are required to further increase the understanding of the
instability that cause the wet belt noise.
Keywords: Poly-V belt, Wet noise, Friction-induced instability
1. INTRODUCTION
In order to lower warranty cost and to improve the comfort of the passenger, car manufacturers
have tried during the last decades to reduce the impact of the parasite noises that can appear in cars.
Numerous studies have been carried out in order to understand the different causes of noise in
automobile. An example is the squeal of wiper blade. Le Rouzic et al (1) showed that the negative
slope of the friction-velocity curve causes appearance of the squeal noise, and Dalzin et al (2)
relates it to its tribological origin. Brake noise, window seal and different squeak and rattle are
other known examples. Elmaian (3) proposes a large review of the phenomenon producing noise in
automobile.
Belt noise is another typical issue for cars and belts manufacturers. Early studies concern the
noise of dry belt and several mechanisms at its origin have been highlighted. Connell et. al (4)
distinguish misalignment and tangential slip noise. The former is due to the radial sliding of the
belt on the side of the pulley groove in case of misalignment whereas the latter is caused by
tangential slippage of the belt in case of an excessive amount of torque in the pulley. Connell (4)
showed that misalignment noise is created by a harmonic oscillation excited by the radial sliding
oscillation with the presence of stick-slip and Dalgarno et. al (5) established that the tangential slip
noise is caused by the appearance of stick-slip giving the impetus for the excitation of lateral
vibration of the belt. Moon and Wickert(6) gives a more detailed study of the stick-slip created by
the misalignment. Sheng et al. (7) formulates mathematical for the previous instabilities adding the
notion of negative slope of the coefficient of friction versus sliding velocity curve as a sour ce of
instability causing the tangential slip noise. Sheng et al. (8) then explains with a phenomenon of
mode-coupling the instability of belt with a coefficient of friction that increases with the sliding
velocity. Sheng et al. synthesized all the previous results in another work (9). However, studies
about the noise generated by wet belts are more rare. Sheng et al. (10) identified that the cause of
1 [email protected] 2 [email protected] 3 [email protected]
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the instability leading to wet belt noise is the negative slope of the friction velocity curve
characteristic of a mixed lubrication regime . A model is also proposed in (11). In another way (12),
Sheng et al. determined that the noise of wet belt during the start up process followed an impulsive
pattern (large spectra) and is caused by the relaxation of friction static force. That force reaches a
maximum due to the possible appearance of capillary force. A last work (13) approaches the
mechanism that produces noise during the start-up process for drying belts.
The goal of the present work is to complete the previous studies about the wet belt noise. Apart
from works (12) and (13), all the studies have been carried out on an SAE test rig. If it approaches
the conditions of functioning of the belt on motors it limits the feasible measurements. To improve
this aspect a specific test rig is used in the following and the focus is made on the detection of the
different friction-induced instabilities that could occur at a belt-pulley interface. A particular
attention has been paid to the apparition of a negative slope in the friction-velocity curve with or
without stick-slip motion.
To reach this goal a specific test rig, described in section 2, has been developed. The vibration
and noise reproduced on this test rig are then detailed in section 3, before the results and analysis
about the detection of negative slope and stick-slip in link with the generation of noise are
presented in section 4 and 5.
Table 0 – Notation
Notation
µ Kinematic coefficient of friction
µ0 Kinematic friction of friction at 0 velocity
a Wrap angle
b Wedge angle of the pulley
Tt , Ts Tension in tight, slack span
vr Relative (sliding) velocity
m, c, k Mass, viscous damping, stiffness
N Normal force
2. Presentation of the test rig LUG
2.1 Measurement setup
The test rig called “LUG” is presented in Figure-1 equipped with a modulus for the specific
study of a belt-pulley contact.
The main specificity of this setup is that it involves only one pulley and that the belt is static.
It is also composed of:
A motor and transmission system to control the rotation of the pulley.
2 tension sensors to measure tension in both tight and slack span
A belt tensioner to maintain minimum tension in the slack span
A peristaltic pump to ensure a controlled water alimentation of the contact
A microphone to record the noise
Both vibrometers and accelerometers can be added to measure vibrations of the belt.
The mechanic of the contact is so modified as there is no adhesive arc along the contact arc and
it leads to the apparition of pure sliding compared to the rolling-sliding dynamic in the sliding arc
of systems with several pulleys and a moving belt.
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Figure 1 – LUG test rig equipped with microphone and vibrometers
2.2 Measure of sliding velocity
As the belt is static the sliding velocity is equal to the rotational velocity of the pulley. This velocity
is piloted via the servomotor AKM servostar 600 and is verified by the measure of a position sensor
fixed around the shaft.
2.3 Measure of the friction coefficient
The friction coefficient is measured experimentally from the data of tension in both tight and slack
span, and of the length of contact arc measured after the initial tension is reached and just before the
rotation. Euler’s formula for poly-V belt is used:
µ= sin( ß) /a *ln(tT /
sT ) (1)
This formula supposes that the coefficient of friction is constant all around the contact arc
and that condition of limit sliding are reached which is not the case in reality. However it is still
widely used for example in the recent work of Cepon et al. (14) and Sheng et al.(13)
2.4 Typical experiment
3 types of poly-V belts are tested. They differ by their coating and are named type A B and C.
For the experiments, a four ribs belt is stretch to 180N (45N/tooth). A rotation of 20rpm is imposed
until the friction coefficient stabilized. Then a continual sweep of the velocity is achieved until high
velocity (250rpm). Friction coefficient, sound pressure level, and vibrations are recorded for each
velocity of the sweep.
Initial tension, length of a velocity step and the gap between 2 consecutives steps of velocity, wrap
angle, pulley radius, maximum and minimum velocity … are examples of parameters that can
modified between experiments.
3. Analysis of the vibrations and validation of the reproduction of the
phenomenon on the LUG test rig
The vibration and noise of wet belts are characterized in the following section. It aims both at
ensuring that the phenomenon reproduced on the test rig is the one that appears on motors and at
describing the wet belt noise. It especially focuses on a frequency and time analysis of the noise and
on the identification of the mechanical vibration at its origin.
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3.1 Characterization of the wet belt noise
Figure-2 shows the power spectral density of the noises for the type of belt C respectively on
motors (above) and on the test rig (below). The signals observed are harmonic. Main difference is
the gap between the natural frequencies of each noise. Their numerical values are given for each
type of belts in Table-1.
The time analysis in Figure-3 shows the signal recorded during tests respectively on motors (left)
and on the test rig (right). For each case the noise appears as a continuous one: it is not scattered
inside a burst. Moreover, the presence of bursts exists mainly for the experiment on motors as it is
linked with its irregular rotation.
Figure 2: Superimposed Power Spectral Density of the recorded noise for belts of type C on motors (upper)
and on the test rig LUG (lower)
Table 1 –Natural frequencies (Hz) of the noise recorded on motors and on the test rig LUG for the different
belts
Test Setup Belt A Belt B Belt C
Motor 1800 1600-1900 1950
LUG 900-950 900-1000 1110
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The domain of frequency within which the noise appears correspond amongst other to the squeal
domain with reference to the classification proposed by Akay (15) for brake noises. Elmaian (3) in
a classification of the automobile noise reduced to squeak, squeal and crunch distinguish squeak
and squeal depending on their time response. Squeak noise is characterized by scattered peaks of
acoustic pressure, which can be visualized by a discontinuous time-frequency response whereas for
the squeal the maximum of acoustic pressure is reached progressively and then the level is
stabilized what lead to a continuous time-frequency response. That’s why it has been considered
that the noise of wet belt both on motors and test rig has the characteristics of a squeal noise.
The presence of harmonics is in first instance linked to the non-linearity introduced by the presence
of friction.
Figure 3: Evolution of the Acoustic Pressure (Pa) with respect to the time when the noise appears, for belt of
type C and for tests on motors (left) and on the test rig LUG (right)
3.2 Identification of the vibration at the origin of the noise
The next section follows the works of Connell et al. (4) and Dalgarno et al. (5) who identified
that the noise is generated by a lateral mode of vibration of the belt, that is to say along a transversal
section of belt. The different modes can involve one or several ribs respectively in the case of
misalignment and tangential slip noise. Using Finite Element Analysis, a comparison between the
natural frequencies identified on the model and the natural frequencies of the noise allow to
determine which of the modes cause the squeal noise. In the following the variation of the number
of ribs of the belt gives us an experimental evidence of the mode of vibration that generates noise.
Experiments were carried out on the test rig LUG where the tension by rib was kept constant for
all experiments. That implies that the global tension must be lowered, especially for experiments
with one rib belt, on level that couldn’t be reached on motor. Table-2 presents the natural frequency
of the squeal noise of wet belts of type C with varying number of ribs. It shows that the number of
ribs don’t modify the natural frequency of the noise. As a consequence, the lateral mode of
vibrations that causes the squeal of wet belts implies each rib independently. The small increase in
frequency for an increasing number of ribs can be explained by a lateral stiffening effect due to the
sealing of the ribs.
Experiments with 2*2, 4 and 6 ribs belts were carried out on motors and the same conclusions were
drawn.
Table 2 – Natural Frequency of the squeal noise for different structure of belt
Natural Frequency of the squeal noise for different structures of belt
Belt Structure 1 rib 2 ribs 4 ribs 4*1 ribs 2*2 ribs
Natural
frequency of
the squeal (Hz)
1115 1125 1138 1115 1138
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As a conclusion, the test rig LUG allows the reproduction of a squeal noise characterized by
numerous harmonics and produced by the vibration of a lateral mode of the belt implying each rib
independently.
The difference of frequency between the squeal on motors and on the test rig is in all probability
due to the different sliding conditions. On the test rig, belts slide all along the wrap angle what
modify the boundary conditions on the belt. Moreover, other type of tests have showed that the
characteristics of the noise and the performance of the belt that depend on their coatings on motors
are also find on the test rig.
4. Relation between a negative slope of the friction-velocity curve and a the
belt instability
The negative slope of the coefficient of friction versus sliding velocity is a usual feature to make
a system unstable. It can create a negative damping in the system, which leads to the appearance of
self-excited vibration that triggers the instability of the system. In the motion equation presented in
Equation-2, the derivative of the coefficient of friction participates to the global damping of the
system.
(2)
Sheng has studied this phenomenon for the noise of wet belts (11). The criterion that he
proposed for the appearance of the instability of the belt is immediately deduced from Equation-2
c / N +¶µ(vr )
¶vr
£ 0 (3)
It makes explicit that when the negative slope is steep enough then the global damping of the
system become negative.
In order to investigate this phenomenon on the test rig LUG, experiments as presented in 2.4 are
carried out.
4.1 Experimental results
Figure 4 presents a comparison of the respective evolution, as a function of the increasing
velocity, of the coefficient of friction, the sound pressure level (in dB) and the derivative of
coefficient of friction with respect to the velocity. For these results a belt of type B was used. The
trends observed for a belt of type C are similar. The criterion of Equation 3 was computed but its
values are equivalent to the values of the derivative of the coefficient of friction as the damping
coefficient is low and the normal force high.
First observations are that the slopes are always very low without preventing from the noise
appearance. The transition in the mixed lubrication regime isn’t reached in the same way as in the
case of wiper blade (1, 2). Both level of coefficient of friction and of slope are also lower than in the
results of other study (10).
The influence of belt coating can be observed in Figure 6, which show the results for the same
experiment but obtained for belt A. The slope is steeper than in the other cases. The link between
the level of slope and the noise appearance (at a velocity of 80rpm) isn’t significant. However the
more the slope is steeper the more the level of acoustic pressure increases.
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Figure 4: Comparative evolution of the coefficient of friction, the sound pressure level and the derivative of
the coefficient of friction with respect to the sliding velocity for an increasing sliding velocity
Figure 5: Comparative evolution of the coefficient of friction, the sound pressure level and the derivative of
the coefficient of friction with respect to the sliding velocity for an increasing sliding velocity
4.2 Analysis and discussion
The slope is slight for most of the experiments but both the instability and the resulting noise
appears. Moreover no obvious correlation can be set between the maximum slope, the level of slope
and the appearance of the instability. The high contact pressure in case of the poly-V belt explains
the slight aspect of the slope, compared to results for the wiper blade. In the case when the slope is
steeper the system is pumped with energy so that the magnitude of the vibration and the sound
pressure level increase.
As a conclusion the negative slope of the friction coefficient versus sliding velocity isn’t
considered as the main phenomenon capable of triggering the instability of the system. However, it
participates to the increase in magnitude of the vibrations.
The occurrence of stick-slip correlated with the appearance of the squeal of wet belts has also been
investigated.
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5. Relation between Stick-Slip occurrence and the belt instability
The occurrence of stick-slip is detected thanks to measurement of displacement and/or velocity of
the vibrations of the belt. Different type of vibrometers has been used and different position along
the wrap angle has been tested.
2 different experiments have been realized:
On one side, both the radial (perpendicular to the belt) velocity and displacement and
tangential (parallel to the belt) velocity were measured at an unique position at the end of
the wrap angle both in the radial (perpendicular to the belt) and tangential (parallel to the
belt) direction. Figure 6 exposed the test setup
On another side, tangential vibrations were measured at 3 positions along the wrap angle.
Only the vibrometers at the entry of the pulley realized both displacement and velocity
measurement otherwise only the velocity was measured. The test setup is exposed in Figure
1. Measurements were realized at point both at the back and on the rib of the belt as
presented in Figure 7
Figure 6: Picture of the test setup using 2 vibrometers on the test rig LUG
Figure è: Picture of the Pulley-Belt contact showing the positions of the reflective patch at the back (left) and
on ribs (left)
5.1 Experimental results
Figure 8 exposed the typical phase plots for the radial vibrations (perpendicular to the belt) for
experiment with belts of type B respectively before (left) and after (right) the squeal has appeared.
In absence of squeal, no limit cycle can be seen on the phase plot and trajectories are not well
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defined. Moreover the magnitude of the vibrations is low. On the contrary, when the noise has
appeared, a limit cycle of higher magnitude is observed. Besides, the upper side of the limit cycle is
flat so there exist a displacement at constant velocity during the cycle. That is a classical featured to
reveal the presence of stick-slip. The same trend was observed on the phase plots of the tangential
vibrations.
For these experiments, the corresponding tangential velocity (orange) and rotation velocity (blue
line) before (left) and after (right) the squeal has appeared are represented on Figure 9 as a function
of the time. Without noisy vibration the tangential velocity of the belt remains far lower than the
rotational velocity. Then the tangential velocity increases abruptly when the noise appears until it
matches the rotational velocity. The oscillations of the tangential velocity are still sinusoidal and
they aren’t flattened at their upper extremity at the level of the rotational velocity what could have
been expected in the presence of stick-slip.
Figure 8: Phase plots of the radial vibrations of belts of types B without noise (left) and with noise (right)
Figure 9 : Tangential velocity of the belt (orange ) compared to computed rotational velocity(blue) before
(left) and after (right) the noise has appeared for belt of type B
On another side, the same experiments have been carried out for belts of type A and C. Although
the apparition of noise also leads to the apparition of a limit cycle of higher magnitude, this limit
cycle is elliptic and not flat on its upper side. The results are shown in Figure 10. Figure 11
presented the corresponding evolution of the tangential velocity and rotational velocity as a
function of the time. In this case, the magnitude of the tangential velocity increases when the noise
has appeared but it remains still far lower that the rotational velocity
Figure 10: Phase plots of the radial vibrations of belts of types A before (left) and after (right) noise appears
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Figure 11 : Tangential velocity of the belt (orange ) compared to computed rotational velocity(blue) before
(left) and after (right) the noise has appeared for belt of type A
5.2 Analysis and discussion:
Figure 8 and Figure 9 show characteristics of the presence of stick-slip. The limit cycle on the phase
plots has the typical flat upper side and the tangential velocity almost equals the rotational velocity,
which suggests that the belt stick at the pulley in the presence of noise. The fact that the oscillation
are not flattened and that the perfect equality between the velocities isn’t reached can be explained
by the position of the measurement points that are not directly in the contact but at the back of the
pulley or on the ribs at the extremity outside the wrap angle. The occurrence of stick-slip when the
instability is triggered and the squeal appears is systematic for belts of type B and the stick-slip
participate so necessarily to it. However for the belt of type A and C, the phase plots and the
comparison of the tangential velocity of the belt and the rotational velocity of the pulley let
conclude that stick-slip doesn’t appear. As squeal still appears in this case it follows that another
phenomenon must create the instability.
6. Concluding remarks
The approach develop in the present work consist in the development of a dedicated test setup for
experimental observations of the noise of wet belts. A similar squeal noise has been reproduced on
the test rig and the vibration of a lateral mode of the belt implying the ribs independently are at its
origin.
The participation of 2 friction-induced instabilities have been investigated leading to the following
conclusions:
The correlation between the level of the slope and the magnitude of the oscillations let
suppose that a negative damping in the system leads to the pumping of energy in the system
leading to the increase of the magnitude of the vibration.
However the slope of the friction coefficient versus sliding velocity curve is generally too
slight and the correlation between the level of slope and the generation of the squeal isn’t
pronounced enough to conclude that the negative slope can trigger the instability of the
system on its own.
Occurrence of stick-slip is obvious for the type of belt B and directly linked to the
instability. However squeal noise appears for the other types of belts without stick -slip.
It suggests that the belt coating is a major parameter in the generation of squeal noise. The
possibility that a specific instability appears for each type of belt directly link with its coating is a
solution. Further study of the tribological properties of the coatings and resulting friction at the
interface are required to specify the role it plays.
In the purpose to find a unique phenomenon for all types of coatings other types of instabilities
can be investigated: mode-coupling, sprag-slip, parametrical or/and forced excitation…
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