Frictional Coefficient Distribution Pattern on Brake Disk-Pad Contact Interface to Reduce Susceptibility of Brake Noise Instabilities Causing Brake Squeal

EB2013-NVH-018

FRICTIONAL COEFFICIENT DISTRIBUTION PATTERN ON BRAKE

DISK-PAD CONTACT INTERFACE TO REDUCE SUSCEPTIBILITY

OF BRAKE NOISE INSTABILITIES CAUSING BRAKE SQUEAL

1Esgandari, Mohammad*,

1Olatunbosun, Oluremi,

2Taulbut, Richard

1University of Birmingham, United Kingdom,

2Jaguar Land Rover Ltd, United Kingdom

KEYWORDS - Brake noise, squeal, friction material, Finite Element Analysis, Complex Eigenvalue

Analysis

ABSTRACT - After decades of investigating brake noise and despite the application of

advanced tools and methods of investigation, brake squeal remains a general problem of the

automotive industry. Finite Element Analysis (FEA) has been employed as the main tool in

numerous studies recently, mainly using the Complex Eigenvalue Analysis (CEA) to predict

the occurrence of brake instability and, hence, brake squeal. However it has been shown that

not all instabilities predicted by CEA do occur in reality. The effective (negative) damping

ratio (expressed in percentage terms) is used as a measure of the strength of instabilities.

The level of effective damping ratio of the predicted instabilities below which the instability

is not prone to cause noise is set at different levels by different researchers with 1% being an

average value in the industry. However, in this study, the acceptable effective damping ratio

percentage is set to be 0.5% and any instability predicted with an effective damping ratio of

more than that is assumed to be prone to causing brake squeal when tested on the car.

This study is based on the hypothesis that variation of frictional coefficient over the radius of

the brake pad is effective in reducing the susceptibility of the brake instability to cause brake

squeal. Various patterns of distribution of Coefficient Of Friction (COF) over the disc pad

contact interface have been investigated, and results are illustrated in terms of four different

scenarios. The successful scenario recommends that increasing the COF radially over the disc

radius will lead to instabilities with an effective damping ratio in the acceptable range.

Exaggerated variation in the COF in the disc-pad contact interface is set to cover the entire

range of COF used in different analyses performed to examine noise level of a brake system,

varying from µ=0.3 to µ=0.7.

The proposed friction distribution pattern reduces the strength of all predicted instabilities

over the frequency range to less than the target value of 0.5%. This suggests that instabilities

predicted for the brake system using the proposed pad material design will not cause brake

noise.

INTRODUCTION

Brake noise has been a topic of research since the early years of disc brake development,

likewise the study of friction material properties. However work linking friction material

properties to brake noise has not yet yielded a practical brake design solution.

Frictional force caused by the brake pads is one of the most significant factors governing the

braking power of the brake system, and hence the friction material used for this purpose is

also of high significance. However, the frictional force caused by sliding the friction surface

of the brake pads on the disc causes energy dissipation in different forms. One undesired form

of energy dissipation is vibration, which leads to radiation of noise that is amplified by the

large flat surface of brake disc [1, 2].

Since a major source of brake noise is coupling of modes [2] which commonly occurs

between the disc and pad, and since the nature of this contact is relatively unstable due to

stick-slip phenomena [3], any control measure in this contact could be a potential help on

limiting the brake noise sources.

There are two conflicting factors to be considered in selecting friction materials. Firstly high

friction to give adequate brake performance [4, 5], and secondly low friction which promotes

low brake noise [6]. Hence, any variation in the COF should be carried out with further

attention, since decreasing it can affect the braking performance and increasing it can

introduce even more instabilities into the system, which means more brake noise [7].

Disc brake systems are conventionally designed using pads with a single friction material

throughout the frictional surface. The specific friction material is chosen based on the

specifications of the brake system, and the braking power required for the vehicle it is being

designed for. However, the uniform friction material will cause different frictional force and

slip rate in different parts of the contact interface. This arises from the tangential speed at that

specific radius and also the slight variation of the pad pressure producing the normal force in

the leading and trailing edges of the pad.

If the variation in frictional force over the contact surface is responsible for exciting the

vibration of the disc due to the uneven distribution of the frictional forces over the disc

surface which, at certain frequencies, results in instability of the brake system, then variation

of the friction material based on a pattern may counteract this effect by equalising the

distribution of frictional forces. This is the hypothesis tested in this study.

This is where the challenge of varying the friction material based on a “pattern” becomes

interesting, since simply changing the material over the entire pad surface merely changes the

force level at which stick-slip occurs which may not have the effect of reducing the vibration

exciting the instability.

Friction material development is already at a reasonably well advanced level [8, 9], from the

points of view of both knowledge of the friction material itself and the manufacturing

processes, whereby manufacturers can limit the frictional behaviour of the brake pad to a

certain value or range, within a reasonable margin of accuracy. Hence, manufacturing a brake

pad with a pattern of COF variation is a realistic proposition.

There are different analytical approaches to investigating brake noise. Complex Eigenvalue

Analysis (CEA) is usually preferred to the dynamic transient analysis, mainly because it

provides results more quickly [10]. In order to analyse the stability of the disc brake system,

CEA results are represented either in terms of the eigenvalue real part or the negative

damping ratio. There has been a debate as to whether the real part or the damping ratio is a

better measure of squeal propensity or the strength of instability. For example Ouyang et al.

[10, 11] have used real part as an indication of instabilities, while damping ratio is used by

Nouby et al. in [12] and correlated with the real part. AbuBakar has briefly explained how the

damping ratio can be recognized as a measure of the strength of instability, relating it to the

terms standing for the damping in the Coulomb friction [13]. Also, Wallner shows there is a

proportionality between them in [14]. It is therefore reasonable to assume that the propensity

for brake instability can be expressed in terms of either the complex eigenvalue real part or

the damping ratio.

Based on expectations and experience of designers or analysts, a certain level of damping

ratio is assumed to be an indication of the value below which brake instability is not likely to

occur. Therefore, in this study the damping ratio reported by the software is taken as an

indication of the level of instability, but assumes a very strict margin as the accepted level of

instability. In the industry, the acceptable level of damping ratio (expressed in percentage) is

usually assumed to be less than 1% or even 1.5%, however, in this study 0.5% is considered

as the maximum allowed value of the damping ratio below which potential instabilities are

suppressed.

Typical values of COF are in the range of 0.3 to 0.7 [15], and this is the range used by many

brake pad designers and analysts. This range of values has also been used in this study.

This study investigates the effect of varying the COF over the radius of the brake pad on the

propensity for brake system instability as indicated by the negative damping ratio determined

from CEA. A value of 0.5% is taken as the limit for the damping ratio below which brake

instability is assumed to be suppressed.

METHODOLOGY

The analysis approach employed for this study is the Finite Element Analysis (FEA). The

brake unit is initially modelled using Computer Aided Design (CAD) software, and then

converted into a FEA model by assigning the appropriate material properties, boundary

conditions and required analysis steps. Figure 1 represents an isometric view of the brake unit

model. ABAQUS FEA package has been used for this study.

Figure 1, Brake corner unit, isometric view

Main components included in the brake corner unit are the disc, caliper housing including

pads and shims and pressurising pistons, the hub and knuckle. Also two mass blocks are

added to the caliper as a brake noise fix.

The squeal analysis is performed using CEA, to predict instabilities of the brake system which

are susceptible to develop brake noise. Then the strengths of predicted instabilities are

evaluated and ranked using the effective damping ratio reported as a result of the analysis,

converted into percentages.

In order to employ damping ratio to study the strength of instabilities a target value of 0.5% is

defined, such that instabilities with damping ratio of less than 0.5% are expected not to result

in brake squeal problems when the brake system is tested in the car or on the dynamometer.

This study looks at the problem only using CAE techniques, which are virtual tools employed

to predict instabilities of the system. An experimental investigation is also planned for the

continuation of the study.

Performance of the different configurations of the brake pad applied to each case of the study

and possible improvements are judged by comparing their results with the basic run, i.e.

uniform brake pad COF.

In the basic run the COF is assumed to be constant over the pad friction surface. The basic run

includes a set of analyses of the brake unit for uniform coefficients of friction of values of 0.3,

0.4, 0.5, 0.6 and 0.7. Analysis is carried out for each COF under brake pad pressures of 2, 5

and 10 bar, in both forward and reverse directions. Figure 2 and Figure 3 show instabilities

predicted under the basic run conditions as previously mentioned, highlighting instabilities in

the unacceptable damping ratio region in frequency neighbourhoods of 2.5, 3.0, 4.1 and 5.1

kHz.

Figure 2, CEA instability prediction for the basic run, sorted based on COF

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Basic Run: COF

COF: 0.3 COF: 0.4 COF: 0.5 COF: 0.6 COF: 0.7

Figure 3, CEA instability prediction for the basic run, sorted based on pressure

A significant advantage of this study over most of the previous publications is that this is one

of the most comprehensive squeal analyses ever presented which includes 30 CEA squeal

runs. This covers all aforementioned COF and pressures in both reverse and forward

directions. Research institutions rarely have access to the required computing power to

perform such an analysis, which can be considered as an advantage of this study.

ANALYSIS

Assuming the brake disc to rotate at a constant rotational velocity, the local tangential

velocity at each point on the disc-pad contact interface varies based on the radius of the

chosen point from the centre of rotation. Since slip is known to cause instability [16], and it is

varying radially [17], one can understand that the uniform friction material undergoing this

different local slip over its surface can be a reason for the mentioned instabilities.

In order to address this problem, one possible solution is making the pad capable of handling

the aforementioned slip by providing different values of friction at radial partitions of the

contact interface.

The concept of the partitioned pad can be implemented in the FEA model of the friction

material. In this study, the pad surface is divided into three and five partitions, and each

partition is assigned a different coefficient of friction. Figure 4 illustrates the partitioned pad,

demonstrating three and five partitions.

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Basic Run: Pressure

2 bar 5 bar 10 bar

Figure 4, Pad friction material partitioning, three and five partitions

Variation of COF over the contact area should be defined in a manner such that it correlates

with the radial variation of local tangential velocity. Hence, two different patterns have been

studied in two different numbers of partitions, resulting in four scenarios. Figure 5

demonstrates all four scenarios along with the COF assigned to each partition.

Figure 5, Scenario 1-4 schematic visualisation

As seen in Figure 5, different patterns include increase of the COF radially (scenarios 1 and 3)

and assigning a higher COF in the intermediate partition (scenarios 2 and 4).

The FEA squeal analysis is performed for the four cases above, each undergoing pressures of

2, 5 and 10 bar both in forward and reverse directions. The reason for this combination is to

try most possible situations of distribution of friction and pressure over the disc-pad interface.

The analysis results are then expressed in terms of damping ratio percentage and compared

with the basic run results which come from the conventional analysis as explained earlier.

RESULTS AND DISCUSSION

Results from the basic run are presented in Figure 2. Results are initially categorised based on

the COF, and the values of pressure applied are as mentioned before. Figure 2 demonstrates

that higher COF values are more likely to cause instability, when the strength of instability

predicted for a specific frequency range is compared for different values of COF. However,

this does not necessarily mean a brake friction material with lower COF will be a good brake

pad, since changing the average COF of a friction material directly affects the braking power.

Hence lowering the COF is not necessarily the solution for a noisy brake in general.

Figure 3 also compares the same instabilities of the basic run, sorted based on the applied

pressure. Comparison of instabilities occurring at a certain frequency caused by different

levels of pressure reveals that although the applied pressure and strength of instability are not

directly related, strong instabilities mainly occurred at the low applied pressure of 2 bar.

Results from different scenarios are presented in this section, each compared with the basic

run results. Figure 6 and Figure 7 represent results for scenarios 1 and 2 (three partitions)

respectively while Figure 8 and Figure 9 represent the results of scenarios 3 and 4 (five

partitions) respectively. In all cases instabilities are predicted at five different frequency

neighbourhoods.

Figure 6, FEA results of the predicted instabilities - scenario 1 compared with the basic run

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Basic Run vs. Scenario 1

Scenario 1 Basic run



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Comparing results from scenarios with three partitions with those of five partitions reveals

that the pads with five partitions are showing more stable behaviour, as the damping ratio

(strength of instabilities) is generally lower in scenarios 3 and 4. Both scenarios 3 and 4 show

instabilities with damping ratios not higher than the target set for the analysis. Also, scenario

4 has fewer instabilities in the higher frequencies of above 3 kHz, as seen in Figure 9.

However, although scenario 3 shows instabilities at more frequencies, the majority of them

have a low damping ratio, with the highest being 0.266% at a frequency of 4129.79 Hz.

Hence scenario 3 is selected as the most successful scenario, showing instabilities with

damping ratio mostly lower than half the target set, which was lower than the commonly

assumed level of 1%. Hence the partitioned pad with five partitions assigned a COF

increasing radially shows significantly lower strength of instability.

CONCLUSION

This study is based on the hypothesis that variation of the pattern of distribution of frictional

coefficient over the radius of the brake pad is effective in reducing the strength of the brake

instability.

The study suggests that variation of frictional coefficient over the radius of the brake pad is

effective in reducing the strength of brake instability.

More specifically, increasing the COF radially over the disc radius in the specified steps

produces instabilities with an effective damping ratio well within the acceptable range. This

low predicted damping ratio is an indication that there is less likelihood that noise will be

generated from the brake system, when tested as a prototype.

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This study suggests that the uniform brake pad friction material is not the best approach from

a brake noise point of view. The proposed friction material distribution pattern can contribute

to reducing the fugitive nature of the brake noise problem, by reducing the strength of all

predicted instabilities to a value much lower than the target value of 0.5%, which is an

indication of less noise in the brake.

Although the proposed friction material patterns are not easy to manufacture compared to

conventional brake pads, there are manufacturing processes which make it possible, although

these are outside the context of this article. The intention is to carry out a comprehensive test

programme to confirm the hypothesis in a future study.

REFERENCES

1. Akay, A., Acoustics of friction. Acoustical Society of America, 2002. 111(4): p. 1525-

1548.

2. Papinniemi, A., et al., Brake squeal: a literature review. Applied acoustics, 2002.

63(4): p. 391-400.

3. Mottershead, J.E., Vibration- and friction-induced instability in disks. Shock and

Vibration Digest, 1998. 1(30): p. 17.

4. Liles, G.D., Analysis of disc brake squeal using finite element methods. Society of

Automotive Engineers, 1989. 891150: p. 1138-1146.

5. Spurr, R., A theory of brake squeal. Institution of Mechanical Engineers Automotive

Division, 1961/62(Proc No. 1): p. 30-40.

6. Day, P.A.J., Friction and Friction Materials, in Braking of Road Vehicles 2009, J.K.

A. J. Day, Editor. 2009, University of Bradford: UK.

7. Liu, P., et al., Analysis of disc brake squeal using the complex eigenvalue method.

Applied Acoustics, 2007. 68(6): p. 603-615.

8. Nishizawa, Y., et al., Influence of Pad Thickness and Surface Roughness on Pad

Stiffness, 2012, SAE International.

9. Hornig, S.A. and U. Von Wagner, Improvement of Brake Squeal Simulation

Reliability by Measurement and Identification of Friction Material Properties, 2012,

SAE International.

10. Ouyang, H., AbuBakar, A., Complex eigenvalue analysis and dynamic transient

analysis in predicting disc brake squeal. International Journal of Vehicle Noise and

Vibration, 2006. 2(2): p. 143-155.

11. Ouyang, H., et al., Numerical analysis of automotive disc brake squeal: a review. Int.

J. Vehicle Noise and Vibration, 2005. 1(3/4): p. 207-231.

12. Nouby, M. and K. Srinivasan, Parametric Studies of Disk Brake Squeal Using Finite

Element Approach. Jurnal Mekanikal, 2009. 29: p. 52-66.

13. Abubakar, A., Ph.D Thesis: Modelling and Simulation of Disc Brake Contact Analysis

and Squeal, in Department of Mechanical Engineering, Faculty of Engineering2005,

Liverpool, United Kingdom: University of Liverpool, Liverpool, United Kingdom.

14. Wallner, D., et al., Numerical and Experimental Parameter Studies on Brake Squeal.

2010.

15. Massi, F., et al., Brake squeal: Linear and nonlinear numerical approaches.

Mechanical Systems and Signal Processing, 2007. 21(6): p. 2374-2393.

16. Behrendt, J., C. Weiss, and N.P. Hoffmann, A numerical study on stick–slip motion of

a brake pad in steady sliding. Journal of Sound and Vibration, 2011. 330(4): p. 636-

651.

17. Wallner, D. and M. Meister, Elaborate Measuring System for Sensitivity Analyses and

In-Depth Investigations of a Squealing Brake System. SAE Int. J. Passeng. Cars -

Mech. Syst., 2012. 5(3): p. 1107-1115.

Frictional Coefficient Distribution Pattern on Brake Disk-Pad Contact Interface to Reduce Susceptibility of Brake Noise Instabilities Causing Brake Squeal

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