Evaluation of Disc Brake Materials for Squeal Reduction

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Evaluation of Disc Brake Materials for Squeal ReductionM. Nouby a , J. Abdo b , D. Mathivanan c & K. Srinivasan ba AU/FRG Institute for CAD/CAM, Anna University, Chennai, 600025, Indiab Mechanical and Industrial Engineering Department, Sultan Qaboos University, Muscat Omanc Director of CAE INFOTECH, Chennai, 600020, India

Available online: 18 May 2011

To cite this article: M. Nouby, J. Abdo, D. Mathivanan & K. Srinivasan (2011): Evaluation of Disc Brake Materials for SquealReduction, Tribology Transactions, 54:4, 644-656

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Tribology Transactions, 54: 644-656, 2011Copyright C Society of Tribologists and Lubrication EngineersISSN: 1040-2004 print / 1547-397X onlineDOI: 10.1080/10402004.2011.587634

Evaluation of Disc Brake Materials for Squeal ReductionM. NOUBY,1 J. ABDO,2 D. MATHIVANAN,3 and K. SRINIVASAN2

1AU/FRG Institute for CAD/CAM, Anna UniversityChennai 600025 India

2Mechanical and Industrial Engineering Department, Sultan Qaboos UniversityMuscat Oman

3Director of CAE INFOTECHChennai 600020 India

A nontraditional evaluation tool is introduced to examine

the effects of different materials, in practical applications, that

are used in fabricating disc brake components for commonly

used or special requirements such as heavy-duty performance

and racing cars. As an extension to earlier finite element (FE)

disc brake models, a detailed FEmodel of the whole disc brake

corner that incorporates the wheel hub and steering knuckle

is developed and validated using experimental modal analy-

sis. Stability analysis of the disc brake corner using the finite

element software ABAQUS is carried out to predict squeal

occurrence also taking into account the negative and positive

damping effects and friction material real surface to increase

the accuracy of prediction. A Taguchi methodbased design of

experiment is used to better assess the contributions of different

materials and its interaction effects for effective reduction of

brake squeal. The results showed that the pad friction material

contributes 56% to the total system instability (squeal genera-

tion). The rotor material contributes 22% of the system insta-

bility. Caliper and bracket materials participate 11 and 11%,

respectively.

KEY WORDSDisc Brake Squeal; Finite Element Analysis; Modal Testing;

Material Modifications; Taguchi Approach

INTRODUCTIONSqueal noise that occurs in disc brakes for automobiles has

been one of the major concerns in the automotive industry dueto the persistent complaint that reduces customers satisfactionwith their vehicles. It is commonly accepted by researchers work-ing in the field of brake noise and vibration that squeal noise ina disc brake is initiated by instability due to friction forces, lead-ing to self-excited vibrations (Van Wagner, et al. (1)). Many re-searchers have worked on eliminating brake squeal in order toimprove vehicle passengers comfort and reduce the overall envi-ronmental noise level (Dai and Teik (2); Nouby, et al. (3); Chen,

Manuscript received December 27, 2010Manuscript accepted May 9, 2011

Review led by Farshid Sadeghi

et al. (4); Gesch, et al. (5); Kung, et al. (6)). Despite these efforts,no general solutions exist. Therefore, it is one of the most impor-tant issues that require a detailed and in-depth study for predic-tion as well as to eliminate brake squeal. The detection of discbrake squeal instabilities and the prediction of amplitudes dur-ing squeal events are complex tasks that have been studied formany years and continue to be a major concern in the automo-tive industry (Kinkaid, et al. (7); Ouyang, et al. (8)). Analysis ofbrake squeal is a difficult task due to numerous factors involvedin the study and the effects of the interaction between the fac-tors. Those factors are rotor disc, friction pads, back plate, ap-plied force, angular velocity, and the temperature. Many studieshave used different techniques to measure and study squeal. Theyfound that the noise is caused by the back plate, pad material,pad geometry, and temperature rises due to friction force (Kung,et al. (9)). In addition, the engagement pressure and speed of ro-tation of the rotor have a significant influence on brake squeal(Farhang and Lim (10)) but are not covered in the present workbecause it mainly focuses on material related influences on brakesqueal.

Finite element models are classically used to perform twokinds of analyses for disc brake squeal: eigenvalue analysis todetect squeal frequencies and time analysis to determine self-excited vibrations during the squeal event. One of the greatestadvantages of a brake finite element model is that the differentparts of the brake system are modeled realistically. Therefore,complex parametric studies based on an eigenvalue analysis areextensively investigated to detect brake squeal in relation to dif-ferent physical parameters (Liles (11); Joe, et al. (12); Liu, et al.(13); Mario, et al. (14); Ouyang and Abu-Bakar (15)). The short-comings of using of complex eigenvalue analysis (CEA) are over-predictions and missing unstable modes in the squeal frequencyrange. To overcome these limitations of CEA and to increase theprediction accuracy, Chen (16) stated that considering positivesystem damping avoids the probability of overprediction while in-troducing negative damping tends to minimize underprediction.Structural modifications including geometric and material modi-fications of a disc brake system are widely used to reduce brakesqueal (Farhang and Lim (10); Liles (11); Joe, et al. (12); Liu,et al. (13); Fieldhouse and Steel (17)).

The literature review indicates that in finite element modeling,researchers vary the geometric details of the finite element (FE)

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Evaluation of Disc Brake Materials for Squeal Reduction 645

brake model. For instance, many researchers have consideredonly a simplified FE model of the disc brake assembly; that is,a disc and two pads (Liu, et al. (13); Mario, et al. (18); Coudeyras,et al. (19)). A few have developed FE models consisting of a ro-tor, caliper, mounting bracket, piston, and brake pads; that is, adisc and two pads (Dai and Teik (2)). Some researchers (Liles(11); Abu-Bakar (20); Papinniemi (21)) used a detailed FEmodelthat consisted of a disc, a piston, a caliper, a carrier, piston andfinger pads, two bolts, and two guide pins. From the literaturereview, it was observed that just a few of the FE models werevalidated at both the individual components and assembly levelbased on modal testing data in order to improve the predictionaccuracy of the disc brake squeal. Of these works, only a fewstudies based on finite element models have considered the sta-bility analysis of brake systems, including the effect of steeringknuckle and wheel hub on squeal occurrence, without validationof all disc brake components or validation brake assembly (Kung,et al. (6)). This leads to the fact that the FE models including asteering knuckle and wheel hub need to be validated as both in-dividual components and assemblies.

An extension of the FE models discussed earlier is a three-dimensional FE model of the disc brake corner that incorporatesa wheel hub and steering knuckle that was developed and val-idated at both components and assembly levels to predict discbrake squeal. In addition, the real pad surface topography, neg-ative frictionvelocity slope, and friction damping were consid-ered to increase the prediction accuracy of the squeal. Finally,the Taguchi method was used to determine optimal materials ofdisc brake components for minimization of squeal propensity us-ing several types of materials for disc brake components as foundin practice. The Taguchi method (Rowlands, et al. (22); Antonyand Antony (23); Maghsoodloo, et al. (24)) is a systematic ap-plication of design and analysis of experiments for the purposeof designing and improving product quality. It can reveal an op-timal setting after a limited number of experiments have beenconducted.

The main contribution of the present work is to present theevolutions of stability analysis with the effects of friction damp-ing (positive damping), frictionalvelocity slope (negative damp-ing), and real pad surface topography, using actual material usedin fabricating disc brake components, considering the effect of asteering knuckle and wheel hub on squeal occurrence and usingthe Taguchi method to determine the significant contributions ofthe material modifications on reducing the squeal propensity andits interactions as well. For damped systems it is possible to ne-glect slight gyroscopic effects because damping is a key parame-ter that requires highly detailed analysis when modeling the oc-currence of instabilities and determines the efficient control ofthe damping structure of the system relative to circulatory andgyroscopic actions (Herve, et al. (25)).

METHODOLOGY AND NUMERICAL MODELFinite Element Model

A surface-to-surface discretization technique was used to de-velop the FE model because it considers the shape of both the

slave and master surfaces in the region of contact constraints andhas the following characteristics that suit our case:

The surface-to-surface formulation enforces contact condi-tions in an average sense over regions nearby slave nodes (padsurface) rather than only at individual slave nodes. The aver-aging regions are approximately centered on slave nodes, soeach contact constraint will predominantly consider one slavenode but will also consider adjacent slave nodes. Some pene-tration may be observed at individual nodes; however, large,undetected penetrations of master nodes into the slave surfacedo not occur with this discretization.

The contact direction is based on an average normal of theslave surface in the region surrounding a slave node.

Surface-to-surface discretization is not applicable if a node-based surface is used in the contact pair definition.

The whole brake corner typically consists of the steeringknuckle assembly, the wheel hub, and the actual disc brake as-sembly. The disc brake assembly consists of a ventilated rotor(disc), a floating caliper with a single piston, an anchor bracket,two bolts, two guide pins, and two brake pads. The brake padmounted on the piston is often referred to as the piston pad, andthe pad on the opposite side is called the finger pad. The brakecorner is connected to the cars suspension system through thesteering knuckle, the wheel hub is connected to the drive line,and the brake cylinder in the caliper is connected to the hydraulicbrake line system. Hence, the brake corner can be looked uponas a subsystem consisting of a number of components interrelatedto each other and to other subsystems in the vehicle.

A detailed three-dimensional FE model of the whole discbrake corner was developed. Figures 1a and 1b show a solidmodel and the FE model of the entire disc brake corner. The FEmodel consists of a disc, a piston, a caliper, an anchor bracket, awheel hub, a steering knuckle, piston and finger pads, two bolts,and two guide pins. All of the disc brake components are mod-eled carefully in order to achieve as accurate a representation aspossible of a real disc brake.

The FE model used up to 19,000 solid elements and approxi-mately 78,000 degrees of freedom (DOFs). The disc, brake pads,piston, wheel hub, guide pins, and bolts were developed usingeight-node linear solid elements, and other components were

Fig. 1Commercial disc brake corner: (a) solid model and (b) FE model.(color figure available online).

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646 M. NOUBY ET AL.

TABLE 1MATERIAL PROPERTIES OF DISC BRAKE COMPONENT

ComponentsDensity(kg m3)

YoungsModulus(GPa)

PoissonsRatio

Disc 7,155 125 0.23Friction material 2,045 2.6 0.3Back plate 7,850 210 0.3Caliper 7,005 171 0.27Anchor bracket 7,050 166 0.27Steering knuckle 7,625 167 0.29Wheel hub 7,390 168 0.29Piston 8,018 193 0.27Guide pin 2,850 71 0.3Bolt 7,860 210 0.3

developed using a combination of eight-node, six-node, and four-node linear solid elements.

Experimental Model: Validation of the FE ModelIn this section two stages were used to validate the FE model

using experimental modal analysis (EMA). The first stage ob-tained dynamic characteristics of the individual disc brake com-ponents with freefree boundary conditions. In the second stagethe dynamic characteristics of the complete assembly with bound-ary conditions are performed. In a recent study (Abdo, et al. (26))the authors considered the influence of various factors, namely,back plate Youngs modulus, back plate thickness, chamfer, dis-tance between two slots, and angle of slots, on the disc brakesqueal. The proposed approach was aimed toward prediction ofoptimal pad design to reduce the damping ratio of the dominantunstable modes through the various factors of the brake pad ge-ometrical construction. Based on this study (Abdo, et al. (26)),the authors used a new pad with a brake pad distance betweenthe two slots equal to 44 mm at a slot angle of 0 and a chamferof the edges equal to 9 mm.

Validation of FE Model at Component Level

The experimental modal analysis at the component level wascarried out up to frequencies of 10 kHz at freefree boundaryconditions. The freefree condition allows the structure to vibratewithout interference from other parts, making the visualization ofmode shapes associated with each natural frequency easier andsimpler for FE model validation. By comparing the experimentaland predicted results, a large difference was found. In order to re-duce the difference, an FE modification was considered. The pro-cess (FE updating) was used to reduce the difference in frequen-cies between predicted and experimental results (Liles (11)). Thebaseline material properties of the disc brake components afterFE updating are listed in Table 1. By comparing the experimen-tal and predicted results it was found that the predicted naturalfrequencies were quite close to those experimentally measured,as shown in Table 2.

Validation FE Model at Assembly Level

The second validation stage was the assembly level test usingthe boundary conditions with applied pressure. In this case, the

individual components were assembled on a brake test rig underbrake pressure of 1 MPa, as shown in Fig. 2.

In the FE assembly model, traditionally disc brake compo-nents are connected by so-called friction springs through a num-ber of imaginary linear spring elements. In recent years, an al-ternative method associated with the direct connection of brakecomponents has been suggested (Bajer, et al. (27)), thereforeeliminating the imaginary springs. Direct contact interaction be-tween disc brake components is represented by a combination ofnode-to-surface and surface-to-surface contact elements (Abdo(28)).

There are three contact features available in ABAQUS (MU-LIA, Dassault systems Europe) and were useful in our work.These features are gap contact elements, surface-to-node con-tact interaction, and surface-to-surface contact interaction. Thecontact algorithm used between disc and pads was a surface-to-surface contact. The surface of the disc was defined as the masterbecause it had a coarser mesh than the pad and the disc was astiffer material. The pad was consequently selected as the slavesurface. For each node on the slave surface, software attempts tofind the closest point on the master surface of the contact pairwhere the master surfaces normal passes through the node onthe slave surface. The interaction is then discretized between thepoint on the master surface and the slave node. After all bound-ary conditions and interactions between all brake components areconsidered, modal analysis is performed at the full assembly un-der the same conditions of experimental. From the analysis re-sults, it is shown that a good agreement was found between thepredicted results and the measured data, as shown in Table 3.

Experimental Setup for Squeal MeasurementsThe measurement of squeal noise of the disc brake system

was conducted using a brake test rig as shown in Fig. 2. A num-ber of tests were conducted and squeal noise was recorded atdifferent speeds and pressures using a 3.7-kW DC motor with avariable-speed drive to control the speed manually. A tachome-ter was used to read the speed of the disc. The braking pressurewas applied using a pressure pump and its value was measured bypressure gauge. In order to measure squeal noise, sound pressurelevel (SPL) measurements were made using a microphone, whichwas mounted 500 mm from the disc brake assembly. The micro-phone output signal was fed to a fast Fourier transform (FFT)analyzer, and the SPL spectrum was calculated using DEWESoft(Radio Shack, USA). The recorded data were plotted as soundpressure level (dB) against frequency (Hz). Any SPL value ex-ceeding 70 dB is considered squeal noise. It was found that ex-perimental squeal frequencies for a number of tests were domi-nant at 1,438, 2,370, 7,442, and 8,557 Hz, as shown in Fig. 3. Atbrake-line pressure of 0.7 MPa and a rotational speed of 5 rad/s,it was also found that there were four squeal frequencies at thesame values, which had higher sound pressure level, as shown inFig. 4.

MATERIAL CONSIDERATIONSIdeally, the materials used in braking systems should exhibit

properties such as good thermal diffusivity and resistance to

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TABLE 2COMPARISON BETWEEN PREDICTED RESULTS AND MEASURED DATA

Components Mode Exp. (Hz) FE (Hz) Error (%) Mode Shape

Rotor 1 1,464 1,453 0.7

2 3,198 3,225 0.8

3 4,992 5,062 1.4

Anchor bracket 1 878 880 0.2

2 1,770 1,755 0.8

3 3,341 3,164 5.2

Caliper 1 2,282 2,293 1.7

2 3,769 3,960 5

3 5,017 5,182 3.2

Brake pad 1 2,819 2,889 2.4

2 7,067 6,735 4.6

Piston 1 7,287 7,392 1.4

Steering knuckle andwheel hub

1 1,232 1,211 1.7

2 2,138 2,242 4.8

3 4,856 4,421 8.9

corrosion, low weight, long durability, friction stability, low wearratio, and good costbenefit ratio. Stiffness of the disc brake com-ponents usually has a significant effect on brake squeal genera-tion. It is necessary to design brake components such that theirnatural frequencies in the audible range are as isolated as possi-ble to avoid mode coupling. In this section, the role of materialproperties for the brake pads, rotor, caliper and anchor bracketin the model output are explored in an attempt to reduce or elim-inate the occurrence of squeal in the automotive brake systemunder evaluation.

Because the focus of this analysis is the brake squeal, the fric-tion material was modeled as a linear elastic material to avoiddifficulties in advecting the nonlinear material modeling dur-ing the adaptive meshing procedure, which was used to simu-late wear in the friction material. Hence, the load-deflection be-havior was kept within the linear zone. This assumption wasmade in most of the previous publications previously referredto. Adaptive meshing in ABAQUS is a tool that makes it pos-sible to maintain a high-quality mesh throughout an analysis,even when large deformation or loss of material occurs. Also, the

TABLE 3COMPARISONS BETWEEN PREDICTED RESULTS AND MEASURED DATA FOR BRAKE ASSEMBLY

Mode 1 2 3 4 5

Exp. (Hz) 1,611 3,222 5,065 7,043 9,130FE analysis (Hz) 1,562 3,174 5,184 6,597 9,452Error (%) 3 1.4 2.3 6.3 3.5

Mode shape

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Fig. 2Experimental modal analysis for disc brake assembly. (color figure available online).

70.0

80.0

90.0

100.0

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000Frequency (Hz)

SPL

(dB)

Fig. 3Results of experimental squeal tests at different operating conditions.

nonlinear load-deflection characteristics of the friction materialused in disc brakes have a significant effect on brake squealpropensity and are well known (Kumar, et al. (29)), but onlylinear stiffness characteristics are used in this work, mainly be-cause, as presented in Kumar, et al. (29) for values of Pois-sons ratio < 0.3, the relationship between the load and de-flection remains linear. In addition, there is only a slight varia-tion in the elastic modulus between the surfaces. Thus, for thiscase it is not considered imperative to include the nonlinearityeffects. Details of the material modifications are given in Ta-ble 4. The mode coupling mechanism is not considered in thiswork due to its diminutive effect and because it is more relatedto the design of the caliper, caliper adapter, rotor, or drum. It is

also evident in the results obtained in this work that the frictionmaterial selection has a greater influence on squeal propensitythan other structural components, because they only affect theeigenfrequencies and not the eigenmodes. A detailed investiga-tion of the dependence of squeal propensity on the eigenfrequen-cies of the structural components has been presented by Huang,et al. (30).

Pad MaterialBrake pads consist of friction materials that are highly filled

composite materials with a very complicated mechanical behav-ior and back plates made of steel. Friction materials are as-sumed to be linear and elastic. In this study, variation of Youngs

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Fig. 4Sound pressure level of brake squeal at pressure of 0.7 Mpa and speed 5 rad/s. (color figure available online).

modulus of the friction material from 0.5 to 4 GPa was simulated.These values of Youngs modulus are in the range readily at-tained with brake pads available on the market. Adaptive mesh-ing is intended to model large-deformation problems. It does notattempt to minimize discretization errors in small-deformationanalyses. However, it is intended for modeling the effects of ab-lation, or wear, of material.

Rotor MaterialBrake rotors are components of disc brake systems used in

vehicles. The size, weight, and other attributes of brake rotorsare highly variable. The material generally used for commercialbrake discs is cast gray iron, which is a material that fits the re-quirements it is intended for, such as acceptable thermal proper-

ties, sufficient mechanical strength, satisfactory wear resistance,good damping properties, and low cost; it is also relatively easy tocast and to machine. Grey cast iron differs somewhat from steelsand most other structural metals in that the elastic modulus canbe varied significantly by changing the carbon equivalent. How-ever, cast iron has a relatively high material density compared toother materials. As a consequence, cast iron brake rotors are of-ten heavy. C/C-SiC is a carbon fiber phase added to a silicon car-bide matrix. The resulting material has increased strength witha lower density and high tribological characteristics. The mostpredominant feature is its ability to withstand high temperatureswithout failure.

Recently, ceramic matrix composites have been consideredfor high-performance brake discs in the automobile industry as an

TABLE 4PROPOSED MATERIAL MODIFICATIONS

Component Material Type Youngs Modulus (GPa) Density (kg m3)

Pads Friction material (soft) 0.5 2,045Friction material (baseline) 2.6 2,045Friction material (stiff) 4 2,045

Rotor C/C-SiC 50 2,100Al-MMC 70 2,800Cast iron (baseline) 125 7,155

Caliper Aluminum 71 2,800Cast iron 171 7,005Steel 210 7,850

Bracket Aluminum 71 2,800Cast iron 166 7,050Steel 210 7,850

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650 M. NOUBY ET AL.

alternative of the conventional cast iron disc mainly due to theirexcellent thermomechanical properties as well as high strength-to-weight ratio.

For weight reduction, one approach utilizes lightweight met-als, such as aluminum rotors with a ceramic coating, or ametal matrix composite (MMC). However, aluminum and otherlightweight metals, when used as brake rotors, often result in un-acceptable performance due to low strength and poor wear resis-tance.

Many efforts have been made recently by different automo-bile manufacturers worldwide regarding the possibility of usingAl-MMCs in place of cast iron for disc brake applications inground transport systems. All of these efforts were undertakenwith the prime aim of utilizing the favorable characteristics of Al-MMCs, such as high thermal conductivity, low thermal expansion,and low relative density when compared with cast iron. The ma-terials selected are shown in Table 4.

Caliper and Anchor Bracket MaterialsBrake calipers and anchor brackets are made of ductile iron.

The carbon content of ductile irons is lower than grey cast iron,and the carbon formation is in spheroidal or nodular form. Duc-tile iron exhibits a proportional or elastic stressstrain relation-ship similar to that of steel but is limited by the gradual onset ofplastic deformation. Ductile iron has tensile strengths of around400 MPa as opposed to high-carbon grey irons, which may beas low as 150 MPa. This, along with an elastic modulus of ap-proximately 170 GPa, makes them the preferred choice for use incast iron components in low-cost applications for which the highthermal conductivity of grey iron is less important. The higherstrength is an obvious benefit in most applications, but the highermodulus is also important because the stiffness of components isproportional to modulus and can be vital in ensuring proper oper-ation and wear of components. The modulus of elasticity for duc-tile iron, measured in tension, varies from 162 to 170 GPa. Somebrake calipers are made from aluminum materials with a mod-ulus of elasticity 70 GPa. The ranges of the caliper and bracketmaterials selected are also shown in Table 4.

STABILITY ANALYSISThe governing equation of the system is

Mu + Cu + Ku = 0 [1]

where M is the mass matrix; C is the damping matrix, which

can include friction-induced damping effects as well as materialdamping contribution; and K is the unsymmetric (due to friction)stiffness matrix. This unsymmetrical stiffness matrix leads to bothcomplex eigenvalues and eigenvectors y. u is the displacementvector. Because of friction, the stiffness matrix has specific prop-erties:

K = KStructure + KFriction [2]

where KStructure is the structural stiffness matrix, KFriction is theasymmetrical friction-induced stiffness matrix, and is the fric-tion coefficient.

For a particular mode the eigenvalue pair is

i1,2 = i ii [3]

where i is the real part, i and is the imaginary part for the ithmode. The motion for each mode can be described as a dampedsinusoidal wave:

{ui} = {Ai} eai t cosi t [4]

Thus, i and i are the damping coefficient (real part) anddamped natural frequency (imaginary part) describing dampedsinusoidal motion. If the damping coefficient is negative, decay-ing oscillations typical of a stable system result. A positive damp-ing coefficient, however, causes the amplitude of oscillations toincrease with time. Therefore, the system is not stable when thedamping coefficient is positive. By examining the real part of thesystem eigenvalues, the modes that are unstable and likely to pro-duce squeal are revealed.

In order to perform the complex eigenvalue analysis usingABAQUS, four main steps are considered. They are given as fol-lows:

Nonlinear static analysis for applying brake-line pressure. Nonlinear static analysis to impose rotational speed on the

disc. Normal mode analysis to extract natural frequency of an un-

damped system. Complex eigenvalue analysis that incorporates the effect of

friction coupling.

A stability analysis using a complex eigenvalue analysis is ex-amined in the following section.

Squeal Prediction ResultsIn this study, a stability analysis using a complex eigenvalue

analysis is examined between 1 and 10 kHz with brake-line pres-sure of 0.7 MPa and a rotational speed of 5 rad/s in order to pre-dict the squeal occurrence of the disc brake. The positive realparts of the complex eigenvalues indicate the degree of instabilityof the disc brake assembly and reflect the likelihood of squeal oc-currence. Complex eigenvalues with positive real parts are iden-tified as unstable modes. The results of the complex eigenvalueanalysis are displayed on a complex plane, as shown in Fig. 5. Noother sources of damping are specified in the baseline case. Themode of frequency range is listed on the vertical axis, and the hor-izontal axis represents the real part of the complex eigenvalue,which is the index of the system instability. All of the frequencieshave zero damping (on the imaginary axis) except a few pairs offrequencies that have been coupled and form a stable/unstablepair. In this case, there are five unstable frequencies predicted at2,777, 7,573, 8,530, 9,453, and 9,722 Hz.

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0

2000

4000

6000

8000

10000

-150 -100 -50 0 50 100 150Real Part

Freq

uenc

y (H

z)

Fig. 5Predicted unstable frequencies for the baseline model. (color figure available online).

Verification of the Predicted ResultsBy comparing the CEA results with squeal test results, it was

found that only three experimental squeal frequencies were closeto the predicted frequencies. Utilizing complex eigenvalue anal-ysis resulted in missing one experimental squeal frequency at1,438 Hz and predicted more unstable frequencies than experi-mental at 9,453 and 9,722 Hz. Similar conclusions were reachedby Chen (16). Therefore, improvement of CEA is required in or-der to reduce the difference between numerical and experimentalresults.

To overcome the limitations of CEA and increase the predic-tion accuracy, three improvement tools will be considered as fol-lows:

1. The first improvement was performed considering the influ-ence of positive damping (friction damping) along with a con-stant friction coefficient to reduce overpredictions. The posi-tive damping term in ABAQUS was activated.

2. The second improvement was performed considering the ef-fect of negative frictionvelocity slope (negative damping),which is considered as one mechanism of squeal noise. Inorder to activate this effect, two values of friction coeffi-cient were considered: the static friction coefficient s = 0.65and the dynamic friction coefficient d = 0.5 measured atspeed 5 rad/s. However, it is well known that the negativefrictionvelocity slope mechanism of vibration formation is

not dependent on the coefficient of friction (Chen and Zhou(31)).

3. The third improvement was performed considering the realpad surface topography, which was measured using a portablestylus-type profilometer (Taylor Hobson Surtronic 3+). Theprofilometer had a microprocessor and a digital scale in-dicator that was used to measure and provide readings ofthe surface. In this study, the roughness parameter consid-ered was surface average height (Ra), which can be mea-sured directly at any point on the surface. The surfaceheight of the brake pad was measured by considering thesame node mapping obtained from FE model. By mea-suring average node height, the data were used to adjustthe axial coordinates of the nodes of the pad surface inthe FE model by moving the node positions in the FEmodel.

A series of experiments was performed to determine sur-face parameters of the pad/disc assembly using a portable stylus-type profilometer as explained above and were implemented inABAQUS by user-defined subroutine FRIC. Surface measure-ments of a brand new pad/disc assembly were made before start-ing the experiment. A series of surface measurements (with con-stant exploration length) was made and assessment was based onthe mean values of these parameters. The asperity summits wereassumed to be spherical and the mean radius p of the pad sur-face and d of the disc surface were computed. The mean radius of asperities and the mean standard deviation of asperities of

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TABLE 5AVERAGE DATA OF THEMEASURED SURFACES

Surface Parameters Pad Disk

Rd (m) 14.1 0.53Rp (m) 74 0.2p (m) 158 214d (m) 158 214 (m) 91.13 91.13 (m) 18.4 18.4

the pad/disc contact surfaces are given as:

1

= 1p

+ 1d

, =

2p + 2d

p = (Rp)p , d = (Rd)dwhere Rp is the maximum height of profile above mean line, Rd isan r.m.s. parameter corresponding to centerline average, and pand d are the standard deviation of height distribution of asper-ities for pad and disc surfaces, respectively. Average data of themeasured surfaces are given in Table 5. In addition, Fig. 6 showsthe 3D residual surface plot of the pad used in one of the tests.

The CEA was performed considering the friction damping,negative damping, and real pad surface. Figure 7 shows thatthe complex results were not symmetrical due to the inclusionof frictional damping. Therefore, complex conjugate pairs werenot easily identified. It is found that there are seven unstablesqueal frequencies predicted at 1,472, 2,339, 2,773, 5,816, 7,383,8,706, and 9,471 Hz. Four of these frequencies with out-of-planemodes were quite close to experimental squeal frequencies, andthe other predicted frequencies had in-planemodes and could notbe recorded, as shown in Fig. 8. Hence, the CEA results with themodification were with a higher confidence level to reduce squealoccurrence.

TAGUCHI METHODIn the present work, a Taguchi technique was integrated to

determine the significant contributions of the material modifica-tions and their interactions with other design parameters to re-duce the squeal propensity. The disc brake corner consisted ofa number of components that were made of different types ofmaterials. The influence of assembly components on squeal is be-ing studied by researchers through various methodologies. Of allcomponents, the disc, pad, caliper, and anchor bracket are be-ing widely targeted for studies. From the literature and previousworks, it is understood that there are different types of materialsthat are employed to manufacture those components. Hence, inthe present study, an attempt was made to determine the influ-ence of material selection for the brake components through theTaguchi method. From a literature review, different types of ma-terials available on the market used for fabricating these brakecomponents were studied for their effects on squeal; other brakecomponents have been assumed to be constant over the study(23).

According to Taguchi, all machines and mechanisms are clas-sified as engineering systems (if they produce a set of responses

Fig. 8Unstable frequencies and mode shapes for the predicted result.(color figure available online).

for a given set of inputs). Those systems can be classified in to twocategories: (1) static and (2) dynamic. A dynamic system has sig-nal factors (input from the end user) in addition to control andnoise factors, whereas in a static system signal factors are notpresent. Optimization of materials of disc brake components isa static system. The diagram in Fig. 9 is called a P-diagram. TheP means process or product according to Taguchi.

In the present work, parameter design was utilized to arrive atthe optimum levels for types of materials in order to minimize thesqueal occurrence during braking. According to Taguchi, twoma-jor tools are employed to achieve any quality goal or any robustdesign (Phadke (32)). They are

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Fig. 63D surface residual of brake pad.

0

2000

4000

6000

8000

10000

-150 -100 -50 0 50 100 150Real Part

Freq

uenc

y (H

z)

Fig. 7Effect of real pad surface including negative and positive damping on predicted results: 1, unstable frequency at 1,472 Hz; 2, unstable frequencyat 2,339 Hz; 3, unstable frequency at 2,773 Hz; 4, unstable frequency at 5,816 Hz; 5, unstable frequency at 7,383 Hz; 6, unstable frequency at 8,706Hz; 7, unstable frequency at 9,471 Hz. (color figure available online).

1. Signal-to-noise (S/N) ratio, which measures quality.2. Orthogonal arrays, which are used to study many parameters

simultaneously.

Taguchi uses the S/N ratio to measure quality characteris-tics deviating from the desired value. The S/N ratio character-istics can be divided into three categories: the nominal-the-best,the smaller-the-better, and the larger-the-better. Because the ob-

jective of this study was to minimize the squeal occurrence, thesmaller-the-better quality characteristic was employed.

Selection of Variables and Their LevelsBased on the detailed literature survey, the following param-

eters were considered for the experiment, as listed in Table 6.

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654 M. NOUBY ET AL.

TABLE 6MATERIAL PARAMETERS AND THEIR LEVELS FORTAGUCHI METHOD

Level

Factors 1 2 3

Friction material (A) Soft Medium StiffRotor (B) C/C-Sic Al-MMC Cast IronCaliper (C) Aluminum Cast Iron SteelAnchor bracket (D) Aluminum Cast Iron Steel

TABLE 7EXPERIMENTAL LAYOUT USING TAGUCHI L9 ARRAY

Test

FrictionMaterial

(A) Rotor (B) Caliper (C)

AnchorBracket(D)

1 1 1 1 12 1 2 2 23 1 3 3 34 2 1 2 35 2 2 3 16 2 3 1 27 3 1 3 28 3 2 1 39 3 3 2 1

Fig. 9P-diagram of disc brake squeal system.

Taguchis Experiments, Data Collection and AnalysisExperiments were conducted as per the Taguchi L9 orthog-

onal array to identify the most significant variables by rankingthem with respect to their relative impact on the squeal occur-rence. The L9 orthogonal array consisted of four control parame-ters at three levels, as shown in Table 7.

The S/N ratio is given by:

= 10 log (MSD) [5]

Fig. 10Main effects plot.

where MSD is the mean square deviation for the output charac-teristic. MSD for the smaller-the-better quality characteristic iscalculated by the following equation,

MSD = 1N

[ni=1 Y

2i

][6]

where Yi is the squeal response (damping ratio) from which theS/N ratio is computed. For the ith test, n denotes the number oftests and N is the total number of data points. The function -logis a monotonically decreasing one, which means that we shouldmaximize the S/N value. The S/N values were calculated usingEqs. [5] and [6]. Table 8 shows the response table for S/N ratiosusing the smaller-the-better approach.

Results and DiscussionFrom Table 9 and from the main effects plot for the S/N ratio

(Fig. 10), it is observed that A3-B2-C3-D2 and A3-B2-C3-D3 arethe optimum combinations for minimum squeal. Similarly, A1-B1-C1-D2 is the combination for maximum squeal. These combi-nations were not included in the experimental runs. Three sets ofmaterials were tested and the results compared for the minimumsqueal that showed perfect agreement with experimental results.The results are listed in Table 9.

A comparison of experimental (measured) results and the FEanalysis (predicted) results are also shown graphically in Fig. 11.Thus, the adequacy of the approach for prediction of squeal wasverified.

TABLE 8RESPONSE TABLE FOR S/N RATIOS USING SMALLER-THE-BETTER

Level Friction Material (A) Rotor (B) Caliper (C) Anchor Bracket (D)

1 22.26 17.93 17.68 16.312 15.67 15.45 17.72 18.113 13.33 17.87 15.87 16.84Delta 8.93 2.48 1.85 1.79Rank 1 2 3 4

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TABLE 9VERIFICATION EXPERIMENTAL RESULTS

ValidationRun Pad Rotor Caliper Bracket S/N Ratio

PredictedSqueal

MeasuredSqueal Difference

1 0.5 C/C-SiC Aluminum Cast 24.71 15 16 12 4 Al-MMC Steel Steel 11.49 3.33 3 0.663 4 Al-MMC Steel Aluminum 10.23 2.33 3 0.66

Fig. 11Comparison between predicted (series 1) and measured (series2) squeal. (color figure available online).

Fig. 12Contributions of material components. (color figure availableonline).

Contribution of ComponentsBased on the Taguchi method the S/N ratio contributions of

material components were computed and plotted, as shown inFig. 12. It was found that the pad friction material contributes56% of the total system instability (generation of squeal), fol-lowed by the rotor material, which contributes 22% of the systeminstability. Caliper and bracket materials contribute 11% each.

CONCLUSIONSThis article presents a methodology for evaluation of differ-

ent types of materials for components of a disc brake system toreduce squeal generation. Various materials used in practice formanufacturing disc brake components were examined. Initially,the FE model was validated at component and assembly levels.Reasonably good agreement was achieved between predicted andexperimental results in terms of dynamic characteristics. Then astability analysis using a complex eigenvalue analysis was per-formed and verified with experimental tests. Subsequently, theanalysis was integrated with the Taguchi method to determine thecontributions of different types of materials and their interactioneffects for effective reduction of brake squeal.

The results showed that the most significant improvement inbrake squeal performance could be achieved by using a combi-nation of rotor material from Rotar Material (Al-MMC), castiron caliper and friction material with elastic properties 2.6 GPa.It was also seen that the pad friction material contributed 56%of the total system instability (generation squeal). The rotormaterial contributed 22% of the system instability. Caliper andbracket materials contributed 11% each.

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Documents

Evaluation of Disc Brake Materials for Squeal Reduction