EFFECT OF CHAMFERED BRAKE PAD PATTERNS ON THE VIBRATION SQUEAL RESPONSE OF DISC BRAKE SYSTEM

Transcription

1 3rd Iteratioal Symposium o Advaced Fluid/Solid Sciece ad Techology i Experimetal Mechaics, 7-10 December. 2008, Taia, Taiwa EFFECT OF CHAMFERED BRAKE PAD PATTERNS ON THE VIBRATION SQUEAL RESPONSE OF DISC BRAKE SYSTEM E-Cheg.Liu 1, Shih-Wei Kug 2, Syh-Tsag Jeq 1*, Chie Gau 1, Hsi-Lue Tsai 3, Cheg-Chig Lee 4, ad Yu-Der Che 4 1 Departmet of Aeroautics ad Astroautics, Natioal Cheg Kug Uiversity, Taia, Taiwa, R.O.C. 2 Dassault Systemes Simulia Cetral, Ciciati, Ohio, USA 3 Departmet of Electroic egieerig, Kao Yua Uiversity, Kaohsiug couty, Taiwa, R.O.C. 4 Aeroautical Systems Research Divisio, Chug-Sha Istitute of Sciece & Techology, Taichug, Taiwa Abstract This paper is cocered with the disc brake squeal problem for automotive vehicles. The purpose of the preset research tries to reduce the istability of the squeal mode ad to improve the comfortless discord volume i the car. I the curret study, the ABAQUS/Stadard (Implicit method) fiite elemet umerical model was costructed to perform the dyamic cotact vibratio aalysis of a disc brake system cotaiig a brake disc, brake pads, caliper, ad brake shoe. Brake pads with specific chamfer patters ad a brake disc with coolig ribs for vetilatio ad heat trasfer were costructed umerically i the preset system. The effect of brake pad chamfer patter o the ustable frequecy distributio, which may result i the brake squeal pheomeo, is studied. A disc rotatioal velocity of 2.5 rad/s was studied umerically whe the pad was uiformly pressurized to 200 psi (1.379 MPa) o the brake shoe. The Laczos method is used to fid the atural frequecies of brake system i questio, ad the use the complex eigevalue method to extract the ustable squeal high frequecies betwee the brake disc ad brake pads for specific chamfer patters with dry frictio. A liig frictio coefficiet of 0.4 was selected to i the curret aalysis i order to determie the ucomfortable brake squeal vibratio frequecies distributio with specific chamfer patters. Keywords: brake squeal, frictio, chamfer, Laczos method, complex eigevalue method. 1. Itroductio Brake squeal problems are always exist i the brake system of the vehicle, there are may egieers ad academics more ad more attach importace to frictio iduced vibratio problem of brake squeal. Brake oise frequecy ca be classified ito three categories frequecy regio. The three categories are judder, groa/moa, ad squeal as show i Figure 1. Amog this frequecy, egieers ad academics used experimetal, aalytical, ad computatioal methods to aalysis ad reduce the brake squeal problems. May egieers ad academics used the complex eigevalue method to predict the brake squeals i the ustable regio. Kug et al. [1] were used the complex eigevalue method for a detailed aalytical study i order to obtai a better uderstadig of this solutio techique. Modal participatio factors were calculated to examie the modal couplig mechaism. Parametric studies were also performed to fid out the effects of frictio coefficiet ad rotor stiffess. I order to reduce or elimiate squeal, it was very importat to uderstad the couplig mechaism so that the key compoet(s) ca be modified accordigly, Kug et al. [2] demostrated a quatitative method to defie system mode shapes usig the cocept of modal participatio factors. This method was implemeted o a frot disc brake system to idetify the modal couplig mechaism associated with its high frequecy squeal. Complex eigevalue aalysis was carried out ad the squeal frequecy was correlated. Shi et al. [3] were used the complex eigevalue aalysis for brake oise aalysis ad oise reductio i GM. Fiite elemet models were validated with compoet modal testig. Also dyamometer ad vehicle test results were compared with fiite elemet results. From several vehicle level brake oise aalyses, their experiece shows that complex mode shapes were capable of depictig the oise geeratig mechaisms, ad the complex eigevalues are able to depict the oise frequecies. Bajer et al. [4] were performed the complex eigevalue extractio at a deformed cofiguratio; oliear effects were take ito accout i the modal aalysis. A example case was used to illustrate the importace of frictio-iduced dampig ad oliear effects i brake squeal aalysis. It was foud that the iclusios of liig wear, geometric oliearities, ad positive as well as egative frictioal dampig effects had sigificat ifluece o the brake squeal predictios. Yue et al. [5] i order to better uderstad the mechaism of squeal geeratio, this study started with the compoet modal aligmet aalysis aroud problem frequecies based o the compoet EMA (Experimetal Modal Aalysis) data i free-free coditio. Liu et al.[6] were preseted a simple fiite elemet model as a rapid egieerig tool for desigig pad shape to reduce high frequecy brake squeal ad discussed the mechaism, effect, ad desig methodology of pad shape o squeal. Liu et al. [7] ad [8] were performed usig the commercial available code ABAQUS/Stadard (Implicit method) to calculate the atural frequecies of brake disc model extract the complex eigevalues of the cotacted brake disc ad pads model. The ustable squeal frequecies of the brake disc compressed by a pair of brake pads were determied. * Correspodig author, Professor, stjeq@mail.cku.edu.tw, Fax: (Taiwa)

2 3rd Iteratioal Symposium o Advaced Fluid/Solid Sciece ad Techology i Experimetal Mechaics, 7-10 December. 2008, Taia, Taiwa Figure 1 Brake squeal rage. 2. Equatio of motio of the disc brake system The equatio of motio for a disc brake system ca be writte as follows: M ]{ u& } + [ C]{ u& } + [ K]{ u} = [ F ], (1) [ exteral where [M] is the mass matrix, [C] is the dampig matrix, [K] is the stiffess matrix, {u} is the geeralized displacemet vector, ad [ F exteral ] is exteral force matrix, respectively. The forcig term [ F exteral ] ca be as the fuctio of the velocity as follows: [ ] = [ f ]{ u& }. (2) F exteral A homogeeous equatio of ca be obtaied by combig equatio (1) ad (2) by movig the forcig term to the left had side [ M ]{ u& } + [ C f ]{ u& } + [ K]{ u} = 0. (3) coditios are applied at the ceter of the hub ad at the bolted locatio of the bracket. Iterfaces betwee compoets are modeled as cotact pairs with master ad slave surfaces. These cotact pair surfaces iclude rotorliig surfaces, caliper-pad surfaces, pisto-pad surfaces, ad bracket-shoe abutmet surfaces. A commercial fiite elemet software Abaqus/Stadard is selected. The aalysis flow chart is show i Figure 9. Several o-liear static steps are performed first to calculate steady state equilibrium of the system i a specific brakig coditio. Withi these static steps, the brake pressure is applied ad rotor agular motio is imposed. The atural frequecies of the system at brakig coditio are extracted by usig the Laczos eigevalue solver. Fially, complex modes are extracted i the complex eigavelue step ad ustable squeal frequecies are idetified. To study the effect of liig chamfer, the origial pad shape (Figure 6) are modified to the ew pad shape (Figure 7 ad 8) as suggested by Ref. [6] (Figure 5). This modificatio icludes 21 mm parallel chamfers, ceter slot, as well as top ad bottom ceter V-chamfer. The fiite elemet model are revised by swappig the ier ad outer pad models with the ew oes. Cotact surfaces are redefied ad the procedure described above is performed agai. Results are discussed i the followig sessio. From equatio (3), the determiatio of istability formulatio is derived as C eq C f ζ = = < 0, (4) 2 MK 2 MK where K ω =, Ceq λ ( D) ζ = =, ad M Cc 2ω Cc = 2 Mω = 2 MK. I additio, ω is the udamped atural frequecy of the disc brake system, ζ is dampig ratio, C is critical dampig coefficiet ad c λ = a + bi is the eigevelues of the brake system, where a is the real part ad b is the imagiary part of the eigevalue. If C < f occurs, the disc brake system will appear egative dampig effect such that the disc brake system occurs ustable pheomeo. 3. Fiite Elemet Model A passeger car frot brake system with a vetilated disc ad sigle-bore floatig caliper is used here as a example [4]. High frequecy squeals were observed i dyamometer tests as show i Figure 2. The fiite elemet model cosists of a rotor, caliper, bracket, pisto, ad pads as show i Figures 3 ad 4. This model is meshed with 26,056 elemets ad 38,120 odes. Figure 2 Dyamometer test results (4). Figure 3 Frot view: Fiite elemet model of a disc brake system. The brake liig material is assumed to be trasverse isotropic. Other compoets are modeled as liear elastic isotropic materials as show i Table 1. Boudary

3 3rd Iteratioal Symposium o Advaced Fluid/Solid Sciece ad Techology i Experimetal Mechaics, 7-10 December. 2008, Taia, Taiwa Figure 8 Rear view of the curret brake pad model. Figure 4 Back view: Fiite elemet model of a disc brake system. Fiite Elemet model Fiite Elemet iput file *Static: Distributio force *Motio: Velocity Figure 5 New pad shape [6]. *Frequecy Extractio *Complex Eigevalues Extractio Results: Brake squeal predictio Figure 9 Aalysis flow chart usig the ABAQUS/Stadard code. Figure 6 Frotal view of the origial pad model Figure 7 Frotal view of the curret brake pad model which cotais 21 mm parallel chamfers, a ceter slot ad the top ad bottom ceter V-chamfers. Table 1 Material properties of a disc brake compoets. Compoet Brake disc (Rotor) Material Cast iro Youg s modulus Poisso ratio Shoe Steel Pisto Steel Caliper Steel Bracket Steel Yield stress (MPa) Ultimate stress (MPa) Results ad Discussio The focus of this study is o the reductio of high frequecy squeals which rages from 5 khz to 16 khz. I order to cover such a wide frequecy rage, 200 modes are requested i the complex eigevalue calculatio. I this case study, the basic parameters chose for the parametric studies are frictio coefficiet ad brake disc rotatio speed. The frictio coefficiet μ = 0.4, ad brake

4 3rd Iteratioal Symposium o Advaced Fluid/Solid Sciece ad Techology i Experimetal Mechaics, 7-10 December. 2008, Taia, Taiwa disc rotatio speed is 2.5 rad/s. The results of complex eigevalue aalysis is i the form of λ, where a = a + bi is the real part ad b is the imagiary part of the eigevalue which presets frequecy of the ustable mode. All calculated eigevalues are the plotted o a complex plae as show i Figure 10. Note that the left half plae shows the stable regio while the right half pla shows the ustable regio. It ca be see that the squeal frequecies of 6, 7, 10, 13 ad 16 khz from the test data (4) are all predicted i the complex eigevalue results as ustable modes. It is also see that the istability of most ustable modes are reduced whe the chamfer desig is applied. Table 2 listed the predicted modes ad their istabilities before ad after the liig chamfer. Frequecy (Hz) Complex Eigevalue Aalysis origial chamfered Stable regio 0 Ustable regio Real Part of Complex Eigevalue Figure 10 Complex eigevalues of origial ad chamfered model. Figure 11 The ustable mode 110 (tagetial mode) at khz. Figure 12 Bedig mode 139 at khz. Figure 11 shows the complex mode shape of a ustable mode 110 at khz. It ca be see that the rotor motio is the secod tagetial mode. Figure 12 shows the pad motio of the chamfered pad for the ustable mode 139 at khz. Further study is eeded to look ito these compoet motios i the ustable modes i order to get the isight of the liig chamfer effect. Table 2 The FEM aalyzed ustable modes ad frequecies correspodig to dyamometer test results (4). 200 psi (1.379 MPa), 2.5 rad/s, ad μ =0. 4 Mode khz Mode khz Mode khz Mode khz Mode khz 5. Coclusio I the preset study, a commercial fiite elemet code - ABAQUS/Stadard (Implicit method) is used to predict the dyamic istability of a cotact vibratio disc brake system before ad after a specific liig chamfer treatmet. This type of liig chamfer (6) cosists of a ceter slot, 21- mm parallel chamfers o both leadig ad trailig side, ad V-chamfers at the top ad bottom ceter. Major squeal frequecies that observed i the dyamometer test (4) are predicted i the complex eigevalue aalysis as ustable modes. The effect of liig chamfer is also predicted ad the results show reductios of istability for may modes. The FEM predicted frequecies of the ustable squeal modes correspodig to test results are , , , 13.3, ad khz. It ca be see that the squeal frequecies of 6, 7, 10, 13 ad 16 khz from the test data are all predicted i the complex eigevalue umerical results as ustable modes. It is also see that the istability of most ustable modes are reduced whe the chamfer desig is applied. Table 2 listed shows the predicted modes ad their istabilities before ad after adoptig the liig chamfer. Further ivestigatio i compoet motios is eeded to get the isight of this liig chage so that

5 3rd Iteratioal Symposium o Advaced Fluid/Solid Sciece ad Techology i Experimetal Mechaics, 7-10 December. 2008, Taia, Taiwa optimum liig shape ca be proposed. This aalysis provides desigers with a powerful aalysis tool for the brake squeal vibratio study of a advaced disc brake system. Ackowledgemet The authors are grateful to the Departmet of Idustrial Techology, Miistry of Ecoomic Affairs (MOEA), Taiwa, R.O.C. for their support of the research preseted uder the Cotract No. 97-EC-17-A-99-R Refereces [1] Kug, S. W., Dulap, K. B. ad Balliger, R. S.: Complex Eigevalue Aalysis for Reducig Low Frequecy Brake Squeal, SAE Paper , [2] Kug, S. W., Saligrama, V. C. ad Riehle M. A.: Modal Participatio Aalysis for Idetifyig Brake, SAE Paper , [3] Shi, T. S., Chag, W. K., Dessouki, O. Jayasudera, A. M. ad Warzecha, T.: Advaces i complex eigevalue aalysis for brake oise, SAE Paper , [4] Bajer, A., Belsk, V. ad Kug, S. W.: The Ifluece of Frictio-Iduced Dampig ad Noliear Effects o Brake Squeal Aalysis, SAE Paper , [5] Yue, Y., Allgaier, R. Jaber, N. A. ad Wag, A.: Brake Noise Study (Part I) Low Frequecy Squeal, SAE Paper , [6] Liu, W., Vyletel, G. M. ad Li, J.: A Rapid Desig Tool ad Methodology for Reducig High Frequecy brake Squeal, SAE Paper , [7] Liu, E. C., Jeq, S. T., Gau, C., Tsai, H. L., Kug, S. W., Lee, C. C., Li, S. C., ad Li, S. W.: Cotact Vibratio Aalysis of a Brake Disc Made of Cast Steel Compressed by a Pair of Brake Pads, paper o. A27-17, the Proceedigs of the 2007 AASRC/CCAS Joit Coferece, PigTug, Taiwa, Nov. 16, [8] Liu, E. C., Jeq, S. T., Gau, C., Tsai, H. L., Kug, S. W., Lee, C. C., Li, S. C., ad Li, S. W.: Eigevalue Aalysis of a Brake Disc Compressed by Brake Pads, 2007 Abaqus Taiwa Users Coferece, Jiaosi, Taiwa, Nov. 7, 8, [9] ABAQUS Theory Maual, Versio 6.7-EF1, [10] ABAQUS Aalysis User s Maual Versio 6.7-EF1, 2007.