Mathematical Modeling & Analysis of Brake Pad for Wear Characteristics

Transcription

1 Intenatnal Cnfeence n Ideas, Impact and Innvatn n Mechancal Engneeng (ICIIIME 07 ISSN: -869 Vlume: 5 Issue: Mathematcal Mdelng & Analyss f Bake Pad f Wea Chaactestcs S. R. Kakad, R.M. Me, D. D. N. Kamble Pf. S. R. Kakad, Depatment f Mechancal Engneeng, SKNCOE, Pune, shaad_kakad@yah.cm Pf. R.M. Me, Depatment f Mechancal Engneeng, SKNCOE, Pune, me.ms@gmal.cm D.D.N.Kamble, Depatment f Mechancal Engneeng, SAOE, kndhwa Pune, dnkamble8@gmal.cm ABSTRACT Rbust bakng esults n heat geneatn whse effects may have cnsdeable mpact n the paametes f the pcess such as wea ate and ceffcent f fctn. In ths pape, the pefmance f the bake s studed f the dffeent mateal. The smulatn f wea and cntact pessue s epted by usng FEA sftwae. The nvestgatn can be extendng f the vefcatn f mathematcal mdel. The FEA sftwae s me effectve as a tl f vefcatn f analytcal cntbutn. The fctn and wea pefmances f bake mateal n dy cndtn ae als epted n the pape. The themal analyss and the stuctual analyss ae fund t be a ce f nvestgatn n study f dsc bake. The cllectve dependent mathematcal mdel s develped t study the cllectve effect n specfc dsc mateal. The applcatn can be extend t valdate a mathematcal mdel and the pedctns can be epted fm the nvestgatn. In ths pape, The Mathematcal mdel f the dsc bake f analyss f wea s develped. The equatns ae desgned t study the effect f paametes lke beakng enegy, beakng pwe, cntact pessue and actuatng fce n the wea f dsc bake. The btaned mathematcal mdel s studed t ept the mdfcatn t mpve the degee f acceptance. The custmze sftwae package lke ANSYS s used t vefy the mdfed analytcal nvestgatn. Keywds: Beakng pwe, Mathematcal mdel, Wea, Fctnal fce4, Bake pad5 etc INTRODUCTION Passenge ca dsc bakes ae safety-ctcal cmpnents whse pefmance depends stngly n the cntact cndtns at the pad-t-t nteface. When the dve steps n the bake pedal, hydaulc flud s pushed aganst the pstn f the calpe, whch n tun fces the bake pads nt cntact wth the t. The fctnal fces at the sldng ntefaces between the pads and the t etad the tatnal mvement f the t and the axle n whch t s munted. The knetc enegy f the vehcle s tansfmed nt heat that s manly absbed by the t and the bake pad. The pad-t-t nteface can be classfed as a cnfmal dy sldng cntact. Dung bakng a pnt n the bake pad s n cnstant cntact wth the t, wheeas a pnt n the t expeences ntemttent cntact. A natual cnsequence f the sldng cntact s that bth the t and the pads ae wn ut, affectng the useful lfe f the bake as well as ts behavu. The bake dsc ( t s usually made f cast n, but may n sme cases be made f cmpstes such as enfced cabn cabn ceamc matx cmpstes. Ths s cnnected t the wheel the axle. T stp the wheel, fctn mateal n the fm f bake pads, munted n a devce called a bake calpe, s fced mechancally, hydaulcally, pneumatcally electmagnetcally aganst bth sdes f the dsc. Fctn causes the dsc f wheel t slw stp. Bakes cnvet mtn nt heat, and f the bakes get t ht, they becme less effectve, a phenmenn knwn as bake fade. []. OBJECTIVE & SCOPE Fg-: Assembly f Dsc Bake. Develpment f mathematcal mdel f the dsc bake f the wea analyss. The equatns ae desgned t study the effect f paametes lke beakng enegy, beakng pwe, cntact pessue and actuatng fce n the wea f dsc bake.. The study f btaned mathematcal mdel t ept the mdfcatn t mpve the degee f acceptance.. The custmze sftwae package lke ANSYS s used t vefy the mdfed analytcal nvestgatn. IJRITCC June 07, (Specal Issue 048

2 Intenatnal Cnfeence n Ideas, Impact and Innvatn n Mechancal Engneeng (ICIIIME 07 ISSN: -869 Vlume: 5 Issue: METHODOLOGY. Analytcal Investgatn. Bake pwe Themal mdelng Regadng t the unfm pessue the cnstant wea bunday cndtn at the cntact suface, tw methds ae avalable f calculatng the bakng heat geneatn ate. Unfm pessue dstbutn n the cntact egn s ften vald when the pad s new. Hweve afte bakng f seveal tmes, assumptn f unfm wea s me pagmatc. In ths study, the pad s used seveal tmes and unfm wea between pad and bake dsc s stablzed, hence the heat flux s just a functn f tme and t s ndependence f the spatal vaables. F a vehcle whch s deceleatng n a level suface fm a hghe velcty V t a lwe velcty V the bakng enegy Eb can be wtten as m( V V I( E b Whee, I s mass mment f neta f the tatng pats, m lcmtve mass and ω s the angula velcty f tatng pats. If the lcmtve stps cmpletely (V = ω= 0 then all the tatng pats wll be expessed elatve t the evlutns f the wheel. Whee, Kcf s the cectn fact f tatng masses and enegy dvded by the bakng tme t, The bake pwe s gven by, E b I m( = Kcf mv R P V w m b R w s the wheel adus. Bakng pwe P b s equal t bakng de dt b P b K cf ma( V at Whee, a s the deceleatn f the lcmtve. The dstbutn f bakng enegy between pad and dsc cannt be pedcted eadly. [5] Fg-: Paamete f Dsc Bake The mdel cnsst f vaus fces n the vehcle dung bakng and cmputes the tme-dependent bakng pwe dsspated, fm the calculated bake tque Tb, and wheel speed ω,.e. Pb =Tb ω =Tb (-Te Slp wheel speed/rllng adus.. Lnea Sldng wea Cnsdeng a blck wth suface aea A, sldng ve fxed suface wth cntact pessue P, whee the c-effcent f sldng fctn fs & defne a lnea wea measue w. [0] The wk dne by fctnal fce fspa dung dsplacement S s fspas fspavt (whee V s velcty & & t s tme. The vlumes f mateal emved because f wea wa s pptnal t the wk (wa α fspavt.e. wa = KPAVt Whee, K s pptnalty fact whch ncludes the c-effcent f fctn fs. The SI unt f K s m.s / (N.m.s w = KPVt Addtnal cectn facts f & f can be ncluded such that: w = ffkpvt Whee, f cectn fact f mtn type IJRITCC June 07, (Specal Issue 049

3 Intenatnal Cnfeence n Ideas, Impact and Innvatn n Mechancal Engneeng (ICIIIME 07 ISSN: -869 Vlume: 5 Issue: f cectn fact f envnment The Fce and the tque equatns ae gven as, w = ffkpvt F p. d. d p.d T f. p. d. d f p. d e T ff p. d p. d _ M x F p(.sn. d. d (cs cs p.d M F These equatns ae appled f unfm wea and unfm pessue cndtns: _ x (cs cs e A. Unfm Wea Cndtn F ( P. ( a T ( f. P. d a ( f. Pa ( IJRITCC June 07, (Specal Issue 050

4 Intenatnal Cnfeence n Ideas, Impact and Innvatn n Mechancal Engneeng (ICIIIME 07 ISSN: -869 Vlume: 5 Issue: B. Unfm Pessue Cndtn e P a P a. d d _ cs cs F ( P. d ( Pa ( a T ( f. Pa. d ( f. Pa ( e a P P a. d. d _ cs cs cs cs. Fce system f ca mdel The Nmal fce FT n the nne and ute faces can be btaned fm the Tque T = FT.R FT= T/Rµ = Ceffcent f fctn FT = Ttal nmal fces n dsc bake = FTRI + FTRO FTRI=FT/ FTRI = µ.fri FRI= FTRI/ µ FRI = P max / A pad bake aea µ = Ceffcent f fctn = 0.5 IJRITCC June 07, (Specal Issue 05

5 Intenatnal Cnfeence n Ideas, Impact and Innvatn n Mechancal Engneeng (ICIIIME 07 ISSN: -869 Vlume: 5 Issue: Fg-: Fces System f ca mdel 4. Bakng Dstance(x The tangental bakng fce actng at the pnt f cntact f the bake and the wk dne elatn s gven by, Wk dne = F T. x Whee FT = FTRI + FTRO x = Dstance tavelled (n mete by the vehcle befe t cme t est. The knetc enegy f the vehcle, K.E. = (mv / Whee, m = Mass f vehcle & v = Velcty f vehcle In de t bng the vehcle t est, the wk dne aganst fctn must be equal t knetc enegy f the vehcle. FT. x = (mv / Assumptn v = 00 km/h = 7.77 m/s m = Dy weght f Vehcle Theefe, x = (mv / F T 5. Themal Mdel The themal cnductvty f the bake pads s smalle than the dsc (Kp < Kd, s ne can cnsde that the ttal amunt f the bakng heat wll be cmpletely absbed by the bake dsc. Ths assumptn leads t hghe tempeatue estmatn f bake dsc. T avd ths ssue, suppse that the bakng peatn tme s sht, hence the pad and bake can be cnsdeed as sem-nfnte slds and the heat geneatn at can be calculated as fllws [6] '' q d d. Cd. K d '' q p p. C p. K p whee λ s the heat geneatn at, q d and q p ae the heat flux absbed by the bake dsc, and pad, ρ epesents densty, C s the specfc heat, K the themal cnductvty and the ndex d and p ndcate dsc and pad, espectvely. The heat flux n the bakng suface can be fund '' qd Kcf. m. a( V at A( Whee, A s the dsc and pad cntact aea.. Sftwae vefcatn A. Backgund Lnea statc analyss s caed ut t get the desed esults. Heat Geneated (Q d = m.cр. ΔT ΔT= Q d /m Cp Fg 4 Smplfed CAD mdel f the studed subsystem IJRITCC June 07, (Specal Issue 05

6 Intenatnal Cnfeence n Ideas, Impact and Innvatn n Mechancal Engneeng (ICIIIME 07 ISSN: -869 Vlume: 5 Issue: RESULT & DISCUSSION The nvestgatn f wea f bake pad s dne and categzed based n analytcal nvestgatn & sftwae vefcatn. The esults ae studed, cmpaed and ae epted. 4. ANALYTICAL RESULT The studes ae pefmed f bakng tme f -6 Sec. It s bseved that f a mn. bakng tme the tque epts the hghe values. As the velcty f vehcle nceases, the tme equed f bakng s als nceases. Snce bakng tme vay wth velcty. Fg.5 Vel. Vs Tque f bakng tme f -6 Sec. Fg.6 Vel. Vs Cntact Pessue (Dy f bakng tme f -6 Sec. Fg. 7 Vel. Vs Cntact Pessue (Wet f f -6 Sec. Fg. 8 Vel. Vs Actve Fce (Dy & Wet f unfm bakng tme Wea & pessue cndtn Fg. 9 Velcty Vs Fces Fg. 0 Vel. Vs Bakng Dstance f bakng tme f -5 Sec. IJRITCC June 07, (Specal Issue 05

7 Intenatnal Cnfeence n Ideas, Impact and Innvatn n Mechancal Engneeng (ICIIIME 07 ISSN: -869 Vlume: 5 Issue: Fg. Heat Dsspatn Vs Fce f Cast n & AL O Fg. Wea Vs Actve Fce f Cast In Fg. Wea Vs Actve Fce f Al O 5. SOFTWARE VERIFICATION The wea f the bake pad mateal s analyzed by usng sftwae package lke ANSYS. Dung the vaatn f velcty, bakng tme s kept cnstant & cespndng wea f cast n bake pad mateal s analyzed. Thee s vaatn f wea f bake pad mateal wth espect t velcty f the vehcle & ts cespndng bakng tme. The statc stuctual analyss s pefmed analyss f ttal defmatn f cast n bake pad mateal. Fg. 4 Wea defmatn f bake pad at velcty 40km/h & 45 km/h wth secnds bakng tme Fg. 5 Wea defmatn f bake pad at velcty 50km/h & 55km/h wth secnds bakng tme IJRITCC June 07, (Specal Issue 054

8 Intenatnal Cnfeence n Ideas, Impact and Innvatn n Mechancal Engneeng (ICIIIME 07 ISSN: -869 Vlume: 5 Issue: Fg. 6 Wea defmatn f bake pad at velcty 60km/h & 65km/h wth secnds bakng tme Fg. 7 Wea defmatn f bake pad at velcty 70km/h & 75 km/h wth secnds bakng tme 6. CONCLUSION Fg. 8 Wea defmatn f bake pad at velcty 80km/h wth secnds bakng tme. The mathematcal Equatns ae develped f nvestgatn f wea f bake pad f vaus mateals. The btaned analytcal esults fm mathematcal equatns ae studed and vefed by usng ANSYS. The equatns ae desgned t study the effect f paametes lke beakng enegy, beakng pwe, cntact pessue and actuatng fce n the wea f dsc bake.. The Investgatn s pefmed n bake pad mateal f unfm pessue cndtn & unfm wea cndtn unde dy & wet cndtn.. The esults ae cmpaed n cmmn scale and the acceptance f mdfcatn shws gd ageement n the ange f 5 t 8 %. REFERENCES [] Jana Kukutschva, Vaclav Rubcek, Mslav Maslan, Dalb Janck and Pete Flp Wea pefmance and wea debs f sem metallc autmtve bake mateals Wea 68 ( [] Andes Sdebeg, Sen Andessn Smulatn f wea and cntact pessue dstbutn at the pad-t-t nteface n a dsc bake usng geneal pupse fnte element analyss sftwae Wea 67 ( [] Saeed Abbas, Jens Wahlstm, Las Olande, Chstna Lassn and Ulf Sellgen A study f abne wea patcles geneated fm ganc alway bake pads and bake dscs Wea 7 ( [4] A. Akay, O. Gannn, F. Mass and A. Seste Dsc bake squeal chaactezatn thugh smplfed test gs Mechancal Systems and Sgnal Pcessng ( [5] Shayang Zhang, Fupng Wang, Cmpasn f fctn and wea pefmances f bake mateal dy sldng aganst tw alumnum matx cmpstes enfced wth dffeent SC patcles Junal f Mateals Pcessng Technlgy 8 ( [6] A.A. Yevtushenk, P. Gzes Axs-symmetc FEA f tempeatue n a pad/dsc bake system at tempeatue-dependent ceffcents f fctn and wea Intenatnal Cmmuncatns n Heat and Mass Tansfe 9 ( [7] A.A. Yevtushenk, A. Adamwcz, P. Gzes Thee-dmensnal FE mdel f the calculatn f tempeatue f a dsc bake at tempeatue-dependent ceffcents f fctn Intenatnal Cmmuncatns n Heat and Mass Tansfe 4 ( IJRITCC June 07, (Specal Issue 055

9 Intenatnal Cnfeence n Ideas, Impact and Innvatn n Mechancal Engneeng (ICIIIME 07 ISSN: -869 Vlume: 5 Issue: [8] Al Belhcne, Mstefa Buchetaa Themmechancal mdellng f dy cntacts n autmtve dsc bake Intenatnal Junal f Themal Scences 60 ( [9] B. Ghadm, F. Kwsay, M. Kham Themal analyss f lcmtve wheel-munted bake dsc Appled Themal Engneeng 5 ( [0] Jans Feldmans, Mathematcal mdelng f dsc bake fctn lnng heat and wea May 008. [] Thmas Valvan and Kwangjn Lee, An Analytcal Methd t Pedct Themal Dsttn f a Bake Rt SAE 000 Wld Cngess Dett, Mchgan Mach 6-9, 000. [] Eskl Lndbeg, Nls-Ek Hln, Pete Ganssn, An expemental study f nte vehcle ughness nse fm dsc bake systems Appled Acustcs 74 ( [] Pete J. Blau, Ban C. Jlly, Wea f tuck bake lnng mateals usng thee dffeent test methds Wea 59 ( [4] Ph Wah Lee, Pete Flp, Fctn and wea f Cu-fee and Sb-fee envnmental fendly autmtve bake mateals Wea 0 ( [5] K. Deepka, C. Bhaska Reddy, D. Ramana Reddy, Fabcatn and Pefmance Evaluatn f a Cmpste Mateal f Wea Resstance Applcatn Intenatnal Junal f Engneeng Scence and Innvatve Technlgy (IJESIT, Vlume, Issue 6 Nvembe 0. [6] Subhass Saka, (D. Pavn P. Rathd, A. J. Md, Reseach Pape n Mdelng and Smulatn f Dsc Bake t Analyse Tempeatue Dstbutn usng FEA, IJSRD - Intenatnal Junal f Scentfc Reseach & Develpment Vl., Issue 0, 04 ISSN (nlne: -06. IJRITCC June 07, (Specal Issue 056