Optimized Braking Force Distribution during a Braking-in- Turn Maneuver for Articulated Vehicles

Transcription

1 56 Opmzed Bakng Foce Dsbuon dung a Bakng-n- Tun Maneuve o Aculaed Vehcles E. Esmalzadeh, A. Goodaz and M. Behmad 3 Downloaded om a 3:04 IRST on Fday Novembe 3d 08,* Faculy o Engneeng and Appled Scence, Unvesy o Onao Insue o Technology, Oshawa, Onao, Canada, ezadeh@uo.ca Auomove Engneeng Depamen Ian Unvesy o Scence and Technology, Tehan, Ian, a_goodaz@us.ac. 3 Auomove Engneeng Depamen Ian Unvesy o Scence and Technology, Tehan, Ian, behmad@yahoo.com Absac Impovemen n bakng peomance and vehcle sably can be acheved hough he use o bakng sysems whose bake oce dsbuon s vaable. Eleconc bakng oce dsbuon has an mpoan and seous ole n he vehcle soppng dsance and sably. In hs pape a new appoach wll be pesened o acheve he bakng oce dsbuon saegy o aculaed vehcles. Fo hs pupose, he mahemacal opmzaon pocess has been mplemened. Ths saegy, dened as an nnovave bakng oce dsbuon saegy, s based on he wheel slps. The smulaon esuls llusae poposed saegy can sgncany mpove he vehcle sably n cuved bakng o deen levels o vehcle deceleaon. Keywods: vehcle dynamcs, bakng oce dsbuon, opmzaon, aculaed vehcles. INTRODUCTION In bake sysem desgn o a vehcle, he s consdeaon should be he bakng peomance. The bakng sysem has o be able sop o educe he vehcle speed as quckly as possble and manan he vehcle avelng decon sable and conollable a any oad condons []. A key aspec o good bakng peomance s ha bakng s balanced. Ths occus when each wheel bakes popoonal o he wegh ha caes. I hs deal s acheved hen he vehcle can use all he avalable oad con and wll have he mnmum soppng dsance whou skddng wheels. heel lock-up pomoes loss o deconal conol, paculaly when occus on dve o ale ales, because he locked wheel canno povde sablzng sde oces []. The load sensng popoonng valve (L.S.P.V employed o adjusng bakng oce among ales o he nomal oces on hose ales and closed acual bake oce o deal bake oce dsbuon. These valves opeae based on he sac delecon o he ea suspenson, bu hey ae no able o compensae o he dynamc load anse beween he on and ea ales [3,4]. Aculaed vehcles sably, much lkes o cas, eques ha he aco on ale locks s, and ollowed by he ale ale, wh he aco ea ale lockng up las [5,6]. In he moden bakng sysems, such as eleconc bake oce dsbuon (EBD sysems, usng sophscaed algohms omed based on slp conol appoach; he bakng oce dsbuon s done nellgeny leads o hghe sably and shoe soppng dsance. In hs pape an nnovave appoach o omulae a new bakng oce dsbuon saegy o aculaed vehcles s pesened whee, he mahemacal opmzaon pocess has been ncluded. The opmzed saegy as he ohe moden bakng oce dsbuon saeges, woks based on wheel slp conol.. CLASSICAL BRAKING FORCE DISTRIBUTION Classcally, o sagh-lne bakng on a level suace n he absence o any aeodynamc eecs, desed bakng n ems o mamum deceleaon s dened as: a ( hee a s dmensonless vehcle deceleaon (guns and, and ae e-oad con coecen o especvely aco on ale, aco ea ale and ale ale. Fo an aculaed vehcle, he ale loads o he aco un ae nluenced by boh he loadngs and bakng oces o he ale un [7]. Usng he emnologes gven n Fgues ( and (, he equaons o oce and momen equlbum Inenaonal Jounal o Auomove Engneeng Vol., Numbe, Januay 0

2 E. Esmalzadeh, A. Goodaz, M. Behmad 57 Downloaded om a 3:04 IRST on Fday Novembe 3d 08 balance yeld as he dynamc ale loads. Fz. y.( Fz ( (3 (4 In he deal condon, namely, a =, all he avalable oad con s ulzed and he bake oces ae decy elaed o he dynamc ale loads. The deal bake oce on each ale can be compued om he ollowng equaons: F F a ( m a a ( y a z F Fz. m ( m y a.(. z Fg.. Dynamc model o he aco un [7].( m ( m ( y a( z ( Fg.. Dynamc model o he ale un [7]. m. a.( z F. z z F ( z a ( m a a m a ( z a a z z ( y F ( z m a a z m a ( y a z a z y. z ( z yz (5 (6 (7 The gaphcal epesenaon o Equaons (5, (6 and (7 o a specc vehcle, s llusaed n gue (3 n empy and laden suaon. Any pon on he Fg. 3. Nomalzed dynamc ales beak oce o classcal dsbuon classcal bakng oce cuve epesens opmum bakng,.e., a condon unde whch he e-oad con coecen o on ale and ea ales ae equal o dmensonless vehcle deceleaon. 3. MODERN APPROACH TO BRAKING FORCE DISTRIBUTION In he moden sysems, known as Eleconc Bake oce Dsbuon sysems (EBD, he bake oces ae dsbued usng an acve eleconc conol sysem whch use wheels slp eedback o conol he bake oce dsbuon. An eleconc bake oce dsbuon ulzes he ABS hadwae o uncon as an nellgen bake popoonng valve. Unlke a adonal mechancal popoonng valve whch s lmed by desgn o knee pon and slope, he EBD algohm eles on closed-loop eedback o connuously mono wheels slp, adjusng bake lne pessue o he ea wheels as appopae. The basc dea o developng he conol algohms o a common EBD sysem s ha he slp deence beween he on ale and he ea ales should be made mnmal o heoecally equal [8]. S S S (8 hee S and S ae especvely on and ea aco wheels slp and S s ale wheel slp. The combnaon o vehcle dynamc equaon dung bakng, longudnal load anse equaons and pue slp magc omula e model [9] ae consdeed and solved smulaneously: F F F ( a hee (9 Inenaonal Jounal o Auomove Engneeng Vol., Numbe, Januay 0

3 58 Opmzed Bakng Foce Dsbuon dung... Downloaded om a 3:04 IRST on Fday Novembe 3d 08 Fg. 4. Compason o classcal bake dsbuon and equal slps dsbuon F D sn( C an an ( B S E ( B S ( B S ( Fz, S (0 By addng he Equaon 8 o Equaon 9 and solve hem numecally we'll gue ou ha he equal slp on he aco and ale wheels esul n a bakng oce dsbuon as same as classcal dsbuon. I s shown n he gue (4 ha he cuve o Ideal bake oce dsbuon lays ove he cuve o equal slps saegy. 4. OPTIMIZED BRAKING FORCE DISTRIBUTION I was shown ha he equal slps saegy s same as he classcal bakng oce dsbuon n sagh lne bakng. Bu s well known ha he bakng oces n a sagh lne bakng ae deen om bakng oces dung a un. The Laeal e oce may decease he e bakng oce; hence bakng oce n bakng-n-un may be smalle han coespondng value n he sagh lne bakng. In addon o ha, hee s a laeal load anse n unng maneuve causng nequaly n he bakng capacy o he sdes wheels o an ale hen s noable ha such a saegy may be able o povde mnmum soppng dsance [0] bu dose no he opmum saegy om he vehcle deconal sably pon o vew. To mpove deconal sably dung bakng, aco ea wheel slp mus be smalle han Tale wheel slp and Tale wheel slp mus be smalle han aco on wheel slp. So, accodng o he above dscusson we have omed a new non-equal slps, opmzed saegy, based on classcal consaned opmzaon heoy. The poposed opmzaon saegy manans he bakng deceleaon o be unchanged when compang o he above adonal saegy bu wll conol he wheels slps n such a way ha hey should :,, be loweed as much as possble. Moeove, he aco ea wheel slps should always be kep lowe han he ale wheel slps and n ode o mpove he vehcle sably he ale wheel slps should always be kep lowe han he aco on wheel slps. Fo hs pupose, he opmzed saegy o he bake n un suaon wll be developed. The consaned opmzaon poblem could heeoe, be saed as ollowng: g hee S l : Fon le wheel slp; S l : Rea le wheel slp; S : Tale le wheel slp; ( S : Fon gh wheel slp S : Rea gh wheel slp S : Tale gh wheel slp And Fl F Fl F F F ( ( a 0 hee g s he objecve uncon whch mus be mnmzed and equaon ( ndcaes he consan equaon whch llusaes he unchanged deceleaon condon. The weghng acos w, and w have been used o conol he amoun o he aco ea wheel slps and he ale wheel slps elave o he aco on wheel slps. Opmzaon pocedue could be omulaed by usng he Lagange echnque. Applng opmzaon pocess and smplyng leads o he ollowng equaons: l ws l S 0 S S w S S l l l S l l S S l w ( S w S l l 0 l 0 ( S w ( S 0 l S l (3 (4 (5 (6 Inenaonal Jounal o Auomove Engneeng Vol., Numbe, Januay 0

4 E. Esmalzadeh, A. Goodaz, M. Behmad 59 Downloaded om a 3:04 IRST on Fday Novembe 3d 08 (7 (8 Based on he combned slp magc omula e model [9], he bakng oce F s a uncon o longudnal slp S, sde slp angle and e nomal oce F z. Nomal oce o each wheel s a summaon o sac vehcle wegh's em and laeal/ longudnal load anses ems. Fo calculang slp angles s consdeed he seady sae consan adus un condon [] as shown n he gue (5 and also s assumed ha he slp angles o boh wheels o each ale ae equal. Fon, ea and ale slp angles can be epessed based on laeal acceleaon a y as ollowng (The ogn o boh aco and sem ale has locaed a he common pon o he h wheel couplng: F ( a 0 l Fg. 5. Lnea Model o Aculaed vehcle [0] S ( l S ( l F F l F ( Lmvd dlm blm bm dm. a y C L ( a b Lma dlm m a dm Lmvd. a L C ( a b L ma Lmd m d m a Lmvd. a y L C ( a b l l F F (9 (0 ( hee C, C and C especvely ae oal laeal sness o on and ea ales o aco and ale ale besdes mv, m and m ae aco mass, ale mass and oal mass especvely. Now he opmzed bakng oce dsbuon o bake-n-un suaon y Slp Slp can be numecally ound ou. By consdeng speced values o longudnal deceleaon a and laeal acceleaon a y, he equaons (3 o ( can be numecally solved o S l, S, S, S l, S and S. The opmzed slps o a specc vehcle, whch bakes on a day bend wh deen longudnal deceleaon and deen laeal acceleaon, have been calculaed and some o hem have been llusaed n he gues (6 and (7. Accodng o he gues as a geneal end, o deen deceleaon values, he opmzed slps o le sde wheels (ousde wheels ae nceased and he opmzed slp o gh sde wheels ( nsde wheels ae deceased compang o sagh lne bakng values (a y =0. I s due o changng he nomal oce o each wheel as a esul o longudnal/laeal load anse. The unequal dsbuon o le/gh wheels slp o each ale, can leads o much moe negave yaw momen, senghenng he unde see behavo o he vehcle. Also s ound ou, by appopae weghng acos adjusmen, he desed wheel slp scheme o each ndvdual wheel as a uncon o longudnal and laeal acceleaons could be acheved. 5. SIMULATUIN FL_Slp Mu=0.9 w=, w= ay=0 ay=0.g ay=0.4g ay=0.6g deceleaon (a/g Fg. 6. Desed slp value o on le wheel TR_Slp Mu=0.9 w=, w= ay=0 ay=0.g ay=0.4g ay=0.6g deceleaon (a/g Fg. 7. Desed slp value o ale gh wheel In ode o evaluae he peomance o he opmzed bakng oce dsbuon saegy a pecse Inenaonal Jounal o Auomove Engneeng Vol., Numbe, Januay 0

5 60 Opmzed Bakng Foce Dsbuon dung... Downloaded om a 3:04 IRST on Fday Novembe 3d 08 Fg. 8. Block dagam o he poposed EBD sysem Fg. 9. Smulaed longudnal deceleaonfgue0. Smulaed laeal acceleaon Fg. 0. Smulaed laeal acceleaon Fg.. Smulaed aculaon angle (Hch compue smulaon has been peomed. The poposed saegy s consdes as a pa o a specc eleconc bakng oce dsbuon (EBD sysem. Fgue 8 llusaes he sysem s block dagam. Accodng o he gue, he sysem s npu s dve s bake pedal oce. Based on pedal oce deceleaon Fg.. Smulaed sde slp angle Fg. 3. Smulaed aco yaw ae cuve, dve s desed deceleaon s calculaed popoonal o pedal oce. In he hghe level o he conol sysem, based on desed deceleaon s value, esmaed oad con and measued laeal acceleaon, desed slp o each wheel s calculaed based on opmzed bakng oce dsbuon saegy. The saegy s ulzed n he om o pe-calculaed lock-up able. In he lowe laye, he desed slps ae acualzed by he slp conolle un, whch can be a common ABS conol algohms. To smulae he vehcle dynamc behavos, a 0 degee o eedom vehcle dynamc model [] wh "Combned Magc Fomula" non-lnea es model [9] has been used. Also o compae he peomance o deen ypes o conol saeges, ou deen vehcles have been consdeed: A vehcle whou any knd o EBD sysem, nomnaed as No Conol. A vehcle equpped wh common EBD sysem, nomnaed as equal slp. A vehcle equpped wh poposed EBD sysem, nomnaed as opmzed Slp. The smulaon sudy consss o bakng dung a sep seeng. In hs sudy, had bakng on a dy oad ( =0.9 has been suded. Smulaneously, 5 degees sep see npu apples o he on wheels. The nal speed s 5 m/s. Fgues (9 o (3 show he smulaon esuls. Inenaonal Jounal o Auomove Engneeng Vol., Numbe, Januay 0

6 E. Esmalzadeh, A. Goodaz, M. Behmad 6 Downloaded om a 3:04 IRST on Fday Novembe 3d 08 Accodng o he gue (9, he me hsoes o he conolled vehcles deceleaon s appomaely he same. Bu n he case o he whou conol vehcle due o necen dsbuon o bakng oce he deceleaon s 5% lowe, leadng o longe soppng dsance. In spe o smla longudnal dynamcs behavo, hanks o opmum bakng oce dsbuon, opmzed saegy can povde much bee laeal dynamc behavo han whou conol o even equal slps saegy. Fgues (0 o (3 llusae especvely he laeal acceleaon, hch angle o he aculaed vehcle, sde slp angle and yaw ae o aco un ha n all ove gues, opmzed saegy has bee laeal dynamc behavos whch mpoves he vehcle sably. 6. CONCLUSION I s well known ha o acheve sable and sae bakng, he aco ea wheels slp mus be less han ale wheels slp and hey mus be less han aco on wheels slp. Accodng o hs smple ule, common bakng oce dsbuon sysems wok based on a smple saegy known as equal slp saegy. In hs saegy he on and ea wheels slps ae heoecally se o he same value. Such a smple saegy canno be peec. By keepng he oal bakng oce unchanged, he on wheels poon can be nceased unlke he ea wheels poon s deceased. On he ohe wod, he on wheels slp se o much hghe value o ea wheels slp leads o moe sably. The ohe neesng pon s unequal bakng capacy o le/gh wheels dung a bakng n un maneuve. So an nellgen bakng oce dsbuon saegy mus egulae he le/gh wheels slps as well as on/ea wheels slps n deen values. Damacally such an appoach can lead o an unequal bakng oce dsbuon no only longudnally bu also laeally. In hs pape usng opmzaon heoy, has been ed o omulae he above menon Idea. The socalled opmzed bakng oce dsbuon saegy keeps he deceleaon value and hence soppng dsance o he vehcle unchanged compang o he classcal bakng oce dsbuon saegy. Bu nellgeny dsbues he bakng oce beween he s wheels unequally, based on he equesed longudnal deceleaon and known laeal acceleaon. The smulaon esuls show much moe sable behavo o he aculaed vehcle usng he opmzed saegy dung had bakng un suaon compang o adonal equal slp saegy. REFERENCES [] G. Ymn, M. Ehsan, eleconc bakng sysem o EV and HEV negaon o egeneave bakng, auomac bakng oce conol and ABS, SAE [] P. Ha, Naonal heavy vehcle bakng saegy dscusson pape, Naonal Tanspo Commsson, ISBN: Febuay 006 [3] L. Palkovcs, A. Fes, "Inellgen eleconc sysems n commecal vehcles o enhanced ac saey ", Vehcle Sysem Dynamcs Vol. 35, no. 4-5, pp May 00 [4] F. Lueck,. Gaand, M. Denholm, "Popoonal valve o skd conol--a logcal pogesson," SAE Pape No , May 969. [5] R. Lmpe, An nvesgaon o he bake oce dsbuon on aco-semale combnaons, SAE 70044, 97 [6] M-. Suh, Y-K. Pak and S-J. Kwon, A Smulaon pogam o he bakng chaacescs o Taco-Semale vehcle, SAE pape [7] R. Lmpe, Bake desgn and saey, SAE Ode No. R-98, 999 [8] P. Fank, Slp conol a small slp values o oad vehcle bake sysems, Peodca Polyechnca SER. MECH.ENG. 000, Vol. 44,No.,PP [9] H.B. Pacejka, "Te and vehcle dynamcs", publshed by Elseve, 00. [0] E. Goehng,, "Evaluaon o he bake-oce dsbuon And Is Inluence on he bakng peomance o lgh commecal vehcles", SAE 80053,980 [] J.R. Ells, Vehcle handlng dynamcs, Mechancal Engneeng publcaons Lmed, London 994, pp. 5-7 Inenaonal Jounal o Auomove Engneeng Vol., Numbe, Januay 0