Vehicle Suspension Inspection by Stewart Robot

Transcription

1 Vehcle Supenon Inpecon by Sewa Robo.Kazem 1,* and. Joohan 2 Downloaded fom a 4:7 IRST on Wedneday Januay 23d an Pofeo,Depamen of Eleccal Engneeng,Shahed Unvey, Tehan, Ian.2 c Suden Eleccal Engneeng Faculy, Souhen Tehan Ilamc zad Unvey kazem@hahed.ac. bac The upenon yem of a vehcle one of he mo mpoan pa whch nvolved n he poce of vehcle degnng. When a vehcle upenon yem degned, he evaluaon of pefomance agan he oad dubance uch a hock and bump ae vey mpoan. The mo commonly ued yem con of fou hydaulc Jack wh mobly n vecal lne wh low peed and low exacude. Th pape offe a new mechanm fo npecng he upenon yem of a vehcle ung a paallel obo called Sewa. Th obo a pecal knd of paallel obo wh capably of movemen n dffeen decon wh hgh peed, accuacy and epeaably. In h pape he upenon yem evaluaed on a quae model of a mulaed vehcle wh conol and gudance of Sewa obo ung PID conolle. The Sewa obo mulae he olaed and uneven bump on a fla oad n ode o evaluae he gven upenon yem, and o nvegae ome cea uch a comfong of he paenge and emanng of he vehcle on he oad. The eul of he mulaon how ha he popoed mehod ha a hgh accuacy, applcably and flexbly a well a mplcy, compaed o cuenly ued mechanm. Keywod: Vehcle upenon, Sewa obo, Quae model of a vehcle, PID conolle. 1. INTRODUCTION The upenon yem of a vehcle he pa beween he cabn of he paenge, cha and he wheel of he vehcle whch adju he eacon of he cabn and cha n accodance o he oad. The upenon yem wee f noduced a an aemp o olve he poblem of he hock o he paenge cabn o he ca due o he anmon of foce fom he bump o he wheel and hen he paenge [1]. In he followng yea n 194 [2], moe mpovemen wee made by Wllam uh n he upenon yem and fnally n 196 ca wh he moden upenon yem wee bul [3] and a evoluon wa ceaed ncludng hock abobe whch wee nalled on flexble wooden ax. pa fom exceponal cae, h knd of png wa ued fo 25 yea n fon upenon yem afe he uh noducon. Then uddenly n 1934 [4], Geneal oo, Cyle, Hudon and ohe agan aed o make new fon upenon png and h me a png nalled fo each wheel ndvdually. Teng and aemen of applcably of each uggeed upenon yem a puu of dffeen ee whch qualfe. So fa vaou way have been uggeed fo eng [5] he upenon yem of vehcle [67]. In he convenonal e fo vehcle upenon yem, hydolc jack ae ued whch have lmaon n peed and movemen. Thee ae alo eveal eng age on he pa of upenon yem whch ae pefomed by manufacung compane bu nce hee eng age ae done ndvdually on each pa, hey canno qualfy he whole upenon yem. Due o he capable of Sewa obo [8], he pape ha popoed o ue hem fo upenon yem npecng. y nallng fou obo a he end of poducon lne and povdng hem o appopae elaed conol ofwae, he e and npecon of upenon yem can be pefomed vey fa and vey exac unde dffeen ccumance. The npecon eul hen can be ued o mpove he upenon yem and poducng a hgh qualy upenon yem. The mulaon ae done wh he ue of Smechanc fom he Smcape oolbox n he TL ofwae. The pape oganzed a follow. The dynamc and knemac equaon of Sewa obo ae analyzed Inenaonal Jounal of uomove Engneeng Vol. 2, Numbe 4, Oc 212

2 243 Vehcle Supenon Inpecon by.. Downloaded fom a 4:7 IRST on Wedneday Januay 23d 219 n Second 2. Secon 3 manly peen he modelng of upenon yem. The oveall eup and mulaon eul ae peened n Secon 4, and fnally Secon 5 conclude he pape. 2. Sewa Robo equaon Thee ae manly wo ype of he manpulao: eal manpulao and paallel manpulao. The eal manpulao ae openended ucue conng of eveal lnk conneced n ee. Such a manpulao can be opeaed effecvely n he whole volume of wokng pace. Howeve, a he acuao n he bae ha o cay and move he whole manpulao wh lnk and acuao, vey dffcul o ealze vey fa and hghly accuae moon by ung uch manpulao. a conequence, hee ae he poblem of bad ffne and educed accuacy. Paallel obo ae decbed a a cloed knemac chan n whch he ool uppoe nalled on he obo bae wh many knemac chan. Due o he hadne and capably of wokng n hgh peed and capably of lfng heavy objec of paallel obo, hee obo aaced a lo of aenon n 199 n cenfc acle and alo n nduy [8]. Solvng he nvee knemac,.e. deemnng he leg lengh once he poon and oenaon of he op plafom ae known, eay o do. Fndng he poon and oenaon of he op plafom wh he leg lengh known, howeve fa moe complcaed. Fuhemoe, he cloed mechancal chan make he dynamc of paallel manpulao hghly complex and he dynamc model of hem hghly nonlnea. So ha, whle ome of he paamee, uch a mae, can be deemned, he ohe, paculaly he fcon coeffcen, can be deemned exacly. ecaue of ha, many of he conol mehod ae no effcen afacoly. In addon, moe dffcul o nvegae he ably of he conol mehod fo uch ype manpulao [14]. Unde hee condon of unceany, a way o denfy he dynamc model paamee of paallel manpulao o ue adapve conol algohm, Fuzzy conol, nellgence echnque, ec. In ome cae he eeache ed o mplfy he obo dynamc and wh condeng ome faco and combnng he mehod baed on dynamc modelng, fndng a fae and moe accuae obo conolle whch fae bu he me conumng calculaon ae ll a man poblem. The dynamc of he paallel obo have a complcaed fomulaon becaue of he cloed loop and knemac ean. Howeve, hee ae a lo of eeache ha wok on he Sewa obo dynamc [911] Knemac In h knd of obo hee ae a goup of mechancal am whch ae all conneced o one plafom n ode o be able o gan he feelng of bendng o echng n dffeen decon wh hgh peed and hgh accuacy. I a mechancal machne wh x jack whch ae locaed n hee pa beween wo plafom, ee Fg. 1. The uppe gd body fomng he moble plafom,, conneced o he lowe gd body fomng he fxed bae plafom,, by mean of x leg. Each leg n ha fgue ha been epeened wh a phecal jon a each end. Each leg ha uppe and lowe gd bode conneced wh a pmac jon, whch, n fac, he only acve jon of he leg [3]. oon of he movng plafom geneaed by acuang he pmac jon whch vay he lengh L of he leg, q, = 1,...,6. So, ajecoy of he cene pon of movng plafom adjued by ung hee vaable. Fg1. 6dof Sewa manpulao Fo modelng he obo, a bae efeence fame ( O, x, y, z ) defned a hown n Fg. 2. econd fame ( O, x, y, z ) agned o he cene of moble plafom, O, and each leg aached o he bae plafom a pon and o he moble plafom a pon Q fo = 1,...,6. The poe of he cene pon, O, of movng plafom epeened by he veco [ ] T ovng Plafom ae Plafom x = x y z α β γ (1) Inenaonal Jounal of uomove Engneeng Vol. 2, Numbe 4, Oc 212

3 .Kazem and. Joohan 244 Downloaded fom a 4:7 IRST on Wedneday Januay 23d 219 whee x, y, z ae he caean poon of he pon O elave o he bae fame and α, β, γ ae he oaon angle, namely Eule angle, epeenng he oenaon of moble fame elave o he bae fame by hee ucceve oaon abou he x, y and z axe, gven by he mace R x ( α ), R ( β ), R ( γ ) epecvely. Thu, he oaon max y z beween he bae and moble fame gven a follow: R = R ( α) R ( β ) R ( γ ) (2) Then he nvee knemac can be analyzed by he epeenaon of any one of leg. y ung he oaon max gven by equaon (2), he poon veco of he uppe jon poon, Q, connecng he Q moble plafom o he leg, q can be anfomed o he bae fame a follow: Q o q = p + R d = 1,...,6 (3) whee o p epeen he poon veco of he cene pon of moble plafom, O, elave o he bae fame, d he poon veco of he pon Q, = 1,...,6, elave o he moble fame. Then he veco q epeenng he leg lengh beween he jon pon fame a follow: whee x y z and Q can be anfomed o he bae Q Q = q = a + q = 1,...,6 (4) a epeen he poon veco of he pon, elave o he bae fame. The leg lengh q, hen obaned by Eucldean nom of he leg veco gven above. So, ung equaon (3) and (4) we can we 2 o T o ( q ) = ( a + p + R d ) ( a + p + R d ) The leg lengh elaed o a gven poe of moble plafom can be obaned fo a ajecoy defned by he poe veco x, gven n equaon (1) Dynamc The NewonEule equaon of he decbed Sewa manpulao can be deved n a moe compac fom a decbed below [1415]:. ( q) q&& + C ( q, q& ) q& + G ( q) = τ (5) Whee, q he genealzed coodnae veco, 6 τ R he genealzed foce developed by he acuao, and G ( q) he gavy veco. The ymmecal and pove defnon max 6 6 ( q) R deemned a: T ( q) = T T (6) whee, = dag ( 1, 2,..., 13) denoe he ma and momen of nea popee of he all heen gd bode n he manpulao, and he genealzed wench veco T = [ T 1 T 2... T 13] T defned n em of he angula and lnea veloce. C ( q, q& ) he coeffcen max of he veco of Cool and cenpeal foce a gven below. T T C ( q, q& ) = T T& + T ΩT (7) whee, Ω = dag ( Ω1, Ω2,..., Ω13) denoe he angula velocy of he all heen gd bode of manpulao. Q Q q d z a O p o y x z O Fg2. Defnng he veco of Sewa obo 3. Supenon Syem odelng y x Fo degnng and modelng of upenon yem hee ae many way uch a nacve upenon, elf adjung upenon [12], emacve upenon [5] and acve upenon [7]. Snce h acle abou he upenon e and mulaon, and no conol Inenaonal Jounal of uomove Engneeng Vol. 2, Numbe4, Oc 212

4 245 Vehcle Supenon Inpecon by.. Downloaded fom a 4:7 IRST on Wedneday Januay 23d 219 uppoed o be done on he upenon yem, a quae model of nacve upenon yem ued. cve upenon yem eque exenal foce o enegy o be able o acve he conol yem pemanenly and conol he foce whch ae anfeed hough he upenon yem. In h pa a econd ode model of quae vehcle upenon yem (of nacve upenon) peened. Th model ha been ued n eveal acle and conan many mpoan chaacec of complcaed model of upenon yem. Fg. 3 how he nacve upenon yem whch placed on a Sewa obo. The dynamc equaon of a pave upenon yem fo elac ma and non elac ma ae decbed a [13] m z&& ( ) + c [ z& ( ) z& ( )] + k [ z ( ) z ( )] = u u m z&& ( ) + c [ z& ( ) z& ( )] + k [ z ( ) z ( )] + u u u u + k [ z ( ) z ( )] + c [ z& ( ) z& ( )] = whee, u u m he elac ma (quae of he ma of (8) cha ma), m u nonelac ma (he ma of wheel goup), c and k ae he dampng coeffcen and he hadne of png n pave upenon, c and k ae dampng coeffcen and conacly of pneumac e. z ( ) and z u ( ) ae movemen of z z u c m m u k elac ma and nonelac ma and z ( ) he movemen of Sewa obo o mulae he movemen of oad a an npu. The ae vaable defned a x ( ) = [ x 1( ) x 2( ) x 3( ) x 4( )] T,whee x ( ) ( ) ( ) 1 = z z u he devaon of upenon pa, x ( ) = 2 z ( ) z ( ) he e devaon, x ( ) ( ) 3 = z& he u velocy of elac ma and x ( ) ( ) 4 = z& u he velocy of nonelac ma. Then he ae pace equaon of he yem can be expeed a follow. x& ( ) = x ( ) + u ( ) (9) whee, =, =, k c c (1) c m m m m u k k c ( c + c ) mu mu mu mu u ( ) = z& ( ) Ca Supenon Wheel z c k Te Sewa Fg3. Pave model of a quae ca upenon yem wh Sewa obo. Inenaonal Jounal of uomove Engneeng Vol. 2, Numbe4, Oc 212

5 .Kazem and. Joohan 246 Downloaded fom a 4:7 IRST on Wedneday Januay 23d 219 Refeence Geneao q Conolle paamee value Fg4. Conol yem confguaon Table 1. Paamee of pave vehcle upenon yem fo quae model m 32 Kg k 18 N/m The yem mulaed n Smechanc oolbox of TL ofwae. The dance beween he wheel ax and he moble plafom condeed a 3 cenmee (non conaced poon e). In ac balance, boh png hown n Fg. 3 wll be conaced. The conacon amoun can be calculaed hough he followng equaon. m g 2 k x = m g x =, g = 9.81m k (11) ( m + mu ) g k x = ( m + mu ) g x = k The ma cene n balance uaon wll be locaed on he z ax whch mean.3 x. The upenon and cha ma of he ca ae alo defned ame a wheel and e goup (a anmon jon and a ma). The naual lengh of upenon condeed a 6 cm (whou any peue due o vehcle wegh). 4. Oveall Seup and Smulaon Reul τ Sewa anpulao Dynamc q q& Combnaon of quae upenon yem model o Sewa obo he nex ep fo ceang a unfed mechancal model. The bae plafom of Sewa obo conneced o he gound and he each wheel of vehcle locaed on one Sewa obo. When he e ouche he moble plafom, he quae vehcle Knemac odel of Sewa c 1 N./m m u 4 Kg x k 2 N/m Supenon Syem Dynamc z y upenon yem model can be combned o Sewa obo model and a unfed mechancal model acheved. fe achevng he whole obo and upenon yem hough he elaon beween he obo uppo lengh and moble plafom, he conol command wll be changed no he uppo lengh command. Then conol of he moble plafom whch condeed a he oad uface n h econ, wll be done by ue of a PID conolle. In h way by a cloed loop conol ucue a Fg. 4, he dffeen oad ccumance ae povded fo npecng he upenon yem. PID conolle condeed fo he obo movemen a follow: K N Gc ( ) = K p + + K (12) d + N Whee, N he fle ably on devave pa whch condeed equal o 1. The conolle uned fo achevng maxmum 2% ovehoo and pemanen eo lowe han 5%. In degnng a upenon yem hee cea ae uually aken no condeaon; (1): paenge comfo, (2): lmaon of devaon n upenon pa, (3): ably o eman on he oad. cceleaon of he elac ma can be eaed a comfo of he paenge,.e. defnng he f oupu of upenon yem, y ( ) ( ) 1 = z&&, a a cea fo comfong of paenge. In ode o peven any ham o he c Inenaonal Jounal of uomove Engneeng Vol. 2, Numbe 4, Oc 212

6 247 Vehcle Supenon Inpecon by.. Downloaded fom a 4:7 IRST on Wedneday Januay 23d 219 paenge and afyng he comfong of avele, devaon ocllaon of he vehcle upenon pa hould be deceaed. So he followng conan can be condeed fo he upenon yem, x ( ) = z ( ) z ( ) z (13) 1 u max whee z max he maxmum accepable devaon of upenon pa n dffeen oad condon. To have a connuou conac beween he e and he oad, equed ha he ac load of he e be geae han dynamc load,.e. k [ z ( ) z ( )] < 9.8( m + m ) (14) u u f we analyze he cloed loop yem (he combnaon of Sewa obo and upenon yem wh he PID conolle) wh ep epone. me =.5 ec. a movemen abou 1 cm n he decon of z ax, commanded o Sewa obo o mulae he oad dplacemen. The op plae movemen of he obo hown n Fg. 5. Fgue 6 and 7 how he dplacemen and acceleaon of cha ma cene epecvely. Devaon of upenon pa, wheel dplacemen, and movemen of he cene of wheel goup ma cene, ae hown n he fgue 8 o 1 epecvely. In geneal a good upenon yem hould be able o abob he foce whch mpoed o he ca by he oad bump and o damp lghly. Road Dplacemen (Top Plae Poon) Fg5. Sep epone of he Sewa obo Fo eng and evaluang he uggeed degn, olaed bump and uneven bump on fla uface oad ae mulaed by he obo and hen comfong of he paenge and emanng he vehcle on he oad, ae nvegaed. Ca Cha Dplacemen [m] Fg6. Devaon of cha ma cene fo ep oad dplacemen Ca Cha cceleaon [m/ 2 ] Fg7. The acceleaon of he ca cha ma cene fo ep oad dplacemen Supenon Deflecon [m] Fg8. Devaon of upenon pa epone fo ep oad dplacemen Inenaonal Jounal of uomove Engneeng Vol. 2, Numbe 4, Oc 212

7 .Kazem and. Joohan Downloaded fom a 4:7 IRST on Wedneday Januay 23d 219 Wheel Dplacemen [m] Fg9. Wheel devaon fo ep oad dplacemen In he f mulaon an olaed bump on a fla uface oad ued o hock he upenon yem. The dplacemen due o oad uface can be epeened a follow [13]: a 2πυ l (1 co( )) 2 l υ z ( ) = (15) l > υ whee a and l ae he hegh and lengh of he bump and υ he velocy of hozonal movemen of he ca. In he pefomed mulaon n h age he above paamee ae condeed a: a =.15 m, l = 5 m, and υ = 6 km h. The cuve nuodal wave fom wh hegh of 15 cm, whee wdh elaed o he hozonal velocy of he ca. Th cuve appled o he obo wo me. The acceleaon of he ca cha hown n Fg. 11 o check comfong of he paenge. Fgue 12 how he dplacemen of cha ma cene elave o he gound uface. The ubulence of he cha ma cene wll connue fo abou 3 econd. The peak of dplacemen of cha ma cene of he ca alo abou 12.5 cm whch le han he peak of oad bump (15 cm). Devaon of upenon lengh alo hown n Fg. 13. The hghe allowable change n he lengh of upenon pa fo he eleced yem z max =.8 m. we can ee n he Fg. 13, he maxmum devaon of upenon pa (abou 11 o 12.5 cm) hghe han allowable ange, o he upenon yem ha encouneed o a poblem fo olaed bump and anfe heavy hock o he png and hock abobe. Noe ha nce he png Te Deflecon [m] Fg1. Dplacemen of he cene of wheel goup ma cene coeffcen of he wheel goup hgh, expeced ha he dplacemen of he oad uface decly anfeed o he wheel ma cene. The ably of he ca o manan on he oad, can be checked by compang he dynamc and ac load mpoed on he e. The ac load can be calculaed hough F = g ( m + m ), whch mple u ha F = 3528 N. The amoun of he dynamc load, calculaed hough Fd = k [ z u ( ) z ( )], hown n Fg. 14. I how ha fo olaed bump wh he nal peed of 6 km h, he e doe no loe conac wh he oad uface. In he nex ep, an uneven bump on fla uface oad ued o npec he eacon of upenon yem o h hock. Fo h pupoe, he followng equaon condeed fo he dplacemen of he oad [13]: l a υ l z ( ) = a (16) υ ohewe whee, a and l ae hegh and lengh of he bump and υ he hozonal peed of he ca. In ou mulaon, he paamee ae condeed a befoe. Snce he mulaon eul how he mla behavo, gnoed o how hem becaue of nceang he numbe of fgue. Ju he cuve of dynamc load on he e hown n he Fg. 15. Inenaonal Jounal of uomove Engneeng Vol. 2, Numbe4, Oc 212

8 249 Vehcle Supenon Inpecon by Downloaded fom a 4:7 IRST on Wedneday Januay 23d 219 Ca Cha Dplacemen [m] Ca Cha cceleaon [m/ 2 ] Tme(Sec Fg11. The acceleaon of he ca cha fo olaed bump Fg12. The dplacemen of cha ma cene fo olaed bump.1. Supenon Deflecon [m] Tme(Sec Fg13. Devaon of upenon lengh fo olaed bump Inenaonal Jounal of uomove Engneeng Vol. 2, Numbe 4, Oc 212

9 .Kazem and. Joohan Downloaded fom a 4:7 IRST on Wedneday Januay 23d 219 Te Dynamc Load [N] Te Dynamc Load [N] Tme(Sec Fg14. Dynamc load on he e fo olaed bump 4 x I how ha, n h cae, he e of he ca loe conac wh he oad uface fo a ho whle. 5. Concluon Th pape peened a new mechanm fo npecng he upenon yem of he vehcle ung paallel obo o called Sewa. I wa mulaed ove a quae model of a ca and he eacon of he upenon yem uch a e, png and hock abobe wee uded. PID conolle wa ued o conol and gudance of he Sewa obo. I wa Fg15. Dynamc load on he e fo uneven bump hown ha any oad deflecon can be mulaed by mpong a uable ajecoy o he obo. The uggeed upenon yem wa evaluaed by applyng olaed bump and uneven bump on fla uface oad. Some opeaon cea uch a comfong of paenge and emanng of he vehcle on he oad, wee nvegaed fo dffeen oad ubulence. The mulaon eul how a afacoy accuacy and applcably fo he popoed yem compaed o he commonly ued yem. In he mo commonly ued yem hee ae fou hydaulc Jack wh mobly ju n vecal decon wh low peed and low accuacy, whle wh he popoed yem able o e he Inenaonal Jounal of uomove Engneeng Vol. 2, Numbe4, Oc 212

10 251 Vehcle Supenon Inpecon by.. Downloaded fom a 4:7 IRST on Wedneday Januay 23d 219 upenon yem agan o any foce n any decon wh hgh peed and hgh accuacy. Refeence [1]. Shgeo Hoe, Takaya Shau and Edwado F. Fukuhma, Popoal Fo Coopeave Robo ``Gunyu'' Compoed of uonomou Segmen, Roboc and uonomou Syem, vol. 17, pp , (1996) [2]. J. Lenacc and. Roh, dvance n Robo Knemac: mechanm and moon, Dodech, The Neheland, Spnge, 26. [3]. J. H. Ryu, Paallel anpulao: New developmen. ITech Educaon and Publhng, 28. [4]. J. P.ele, Paallel Robo (Sold echanc nd I pplcaon), Spnge,26. [5]... Peng, X.Q. Huang, Smulaon Te ehod fo Half Semacve Vehcle Supenon aed on he Heachcal odelng ehod, IEEE Inenaonal Confeence on: Vehcula Eleconc and Safey, ICVES, 26. [6]. P. G. Wgh and D.. Wllam, The applcaon of cve Supenon o Hgh Pefomance Road Vehcle, Poccedng of IECH Confeence on copoceo n flud powe engneeng, echancal Engneeng Publcaon, London, [7]. D.. Colla and... boul Nou, Thoecal Compaon of Vaou cve Supenon Syem n Tem of Pefomance and Powe Reouemen, Poceedng of IECE Confeece on dvanced Supenon, Ocobe [8]. V.E. Gough and S. G. Whehall, Unveal Type Te achne, n Poc.9h In. Tech. Conge FISIT, 1962, pp [9]. Z. Geng, L. S. Hayne, J. D. Lee and R. L. Caoll, On he Dynamc odel and Knemac naly of cla of Sewa Plafom, Roboc and uonomou Syem, Vol. 9, No. 4, pp , [1]. G. Lebe, K. Lu and F.L.Lewe, Dynamc naly and Conol of a Sewa Plafom anpulao, Jounal of Roboc Syem, Vol. 1, No. 5, pp , [11]. C. D. Zhang and S.. Song, n effcen ehod fo The nveed Dynamc of anpulao aed on he Vhal Wok Pncple, Jounal of Roboc Syem, Vol. 1, No. 5, pp , [12]. T. K. Gae, K. Newon and W. Seed, oo Vehcle, 13h Edon, uewoh Henemann, 2. [13]. D. Hova, Suvey of dvanced Supenon Developmen and Relaed Opmal Conol pplcaon uomaca, 33, pp , [14]. H. Fang,. Zhou, H. Xu, and Z. Feng, Sably analy of ajecoy acng cono1 of 6dof paallel manpulao, Poceedng of he 3d Wold Conge on Inellgen Conol and uomaon, IEEE, Vol. 2, pp , 2. [15]. W.. Khan, V.N. Kov, S.K. Saha, and J. ngele, odula and ecuve knemac and dynamc fo paallel manpulao, ulbody Syem Dynamc, Vol. 14, No.3 4, pp , 25. Inenaonal Jounal of uomove Engneeng Vol. 2, Numbe 4, Oc 212