Damper Tuning with the use of a Seven Post Shaker Rig

Transcription

1 SAE TECHNICAL PAPER SERIES Dme Tuning wih he ue of Seven Po She Rig Heni Kowlzy ARC Indinoli-Reynd Mooo SAE 00 Wold Conge Deoi, Mihign Mh 4-7, Commonwelh Dive, Wendle, PA USA Tel: F:

2 The ene of hi ISSN ode he oom of hi ge indie SAE onen h oie of he e my e mde fo eonl o inenl ue of eifi lien Thi onen i given on he ondiion, howeve, h he oie y e ile oy fee hough he Coyigh Clene Cene, In Oeion Cene, Roewood Dive, Dnve, MA 093 fo oying eyond h emied y Seion 07 o 08 of he US Coyigh Lw Thi onen doe no eend o ohe ind of oying uh oying fo genel diiuion, fo dveiing o omoionl uoe, fo eing new olleive wo, o fo ele Quniy ein e n e oined fom he Cuome Sle nd Sifion Demen To eque emiion o ein ehnil e o emiion o ue oyighed SAE uliion in ohe wo, on he SAE Puliion Gou All SAE e, ndd, nd eleed oo e ed nd indeed in he Glol Moiliy De No of hi uliion my e eodued in ny fom, in n eleoni eievl yem o ohewie, wihou he io wien emiion of he ulihe ISSN Coyigh 00 Soiey of Auomoive Enginee, In Poiion nd oinion dvned in hi e e hoe of he uho nd no neeily hoe of SAE The uho i olely eonile fo he onen of he e A oe i ville y whih diuion will e ined wih he e if i i ulihed in SAE Tnion Fo emiion o ulih hi e in full o in, on he SAE Puliion Gou Peon wihing o umi e o e onideed fo eenion o uliion hough SAE hould end he mnui o 300 wod of ooed mnui o: Seey, Engineeing Meeing Bod, SAE Pined in USA

3 Dme Tuning wih he ue of Seven Po She Rig Coyigh 00 Soiey of Auomoive Enginee, In Heni Kowlzy ARC Indinoli-Reynd Mooo ABSTRACT Re nioning odie hve egun o dilly limi he nume of dy ville o e em fo eing in ode o onin o Due o he limied moun of ime ville i h eome ineingly diffiul o eloe nd eloi ll of he oile hnge h n e mde o he in ode o imove i efomne Thu even o eing i eoming moe widely ued y e em o oimize hei uenion efoe iving he e A even o ig, he nme imlie, omie even uo Fou uo e ued o imule he od inu, while he ohe hee uo e ued o imule downfoe nd ineil loding The ig he ARC i le of eoduing viou wvefom, inluding he iliy of imuling inu Thi e deie modl eing of he, whee he mode of inee e he igid ody mode of he : heve, ih nd oll Fuue wo will e onened wih eul ed on imulion eing Thi e deie how even o ig i ued o oimize he uenion of e A que model well even degee of feedom model wih ung m feedom of heve, ih nd oll, nd veil feedom of eh unung m, will e develoed Simulion eul fom he model will e ued o illue he inile involved when uning he uenion of e The eul of he imulion will e eled o he el wold y howing eul oined fom n ul even o e of Chm INTRODUCTION Thi e deie he ue of he even o ig he Auo Reeh Cene ARC in Indinoli o une e uenion Thi filiy h een in oeion ine ely 999 nd i ued y em in vied mooo egoie nging fom oen wheel e o o The ARC i e filiy oniing of 50% olling od wind unnel nd even o he The even o he i uni mnufued y Sevoe lede in hyduli e equimen Sevoe uenly ovide even o he o mo of he Fomul em, well develoing he fo NVH nd eimi eing The Sevoe yem diffe fom mny ohe he in h i i ue even o yem Mny he ig e fou o ig h hve een eofied wih ing h llow fo he liion of i eo lod The min dw o hi mehod i h y hing ing fom he gound o he he dynmi of he e leed The Sevoe yem on he ohe hnd ue n ive onol yem h i uned o hve miniml im on he dynmi of he In he ing induy, dme uning i een omewh of n A foe-veloiy uve fo dme i loely guded ee Dme enginee e hee uve on ye of eeiene of wh iul need Someime, when fed wih new iuion dme enginee will ely on heoy ed on que

4 model Howeve, oh of hee mehod hve hei hooming Dme ed on eeiene e uully develoed fom dive feed, hu hey my o my no e nfele o ohe dive o Dme ed on imle line model do no e dvnge of non-line iliie of moden e dme In ode o fully undend he non-line dynmi of he vehile, non-line model of oh he nd dme mu e eed The ime equied o uild nd vlide model of hi omleiy i eyond he udge of mo e em, hu he even o ig i ueful ool fo he em o ue in he oimizion of hei uenion In ode o ee meningful e nd nlyi oedue fo ny yem, i dynmi mu e undeood le i level Simulion n e ued o undend he dynmi of he yem Thee imulion n e ueful in deviing e mehod nd nlyi oedue A he ARC we hve develoed i model of he veil dynmi of he in ode o imove ou eing mehodology on he he ig Thi e deie he model, how hey ele o he eul oeved on he ig, nd finlly he eul of n ul e e deied illuing he vlidiy of he finding of he model The moun of d olleed on he even o ig n quily eome ovewhelming; he model deied in hi e hve llowed u he ARC o fou ou nlyi of he d geneed y he even o ig TEST PROCEDURE Ou uen eing mehodology oni of eiing he wih we ine whee ll he wheeln e in he heve inu nd minimizing he ih nd heve We hve een ueful uing hi fom of oimizion wih vied fom of mooo nging fom high downfoe oen wheel e o NASCAR Winon Cu The fi e in he e oedue i o deemine he inu o he Fi he downfoe level e deemined fo given oneing enio Then he wheeln inu mliude i vied unil he owe el deniy PSD of he dme dilemen ignl i imil o wh i een on he Sine he inu we e uing i no he me he inu of he ufe, he PSD will no ely mh The im i o no ove o unde eie he One he inu mliude h een hoen he oimizion n egin In i mo i fom, he ole uoe of uenion dme i o diie he enegy oed in he ing If hi wee i only uoe, hen he oimizion of he dme would e elively imle endevo nd would equie only minimizing he eonn eone of he viou mode Howeve, in n uomoile uenion he dme eve eondy uoe, onolling lod nfe in nien mneuve How he lod nfe i onolled y he dme i iil in giving he dive he feed h he need o dive he i limi In wih gound effe eodynmi, he dme i lo ued o onol he iude of he The uning of he dme fo he le wo equiemen i guided y dive feed Tuning fo he eonn eone n e ied ou wih he hel of he even o he Alhough he end eul i no neeily dme omleely oimized o minimize eonn eone, hee eone e uully edued unilly hough he oue of e eion he he MODEL DERIVATIONS The following eion deie he veil dynmi of, nd how wh n e done o oimize i eone Thee model illue he eul h n e eeed fom he oimizing wo done on he ig QUARTER CAR VEHICLE MODEL Alhough que model i vey imlified eeenion of i i vey oul in he lieue of uenion eeh i The eon fo hi ouliy i h i imliiy llow fo loed fom oluion nd hu led o gee undending of he yem A que

5 model h een develoed nd ued o gin ome inigh ino he ehvio of e uenion Figue how he geomey of he que model deived in hi eion T m m 3 The effe of he uenion geomey e ouned fo in he uenion iffne oeffiien Thi i n vege veil e whih oun fo ny iing e heii of he uenion The oenil enegy of he yem i given y eqn 4 U 4 Figue - Que C Model The que model i ued o udy he ehvio of he yem ound i equiliium e; heefoe, he dilemen e en o e zeo i equiliium The vile of he model e defined : - Dilemen of Sung m fom equiliium oiion Dilemen of unun m fom equiliium oiion uenion iffne uenion dming ie veil iffne ie dming The equion of moion n e deived uing Lgnge Equion fo holonomi yem wihou eenl foe d d d d T T U R T T U R 0 0 The inei enegy of he yem i given y eqn 3 The non-line heii of he dme hve een lumed ino he dming oeffiien Thi inlude he effe of uenion geomey well he diffeene in um nd eound dming The Ryleigh diiion funion of he dme nd dming of he ie i given y eqn 5 R 5 Suiuing eqn 3,4 nd 5 ino nd yield he equion of moion fo he que m 0 6 m 0 7 Roo Lou Anlyi of Dming Coeffiien The oo lou oedue n e ued o udy he effe of mee on he eone of he yem Hee, he effe of vying he dming oeffiien i udied Tie dming h een negleed in he uequen nlyi of he que in ode o imlify he mhemi; hi i vlid umion ine ie dming i muh le hn h ovided y he dme, nd i deee wih olling eed ii Figue how he oo lou fo que model of yil Chm in ee

6 oue onfiguion The mee ued fo he oo lou e fo fon one nd e hown in Tle in he endi whee he ie iffne i muh highe hn he uenion iffne Figue The oo lou how he effe of vying he dming oeffiien of he que model The ole jeoy fo he unung m how h deque dming, dming io of, n e hieved y ineing he dming oeffiien Thi ou when he ole eled o he unung m moion i on he el i The me on figue how he dming oeffiien of 49 l/in/ [858 N/m/] h eul in well dmed unung m mode he me i on he el i, howeve, hi moun of dming only eul in dming io of ou fo he ung m Convenionl widom would indie h ineing he dming oeffiien would imove he iuion nd dmen he ody mode In f he ooie eul The oo lou nlyi how h ineing he dming oeffiien will deee he dming of he ung m mode The eon fo hi limiion i h he iffne of he ie i he me ode of mgniude he ing iffne Ineing he dme iffne y ineing he dming oeffiien will limi he movemen of he uenion, nd will inee he deeion of he ie, o h he ung m hen oune on he ie The mnifeion of hi henomenon i nown in he ing ommuniy loing he ho In on o hi iuion we n emine enge uenion, Figue 3 Figue 3 how he oo lou fo yil od uenion, he mee ued e hown in Tle in he endi The oo lou how h he dming io fo oh mode move loely ogehe he dming oeffiien i ineed The que me how he uen oo fo dming vlue of 65 l/in/ [383 N/m/] Fo hi moun of dming he unung m mode i ovedmed, he ole i on he el i, nd he ung m mode i lmo well dmed wih 8 dming io Thu he dme dmen oh mode elively eqully Unlie he e, he ie of enge e quie iffe hn he uenion ing, hu ineing he dming doe no inee he dilemen of he ie unilly Howeve, hi ing ou ohe diffiulie, ine ineing he dming oeffiien o dmen he ung nd unung me will eul in ineed nmiiiliy of od viion o he enge ommen SEVEN DEGREE OF FREEDOM DOF CAR MODEL Alhough he heve eone of he n e eily undeood wih he que model, even DOF model how he ineion of he diffeen mode The i modeled n indeendenly ung, igid ody wih ih nd oll moion ou

7 i inil e The uenion geomey effe e negleed, ee fo moion io onideion The moion io i ued o genee n equivlen veil ing iffne nd dming he wheel Figue 4 how he geomey of hi model Figue 4 Seven DOF C Model The vile of he model e defined : veil dilemen of ung m ih ngle of ung m oll ngle of ung m veil dilemen of fon lef ie f veil dilemen of fon igh ie l veil dilemen of e lef ie veil dilemen of e igh ie y veil inu fon lef ie y f veil inu fon igh ie y l veil inu e lef ie y veil inu e igh ie m ung m I ih inei I oll inei m fon lef ie m m fon igh ie m m l e lef ie m m e igh ie m fon lef uenion iffne f fon igh uenion iffne l e lef uenion iffne e igh uenion iffne fon lef dming oeffiien f fon igh dming oeffiien l e lef dming oeffiien e igh dming oeffiien fon lef ie iffne fon igh ie iffne l e lef ie iffne e igh ie iffne fon lef ie dming oeffiien fon igh ie dming oeffiien l e lef ie dming oeffiien e igh ie dming oeffiien dine fom g o fon le dine fom g o e le fon widh e widh Agin we ue Lgnge Equion o deive he equion of moion The inei enegy of he yem oni of he nlionl enegy of he me well he oionl inei enegy of oll nd ih of he ung m The inei enegy i given y eqn 8 T m I I m m f ml l m 8 The oenil enegy of he yem i given y eqn 9 U f f l l y f f y y l y l l 9 The Ryleigh diiion funion of he dme nd dming in he ie i given y eqn 0 R f f l l y f f y y l y l l 0

8 Suiuing ino Lgnge equion eul in he equion of moion fo he 7 DOF model The equion of moion n e found in Aendi B SEVEN POST RIG DATA ANALYSIS The ig inumenion n inlude u o 40 hnnel of vehile d nd i i ey o eome ovewhelmed wih he nlyi In ode o imlify he nlyi, only few mee e ed, nd when fuhe nlyi i wned he emining hnnel e nlyzed Mo of he d eduion ou in he fequeny domin Comue ofwe h een wien in Ml uing he ignl oeing oolo in ode o uome he nlyi oedue The nlyi oni of oining he fequeny eone funion FRF of he mjo mode of he vehile; eifilly he heve, ih nd oll mode of he ung m well he veil mode of he unung m Thi eion diue how hee FRF e oined In he uequen eion he equivlen eone will e oined fo he 7 DOF model The FRF i given y Hf in eqn Y f H f * X f whee Yf i he yem eone nd Xf i he inu ignl, oh of hee ignl e meued nd hu eqn n e olved fo Hf Uing he nfe funion eime funion TFE in Ml ignl oeing oolo olve fo Hf Thi funion divide he d ino oveling lo, window he d wih Hnning window o edue lege nd finlly fom he nfe funion uing he H eime of he FRF The H eime i given y eqn H G G f f XY XX whee G y f i he o-eum of X nd Y nd G f i he uo-eum of X The H eime give he e eime of he nfe funion if he noie only onmine he meuemen of he ouu Y of he yem iii In he e of he even o ig, he inu ignl e eed y he onol yem o heefoe n e umed o e noie fee Fo he diuion in hi e udy we e only onened wih heve nd ih moion ine he i ymmei in he oll i, hu only wo eleomee e uffiien o deie he moion of he One eleomee i led long he eneline of he on he fon le line, nd nohe one i led on he eneline long he e le line Fom he geomey of he loion of he eleomee we n define he following heve nd ih given y eqn 3-4 * FonAel * ReAel Heve InuAeleion FonAel ReAel Pih InuAeleion 4 3 Eqn 6, he on h lod mgnifiion nfe funion, how how well he ie i e in on wih he od A lod ell in eh wheeln meue he veil foe eh on h Sine he longiudinl nd lel foe geneion of he ie i ooionl o he veil lod, minimizing he viion of he on h lod led o moe onn lel nd longiudinl foe geneion Looing hi gh fo he fon nd e i i ueful when ming djumen o imove iul e of hndling Fo emle, o imove ion of he e wheel he on lod viion he e would need o e minimized ConLo d ConP hlodmgn ifiion 6 InuAel Idelly, n oimized would hve he lowe oile FRF fo ll of he ove The eul of he imulion will how h ll of he FRF nno e minimized onuenly

9 7 DOF CAR MODEL DATA ANALYSIS The equion of moion of he 7-DOF model n e ineged numeilly o find he eone of he o given inu A MATLAB ogm h een wien in ode o omlih hi The inu o he imulion n e he me h ued on he even o ig, hu llowing fo die omion of he eul The ouu of he imulion e he ime domin eone of eh of he degee of feedom of he model The ime domin ouu of he imulion e ued inu o he nfe funion eime funion TFE o find he FRF The igid ody moion of he model e given y he dilemen of he ung m, X, he ih ngle, The FRF e hen found uing eqn 7-8 X Heve 7 Pih Y Y 8 Sine he inu i ue heve dilemen ll fou wheel dilemen will e he me nd hu i i uffiien o ue he dilemen of one of he one, in hi e we hoe he fon lef wheelm, Y ROAD INPUT MODEL The od inu ued fo modl eing i we ine of onn mimum veloiy The mliude of he we ine i hoen o h he dme eone on he ig i imil o h een he The owe el deniy PSD of dme veloiy d logged he i he ge eone The od mliude i hen vied unil uile mh i found Thi oe ou ofine nd equie he ue o me judgmen o when uile inu h een found Bed on he eeiene of he ARC ff hi oedue will uully equie only few ieion o odue eonle inu The onn mimum veloiy inu i ed on he oeie of el od ofile Wong iv give he PSD of dilemen of od ofile : S N Ω C Ω 0 whee Ω i he il fequeny in yle e mee o e foo, nd C nd N e uled fo diffeen ufe The vlue N n nge fom o ou 4 deending on he od ufe heii If we ume h he i velling ove he od onn veloiy V, hen he PSD of he od in Hz n e found y uiuing: f Hz V m / Ω whih eul in PSD in he fequeny domin of: S N f C f / V Rell h o find he veloiy PSD fom he dilemen PSD i i only neey o mulily y he fequeny in he fequeny domin, hu if we ume N he veloiy PSD eome: S f C V 3 V whih i indeenden of fequeny nd ou umion of onn mimum mliude veloiy we ine i vlid SIMULATION RESULTS FOR 7 DOF CAR MODEL I i ueful o udy he eul of line imulion o gin inigh ino he dynmi of he yem, lhough lely he imulion e limied ine he el inlude mny non-line elemen The line imulion n e ued o give quliive eeenion of wh hen when hnge e mde o dming level; figue 5 how n emle whee imulion h een un o udy elive dming level In hi emle, he fon

10 nd e dming level e vied nd he effe on he mimum of he heve nd ih fequeny eone funion e loed in onou lo The y-i i he fon dming oeffiien in l/in/ nd he i i he e dming oeffiien lo in l/in/ The mee ued fo he eul of figue 5 e hown in Tle in he endi The mee oeond o he eed in he e udy eion Alhough he eul e fo ingle eu of ing, he end i eeenive fo he nge of ing ommonly ued in Chm The onou of mimum heve eone how he lowe eone o e oughly 75 Rell fom he oo lou udy h he heve eone of he i limied y he ie iffne Theefoe i i no uiing h djuing he dming nno fuhe edue he heve eone Anohe eul whih i eviden in he onou lo i he neeiy o ie omomie eween heve nd ih eone Figue 5 how h i i no oile o hieve minimum ih nd minimum heve onuenly In ode o minimize he ih eone of he i i neey o inee he e dming, howeve, hi i deimenl o heve eone Thu judgmen ll mu e mde o whih eone i mo imon Figue 5 LIMITATIONS OF LINEAR MODELS Alhough he 7 DOF model i v imovemen ove he ¼ model, i i ill imlified line model The enefi of hi model i h i give quliive iue of wh effe elive dming level will hve on he dynmi of he Anohe enefi i in he udy of mee uh CG oiion, ih inei, o wheele Thee hnge e hnge h e ouinely mde o Chm y ll nd uenion geomey djumen The line model give qui indiion o he mei of he ooed hnge The line model h een ued minly o undend he dynmi of he I how he elii limi o whih he eonne n e edued, hu we do no we ime needlely ehing fo ee nd ee eone The min limiion of he model i h i doe no ovide fo non-line dme Re dme e fully djule in omeion nd eound well low nd high eed nge Re em do no hve he eoue o ee fully non-line imulion, hu he non-line effe e ee udied uing he even o he CASE STUDY Thi eion deie he oimizion oedue ued on Chm nd ie i o he eul of he elie eion of hi e A diued in eviou eion, he inu ued o eie he i ue heve inu The inu o he wheeln i we ine ing 5 Hz nd oing 0 Hz, wih onn mimum veloiy of 00 mm/ The onn mimum veloiy i equivlen o uming N in he od inu model eened elie Rell h he oo lou nlyi how h wheelho i no mjo onen fo Chm, hu he nlyi of he oimizion i minly eneed on oimizing he ung m mode, heve nd ih Deending on he eed, oll i lo onideed, howeve, fo Chm he oll eone i vey mll nd in ny e hi d efe o ymmei eu fo ee oue whih doe no ehii oll omonen when eied in heve

11 A he eul of he eviou eion howed, heve nd ih nno e minimized onuenly, hu we end o onene on minimizing he ih eone Thi i onien wih eul ulihed y ohe uho, uh fo emle Kz & Floyd v The enefi of eduing ih eone e o e wofold Fi fo whih hve eodynmi ih eniiviy limiing ih will eul in moe le eodynmi lom y eduing he movemen of he eodynmi ene of eue Seond, hee i lo gin of mehnil gi nd iliy whih i eoed y he dive To undend hee eul, onide wh hen when he ihe noe down; he fon ing will e omeed, nd hu he veil lod he fon ie will inee Thi will inee he lel foe of he fon ie Howeve, he me ime he e ie nd hu lowe he veil lod he e ie, loweing he lel foe Sine i of ie eqully loded will odue he gee moun of lel foe fo given moun of ol veil lod i i ey o ee h minimizing he ih eone will eul in he ovell gee lel foe Alo, if he i oilling in ih, he mehnil ene of eue will move whih he dive onide n unle iuion Figue 6 & 7 e indiive of he eul oined fom eion he even o he ig Figue 6 how he heve eone of he Noie h hee h een ligh inee % in heve eone, ignling ligh lo of onol of he heve mode Howeve, figue 7 how lge imovemen in he ih eone of he 43% Unfounely due o eniive nue of he infomion ovided y dme uve we nno ulih he ul dme uve h wee ued o ive hee eul Howeve, he uequen diuion uing he line model hould me he lien oin of he oimizion eviden Figue 6 Figue 7 Figue 8 how he me eul Figue 5 u wih limied nume of onou o how moe lely he oeing ondiion fo hi e udy The lo w geneed y uing he mee fo he diued in hi eion The ow on figue 8 how he dieion he dieion h need o e en in ode o imove he ih eone of he, le fon dming nd moe e dming Fo hi e we loweed he fon eound dming lighly nd ineed he e eound dming, hi odued he oimized eu of figue 6 & 7 Noe h ou imulion w no ued o find ou olue vlue of dming equied, u ined i eved guide o wh djumen hould e mde o he dming level in ode o imove he eone of he The finl dming djumen mde o he e ed on he ig eul nd in onulion wih he e enginee The e enginee ovide he feed of wh n e eeed y hnging ein heii of he dming uve In hi e i w fel

12 h ineing he e eound dming would e he mo effeive wy of ineing he e dming level; hu he finl eul i ominion of he ig imovemen while minining he oe feel of he dme fo he I i ineeing o noe h lhough he h mny non-line elemen menioned in eviou eion, i ehii FRF whih e line ou i oeing oin In ohe wod, one he eiion level nd downfoe level h een fied he eone i quie line Fo emle, lhough he moion io inee quie unilly fo hee none of he iffening ing eone heii n e een in he FRF he imulion e imle line model hey e uffiien o undend he dynmi of he vehile h we hve eed Poduing fully non-line imulion i eyond he iliy nd eoue of mo e em, he ue of he even o he ig elimine he need fo uh imulion CONTACT Heni Kowlzy Vehile Dynmi Enginee Auo Reeh Cene-Reynd Mooo 40 Chmionhi Dive Indinoli, IN howlzy@eyndnom APPENDIX A CAR PARAMETERS Due o he onfidenil nue of ing, he mee hown in Tle e no e vlue, ined hey e eeenive vlue of een dy Chm e Tle SUMMARY Figue 8 The even o ig h een vey ueful ool in he uning of e uenion I h een ued o uefully oimize he dme on mny diffeen ye of nging fom oweful gound effe uh Chm o NASCAR Winon Cu The model deied in hi e how he dynmi of he nd how hey e eled o he oimizion oe h i ied ou on he he ig The ue of imulion h llowed u o ee undend he dynmi of he vehile nd i h enled u o me egi deiion on he e oedue nd nlyi on he even o he The imulion eened in hi e how ome of he limiion h e een when eming o oimize he eone of he y uning of he dme Alhough Chm See Coue Pmee Fon Siffne Re Siffne Suenion Suenion Fon Tie Siffne Re Tie Siffne Sung M Fon Unung M Re Unung M Pih Inei 574 N/m N/m 3534 N/m N/m 690 g 35 g 40 g 50 g m^

13 Roll Inei 5 g m^ CG o Fon Ale 7 m CG o Re Ale 4 m Tle Tyil Penge Que C Pmee vi Suenion Siffne N/m Tie Siffne N/m Sung M 00 g Unung M 00 g APPENDIX B - SEVEN DOF EQUATIONS OF MOTION 0 l l f f l l f f m 0 l l f f l l f f I 0 l l f f l l f f I 0 y y m

14 m f f f y f f f f y f f 0 m l l l l l y l l l l l y l l 0 m y y 0 i Chlni, R M, Ride Pefomne Poenil of Aive Suenion Syem- P :Simlified Anlyi Bed on Que C Model ASME Symoium on Simulion of Gound Vehile nd Tno Syem CA, 986 ii Gen, G, Moo Vehile Dynmi: Modeling nd Simulion iii Rndll, RB, Fequeny Anlyi, 3 d ed, Büel & Kje 987 iv Wong, JY, Theoy of Gound Vehile, nd ed, Wiley Ineiene 993 v Kz, JL, Floyd, R S, Ue of Simulion o Tune Re C Dme SAE vi Clnoe ME653:Vehile Dynmi, D EH Lw, Clemon Univeiy Mooo Engineeing Pogm