MODELLING AND EXPERIMENTAL ANALYSIS OF MOTORCYCLE DYNAMICS USING MATLAB

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1 MODELLING AND EXPERIMENTAL ANALYSIS OF MOTORCYCLE DYNAMICS USING MATLAB P. Florn, P. Vrání, R. Čermá Fculy of Mechncl Engneerng, Unversy of Wes Bohem Asrc The frs pr of hs pper s devoed o mhemcl modellng of moorcycle dynmcs. A nonlner 5DOF model of moorcycle s developed usng Lgrnge equons. Ths pproch enles o smule lrge dsplcemen nlyses s well s he conc eween res nd rod. The se of nonlner dfferenl equons s solved usng consn verge cceleron mehod n MATLAB. The resuls of mulody dynmcs smulon re verfed usng VI-Moorcycle plugn for Adms/Cr nd hey re used s oundry condons for FEM nlyses. The second pr of hs pper s focused on expermenl nlyss of moorcycle dynmcs. A mesurng sysem connng hree cceleromeers ws developed nd used for rder vron exposure nlyss. D from 1.6-lomeer esng rc were processed usng MATLAB nd evlued ccordng o ČSN ISO Nonlner mhemcl model of moorcycle Frs sep of he soluon process s o develop nonlner mhemcl model of moorcycle. A plnr 5-degre-of-freedom model ws proposed wh followng generlzed coordnes: x frme horzonl rnslon; y frme rnslon; φ frme pch ngle; y fron ssemly vercl rnslon; y rer ssemly vercl rnslon. A scheme of he model connng generlzed coordnes s well s oher prmeers s shown n Fg. 1. x m,i T ϕ,,l,,l m red y y m red y Fgure 1: Scheme of he model The generlzed coordnes re ncluded n vecor q s shown n equon 1. x y y y T,,,, q (1) Lgrnge equons (eq. ) were used o develop equons of moon of he sysem. d d E q E q E p q R q Q ()

2 Where E, E p nd R represen nec energy funcon, poenl energy funcon nd Rylegh dsspon funcon of he sysem. red red m m I m m M () sn sn sn sn K () sn B (5) The sffness mrx nd he dmpng mrx re oh no consn nd depend on he generlzed coordne φ whch mens he sysem s nonlner nd le o provde more ccure resuls s dsplcemens ncrese. However, hs lso plces requremens on he negron mehod of he moon equons self. 1.1 Tre conc model Inercon eween res nd rod s sgnfcn source of forces h c on he frme. In hs cse longudnl drvng nd rng forces re negleced nd he ey s s o on norml conc forces. As sed prevously he whole model s plnr herefore lerl cornerng forces re no en no ccoun eher. The model of he re conc s shown n Fgure. rod(x) rod(x 1 ) rod(x ) r pneu c x1 S pneu () x y Fgure : Tre conc model

3 Le s ssume h he locon of re cener n nown ny me. In cse h ny pon of rod surfce s closer o he re cener hn re rdus conc pressure exerng on he re cn e clculed s p pc (6) Where p descres sffness chrcerscs of he re nd c s he dfference eween he re rdus nd he dsnce. Dfferenl norml force cn e oned ccordng o eq. 6. dn cds (7) p Dfferenl ds reles o re rc. Dfferenl norml force s lwys perpendculr o he rod surfce. For our prolem s crucl o deermne s componens n horzonl nd vercl drecon. Ths cn e ccomplshed y usng dervve of rod funcon s descred n he followng equons. dn dn x x drod pc sn rcn dx dx (8) drod pc rcn dx dx (9) In order o deermne he componens of he cul norml force, negron s conduced s he very ls sep. xs pneu rpneu N dn x (1) x x S r pneu pneu ys pneu rpneu N dn y (11) y y S r pneu pneu The re conc model proposed ove s sed on elsc conc model. Tre hyseress effecs cn e en no consderon s well ssumng dmpng forces hve smlr chrcer o norml conc forces s sed n he followng equon. N cn (1) The vrle from prevous equon reles o re deformon re. Numercl negron of he equons of moon Once we cqured he forces cng on res we cn proceed o he soluon process of he moon equons wh MATLAB. Se of 5 nonlner ordnry dfferenl equons s summed up n he Equon 1. Mq Bq Kq fn q,q, (1)

4 Consn verge cceleron negron mehod ws used due o s relve smplcy nd numercl sly. Ths mehod s predcor-correcor sed s he sysem n queson s nonlner. A rod funcon ws desgned usng modfed sn funcons o represen n oscle whch s supposed o cuse loss of conc eween he res nd he rod. In hs wy jump of moorcycle cn e smuled. hegh [mm] 1 Fgure : Rod profle Consn verge cceleron mehod s sed on n ssumpon h he cceleron s consn eween wo pons n me (Equon 1). q 1 q q (1) By negron of he prevous equon we on formuls for veloces nd dsplcemens. q q q q (15) q q q q q (16) Susung Equons 1 nd 15 no Equon 1 leds o: ~ Zq f (17) Therefore he cceleron n he nex me sep s clculed s: q 1~ (18) Z f Acceleron resuls re shown n he fgures elow. In Fgure here re cceleron resuls of he frme. The nl seep ncrese reles o he egnnng of he oscle. As he cceleron drops o pproxmely -1 ms - mens h he res los conc wh surfce. The pe vlues occur fer lndng rechng 6 ms -. Acceleron resuls of fron nd rer ssemly n Fgure 5 cn e explned n smlr wy.

frme 5 fron ssemly rer ssemly 15 cceleron [m*s-] 1 cceleron [m*s-] 1 5-5 -1-1 - me Fgure : Frme cceleron resuls -15 me Fgure 5: Fron nd rer cceleron resuls The mhemcl model h ws developed provdes

5 frme 5 fron ssemly rer ssemly 15 cceleron [m*s-] 1 cceleron [m*s-] me Fgure : Frme cceleron resuls -15 me Fgure 5: Fron nd rer cceleron resuls The mhemcl model h ws developed provdes resonle resuls; however, furher verfcon s necessry. In order o do so, ADAMS/VI-Moorcycle module ws used o compre resuls. In Fgure 6 here s moorcycle model n VI-Moorcycle nerfce runnng over n oscle defned n he sme s n he MATLAB model. In Fgure 7 here re cceleron resuls of fron ssemly n ADAMS nd MATLAB. In hs smulon re dmpng properes were negleced n MATLAB whch explns he ey dfference eween oh curves. Fgure 6: VI-Moorcycle model Fgure 7: Fron ssemly cceleron resul comprson Expermenl nlyss A mesuremen sysem ws desgned n order o fulfll wo purposes lsed elow y usng nexpensve prs used n uomove pplcons. 1) Mesurng dynmcs of moorcycle n moon n order o verfy compuonl model ) Evluon of moorcycle vrons effecs on he rder y pplcon of ČSN ISO61 nd ČSN EN ISO 59 sndrds For d loggng DL1 MKdlogger ws chosen. Advnges of hs dlogger re he possly of connecng up o 1 exernl sensors nd he possly of loggng d from vehcle conrol un.

Fgure 8: Dlogger DL1 MK [] In order o on relonshp eween oupu volge of cceleromeers nd

Durng hs expermen ech xs ws exposed o posve nd negve grvonl cceleron s well s o zero

By ssc evluon of hese hree pons lner relon eween oupu volge nd moun of cceleron ws

1 Processng of he mesured dgl sgnls To smplfy he processng of mesured sgnls GUI ws

6 Fgure 8: Dlogger DL1 MK [] In order o on relonshp eween oupu volge of cceleromeers nd vlues of cceleron smple expermen ws done. Durng hs expermen ech xs ws exposed o posve nd negve grvonl cceleron s well s o zero cceleron. By ssc evluon of hese hree pons lner relon eween oupu volge nd moun of cceleron ws oned. Fgure 9: Oupu sgnl of wo xs cceleromeer.1 Progrm N. 1 Processng of he mesured dgl sgnls To smplfy he processng of mesured sgnls GUI ws creed. Mn purpose of hs progrm s o conver mesured sgnls from volge o uns of cceleron y usng prevously compued lner relon. The GUI lso hs funcons med mnly verfyng funcon of sensors nd evluon of mesured d. Fgure 1: GUI nd evluon of mesured d

7 . Progrm N. Evluon of d y he mehodc of ČSN ISO 61 sndrd Ths progrm s processng oupu d of progrm N. 1 y usng ČSN ISO 61 sndrd, med effecs on helh nd comfor. The oupus of hs progrm re frequency specrum of every xs of cceleromeers, summed up moun of vrons (for comprng wh lm moun c ), effecve vlues of weghed vrons hw j nd conrollng fcor. Verfcon of hs progrm ws mde y he followng genered npu sgnl: 5 sn1 sn x,7 sn 19 (19) y x rnd n sze () Fgure 11: Oupu of he FFT lgorhm oned y usng genered npu. Progrm N. Evluon of d y he mehodc of ČSN EN ISO 59 sndrd Ths progrm s processng oupu d of progrm N. 1 y usng ČSN EN ISO 59 sndrd. Oupus of hs progrm re effecve vlues of weghed vrons nd ol dly exposon o vrons A(8). Ths evluon process cn e used only s reference o compre dfferen moorcycles. Precse evluon s no relevn ecuse he vlues recommended y hs sndrd re no men for moorcycles. Fgure 1: Rw mesured d n sw rceechnology Anlyss 8.5

8 Concluson The mhemcl model of moorcycle h ws developed s n good greemen wh commercl sofwre VI-Moorcycle. Is oupus mgh e used for consequenl FEM smulons. Furher developmen of hs model s plnned n order o conduc hree dmensonl nlyses. As fr s expermenl nlyss s concerned, correc funcon of developed progrms ws esed on d oned y mesurng dynmcs of he rel moorcycle rdng on pulc rods. Unforunely, usge of hs sysem s nowdys lmed y nsuffcen smplng frequency of dlogger nd low ndwdh of used cceleromeers. Boh ssues re currenly eng solved. References [1] D. E. Newlnd. An Inroducon o Rndom Vrons, Specrl nd Wvele Anlyss. Longmn Scenfc & Techncl, Essex, U.K., hrd edon, 199. [] J. Dupl. Výpočové meody mechny, ZČU FAV,. [] Rce echnology dlogger DL1 MK [onlne]. [c ]. Avlle :hp:// [] V. Cossler. Moorcycle Dynmcs. Lulu Press, U.K., 6. [5] T. Fole. Moorcycle Hndlng nd Chsss Desgn, he r nd scence. Spn,. [6] P. Florn. Modelng of moorcycles nd her componens, Mser s hess, Unversy of Wes Bohem, Plsen, 15. [7] P. Vrání. Expermenl nd compuonl echnques for modelng of moorcycles nd her componens, Bchelors hess, Unversy of Wes Bohem, Plsen, 15. Ing. Pvel Florn pflorn@s.zcu.cz Bc. Pvel Vrání vrnp@sudens.zcu.cz Ing. Romn Čermá, Ph.D. rcerm@s.zcu.cz

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