VEHICLE PLANAR DYNAMICS BICYCLE MODEL

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Antonia Pitts
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1 Auptions -Do, VEHE PANA DYNAMS BYE MODE o tel, (esued o instntneous cente o ottion O) o Yw, (wt Globl Ais) ongitudinl elocit is ued to be constnt. Sll slip ngles, i.e. ties opete in the line egion. No e wheel steeing. No ligning oent in both ties. No od gdient o bnk ngle. Thee e onl two wheels, one in the ont nd one in the e. No ltel nd longitudinl lod tnse No olling nd piting otion No is o suspension coplince eects Nottions tel Acceletion o og in the G e tel Acceletion o og in the B e. (clculted) (ued to be esued) Yw te (ued to be esued) ongitudinl Velocit o Vehicle (ued to be known) ont/e Tie oneing Stine, (ued to be known) ont/e Tie Slip Angle, (clculted) ont Steeing Angle (ued to be esued) ont/e Wheel Velocit Angle Distnce o og to e/ont Aels θ, θ (clculted), (ued to be known) Vehicle ength (clculted) od dius Gukn Edogn, Ph.D.

No ltel nd longitudinl lod tnse No olling nd piting otion No is o suspension coplince eects Nottions tel Acceletion o og in the G e tel Acceletion o og in the B e.

2 Sste Model tel oce Equilibiu l Moent Equilibiu l tel Acceletion in the G e e Tie ont Tie tel oces in the B e c cos c cos tel oces in the W e c c Slip Angle θ θ Velocit Angle θ tn θ tn Ect tel oce Blnce ( θ ) cos ( θ ) ( ) tn cos tn cos c cos cos cos c cos cos Gukn Edogn, Ph.D.

W e c c Slip Angle θ θ Velocit Angle θ tn θ tn Ect tel oce Blnce ( θ

3 Gukn Edogn, Ph.D. Appoite tel oce Blnce ( ) ( ) 0 Appoite Moent Blnce Stte Spce epesenttion (J hpte 0 pge 6 - Eqution 0.84) 0 entiugl oce nd tie oces lso he longitudinl coponent in the BODY is.

4 Gukn Edogn, Ph.D. dt d 0 The Othe Vesion: ˆ cos ˆ sin ˆ

5 Gukn Edogn, Ph.D. Sted Stte Steeing Angle GEOMETY ONSTANT entipetl/tel Acc. 0 ZEO Angul Acc. ONSTANT ONSTANT Unde-stee gdient o Unde Stee > > > 0 o Neutl Stee 0 o Oe Stee < < < 0

6 Vehicle Side Slip Angle Estition ˆ d dt This looks ok, but we would like to use senso esueents. ˆ ( ) ( cos sin) sin cos sin cos ( sin cos ) sin cos ( sin cos ) sin sin cos cos sin sin cos cos sin cos sin cos Now we cn use w te nd cceletion sensos to estite the w te s below. ˆ ˆ sin cos ˆ Miu Vehicle Side Slip Angle t is stuting unction o the cteistic elocit. < > k ( k k ) ( k k ) k Gukn Edogn, Ph.D.

cos sin cos Now we cn use w te nd cceletion sensos to estite the w te s below.

7 Yw te Estition This is ctull the sted stte esponse, i.e. the gin, o the tnse unction between the steeing input nd the w te output. Deition o the boe eqution nd the hcteistic Velocit Miu Yw te d es d es cos ( ) ( 0 ) We ue tht sin cos sin ( sin ˆ ) d es sin o og dws peect cicle duing neue. o The dil cceletion is in the diection o the dil oce cting on the og. o The dil cceletion is esued s the c tels ound cicul tjecto. o The longitudinl cceletion o the c esued long the longitudinl is o the ehicle lso contibutes to the dil cceletion o the og. o All the cceletion is spent o the w otion, no ltel tnsltion eist whi lso ens tht the og sts on the cicul tjecto. o The dil cceletion coesponds to iu w te. Note tht dil nd ltel cceleoetes do not point t the se diection. Gukn Edogn, Ph.D.

o The dil cceletion is in the diection o the dil oce cting on the og. o The dil cceletion is esued s the c tels ound cicul tjecto.

8 3 tne ede w te hespldik.biccle odel sted stte.m wte Steeing Pd deneleinden ile i kistiip gini bulduk son biccle odelin steeing input/w te output (gini oln) tnse onksionundn gecidik (bi det dh stution unction en son isle olk) 3.4W odelden gelen gecege dh kin w te bide Gukn Edogn, Ph.D.

odelin steeing input/w te output (gini oln) tnse onksionundn gecidik

9 cle ll close ll clc % Wht is the spling tie in [s]? dt 0.; % [sec] % Wht is the longitudinl elocit o the ehicle og in [/s]? 0; % [/s] % Wht e the ehicle petes? % Al oeo Pete Set 400; % [N/d] 8567; % [N/d].8; % [].5; % [] 58; % [kg] 430; % [kg^] unction [,d] biccle(,,,,,,,dt) -()/(*); -(*-*)/(*^)-; -(*-*)/; -(^*^*)/(*); Ac [ ; ]; b /(*); b */; Bc [b; b]; c ee(); Dc eos(,); [Ad,Bd,d,Dd] cd(ac,bc,c,dc,dt); d (Ad,Bd,d,Dd); set(d,'ne','bye MODE') set(d,'nputne',{'delt_'}) set(d,'sttene',{'bet','psi_dot'}) set(d,'outputne',{'bet','psi_dot'}) set(d,'ts',dt) */()/-*/()/; Gukn Edogn, Ph.D.

$ee(); Dc eos(,); [Ad,Bd,d,Dd] cd(ac,bc,c,dc,dt); d (Ad,Bd,d,Dd); set(d,'ne','bye MODE') set(d,'nputne',{'delt_'})$

2.016 Hydrodynamics Prof. A.H. Techet

2.016 Hydrodynamics Prof. A.H. Techet .016 Hydodynmics Reding #5.016 Hydodynmics Po. A.H. Techet Fluid Foces on Bodies 1. Stedy Flow In ode to design oshoe stuctues, suce vessels nd undewte vehicles, n undestnding o the bsic luid oces cting