OPTIMIZATION OF CAR YAW BEHAVIOUR USING ACCTIVE SUSPENSION ELEMENTS SVOČ FST 2011

Transcription

1 PTIMIZATIN F CAR YAW BEAVIUR UING ACCTIVE UPENIN ELEMENT VČ FT 0 Marin Vček Universiy of Wes Bohemia Univerini 8, Pisen Cech Reubic ABTRACT This work, which is a ar of my Ph.D. hesis, is a summary of ossibiiies of overseer and underseer resricions and a mahemaica mode for souion of seady sae cornering. There are exanaions of basic rincies of overseer and underseer in he hesis. The main consrucion souions are seeced wih he he of Engineering Design cience knowedge, imroving car yaw behaviour. KEYWRD Car yaw behaviour, eady sae handing, usension eemens, Momen of ineria, verseer, Underseer INTRDUCTIN There are hree siuaions which may occur during cornering. When he car is moving on a saic radius during cornering, i means neura seer. verseer means ha he car urns more han is required and underseer means ha he car urns ess han is required. The hesis deas wih basic rincies of overseer and underseer (car yaw behavior). The robem wih overseer and underseer is shown on a simified mode of seady sae cornering (veociy and urning radius are consan). The car yaw behaviour for seady sae cornering is shown on a grahica ane mode, which is described by hree main baance condiions. We need o know a he characerisics of he vehice (weigh disribuion, yre characerisics, seering geomery, susension siffness and geomery, ec.) for souion of hese main baance condiions. Therefore his souion gives us an idea of he car behaviour during cornering and shows ossibiiies for imroving vehice handing sabiiy. PRBLEM LVING This hesis describes robems wih car yaw behaviour for case of seady sae handing (deendencies are shown for urning radius 50m). In he hesis, acive design souions for imroving car handing sabiiy are shown (wih my design souion roosas). BAIC PRINCIPLE F VERTEER AND UNDERTEER Figure : Possibiiies of car behaviour during cornering Figure shows hree ossibiiies of car behaviour, which may occur during cornering. The firs siuaion shows neura seer. This is an idea siuaion when he car kees required direcion (moving on saic radius R). We can say ha he car is behaving according o idea Ackermann heory. The second siuaion is underseer when he car urns ess han is required. This is yica for cars wih fron engine and fron whee drive when is cornering seed is oo fas. The driven

2 whees are more oaded by he addiiona forces and yres canno fuy ransfer his oad on he road. The hird siuaion is overseer. verseer means ha he car urns more han is required. This is yica for oo fas cornering in cars wih rear whee drive. verseer is he mos dangerous siuaion for car handing because i can cause unconroabe si. Figure : Definiions of he car behaviour during cornering We usuay use abiiy facor K o exain car behaviour in cornering. This facor is given by he formua: K C m C' C' C () R [m] urning radius v [m/s] whees veociy a [ ] si ange ( = fron axe, = rear axe) m [kg] car weigh C α [N/rad] cornering siffness of rear axe (by virue of yre siffness) C α [N/rad] cornering siffness of fron axe (by virue of yre siffness and neumaic caser) [m] axe base, [m] horiona disance beween he rear/fron axe and he vehice cenre of graviy The sabiiy facor K deends on weigh disribuion and on cornering siffness of axes. When he K is equa o 0, i shows neura seer. Neura seer is characeried by he si ange on he fron whees is he same as he si ange on he rear whees. (i ange is ange beween whee ongiudina ane and rea moving direcion. i ange is caused by yre deformaion i wi be shown in Figure 9). In his case of neura seer, si ange is equa o ero. When he sabiiy facor is ess han ero, i shows overseer and si ange on he fron whees is ess han he si ange on he rear whees. The car urning radius is ess han in he case of neura seer. The hird siuaion is underseer. There K is greaer han ero and si ange on he fron whees is greaer han he si ange on he rear whees.

3 Figure 3: Forces a yre conac area Figure 4: Kamm circe of friciona forces The foowing forces acing on he yre conac area are imoran for good handing sabiiy: [N] driving force B [N] braking force [N] cornering (aera) force R [N] resuan force a ire conac area Z [N] verica whee force m [-] fricion coefficien Resuan force is resuan of aera force and braking force (Figure 4) or aera force and driving force (in case of seady sae handing). Figure 4 shows Kamm circe of friciona forces. The radius of his circe is he roduc of verica whee force and fricion coefficien (beween yre and road). We mus ensure ha he resuan force R is no bigger han he radius of he Kamm circe of friciona force o avoid a si. DEIGN LUTIN IMPRVING CAR YAW BEAVIUR There are many souions ha imrove car yaw behaviour and car handing sabiiy. ere is a is of he main acive devices: - acive body ro - which changes weigh disribuion in cornering - acive and adaive susension uni - imroves yre conac wih road - acive susension geomery - for exame acive whee camber which changes aera force - acive aerodynamics - increases verica whee oad in high seed - seering of rear whees - decreases si anges and imroves car handing sabiiy - eecronic sabiiy rogramme - brakes seeced whees so ha i eiminaes momen of ineria - acive differenia - divides he driving orque among he whees wih he he of mui-disk cuches - acive ro sabiiaion - device which changes siffness of susension sabiier and eiminaes body ro during cornering - acive seering - changes fron whee anges deending on veociy and adhesion - and many anoher souions... Figure 5: EP (Eecronic sabiiy rogramme) [4] 3

4 I used mehods of Engineering Design cience and muicrieria evauaion for evauaing he design souion and I chose Eecronic abiiy Programme (EP) as he mos effecive design souion for eiminaing of overseering and underseering. The seering of he rear whees was he second bes design souion. Therefore I woud choose EP and I woud ike o imrove is funcion wih my own souion. ere are my design souion roosas: - Acive moving wih a mass i means ha we can change weigh disribuion by changing osiions of some of he weigh, baery ec. - Acive ars of chassis changing fricion beween road and car: - side-ou or shooing devices in chassis (for exame airbags wih surface wih high fricion coefficien) - suying some medium o yre conac area for increag fricion - changing yre siffness and exansion of yre conac area (ug of eecric or magneic fieds) - Indeenden seering of a whees The indeenden seering of a whees is robaby he bes souion for ug in vehices and I woud ike o dea wih his souion in he nex ars of my Ph.D. hesis. MATEMATICAL MDEL F TEADY TATE ANDLING Figure 6: Genera ane mode of vehice cornering We can use a genera ane mode o invesigae he effecs of forces on he vehice during cornering. In case of seady sae vehice handing we can use hese simificaions and assumions: - Car veociy and radius of urning are consan - Acceeraion is equa o ero (i means ha he acceeraion resisance and momen of ineria are ero) - Car mode wih fron whee drive wih common differenia (driving forces are he same and ac ony on he fron whees). - Car is driving on eve ground, which means ha he cimbing resisance is ero. - Veociy of wind is equa o ero - Negigibe gyroscoic momen of he whees - Fricion coefficien is he same for a whees 4

5 5 From he review mode, we can wrie hese hree baance condiions for seady sae vehice handing: ) Force baance in he direcion of X axis: 0 o v f f f f F () ) Force baance in he direcion of Y axis: 0 o f f F (3) 3) Momen baance around he Z axis: 0 f f f f f f Mvr Mvr Mvr Mvr (4) We need o know some imoran unknowns and deendencies for soving hese main hree equaions. The firs unknowns are he verica whee forces. I chose an ideaied sma rivae (assenger) car as a mode for soving. The mode has MacPherson susension in fron and raiing arm susension in back. This deermines he osiion of he ro axis. Figure 7: Mode of susensions When we know he siffness of he susension, we can deermine he ange of body ro and change of verica whee oad. Afer incuding aerodynamic if, we ge he foowing grah (for a urning radius) wih verica whee forces which deend on veociy.

6 Figure 8: Verica whee forces her unknowns for soving he hree main equaions are aera forces and sef-aigning momens of he whees. The aera force (Figure 9) is generaed during car cornering and i is a resuan of he deformaion forces in he yre. Figure 9: Laera force In Figure 9 we can aso see si ange. i ange as menioned above is he ange beween he ongiudina whee ane and he rea moving direcion and i is creaed by he yre deformaion. Laera forces and sef-aigning momens deend on he ye of yres and on he whees and seering geomery. ere are some of hese deendencies. Firs deendence (Figure 0) shows yre cornering force characerisic (for yre sie: 55 R3). The yre cornering force characerisic is oed on a 3D char wih deendence of aera cornering force, si ange and verica oad []. Figure shows how he cornering force deends on whee camber and verica oad []. 6

7 Figure 0: Tyre cornering force characerisic Figure : Camber hurs We ge he foowing deendence of whee camber and mean seering ange from known susension geomery (his is shown in Figure ). Figure : Deendence of whee camber and mean seering ange The nex char (Figure 3) shows deendence beween seering ange on he ef and on he righ whee. This deendence is given by he seering geomery. Figure 3: Deendence of seering anges 7

8 The as hing we need is he deendence of si anges and seering anges. Figure 4 shows his deendence which is given by he foowing equaions. Figure 4: Deendence of si anges and seering anges Z R g Z ; R / P R g( P P) ; R / Z P Z R g Z (5), (6) R / Z P R g( P P) (7), (8) R / P Now, we have a unknowns and heir deendencies for soving he hree revious main equaions (),(3),(4). I soved hese hree equaions for he foowing arameers ug Microsof Exce and MATLAB. Figure 5: Enered arameers (/) 8

9 Figure 6: Enered arameers (/) Grahica mode in Figure 7 shows obained anges, forces and Kamm circes. ere are he resuing characerisics for radius 50m: Figure 7: Grahica mode of obained characerisics Figure 8: Deendence of resuan forces and friciona forces for each whee vs. car veociy 9

10 Figure 8 shows deendence of resuan forces R for each whee and sies of Kamm circes of friciona forces. Veociy, where he resuan force is bigger han radius of Kamm circe of friciona forces means oss of adhesion. The foowing char (Figure 9) shows he same deendence for axes as a comex. Figure 9: Deendence of resuan forces and friciona forces for axes vs. car veociy The as char shows deendence of seering and si anges for each whee. Figure 0: Deendence of seering and si anges for each whee vs. car veociy CNCLUIN AND RECMMENDATIN The obained characerisics give us an idea of car behaviour during cornering (for exame: veociy of oss adhesion) and shows ossibiiies for imroving vehice handing sabiiy. owever, hese characerisics resu from a simified mahemaica mode and hey shoud be verified wih some of sofware anayses or wih some exerimens. Tha is he aim of furher research for my Ph.D. hesis. ACKNWLEDGMENT This hesis was suored by he P VK rojec number CZ..07/.3.00/ REFERENCE A Book Pubicaion: [] E. Tönük, Y.. Ünüsoy: Predicion of auomobie ire cornering force characerisics by finie eemen modeing and anaysis, Ankara, 00. []. adeghi, M. T. Ahmadian: Tire Modeing wih Noninear Behavior for Vehice Dynamic udies, harif Universiy of Technoogy, 00. [3] F. Vk: Dynamika moorových voide, Brno, 003. [4] Z. Jan, B. Ždánský: Výkadový auomobiový sovník, Brno, 007. B Inerne sources: [4] h://cs.auoexicon.ne 0