ACTIVE REDUCTION OF OVERSTEER AND UNDERSTEER USING SUSPENSION ELEMENTS SVOČ FST 2013

Transcription

1 ACTIVE REDUCTIN F VERTEER AND UNDERTEER UING UPENIN ELEMENT VČ FT 03 Marin Vček, Universiy of Wes Bohemia, Univerini 8, Pisen Cech Reubic ABTRACT This aer, which is a ar of my Ph.D. hesis, consiss of a basic exanaion of car yaw behaviour and shows exames of design souions reducing car overseer and underseer. There is a sofware mode of a sma assenger car creaed wih Adams Car, which is verified by a mahemaica mode of seady sae cornering. The main emhasis of he aer is aced on my roosed souion reducing overseer and underseer ug acive seering eemens. KEYWRD verseer, Underseer, usension eemens, MC Adams Car, eering. 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 robem wih overseer and underseer reaes o car safey. The rocesses ha occur during cornering are described ug a sofware mode, which is verified by a mahemaica mode of seady sae handing. This aer gives an idea of he car behaviour during cornering and shows ossibiiies for imroving vehice handing sabiiy. BAIC PRINCIPLE F VERTEER AND UNDERTEER There are hree ossibiiies of car behaviour, which may occur during cornering. The firs siuaion is 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 whees are more oaded by he addiiona forces and yres canno fuy ransfer his oad on o he road. The hird siuaion is overseering. 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. [6] We usuay use abiiy facor K o exain car behaviour in cornering. This facor is given by he formua: K C = m α C' α C' C α α () 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 he weigh disribuion and on cornering siffness of axes. When K is equa o 0, i shows neura seer. When he sabiiy facor is ess han ero, i shows overseer. The car urning radius is ess han radius for neura seer. The hird siuaion is underseer, when K is greaer han ero and car urning radius is greaer han radius for neura seer.

2 Figure : Forces a yre conac area [6] Figure : Kamm circe of friciona forces [6] 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 [-] adhesion coefficien Resuan force is resuan of aera force and braking force (Figure ) or aera force and driving force (in case of acceeraing). Figure shows he Kamm circe of friciona forces. The radius of his circe is he roduc of verica whee force and adhesion 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 REDUCING VERTEER AND UNDERTEER There are many common souions ha imrove car yaw behaviour and car handing sabiiy. ere are few seeced 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 (orque vecoring) - 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 - eecronic brake disribuion or cornering brake conro divides braking ressure among he whees in cornering - and many anoher souions... Figure 3: EP (Eecronic sabiiy rogramme) [5]

3 The mos effecive design souion eiminaing overseer and underseer is oday Eecronic abiiy Programme (EP), which is shown in Figure 3. FTWARE MDEL AND MATEMATICAL MDEL Figure 4: Vehice assemby in MC Adams Car 0 I made a sofware mode in he rogram Adams Car 0 o simuae various driving siuaions. In he Figure 4 is shown fu assemby of a sma assenger car, which consiss of hese creaed subsysems: fron susension (MacPherson), rear susension (raiing arm), seering (rack and inion), whees (Pacejka mode 75/70 R3), body (defined as mass roeries), owerrain (fron whee drive). To evauae sofware mode I creaed a mahemaica mode of seady sae handing. I means a mode for consan radius cornering (see Figure 5). To find a veociy where he oss of adhesion occurs for urning radius 50 meers, was an objecive of my cacuaion. Figure 5: Iusraion of seeced moion rajecory for seady sae handing I used he foowing ane mode (Figure 6) o invesigae forces effecs on he vehice during cornering. In he case of seady sae vehice handing we can use hese simificaions and assumions [6]: - 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 Figure 6: Genera ane mode of vehice cornering [6] 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 = α o v f f f f F () ) Force baance in he direcion of Y axis: 0 = α 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 many imoran unknown deendencies and reaions for soving hese hree main equaions. I soved hese hree equaions ug Microsof Exce and MATLAB. I used he same foowing enered arameers for he mahemaica and sofware mode of seady sae handing o ensure sime comarison. The modes were differen ony in he yre sie because I did no find he yre characerisic for he same sie of yres. 75/70 R3 yres were used for he sofware mode, and 55/70 R3 for he mahemaica mode.

5 Modes arameers: Figure 7: Modes arameers [6] The comarisons of obained characerisics of he mahemaica and sofware modes are reresened in he foowing chars. Grahica mode of seady sae handing in Figure 8 shows obained anges, forces and Kamm circes. Figure 8: Grahica mode of obained characerisics ere are he resuing characerisics of seady sae handing for radius 50m. The bue coours reresen he mahemaica mode and red coours are used for he sofware mode creaed in he MC Adams Car.

6 Figure 9: Deendence of seering anges bi vs. car veociy v Figure 0: Deendence of si anges ai vs. car veociy v Figure : Deendence of resuan forces Ri and friciona forces Zi*m for axes vs. car veociy v The as deendence shows resuan forces and friciona forces (radiuses of he Kamm circes) for he fron and rear axe. The veociy, where he resuan force of an axe is higher han friciona force means oss of adhesion. In Figure you can see ha oss of adhesion for fron axe occurs a 70 km/h for he mahemaica mode and a 73 km/h for he sofware mode. These simiar resus show ha he mahemaica mode and sofware mode in he Adams Car are robaby correc. ma differences may be caused by sighy wider yres in he Adams Car. PRPED LUTIN REDUCING VERTEER AND UNDERTEER I creaed a new device in Adams Car ha can he reduce overseer and underseer. I imemened roaion acuaors o he whee carriers of he fron susension (see Figure ). These roaion acuaors change oe ange according o aera acceeraion a y, car veociy v and seering anges b when he oss of adhesion is near.

7 Figure : Roaion acuaor in he fron susension The funcions shown in he Figure 3 were deveoed o conro wo acuaors. The conro funcions use arcg deendence, which I obained by a ong ime oimiaion. Figure 3: Acuaors conro funcions The acuaor conro funcions are based on he Ackermann heory, which says ha he roaion axis of a whees shoud be aimed a one oin. Bu i is no ossibe in fac due o si anges, seering geomery and susension rave. Therefore I deveoed he acuaors changing seering anges (oe anges) indeendeny on he fron whees, which can imrove safey and handing sabiiy a high seeds. I erformed a few ess and manoeuvres wih he acuaors and wihou he acuaors o demonsrae acuaors effecs. I ried ou hese ess: - eady sae handing (consan radius cornering) - I ane change manoeuvre (AVTP 03 60) - INE wave seering (IN seer) - udden seering-ange change (ram seer) - Drifing es I erformed he ess for various inu arameers. The esing car wih he acuaors had faser seering reacions in a cases. i occurred a higher seeds and he car was sabiised earier when he oss of adhesion occurred. In he foowing icure is an exame of he resus for seady sae handing es. The es wih and wihou he acuaors was erformed for iniia radius 50 meers. Figure 4: Resus of seady sae handing es wih and wihou acuaors

8 Deendence in Figure 4 shows aera acceeraion, cornering radius and acuaor behaviour deend on veociy. The veociy a which aera acceeraion and cornering radius suddeny changes shows oss of adhesion. In he deai (Figure 5) you can see ha he oss of adhesion occurs a higher seed wih he acuaor. The difference is aroximaey 0.5 km/h. Bu i is aso imoran ha he car is sabiied earier wih he acuaor. The difference in cornering radius is greaer han 4 meers. Figure 5: Deai of he resus of seady sae handing es CNCLUIN AND RECMMENDATIN The obained characerisics give us an idea of car behaviour during cornering and show ossibiiies for imroving vehice handing sabiiy. My roosed souion indeendeny changes seering anges (oe anges) on he fron whees hereby imroving car driving sabiiy eseciay in cornering. The souion may be creaed by various design conces an i is ossibe o combine his souion wih oher exising souions imroving he acive vehice safey. 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] Reime, J., emu,., Beer, J. W.. The Auomoive Chassis: Engineering Princies, Reed Esevier and Professiona Pubishing Ld, 00. IBN [4] F. Vk: Dynamika moorových voide, Brno, 003. [5] Z. Jan, B. Ždánský: Výkadový auomobiový sovník, Brno, 007. B Conference Proceedings [6] M. VLČEK, imiaion of Car Yaw Behaviour Ug Acive usension Eemens. Proceedings VČ 0. Peň: ZČU-FT, 0, s. -. IBN The arice has been suored by he form of rofessiona advice wihin framework of he Projec No. CZ..07/.3.00/ Pouariaion of research and deveomen in mechanica engineering and is resus (Pouar) and co-financed by Euroean ocia Fund and a sae budge of he Cech Reubic.