The influence of vehicle body roll angle on the motion stability and maneuverability of the vehicle

Transcription

1 Article citation info: PAZEWSKI, K., WNĘK, H. The influence of vehicle bod roll angle on the motion tabilit and maneuverabilit of the vehicle. Combution Engine. 2017, 168(1), DOI: /CE Krzztof PAZEWSKI Henrk WNĘK CE The influence of vehicle bod roll angle on the motion tabilit and maneuverabilit of the vehicle The article dicue the impact of deign olution of vehicle upenion into angle of bod roll. It wa hown which tpe of upenion i better from thi point of view. There were examined the dependence of the upenion parameter on the vehicle bod roll angle. The influence of camber angle on the force tranmitted to the tire contact with the road urface wa analed. The lateral force were meaured on the tet tand. There wa teted dependenc of lateral force from the idelip angle for different angle of camber. Wa analed change of lateral force generated b camber angle on the vehicle which wa made on a cale ~ 1:5 during tet carried out on the teting track. For thi purpoe, two tet have been elected: firt one allowing the meaurement in tead motion condition, the econd one with dnamic change of direction of vehicle motion. The graph how the effect of camber angle on the controllabilit and tabilit of the vehicle motion. Ke word: tabilit of vehicle motion, upenion, the interaction of the road and tire, the roll angle of vehicle bod 1. Introduction One of the tak of the upenion of the vehicle i the appropriate wheel movement relative to the vehicle bod. The controllabilit and tabilit of vehicle motion i influenced b: the tiffne and damping of upenion element, upenion kinematic motion and change the wheel angle. The olution of deign of upenion affect the load and wheel inclination while performing variou maneuver b the vehicle. During analzing the interaction of the wheel with the road urface, it can be determined which of the upenion contruction i the mot preferred for ue in variou tpe of vehicle. For thi purpoe, wa conducted the tud of dnamic of the phical model in a cale of 1:5, in which were aembled variou tpe of upenion on the front and rear axle. Thi model fulfill criteria of imilarit to medium truck [1, 2, 11, 14]. Tire parameter were determined during the tet on the tet tand: tiffne in the longitudinal direction, tranvere and radial and angular tiffne. In addition, were compared variou parameter of the vehicle upenion: vertical tiffne and roll tiffne while maintaining the gro vehicle weight and moment of inertia. During the teting on the teting track were analzed behavior of the vehicle during tet: the firt one driving on the circle track (quai-tatic driving condition) and the econd one udden change of vehicle direction (dnamic driving condition) [5, 6]. The tud allowed to determine the effect of the upenion on the vehicle behavior [10]. 2. Influence of the kind of upenion on the co-operation of the tire with the road urface The total force tranmitted b the wheel on the road urface conit of the normal force and tangential force (driving or braking, and lateral force). The maximum value of tangential force are limited b the condition of the adheion [13]. The lateral force depend on the wheel angular tiffne and it inclination. Figure 1 how a comparion of different kind of vehicle upenion during driving in a circular track. Fig. 1. Comparion of vehicle with different kind of upenion on a curvilinear track [own tud] In the cae of dependent upenion, camber angle i uuall maller than that of the car equipped with the double wihbone in upenion. Supenion equipped with McPheron' column, generate lightl le camber angle. The vehicle bod inclination angle depend on the kinematic and tiffne of the upenion and are uuall maller for vehicle equipped with dependent upenion. The ue of anti-roll bar increae the angular tiffne of the vehicle. The anti-roll bar increae the angular tiffne of the upenion on the axi of the vehicle and protect it from exceive angle of bod roll. During driving on a bend of the road, vehicle under the influence of the centrifugal force incline toward the outer wheel. The anti-roll bar operate to reduce the difference of intantaneou load on the elatic element of upenion of the wheel on one axle and reduce roll angle [13]. In vehicle equipped with upenion with rigid axle change camber depend on the uceptibilit of the tire and the road urface irregularitie. In the cae of vehicle with independent upenion angle of wheel inclination depend on the upenion geometr change reulting from the vertical movement of wheel and the lateral inclination of the upenion. Figure 2 how the camber angle according to the inclination of the vehicle bod for different kind of upenion: double wihbone, McPheron' column, and rigid axle [own tud] The parameter of the vehicle upenion For the anali were choen dependent upenion currentl ued in SUV, van and truck, and an independent upenion with double wihbone of different length ued in paenger car and van. The tet method wa ued to COMBUSTION ENGINES, 2017, 168(1) 133

2 The influence of vehicle bod roll angle on the motion tabilit and maneuverabilit of the vehicle determine the vertical and angular tiffne of the upenion and roll damping of upenion. The meaurement reult of upenion tiffne are given in Table 1. Table 1. Comparion of parameter of the vehicle phical model equipped with variou tpe of upenion [own reearch] Parameter Dependent upenion Independent upenion front axle rear axle front axle rear axle Vertical tiffne K, N/m Vertical tiffne K t, N/m Supended ma m, kg 9,329 13,688 8,839 13,818 Unupended ma m u, kg 1,667 1,648 2,662 2,783 The following figure how the impact of vehicle bod inclination angle to the wheel camber angle for different tpe of upenion, taking into account the correction caued b the anti-roll bar. Fig. 2. The angle of wheel camber γ a a function of vehicle bod roll angle for different tpe of upenion (including the impact of tire deflection) [own reearch] Fig. 3. The wheel camber changing γ reulting from vehicle bod roll angle equipped with upenion with double wihbone [own reearch] Fig. 5. The inclination of the vehicle caued b the lateral force [11] The impact of tire deflection wa omitted. Taking equation for the um of lateral force and equation for the um of moment about the roll centre it can be determined the impact of the location of centre of gravit on roll angle of the vehicle. F f (r) m (V& in β + V β& co β + V ψ& co β) m a M D + m (h m g (h & K K _ ARB (V& in β + V β & coβ + V ψ& coβ) ) co 0 ) in + For mall roll angle it can be aumed that in and co 1, and that the lateral offet of centre of gravit, caued b inclination of the bod, i o mall that can be neglected. The equation (2) wa ued to determine how the lateral acceleration affect on the roll angle of the vehicle bod (auming that the lateral motion of the vehicle bod i relativel low). M 1 (m a b b D & K K (h _ ARB ) 0 ) (1) (2) (3) a D & + (K + K m (h _ ARB ) ) (4) Hence, the implification: 1 (a (h ) m D & ) (5) K + K _ ARB Fig. 4. The wheel camber changing γ reulting from vehicle bod roll angle equipped with McPheron upenion [own reearch] 2.2. The parameter of the vehicle upenion Figure 5 chematicall how the inclination of the car due to a lateral force. Analing the equation (5) it can be tated that the roll angle of the vehicle bod to a large extent, determined b the lateral acceleration, the ditance from vehicle centre of gravit to the roll centre and ratio of the ma to the roll tiffne of the upenion (including the influence of the anti-roll bar). 134 COMBUSTION ENGINES, 2017, 168(1)

3 The influence of vehicle bod roll angle on the motion tabilit and manoeuvrabilit of the vehicle Taking into account the deflection of tire, it will reult in an increae in the roll angle of a few percent for truck to everal percent for paenger car. Baed on of reearch carried at the Laborator of the Department of Internal Combution Engine and Vehicle in Univerit of Bielko- Biala, wa determined the maximum roll angle t, reulting from the deflection of tire: for paenger car ~ 1.3 and for truck ~ 0.7. Figure 6 8 how the influence of the lateral acceleration, ditance of centre of gravit from the roll centre and the upenion roll tiffne and damping. Fig. 6. The impact of lateral acceleration on the vehicle roll angle (for a full-ize vehicle) [own reearch] Fig. 7. Impact at vehicle roll angle of ditance from centre of gravit to the roll centre (for a full-ize vehicle) [own reearch] On the vehicle roll angle alo affect the product of roll rate and roll damping tiffne, in the dnamic tate, it create a temporar decreae in the roll angle. In Figure 8 i hown a dahed line, which repreent the poible impact of roll rate and roll damping to temporaril change the roll angle (e.g during turning manoeuvre). The maximum value of the roll angle for car and truck i about 4 to 7, with the larget impact on the roll angle ha lateral acceleration ~56%, lightl lower ditance from centre of gravit to roll centre ~46% and the minimum ratio of weight to upenion roll tiffne ~8%. Taking into account the deflection of the tire can change the roll angle to ~4%. Moment of inertia of the vehicle bod will caue a dela of rolling. The ue of anti-roll bar of the front and rear axle will caue a reduction in the roll angle of up to 30%. On the bai of thi anali, it can elect the appropriate tpe of vehicle upenion with high and low located centre of gravit above ground. In the port vehicle and paenger car ditance from the centre of gravit to the roll centre i relativel mall and can be ued upenion, in which the effect of vehicle bod inclination on the roll angle i greater. In car with a high located centre of gravit for example SUV and truck hould be ued upenion, in which the inclination of the vehicle bod ha a little effect on the wheel camber angle. 3. The impact of wheel camber angle on the tranmiion of force on the tire contact with the road Change in camber angle caue a change in footprint the tire contact with the road and affect on change of the value of lateral force tranmitted to the road [8,9]. Becaue the ide force i limited b the term of adheion, and depend on the wheel load, the cornering tiffne K i will not be contant and will var. Lateral force between wheel and ground depend on the idelip angle and camber angle γ and i decribed b equation (6a) [4]. For larger idelip angle R. Jazar [7] recommend the ue of a implified equation (6b), taking into account the non-linear curve of the lateral force: F i K i i + K γi γ i (6a) where i an index indicating the i-th wheel Fig. 8. The impact at vehicle roll angle of the roll tiffne of upenion (for a full-ize vehicle) [own reearch] 2 1 K 1 K F K K γ γ (6b) 3 FM 27 FM The wheel camber angle will caue a change of the tire footprint on the roadwa and thu the formation of the lateral force component depend on the camber angle γ. In addition, will appear ome point hift reaction force F z from the wheel axi. In Figure 10b wa hown the impact of wheel camber angle on the tire footprint hape on the roadwa. When vehicle i driving with lateral acceleration under tead tate condition (e.g. during cornering), on the vehicle operate the centrifugal force, which can be determined COMBUSTION ENGINES, 2017, 168(1) 135

4 The influence of vehicle bod roll angle on the motion tabilit and maneuverabilit of the vehicle from equation F m a. Thi lateral force can be decompoed into component acting on the front and rear axle. F F + F (7) f The force acting on the front and rear axle, for mall idelip angle of wheel, can alo be determined from equation: a 2 Ff F (8a) L F a r w 1 r F (8b) L w Baed on the anali equation (6b) can be een that when the vehicle i moving on the curvilinear track under tead tate condition (fixed ide force), the increae of camber angle, will affect the decreae value of lateral force and at the ame value of thi force the value of wheel idelip angle will be increaed. Sidelip angle of the wheel can be determined from equation (9a) and (9b) [3]. f W g K r W g K K f γf a γf f K f (9a) K r γr a γr r Kr (9b) The were defined functional dependencie of wheel camber angle a a function of vehicle bod roll angle and a vehicle bod roll a a function of lateral acceleration, baed on the reult of reearch and anali for variou tpe of upenion. The value of tire cornering tiffne and camber tiffne were determined from meaurement on the tet tand [10]. 4. The impact of wheel camber angle on the tranmiion of force on the tire contact with the road Lateral force meaurement were conducted on a tet tand [10] uing the tire ued in phical model for variou wheel idelip angle at fixed value of camber angle γ (in the range of 0 to 10 deg). Fig. 9. a) Lateral force on the wheel contact with the road F at variou wheel camber angle γ, depending on the wheel idelip angle (for a full-dimenional vehicle) [own reearch], b) The lateral and vertical force and a footprint of the contact on the road urface caued b wheel camber angle Figure 9a how a comparion of the lateral force determined from the equation (6b), and obtained from meaurement on the tet tand [10]. The lateral force F decreae with increaing camber γ from a few to everal percent, proportional to the wheel idelip angle. The value of angular tiffne of tire and camber tiffne were determined on the bai of meaurement which were made on the tet tand. The value hown in table 2 were obtained from meaurement and were multiplied b cale factor of imilarit (for full-dimenional vehicle). The impact of the vehicle bod roll angle on tabilit and teerabilit of the vehicle were verified during the tet of phical vehicle model at cale ~1:5, conducted on the tet track. Table 2. The tiffne of tire for full-dimenional vehicle determined on the bai of the tire of the phical model [own reearch] Parameter Front axle Rear axle Vertical tiffne K z, N/mm Lateral tiffne K, N/mm Cornering tiffne K, N/rad Camber tiffne K γ, N/rad The influence of the vehicle bod roll angle on the tabilit and teerabilit of the vehicle were verified during the tet of the vehicle model in a cale performed on the tet track. 5. Anali of influence of the camber angle on the dnamic of vehicle motion baed on tet of the phical model 5.1. Meaurement of tabilit and teerabilit performed with uing the vehicle model During meaurement of tabilit and teerabilit of vehicle are ued tandardized reearch tet: driving in a circular path at a tead-tate condition (ISO 14792) [5], tep teering input (ISO 14793) [6], dnamic tabilit of the vehicle motion (AVTP tet of avoid an obtacle on the road) and other [12]. For tud were choen two tet baed on the driving on a circular path in tead-tate condition and tet of a repone on udden change of the teering wheel rotation. For teting wa ued a phical model of the vehicle made on a cale ~1:5, which fulfilled criteria of imilarit to the commercial vehicle (LCV) [11,14]. Uing the theor of imilarit, were choen the trajector and the parameter of motion to the cale of the vehicle. The run of the tet ha been programmed in the controller of model. On the vehicle model wa mounted meauring equipment VBOX 3i Racelogic baed on GPS technolog, allowing for regitration of the trajector and parameter of the motion: velocit, longitudinal and lateral acceleration, angular velocit of vehicle motion about axi paing through centre of gravit and roll angle of the vehicle [15]. Figure 10 how a model prepared for the tet. During the tet on the model were aembled variou tpe of upenion and additionall alo were mounted anti-roll bar on the front and rear axle. 136 COMBUSTION ENGINES, 2017, 168(1)

5 The influence of vehicle bod roll angle on the motion tabilit and manoeuvrabilit of the vehicle ion on the front axle and dependent on the rear one (green curve) roll angle reached up to 9 in the initial phae of the manoeuvre, order then to decreae to 4. While a vehicle wa equipped with a upenion with rigid axle (red curve) the roll angle were of ~7 to fall in the final phae to 2.5. Fig. 10. The phical model of the vehicle on a cale ~1:5 with mounted meauring apparatu 5.2. Anali of influence of camber angle on the vehicle tabilit and teerabilit During the tet, after the tart the vehicle wa moving traight for about 3 econd to achieve the required peed and then performed a manoeuvre of turn right and for about four econd wa moving along a circular path, would then return to the traight track and top. Steering angle of wheel, velocit and duration of individual manoeuvre were programmed and performed b the controller. Thi tet allow for conducting reearch under condition of dnamic change of motion direction and during the driving on a circular path in tead-tate condition. Figure 11 how the run of the velocit during tranient and tead-tate motion. Fig. 12. The run of the vehicle bod roll angle during the tet. [own reearch] Figure 13 how influence of the camber angle on the ide lip angle of wheel. Fig. 13. The influence of camber angle γ on the difference of wheel ide lip angle [own reearch] Fig. 11. The run of vehicle motion velocit during the tet. [own reearch] The following figure how the vehicle bod roll angle (Fig. 12) depending on mounted upenion in the vehicle. The red curve how the vehicle bod roll angle with mounted dependent upenion at front and rear axle. The curve of blue colour how the vehicle bod roll angle with independent upenion for both axle and the green one how the vehicle with independent upenion (two wihbone) mounted on the front axle and with the rear rigid axle. The bod roll angle are greatet in a vehicle with independent upenion ~13 and the mallet in the vehicle equipped with dependent upenion ~7. In the firt cae, with the independent upenion on both axle, the roll angle in the initial phae of the turning reached to 13 and then decreaed up to 6. In the cae of independent upencombustion ENGINES, 2017, 168(1) Camber angle have an influence on the ide lip angle, and their change doe not exceed ~3 for a vehicle equipped with an independent upenion on both axle, ~1.75 for the vehicle with independent upenion on the front axle and dependent on the rear one, and ~0.3 for a vehicle equipped with dependent upenion on both axle. Figure 14 how difference of ide lip angle of wheel of the front and rear axle for different upenion tpe mounted on the vehicle. The vehicle equipped with different upenion on the front and the rear axle had overteer characteritic. The vehicle had underteering characteritic for other combination of the upenion. Vehicle with different upenion of front and rear axle in the initial part of the tet (dnamic change of the direction of motion) clearl tightened the turn. A vehicle equipped with independent upenion on both axle in the initial part of the tet increaed the radiu of curvature of the track. A vehicle equipped with a dependent upenion to a much leer extent increaed the radiu of the track. In 137

6 The influence of vehicle bod roll angle on the motion tabilit and maneuverabilit of the vehicle the part of the tet, while the vehicle wa moving in teadtate condition, radii of curvature of the track were ver imilar. Fig. 14. The influence of roll angle on the difference of wheel ide lip angle of front and rear axle. [own reearch] Fig. 15. The influence of anti-roll bar on the vehicle bod roll angle. [own reearch] The application of anti-roll bar in the upenion of vehicle reduce the roll angle (Fig. 15). During the tet of the model ha been oberved reducing of the vehicle roll angle more than 1 degree (about 15%). Thi wa due to increae reaction force on the unloading wheel (at large roll angle, even up to 40%) and in reult the improvement of lateral tabilit. The ue of anti-roll bar allowed the tranfer the larger driving force during the intene turn manoeuvre (even at high lateral acceleration). During the Nomenclature idelip angle of wheel, o, rad difference of wheel idelip angle of front and rear axle, o, rad difference of wheel idelip angle caued b camber angle, o, rad β vehicle lip angle, o, rad γ camber angle of wheel, o, rad roll angle of the vehicle bod, o, rad roll angle of the prung ma, o, rad t roll angle of the vehicle bod caued b tire, o, rad &. roll rate of the vehicle, 1/ road tet wa oberved a light decreae of the trajector radiu of the vehicle motion, reulting from better load ditribution on the ide of the vehicle. 6. Summar and concluion In vehicle equipped with upenion with rigid axle the change of the camber angle reult from the compliance of the tire and the road urface irregularitie. In the cae of vehicle with independent upenion the camber angle alo depend on the upenion geometr change reulting from it the vertical movement and from the vehicle bod roll angle. Change of camber angle will change the contact patch the tire with the road and affect to change of the ize of lateral force tranmitted on the road urface. On bai of conducted tet and tudie it can be concluded about chooing the right tpe of upenion for vehicle with high and low centre of gravit poition. In the port vehicle and claical paenger car the ditance between the roll axi and the centre of gravit i relativel mall and can be ued upenion, in which the influence of vehicle bod roll angle on the camber angle i greater. In car with a high poition of gravit centre, for example multipurpoe vehicle (SUV port utilit vehicle) and truck (CV commercial vehicle) hould be applied upenion, in which the vehicle bod roll angle ha little effect on camber angle. Larger camber angle effect on increaing the ide lip angle. The application of different upenion can caue variation of ide lip angle difference of front and rear axle and thereb affect on underteer and overteer of the vehicle. Thi i particularl apparent when dnamicall change direction of the vehicle motion. During the driving in a circular path at tead-tate condition influence of the applied upenion i much le felt. The ue of independent upenion on the front and rear axle in truck reult in a ignificant increae in vehicle roll angle, which increae the rik of vehicle rollover and deteriorate the propertie of vehicle motion, both in quai-tatic and dnamic condition. The ue of anti-roll bar on the front and rear axle reult in decreae the vehicle roll angle and thereb improving cooperation the wheel with the road urface, and increaing teerabilit and tabilit of the vehicle. ψ&. aw rate of the vehicle, 1/ a 1, a 2 ditance of the centre of gravit from the front/rear axle, m a x longitudinal acceleration (a x V & ), m/ 2 a lateral acceleration, m/ 2 b wheel tread, m b lateral eparation between the pring, m C γ tire camber tiffne, N/rad C tire cornering tiffne, N/rad C z tire vertical tiffne, N/m tire lateral tiffne, N/m C 138 COMBUSTION ENGINES, 2017, 168(1)

7 The influence of vehicle bod roll angle on the motion tabilit and manoeuvrabilit of the vehicle D roll damping of upenion, Nm/rad F L(R) vertical force acting a a reult of the deflection of the left (right) pring, N F f, F r lateral force acting on the front/rear wheel, N F L(R) lateral force acting on the left wheel (right), N F M maximum value of the lateral force, N F zl(zr) vertical force acting on the left wheel (right), N g gravit acceleration, m/ 2 h ditance between the center of gravit and the roll center, m h height of the center of gravit above the ground, m h the height of the roll center above the ground, m i an index the roll tiffne of upenion, Nm/rad K K _ARB additional roll tiffne upenion caued b a anti-roll bar, Nm/rad k upenion tiffne, N/m k t vertical tire tiffne, N/m k cornering tire tiffne, N/rad L w wheelbae (L w a 1 + a 2 ), m M um of moment about the roll centre, Nm m ma of vehicle (m u + m ), kg m prung ma of vehicle, kg m u unprung ma of vehicle, kg R roll centre point, r the radiu of the track, m R, R z the reaction operating in the roll centre, N V the peed of a moving vehicle, m/ W f, W r load of front/rear axle, N Bibliograph [1] BAKER, W.E., EESTINE, P.S., DODGE, F.T. Similarit method in engineering dnamic. Theor and practice of cale modeling. 9th ed. New Jere: Spartan Book. 1978, [2] BUCKINGHAM, E. On phicall imilar tem: Illutration of the ue of dimenional equation. Phic Review. 1914, 4, [3] GILLESPIE, T.D. Fundamental of vehicle dnamic. 1t ed. Warrendale: SAE. 1992, [4] GUZEK, M., LOZIA, Z., REŃSKI, A. The influence of angular tiffne of upenion on the lateral tabilit of the two-axle vehicle on the example of light comercial vehicle. Zezt Naukowe Inttutu Pojazdów. Politechnika Warzawka. 1998, 3, [5] ISO 14792:2003. Heav Commercial vehicle and Articulated Bue. Stead tate circular tet. [6] ISO 4138:2012. Paenger car. Stead-tate circular driving behavior. Open-loop tet method. [7] JAZAR, R.N. Vehicle dnamic. Theor and application. 2nd ed. New York: Springer. 2008, [8] LOZIA, Z. A two-dimenional model of the interaction between pneumatic tre and an uneven road urface. Vehicle Stem Dnamic: International Journal of Vehicle Mechanic and Mobilit. 1988, 17(1), [9] LUTY, W., PROCHOWSKI, L. The poibilit of tranferring lateral force b the tire of a truck on a bend of the road. Zezt Naukowe Inttutu Pojazdów. Politechnika Warzawka. 2004, 3(54), [10] PAZEWSKI, K., WNĘK, H. The tre characteritic of phical model ued to invetigate vehicle lateral tabilit. Proceeding of the Intitution of Mechanical Engineer, Part D: Journal of Automobile Engineering. 2015, 229(10), [11] PAZEWSKI, K, WNĘK, H. Uing mobile caled vehicle to invetigate the truck lateral tabilit. Ekploatacja i Niezawodnoc Maintenance and Reliabilit. 2013, 15(4), [12] PIENIĄŻEK, W. Selected iue of reearch on the vehicle tabilit and teerabilit. Zezt Naukowe Inttutu Pojazdów. Politechnika Warzawka. 2010, 3(79), [13] REŃSKI, A. Vehicle active afet. The upenion, teering and braking tem. 1t ed. Warzawa. Oficna Wdawnicza Politechniki Warzawkiej. 2011, [14] ROMANISZYN, K.M. Mobilne modele amochodów do badań tateczności. Logitka. 2012, 3, [15] ROMANISZYN, K.M. Comparion of dnamic parameter of a pecial-purpoe vehicle with different centre of gravit location. Zezt Naukowe Inttutu Pojazdów. Politechnika Warzawka. 2010, 1(77), Krzztof Parczewki, DSc., DEng. Facult of Mechanical Engineering and Computer Science at Univerit of Bielko-Biała. kparczewki@hth.bielko.pl Henrk Wnęk, DEng. Facult of Mechanical Engineering and Computer Science at Univerit of Bielko-Biała. hwnek@ath.bielko.pl COMBUSTION ENGINES, 2017, 168(1) 139