AN ACTIVE STEERING SYSTEM FOR ROAD VEHICLES

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1 esearch Article IJAAT 207 International Journal o Advances on Automotive and Technology Promech Corp. Press, Ianbul, Turkey Vol., No., pp. -5, January, Manuscript eceived May 20, 206; Accepted June 0, 206. This paper was recommended or publication in revised orm by Co-Editor Ya Karagoz AN ACTIVE STEEING SYSTEM FO OAD VEHICES *Waizuddin Ahmed Concordia University Montreal, Quebec, Canada Vaibhav awat Tata Motors Pune, India Keywords: Vehicle handling, Active eering, Independent eering, Steering mechanism * Corresponding author: Phone: Ext. 7932, Fax: address: waiz@alcoconcordia.ca ABSTACT Active eering syems or road vehicles are designed to generate and deploy a required angle at the wheels to realize a predetermined target response or a eering input at any orward velocit For a typical vehicle with conventional eering syem and undereer characteriics, this will demand an increase (correction) in the wheel eer angle as the velocity is increased. On the other hand, a handling maneuver at high speeds will lead to signiicant load shit rom the inner to the outer wheel, which diminishes the ability o the inner tire to develop lateral orce even i the eer angle is increased. This limits the perormance potentials o active eering syem i corrections are provided at both wheels ollowing a ixed eering geometr ecent udies have proposed active independent eering control where the eering correction can be introduced independently at a selected wheel. Such control rategy can thus also consider the tire work load at each wheel and in doing so, the correction can be applied to each wheel ensuring that none o tires approach its saturation limit. This paper presents sample results rom a -wheel vehicle handling model to demonrate the eectiveness o the active independent eering syem over the ixed ratio conventional active eering syem. A possible ail-sae mechanism that can be utilized to realize such control is also presented. INTODUCTION oad vehicle eering mechanisms are designed to closely ollow the Ackerman eering ratio, which is based on eer angle required at the inner and outer wheels or pure rolling at low speeds. At high speeds, dynamics o a vehicle inluences the vertical load on each tire, which intern eects the slip angle and causes the vehicle to ollow dierent paths at dierent speeds or an identical eering input. This phenomenon due to compliance o pneumatic tires known as undereer characteriics [] can be neutralized by actively controlling or modiying the eer angle at the wheel depending on orward speed. The concept o Active Steering Control [2] has been explored or over a decade ago and has gained a new momentum in recent years [3, ]. The rategy in such syem is to monitor vehicle ate parameters and eering command rom the driver, based on which a corrective eer angle is computed and applied to the eer angle at the wheels. The undereer eect can thus be neutralized requiring same eer input or same turn regardless o orward speed. Such handling characteriics can signiicantly reduce driver skill requirements and would be essential or automations. Any high speed handling maneuver, however, introduces a load shit rom inner to outer wheels. The resulting reduction in normal load on inner tire not only reduces its ability to generate lateral orce, but also decreases the slip angle at which maximum lateral orce can be generated []. Thus, inner tire s rictional orce is prone to saturate while outer tire may ill have reserved ability to generate more lateral orce. The eer angle at the inner tire is thereore critical in determining the extent o active eering control that can be applied. In order to improve handling perormance at high speeds, anti-ackermann geometry is employed in race cars, where primary concern is higher lateral orces at high speed turning [5]. For conventional active eering syem, ce the corrective input is applied to both the wheels ollowing the Ackerman geometry, it is expected that there will be signiicant dierence in the tire work-load [6] at the inner and outer tires, which is a major concern in vehicle handling and saety [7]. A perormance parameter, tire work-load [6, 8] is convenient or comparing tire riction orce utilization. Tire work-load is deined as the ratio o total orces being generated

2 esearch Article rom the tire and maximum ability o generating orces at any given time. The perormance o an active eering syem can be maximized by introducing dierent corrective measure at the inner and outer wheels such that the target response is realized while the tire with lower work-load is given larger corrective measure. Such a control rategy would require an independently controllable eering syem, reerred to here as Active Independent Front Steering (AIFS) syem. Simulation results obtained or a -wheel ull vehicle handling models with active and active independent eering syems. A simple Proportional Integral (PI) controller is utilized to generate corrective eering or the inner and outer wheels such that the target is realized while attempt is made to equalize the tire workloads o both the tires. Simulation results generated or AIFS or a rounded ep and usoidal lane change maneuvers are compared to demonrate the eectiveness o AIFS syem. A major challenge in realizing the concept o AIFS syem is in designing a ail-sae mechanism that can provide a means or active control o the inner and outer wheel s eering angle independentl Va majority o udies with active eering syem proposes the use o Steer-by-Wire (SBW) and signiicant research are being carried out by automotive indury on this concept [9, 0]. Such syems are whoever not yet accepted as a ail-sae syem or eering applications. An innovative mechanical syem utilizing planetary gears proposed in [, ] or the AIFS concept is presented as a viable mechanism or active eering technology o the uture. FOU-WHEE VEHICE MODE Equations o Vehicle Motions Handling udy with active eering syem will typically employ a bicycle model [] o road vehicle without regard to lateral load shit or tire s saturation limit. To examine the concept o AIFS, it is essential to utilize a -wheel vehicle handling model that includes tire non-linearity and dynamic lateral load shit. For the present inveigation, a simpliied but adequate -wheel vehicle model is utilized that includes roll load shit and nonlinear magic ormula [] tire model. For simplicity, an in-plane model is retained that neglects bounce, pitch and roll motions o the vehicle. The 3-DOF (longitudinal, lateral and yaw motions) model along with tire lateral orces is shown in Figure. With reerence to Figure, the inal expressions or the equations o motion are: m a m a I z x y F. F cos( ) F cos( ) F F. M F ( ) F i... F. b cos( ) T ( ) b cos( ) T ( ) c F F ( ) () where are the eective eer angles or let and right wheels. The tire lateral orces (F yi) and aligning moments (M i) are computed rom well-eablished non-linear Pacejka s Magic Formula [2] tire model. The coeicients o the magic ormula used are those corresponding to a medium size car tire provided in [2]. The basic eering command or right ( ) and let ( ) wheels are based on ideal Ackermann geometry and obtained as a unction o driver eering command ug the ollowing relations:, tan tan cos cos T T ; Fig. : Vehicle yaw-plane model. In this inveigation, a tire s ability to generate handling or cornering orce is deined by tire workload deined as: 2 2 Fy Fx Tire work-load = (3) F z Where F x, F y, F z are inantaneous tire orces in the longitudinal, lateral and vertical directions, respectivel For coeicient o riction μ =, the tire workload approaching unity would be considered as the saturation limit or a tire when its ability to generate urther orce is diminished. When tire magic ormula [] is used, however, the coeicient o riction is also a unction o normal load. In this inveigation tire work-load at the inner tire with reduced normal load thus approaching 0.9 is considered (2) 2

3 esearch Article to be the saturation criteria. Detailed derivations or the vehicle and tire model are presented in []. Control Syem oad vehicles or general use are designed with pro- Ackerman eering geometry and undereer characteriics. In simple terms, the control synthesis or active eering syem are based on computing the neutral-eer yaw rate or a given eering angle (target) and comparing it with the inantaneous actual yaw rate to determine the yaw rate erro The yaw rate error is then used to eablish a corrective eer angle which is then added to eer angles given in Equations (2). In order to realize the advancement proposed through AIFS, the corrective eering angle should be primarily added to the outer wheel with lower workload. In the event the inner tire reaches saturation or the tire workload approaches unity, the angle or the inner tire should be reduced while that o the outer increased urthe The initial results presented in this paper are obtained or corrective angle applied to the outer wheel only in order to demonrate the eectiveness o AIFS syem. The controller thus mu ir identiy the outer wheel prior to any corrective action taken. Ug simple PI controller, the corrective eer angle or the outer wheel is eablished rom: c k k2 where the corrective eering actor error and k, k 2 are PI gains. () is a unction o yaw rate ESUTS AND DISCUSSION The parameters used or the handling simulation o vehicle are presented in Table I. A eady turn simulation is carried out or a eering command o 5.73 degrees (0. radians) in the orm o rounded ep input reached in 2.0 seconds. Simulations are carried out or active eering control reerred to as Active Front Table Parameters or Handling Simulations Symb Magnitude Quantity ol and Unit m mass o the vehicle 530 Kg Iz moment o inertia about z axis 3500 Kg.m 2 Wheel base 2.8 m b Diance o CG rom ront axle.3 m c Diance o CG rom rear axle.5 m hcg Height o CG rom ground 0. m T Hal Track Width - ront axle 0.7 m Tr k k2 Hal Track Width - rear axle Controller proportional gain Controller integral gain 0.7 m Steering (AFS), where the correction is added to both wheels without altering the eering geometry, and AIFS where the correction is added to the outer wheel onl Sample results or a conant orward velocity o 5 m/s (5 km/h) are shown in Figures 2 to. The eering input and the eer angles generated by both AFS and AIFS syems are shown in Figure 2. The results show that the AIFS correction was achieved by increag the outer (right) wheel eer angle alone to 8 degrees, while or AFS both the inner and outer wheel angles were increased above 7 degrees. Steering input and Output, (deg) Driver eering commnad AFS-ight, Outer AFS-et, Inner AIFS-ight, Outer AIFS-et, Inner Time (Sec) (sec) Fig. 2: The eering angle generated at each wheel The AFS by design maintained the Ackerman eering ratio and the increase was necessary to realize the target at this speed. In doing so, the inner wheel with reduced normal load quickly approach saturation as can be seen in Figure 3 where work-load at each ront wheel are compared. On the other hand, or AIFS, the workload o both tires is close to each othe With independent controllability o AIFS syem, it is possible or the controller to reduce the eer angle o the inner (let) wheel while increase that o the outer (right) wheel urther to realize the target. And in doing so, the workload will be equalized. Tire Work oad, Compare AFS-ight, Outer AFS-et, Inner AIFS-ight, Outer AIFS-et, Inner Time (sec) 0 5 Fig. 3: Tire work-load comparison or AFS and AIFS MECHANISM FO AIFS Va majority o udies with active eering syem proposes 3

4 esearch Article the use o Steer-By-Wire (SBW) and signiicant research are being carried out by automotive indury on this concept. As shown in the general layout o SBW in Figure 5 [3], there is no mechanical connection between the eering and road wheel, and thus any active correction can be easily introduced through the eering actuato Such syem can also be easily extended to provide independent correction o inner and outer wheels. Fig. 5: Steer by wire syem [] However, or obvious reasons, such syem without mechanical linkage is not yet considered to be a ail-sae, economical or reliable or automotive applications [9]. Consequently, there are no production cars available that depend only on SWB technolog To the be o the author s knowledge, there are no eering mechanism other than the one reported in [], that is readily applicable or an AIFS syem where the angle o each wheel can be controlled independentl This patented [] mechanism utilizing tandem planetary gear rack syem or application to AIFS syem is summarized in the ollowing. A 3D model o the proposed mechanism developed in graphics design sotware, Maya is shown in Figures 6 and 7. The model only represents the mechanical connections between various parts and is not precise in terms o kinematical analysis. Fig. 6: AIFS mechanism, ull view As seen in these igures, the input rom the eering column goes to the sun gear o the ir planetary gear syem and then goes through the planet carriers to connect to the sun gear o the second planetary gear syem. The planet carriers o both gear syems are attached to individual pinion gears which move the racks or each wheel. The annulus o each gear syem is also meshed with an electronic moto Both o these motors are controlled independently by the compute The planet gear syems and the racks used or both wheels have same design parameters which makes this mechanism symmetrical or both ront wheels. The mechanical connection between the eering wheel and the road wheels is maintained through the planet gear, thus making it ail-sae. In case o any electronic ailure, the annulus o both planet gear syems can be locked at a reerence, thus converting it into a conventional eering syem. The input rom the eering will rotate the sun o each planetary syem while the carriers will be attached to the respective rack. As shown, each rack will control the eer angle o one ront wheel. The motors or each wheel will be normally locked in place and the let and right wheel angles will be based on Ackerman geometr ack-pinion 2 Planetary gear syem Controller motor 2 Planetary gear syem 2 ack-pinion Controller motor Driver eering command Fig. 7: AIFS mechanism, planetary gear and controller When active control o one wheel will be required, the controller will send signal to the respective motor to turn the annulus while the sun is held in place by the eering wheel position. Thus the carrier o the controlled wheel will only turn to move the rack giving the required correction in the angle o that wheel onl The syem is designed such that any correction done by the controller and motor to one or both wheels will not be elt by the driver at the eering wheel. In act even when there is no eering input, the control motors will be able to introduce eering angle at the wheels simultaneously or independently to realize unctions other than eering maneuvers. For example, a controlled eering angle can be introduced to a selected wheel to generate lateral orce in order to enhance ability without any eed back to the driver through the eering wheel. Similarly unlike conventional syem, automatic parking unction can be realized without any eedback at the eering wheel.

5 esearch Article CONCUSION Although the concept o active eering control has been explored or some time, it has been revitalized recently through the development o electronics, sensor technologies and vehicle control syems. The concept o AIFS with appropriate controller can be designed or a vehicle to realize target response to a handling command similar to conventional AFS syem. AIFS can however, enhance the perormance limits o AFS by increag the tire s capability as it tends to equalize the workloads o the tires. An AIFS can thus maximize a vehicles handling perormance limited only by lateral slide or roll over o the vehicle. The mechanism presented or application o AIFS concept has the capability o providing independent control o wheel eer angle without any eedback to the operator and in a ail-sae manne The design urther possesses signiicant potential or numerous handling and ability control applications or a road vehicle. Although it is not inveigated in this udy, it may be more advantageous to use AIFS or Dynamic Yaw Control application rather than the conventional selective brake based syem. NOMENCATUE a x ongitudinal acceleration o the vehicle CG a y ateral acceleration o the vehicle CG b, c Diance o CG rom the ront and rear axles G yaw Yaw-rate gain h cg Height o CG above the ground Mass moment o inertia o the vehicle (z) axis I zz K us Undereer coeicient Wheel base m Mass o the vehicle M i.j i=, r; j=, ; aligning moment on ront/rear ight/et adius o the curved path re eerence radius o the curved path V Forward velocity o the vehicle W Weight o the vehicle x, y, Vehicle co-ordinate syem α i.j i=, r; j=, ; Tire side slip-angle, ront/rear-ight/et δ, δ Steering angle at let and right wheels δ Driver eering command μ Coeicient o riction between tire and road surace. Vaibhav awat,. "Active Independent Front Steering or Yaw-ate Control and Tire Work-oad Equalization in oad Vehicles", MASc thesis, Concordia University, Montreal, Canada (2007). 5. Ganey III, E. F. and Salinas, A.. "Introduction to Formula SAE Suspension and Frame Design"; SAE paper no. 9758, (997). 6. Velardocchia, M., Morgando, A. and Sorniotti,. A. Four- Wheel-Steering Control Strategy and its Integration with Vehicle Dynamics Control and Active oll Control, SAE paper no , (200) 7. Cech, I. Anti-oll and Active oll Suspensions ; Vehicle Syem Dynamics, (33), (2000), (pp. 9 06) 8. Mokhiamar, O. and Abe, M. Eects o Model esponse on Model Following Type o Combined ateral Force and Yaw Moment Control Perormance or Active Vehicle Handling Saety ; JSAE eview, 23 (), (2002), (pp ) 9. Dominke, P. and uck, G., "Electric Power Steering-the Fir Step on the Way to" Steer by Wire," SAE Technical Paper No , (999). 0. Amberkar, S., et al., "A Control Syem Methodology or Steer-by-Wire Syems," SAE Paper No (200).. A.K.W. Ahmed, V. awat, and.b. Bhat, Vehicle Steering Mechanism or Active Independent Front Steering Syem, Proceed o 3rd Int. Con. on Mech., Production and Automobile Engineering (ICMPAE'203) January -5, (203), Bali, (Indonesia), pp Pacejka, H.B., Bakker, E., and Nyborg,. Tyre Modeling or Use in Vehicle Dynamics Studies ; SAE paper no. 8702, (987). 3. Yih, P. and Gerdes, J.C., "Steer-by-Wire or Vehicle State Eimation and Control," Proceed. o the 200 Int. Symposium on Advance Vehicle Control, Netherlands, (200).. A.K.W. Ahmed, V. awat,.b. Bhat, Steering Syem and Method o Independent Steering o Wheels. U.S. Patent No. 8,26,62, Issued February 28th, 202. EFEENCES. Wong, J.Y., Theory o Ground Vehicles ; th Edition, Wiley-Interscience, New York, NY, USA, (2008) (pp ) 2. Ackermann, J., Odenthal, D. and Bunte, T., Advantages o Active Steering or Vehicle Dynamics Control, 32nd International Symposium on Automotive Technology and Automation, Vienna, Auria, (999) (pp ) 3. J.Y. Zhang, J.W. Kim, K.B. ee and Y.B. Kim, "Development o an active ront eering (AFS) syem with QFT control", Int. J o Automotive technology, Vol.9, No.6, (2008), (pp ) 5