Research on Vehicle Dynamics Simulation for Driving Simulator Fang Tang a, Yanding Wei b, Xiaojun Zhou c, Zhuhui Luo d, Mingxiang Xie e, Peixin Li f

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1 Advanced Materials Research Vols (2011) pp Online available since 2011/Aug/16 at (2011) Trans Tech Publications, Switzerland doi: / Research on Vehicle Dynamics Simulation for Driving Simulator Fang Tang a, Yanding Wei b, Xiaojun Zhou c, Zhuhui Luo d, Mingxiang Xie e, Peixin Li f Zhejiang University, State Key Lab of Fluid Power Transmission and Control, , Hangzhou, China a tangfang008@163.com, b weiyd@zju.edu.cn, c sky@zju.edu.cn Keywords: driving simulator, multi body dynamics modeling, real-time simulation, Vortex Abstract. In order to fulfill the requirement of vehicle dynamics performance and real-time capability in driving simulator, modeling and simulation method of a four-wheeled vehicle model based on multi body dynamics software Vortex was studied. Fundamental construction and dynamics properties of the model such as body, chassis, wheels, power train, suspension and tyre model were described. The model was tested to simulate on the C grade of road. The results indicate that the model and simulation method can well represent vehicle dynamics performance and high real-time capability of simulation, and is worthy to apply to driving simulator in the future. Introduction In recent years as the national economy has grown in a high speed, amount of vehicle requirement has grown much faster. This situation makes the highway traffic with fast velocity, but with more traffic jam. Therefore, drivers are expected to face higher risks in complex traffic condition. Due to this safety concern, research on close loop system of vehicle-driver-environment is especially important [1-3]. Driving simulator can easily provide various kinds of traffic condition to study the vehicle-driver-environment system. According to its purpose, driving simulator can be separated in two types. The first type is training simulator which has vivid 3D environment, sound and so on, but is lack of vehicle dynamics simulation and force feedback system, like MCGI-9410T computer imaging system developed by Beijing University of Aeronautics and Astronautics, training simulator made by Wuhan University of Technology and Huangshi Institute of Technology [4]. The other type is development simulator like National Advanced Driving Simulator (NADS) made by University of IOWA [5] and Automobiles Dynamic Simulation Laboratory (ADSL) developed by Jilin University [6]. It uses mathematical model to analyze and study vehicle dynamics performance, driving stability and braking performance, to optimize vehicle design and manufacturing. Dynamics performance and real-time capability are both required for driving simulator, but they are conflicting because complex dynamics may increase time of each simulation step. In order to meet needs of vehicle dynamics performance and real-time capability in driving simulator, fundamental modeling and simulation method of multi body dynamics software Vortex is introduced. Based on Vortex, a four-wheeled vehicle is modeled including vehicle simplification and dynamics. The vehicle model is used to simulate on the C grade of road to test its dynamics performance and real-time capability. Multi body dynamics software Vortex Vortex is a multi body software developed by CM-LABS Canada. Based on the fundamental laws of physics, Vortex is optimized for real-time simulation, delivering both accuracy and high performance in numerous real-world applications. It can put vehicles, robots, heavy equipment and more into high-fidelity synthetic environments for operator training, mission rehearsal, virtual prototyping and testing. With highly flexible SDK, Vortex can add accurate physical motion and interactions to objects in visual-simulation applications [7]. Basic contents of Vortex s virtual physics world include Frame, Universe, Part, Constraint and MaterialTable. Where, Frame is used to update state (e.g. position) of all Parts after every simulation step, Universe contains environment state (e.g. gravity), definition and relation (e.g. Constraint) of All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, (ID: /08/11,23:57:43)

2 Advanced Materials Research Vols all Parts, Part defines a part s physics property (e.g. shape, material, mass), Constraint defines restriction (e.g. hinge) between two parts, MaterialTable defines a series of materials and contact properties. A typical Vortex simulation flow diagram is shown in Fig. 1. create Frame set Constraint for two parts create Universe set Universe state create MaterialTable create Part set force or torque to Part make one simulation step exit? yes no release Frame Figure 1. Vortex simulation flow diagram Figure 2. Vehicle model of Audi A6 Vehicle dynamics modeling The following section describes the method of modeling a four-wheeled vehicle Audi A6 using multi body dynamics software Vortex, including vehicle simplification and vehicle dynamics. Vehicle Simplification. Audi A6 is a four-wheeled vehicle, it is a complex system including body, chassis, power train, suspension, wheels, steering system and so on. Modeling such a vehicle with complex structure and many degree of freedom may make Vortex vehicle dynamics simulation more complex than necessary. Therefore, some simplification must be done before modeling. Define right-handed right angle coordinates system XYZ, origin is set to center of vehicle, Y axis is vehicle s forward direction, Z axis is vehicle s height direction. Simplification 1: Body and chassis of vehicle is set as rigid body, assembled together as a Vortex Part, with mass of 1500kg. Center of mass is set to position in front of origin (+Y axis). This simplification is selected to reduce the computational burden caused by including more bodies and degree of freedom. Simplification 2: Each wheel is set as a Vortex Part, with mass of 20kg, not rigid body but Pajecka Magic Formula Tyre Model [8, 9]. Center of mass is set at center of wheel. Front wheels are set to be power wheels. Simplification 3: Suspension is set as Vortex Constraint to connect body and wheels. The system of body, suspension and wheel is set as a vibration system with two degree of freedom [10]. The overall Audi A6 model is shown in Fig. 2. where F.S is front suspension, R.S is rear suspension, L.F.W.P is left front wheel Part, R.F.W.P is right front wheel Part, L.R.W.P is left rear wheel Part, R.R.W.P is right rear wheel Part, F.A is front axle, R.A is rear axle, P is power train and C.P is chassis Part. Power train. A power train system often includes engine, torque converter, transmission gearbox, differential and final drive [11], shown in Fig. 3. To model power train by Vortex, create Parts and Constraint is not necessary, but more attention should be paid to input and output relation of each component.

3 1948 Advanced Design Technology Figure 3. Power train construction The engine is modeled using a shaft and a torque table. The shaft is a rigid body with specified mass and inertia. It can be attached longitudinally or transversally to the chassis [11]. Bilinear interpolation is used by the torque table to describe the amount of torque the engine can provide at the current speed (rpm) and for a given throttle input: T = F( ϕ, n ) (1) e f e where T e is indicated engine torque, φ f is throttle input, n e is engine speed (rpm) and F is torque table function. The torque converter is assumed inertialess and always working. The relation of torque converter input and output is: T tco = γt (2) tci where γ is torque ratio, T tci is torque converter input torque and T tco is torque converter output torque. The transmission connects torque converter and differential. Audi A6 gearbox has five forward gears. Audi A6 vehicle model parameters are shown in Table 1. Table 1. Vehicle model parameters max speed [km/h] 220 body mass [kg] km/h time [s] st gear ratio nd gear ratio rd gear ratio th gear ratio th gear ratio final drive Suspension and wheels. The system of body, suspension and wheels is simplified as a vibration system with two degree of freedom, shown in Fig. 4. Figure 4. Vibration system Figure 5. Simulation on C grade of road System kinematics equation is [10]:

4 Advanced Materials Research Vols m z + C( z z ) + K( z z ) = 0 (3) m z + C( z z ) + K( z z ) + K ( z q) = 0 (4) t 1 where m 2 is body mass, m 1 is wheel mass, K is spring stiffness, K t is wheel stiffness, C is damping coefficient, z 1 is wheel vertical displacement, z 2 is body vertical displacement and q is road rolling. The suspension system is modeled using a map describes the relation among spring stretching quantity, stiffness and damping coefficient. The relation could be linear or non-linear. Tyre model. In Vortex simulation, the user can implement many kinds of tyre model (e.g. Magic Formula and Fiala Tyre Model). The Magic Formula Tyre Model is used to model Audi A6. The equation of Magic Formula Tyre Model [8, 9] is: Y = y+ S v (5) y= Dsin{ C arctan[ Bx E( Bx arctan Bx)]} (6) x= X + S h (7) where Y separately represents lateral force, longitudinal force and aligning torque, X is slip angle and slip rate. Assuming Y as lateral force to explain other parameters, B is stiffness factor, C is shape factor, D is peak factor, E is curvature factor, S v is vertical drift and S h is horizontal drift. By setting these parameters, the user can obtain desired tyre to use in the dynamics simulation. Simulation validation Real-time capability and dynamics fidelity are two requirements for driving simulator, but they are conflicting because complex multi body dynamics may increase time of each simulation step. Therefore, making a simulation to test these two requirements is necessary. According to statistics, almost all high-grade highways in China belong to three grades: A, B and Speed/km.h - 1 COM Z displacement/m Time/s a) Speed/km.h COM Y displacement/m b) d) Figure 6. a) Vehicle speed; b) center of mass displacement curve 1; c) center of mass displacement curve 2; d) system frame rate COM Z displacement/m Frame rate/fps c) Time/s

5 1950 Advanced Design Technology C, while B and C grade account for more [12]. Therefore, Audi A6 vehicle dynamics model is used to simulate on the C grade of road, shown in Fig. 5. Simulation computer software environment is Windows XP SP3 and Visual Studio 2008, hardware environment is Intel E GHz,2.0G DDR2 800,GeForce 9500GT During the simulation, the vehicle model Audi A6 accelerates from 0 km/h with maximum throttle input to the maximum gear ratio and maximum speed. Vehicle speed, vehicle displacement of Y and Z axis and simulation system frame rate (FPS) are saved, shown in Fig. 6. In Fig. 6a, the maximum speed of Audi A6 is 210km/h, 4.5% lower than the design maximum speed 220km/h. Accelerating ability of the vehicle is good, accelerating time of 0-100km/h is about 11s, 10% more than design time, during the simulation, with the increase of gears and velocity, acceleration is decreasing. These above differences are in the reasonable range. Fig. 6b is vehicle center of mass displacement curve of Z axis, which aggravates while speeding up. Fig. 6c reflects the vibration of the vehicle on C grade of road. As shown in Fig. 6a, 6b and 6c, this model can satisfy vehicle dynamics performance requirement of driving simulator. Fig. 6d is the frame rate of simulation system, although it has some rise and fall, the lowest frame rate reaches 36 FPS, average frame rate is 52 FPS. This model simulation system has great real-time capability, can preferably satisfy real-time capability requirement of driving simulator. Conclusions After making certain simplification of a four-wheeled vehicle, an Audi A6 vehicle model is built based on multi body dynamics software Vortex. The vehicle model is used to simulate on the C grade of road. The result indicates that the model can well represent dynamic process of a four-wheeled vehicle running on the road. Average frame rate of simulation is 52 FPS. The simplified vehicle model and simulation method can satisfy dynamics performance and real-time capability requirement of driving simulator, can be worthy to apply in the future. References [1]. Yang, X., C. Zong and Z. Hu: Automotive Engineering, 16(1994), p (In Chinese). [2]. Hirata, T., T. Yai and T. Takagawa: Tsinghua Science and Technology, 12(2007), p [3]. N. Ying: Journal of Hubei Automotive Industries Institute, 16(2002), p. 7-10(In Chinese). [4]. Dingfang Chen, Y.N.L.X.:The Distributed Interactive Vehicle Simulation System for Driving Training. (2009), Beijing: Science Press(In Chinese). [5]. Heydinger, G.J., et al.: Journal of Automobile Engineering, 216(2002), p [6]. K. Guo, Y. Zhao and X. Guan: Journal of Highway and Transportation Researeh and Development, 12(1995), p (In Chinese). [7]. Information on [8]. Pacejka H. B. and R.S. Sharp: Vehicle System Dynamics, 3-4(1991), p [9]. B., P.H.: The Tyre as a Vehicle Component, in Proc. XXVI FISITA Congress. (1996): Prague. [10].Zhisheng, Y.: Vehicle Theory. (2009), Beijing: China Machine Press(In Chinese). [11].CM-LABS: Vortex Documentation. (2009). [12].Xiandong Liu, Zhidang Deng and F. Gao: Journal of Beijing University of Aeronautics and Astronautics, 29(2003), p (In Chinese).

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