车辆纵向非光滑多体动力学建模与数值算法研究

在建立车辆纵向多体系统的动力学模型中, 将车身与车轮视为刚体, 两者通过减振器链接; 将传动系统视为一个圆盘通过扭簧和阻尼器与驱动轮连接; 将车轮与路面间的接触力简化为法向约束力、摩擦力和滚阻力偶,其中摩擦力的模型采用库仑干摩擦模型. 采用笛卡尔坐标作为该系统的广义坐标用于描述该系统的位形, 给出系统单双边的约束方程, 应用第一类拉格朗日方法建立了系统的动力学方程. 由于摩擦与滚阻的非光滑性, 使得该系统动力学方程不连续. 为便于计算, 建立了车轮与路面接触点的相对切向加速度与摩擦力余量的互补条件、车轮角加速度与滚阻力偶余量的互补条件, 以及车轮轮心法向加速度与路面法向约束力的互补条件. 将接触—分离、黏滞—滑移的判断问题转化成线性互补问题的求解, 并给出了具有约束稳定化的基于事件驱动法的数值计算方法. 最后, 应用该方法对车辆纵向多体系统进行了仿真, 分析了输出扭矩、摩擦及滚阻系数对其动力学行为的影响. 

RESEARCH ON MODELING AND SIMULATION OF LONGITUDINAL VEHICLE DYNAMICS BASED ON NON-SMOOTH DYNAMICS OF MULTIBODY SYSTEMS

A method for modeling and simulation of longitudinal vehicle dynamics is presented based on non-smooth dynamics of multibody systems in this paper. The vehicle is the multi-rigid-body system which consists of a vehicle body, wheels and transmission system. It is assumed that wheels are linked with the vehicle body by shock absorbers and the transmission system is treated as the disk connecting with driving wheels by spring-damper system. The friction and the rolling resistance between wheels and the road are taken into account and the Coulomb's friction law is used to describe the frictional forces. Firstly, the lateral and bilateral constraint equations of the system are given in generalized coordinates of the system and the dynamical equations of the system are obtained by Lagrange's equations of the first kind. Secondly, the complementary formulations of friction law, rolling resistance law and contact law between wheels and road are given in order to determine state transitions from contact to separation and sticking to slipping. Based on the event-driven scheme, the problem of state transitions is formulated and solved as a horizontal linear complementarity problem (HLCP). The algorithm for solving these non-smooth DAEs is presented. The Baumgarte stabilization method is used to reduce the constraint drift. Finally, the multibody system of a vehicle is considered as an illustrative application example to analyse its dynamical behaviour affected by the engine output torque, the friction coeffcient and the rolling resistance coeffcient between wheels and road. The numerical results show that the phenomenon of the stick-slip between driving wheel and road occurs continually when the coeffcients have special values.