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 引用本文: 宋宁宁, 赵剑, 公爵, 李琳辉, 彭海军. 车辆在非光滑路面的接触动力学分析方法研究. 力学学报, 2024, 56(6): 1762-1774.
Song Ningning, Zhao Jian, Gong Jue, Li Linhui, Peng Haijun. Resrarch on the contact dynamic analysis method of vehicle on nonsmooth road surface. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(6): 1762-1774.
 Citation: Song Ningning, Zhao Jian, Gong Jue, Li Linhui, Peng Haijun. Resrarch on the contact dynamic analysis method of vehicle on nonsmooth road surface. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(6): 1762-1774.

## RESRARCH ON THE CONTACT DYNAMIC ANALYSIS METHOD OF VEHICLE ON NONSMOOTH ROAD SURFACE

• 摘要: 车辆接触动力学研究有助于更加全面地了解整车力学性能, 对整车稳定性和座舱舒适性设计具有指导性作用. 文章基于非光滑多体系统理论, 对车辆系统展开接触动力学研究. 考虑到车辆在行驶过程中, 轮胎是与地面接触的唯一部件, 轮胎动力学模型对整车动力学分析发挥着重要的作用. 首先, 借助于张拉整体结构的思想, 建立轮胎的等效模型. 然后, 采用拉格朗日乘子方法, 将约束方程引入到拉格朗日函数中, 并基于第二类拉格朗日方程, 推导得到整车系统的一般动力学方程. 由于接触碰撞的存在, 会导致车辆的状态变量呈现出非连续性. 利用牛顿碰撞定律, 建立了碰撞响应的非光滑数学列式, 并利用光滑化的Fischer-Burmeister函数将非光滑数学列式进行等效替换, 以提高计算效率. 其次, 将摩擦响应的求解转化为优化问题进行描述, 以避免求解摩擦方向时出现奇异. 另外, 将车辆系统的一般动力学模型分解为光滑部分与非光滑部分进行求解, 并利用广义α离散策略给出了详细的求解流程. 最后, 对整车系统展开了多工况的接触碰撞数值仿真, 分析了不同工况下的接触响应对整车动力学性能的影响, 验证了所提方法的有效性.

Abstract: The study of vehicle contact dynamics contributes to a more comprehensive understanding of the mechanical performance of the entire vehicle, and has a guiding role in the design of vehicle stability and cabin comfort. Therefore, this article is based on the theory of non smooth multi body system to conduct contact dynamics research on vehicle systems. Taking into account that the tire is the only component in contact with the ground during the driving process of vehicle, the tire dynamics model plays a crucial role in the overall vehicle dynamics analysis. First of all, this article establishes a multi body dynamic model of tires based on absolute coordinate modeling method. Then, by means of the Lagrange multiplier method, the constraint equation is introduced into the Lagrange function, and based on the second type of Lagrange equation, the general dynamic equation of the entire vehicle system is derived. Due to the presence of contact collisions, the state variables of the vehicle may exhibit discontinuity. In this paper, the Newton impact law is used to establish a non smooth mathematical formulation for impact response, and the smoothed Fischer-Burmeister function is used to equivalently replace the non smooth mathematical formulation to improve computational efficiency. Secondly, this article transforms the solution of friction response into an optimization problem for description, in order to avoid singularity when solving the friction direction. In addition, the general dynamic model of the vehicle system is decomposed into smooth and non smooth parts, and a detailed solution process is given based on generalized-α method. In the end, numerical simulations of contact collisions under multiple operating conditions are conducted on the entire vehicle system, and the impact of contact response under different operating conditions on the vehicle's dynamic performance is analyzed, and verified the effectiveness of the method proposed in this article.

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