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基于Hertz弹性接触理论,分别推导了变截面梁单元和车辆动力方程,然后根据分析目的提出了系统方程组装和求解思路,解决了传统分析中“车轮密贴”假设和结构简单的不足。新方法系统质量和阻尼矩阵不再时变,采用Newmark-β方法直接求解,不需迭代,并采用自动半步长法准确确定接触状态发生改变时刻。数值算例表明,新方法能更为精细分析系统动力响应,并能准确模拟脱离现象。应用新方法分析了两种不同车辆模型对耦合系统动力响应的影响,结果表明:整车模型能直接准确获得车辆动力响应;若采用集总车辆模型,可采用将其前后两簧上质量加速度平均的方法近似评估车体加速度。
Based on the Hertz elastic contact theory, the beam element and vehicle dynamic equation of variable cross section are deduced separately. Then, the idea of assembly and solution of system equations is proposed according to the purpose of analysis, which solves the shortcomings of traditional “wheel close” assumption and simple structure. The new method is based on the Newmark-β method to solve the system quality and the damping matrix without iteration, and the automatic half-step method is used to accurately determine the moment when the contact state changes. Numerical examples show that the new method can analyze the dynamic response of the system more accurately and simulate the phenomenon of detachment accurately. The effect of two different vehicle models on the dynamic response of the coupled system is analyzed. The results show that the vehicle model can directly obtain the dynamic response of the vehicle. If the lumped vehicle model is used, the average acceleration of the two sprung mass can be averaged The method approximates body acceleration.