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研究了铁路车辆系统中存在的非线性因素,介绍了修正双步长显式法,给出了该算法的数学表达式。基于简化的非线性车辆系统动力学模型,利用铁路车辆系统中的5个典型非线性算例,对比分析了修正双步长显式法、Newmark法、Wilson-θ法、Runge-Kutta法、翟方法和精细积分法,指出了这些算法在非线性铁路车辆系统中的适用范围。研究结果表明:Newmark法和Wilson-θ法不适用于非线性铁路车辆系统;Newmark法、Wilson-θ法和Runge-Kutta法在包含非线性垂向轮轨力的车辆系统中会产生虚假振荡;仿真时间为2s,时间步长分别为0.4、0.1、0.01ms时,修正双步长显式法的耗时分别为0.198、0.829、7.772s,在6种算法中耗时最短或较短;当非线性铁路车辆系统的自由度较大时,推荐采用修正双步长显式法和翟方法。
The nonlinear factors existing in the railway vehicle system are studied. The modified two-step explicit method is introduced and the mathematical expression of the algorithm is given. Based on the simplified nonlinear vehicle system dynamics model, five typical nonlinear examples in railway vehicle system are compared and analyzed. The modified two-step explicit method, Newmark method, Wilson-θ method, Runge-Kutta method, Method and the precise integration method, pointed out the application of these algorithms in the nonlinear railway vehicle system. The results show that the Newmark method and the Wilson-θ method are not suitable for nonlinear railway vehicle systems. Newmark method, Wilson-θ method and Runge-Kutta method produce false oscillations in a vehicle system with nonlinear vertical wheel-rail force. When the simulation time is 2s and the time steps are 0.4, 0.1 and 0.01ms respectively, the time-consuming of the modified two-step explicit method is 0.198, 0.829 and 7.772s, respectively, which takes the shortest or short time in the six algorithms. Nonlinear system of railway vehicles with greater freedom, it is recommended to use modified double-step explicit method and Zhai method.