The characterization of wheel-rail contacts is a key issue in railway system dynamics. In this work, complete formulations of a wheel-rail contact element are presented in coupling matrices, where the time-varying excitation sources, e.g., track irregularities, are coupled as the inner degrees of freedom (DOFs) with already-known values and the complex system differential equations in classical vehicle-track related dynamics, namely the force equilibrium models, are avoided, and consequently improving the modelling versatility. The novelty of this work is effectively integrating the wheel-rail coupling dynamics model and the energy variation method. The solution accuracy and stability of wheel-rail contacts in train-track dynamics can be both guaranteed. In the first numerical example, a two DOFs system is established by classical force equilibrium method and this present matrix coupling method. Through comparisons between different solution methods, it is shown that this present method shows high stability and precision even at large time step sizes. By comparing to results from commercial software and experiments in-site, the accuracy of the proposed matrix coupling method has also been proved.

中文翻译：

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车轨动力学分析中轮轨接触单元的矩阵公式


轮轨触点的特性是铁路系统动力学中的一个关键问题。在这项工作中，在耦合矩阵中提出了轮轨接触元件的完整公式，其中时变激励源，例如轨道不规则性，作为具有已知值的内部自由度 （DOF） 耦合，避免了经典车辆轨道相关动力学中的复杂系统微分方程，即力平衡模型，从而提高了建模的多功能性。这项工作的新颖之处在于有效地整合了轮轨耦合动力学模型和能量变化方法。在火车轨道动力学中，轮轨接触的求解精度和稳定性都可以得到保证。在第一个数值示例中，通过经典的力平衡法和目前的矩阵耦合方法建立了一个双自由度系统。通过不同求解方法之间的比较，表明该方法即使在大时间步长下也表现出高稳定性和精度。通过与商业软件和现场实验的结果进行比较，所提出的矩阵耦合方法的准确性也得到了证明。