轮轨系统接触问题是一类三维的移动接触问题，接触区域的位置和状态随车轮运行有大范围的运动变化，准确且高效地仿真轮轨之间的接触作用力对轮轨系统的设计和维护有着重要意义。若采用基于Lagrange 描述的传统多体动力学方法求解这类接触区域随时间变化的问题，所有可能发生接触的区域都必须离散成密网格以保证接触求解的精度；此外考虑到接触位置一般提前未知，需通过接触检测算法获取；再加上碰撞过程积分步长通常较小，导致整个系统自由度多，计算效率低。针对这些问题，本文对仿真轮轨接触动力学开展了以下三项研究：建立了一种基于ALE描述的车轮和轨道柔性体模型。通过仅在车轮和轨道的接触区域内布置ALE 网格节点并约束两者网格随接触位置移动进行同步运动，可以将车轮的滚动运动分解为网格节点在空间中的平面运动以及物质点相对网格节点绕中心的环向流动，将轨道原本没有的大范围刚体运动分解为ALE网格节点随车轮位置的平面刚体运动以及物质点相对网格节点的径向流动。当车轮在轨道上通过接触滚动若干周期时，只需在固定的接触位置布置密网格以保证计算精度，而在远离接触区域的网格可以用疏网格代替以减少系统自由度，极大提高计算效率。建立了一种使用自由模态综合法减缩的轮轨柔性体模型。相比于常用的固定界面模态综合法，使用自由界面模态综合法减缩柔性体变形模态，不需要引入大量界面节点对应的约束模态进入模态集，界面约束模态通过除去低阶振动模态后的高阶补偿模态替代界面附着模态。同时，大量接触界面节点对应的位移模态坐标也转换为高阶补偿模态对应的界面节点力坐标，与系统整体自由度解耦，既降低了系统自由度、提高了轮轨接触的数值计算效率，也避免了固定界面模态综合法中的高频截断误差，提高了轮轨接触作用力的计算精度。提出了一个结合Hertz模型的虚拟嵌入法向接触模型和LuGre切向摩擦模型的适用轮轨滚动接触的计算方法。Kalker接触理论因存在弹性无限半空间假设的局限性、接触区域整体迭代计算量巨大等缺陷导致难以实时仿真含波磨的轮轨接触问题。本文提出的接触模型利用ALE描述下接触网格固定的优势，实现了在接触区域内离散Gauss点上的Hertz和LuGre接触模型。并与Kalker理论在同一钢轨波磨工况下进行数值准确性和计算效率的对比。

The wheel-rail system contact problem is a kind of three-dimensional mobile contact problem. The position and state of the contact area change with the wheel movement in a large range. The accurate and efficient simulation of the contact force between the wheel and rail is of great significance for the design and maintenance of the wheel-rail system. If the traditional multibody dynamics method described by Lagrange is used to solve this type of problem of contact area change over time, all areas that may be in contact must be discretized into dense grids to ensure the accuracy of contact solution. Considering that the contact position is generally advanced unknown, it needs to be obtained through the contact detection algorithm. The integral step length of the collision process is usually small, resulting in many degrees of freedom in the entire system and low calculation efficiency. In response to these problems, this thesis carried out the following three studies on wheel-rail contact dynamics simulation:A flexible body model of wheels and track based on ALE description is established. By only arranging the ALE grid nodes in the contact area of the wheel and the track and constraining the two grids to move in synchronization with the contact position, the rolling motion of the wheel can be decomposed into the plane motion of the grid node in space and the relative material point. The grid nodes flow in a circular direction around the center, which decomposes the large-scale rigid body motion that the track does not originally have into the plane rigid body motion of the ALE grid node with the position of the wheel and the radial flow of the material point relative to the grid node. When the wheel rolls through contact for several cycles on the track, it is only necessary to arrange a dense grid at a fixed contact position to ensure the calculation accuracy, and the grid far away from the contact area can be replaced with a sparse grid to reduce the degree of freedom of the system and improve calculation efficiency.A wheel-rail flexible body model reduced by the free-boundary mode synthesis method is established. Compared with the commonly used fixed interface modal synthesis method, the free-interface modal synthesis method is used to reduce the deformation modes of the flexible body. There is no need to introduce a large number of constrained modes corresponding to interface nodes into the mode set. The constrained modes of the interface are removed by the higher-order compensation mode called the interface adhesion mode by removing the vibration mode. At the same time, the displacement mode coordinates corresponding to a large number of contact interface nodes are also converted into the interface node force coordinates corresponding to the higher-order compensation modes, which are decoupled from the overall degrees of freedom of the system, which reduces the degree of freedom of the system and improves the numerical efficiency of wheel-rail contact. The proposed method also avoids the high-frequency truncation error in the fixed interface modal synthesis method, and improves the calculation accuracy of the wheel-rail contact force.A method for calculating wheel-rail rolling contact that combines the virtual embedded normal contact model of the Hertz model and the LuGre tangential friction model is proposed. The Kalker three-dimensional elastic non-Hertz contact theory is difficult to simulate the wheel-rail contact problem with corrugation in real time due to the limitations of the elastic infinite half-space assumption and the huge amount of iterative calculations in the overall contact area. The contact model proposed in this paper takes advantage of the fixed contact grid under the ALE description, and realizes the Hertz and LuGre contact models on discrete Gauss points in the contact area. The numerical accuracy and calculation efficiency are compared with Kalker theory under the same rail corrugation condition.