In order to facilitate the research on the geometrical relation of wheel-rail contact, the geometrical calculation of three types of typical wheel-rail 3D contact, including wheel-rail contact on straight line, wheel-rail contact on curve and wheel-rail roller contact, was converted into 2D contact of parallel projection contour for wheel-rail contact on straight line and rotating projection contour for wheel-rail curve and wheel-rail roller contact. Based on the characteristics of wheelset revolution solid, the calculation formula for the bottom contour of wheelset under different projection directions was respectively derived. The solving steps and 2D synchronous iterative procedure suitable for the calculation of wheel-rail 3D contact were presented. Taking the relationship between S1002CN tread wheelset and 3D contact geometry of 60 kg · m-1 rail for example, the wheel-rail 3D contact geometry on straight line, 300 m radius curve and the roller test rig with 900 m radius track wheel was simulated and analyzed. The results show that, by taking the deflection angle of wheel-rail contact point relative to wheelset bottom generatrix as the calculation parameter enables the calculation method of wheel-rail contact geometry based on the projection contour simple and easy to use. The geometrical relationship of wheel-rail 3D contact on straight line and the one on curve is similar, and can be approximated by wheel-rail 2D geometrical relationship when the yaw angle of wheelset is less than 5~10 mrad. When the wheelset has big lateral displacement, the deflection angle of contact point can be regarded as the linear function of wheelset yaw angle within a certain scope. 2D synchronous iteration can effectively realize the geometrical calculation of wheel-rail 3D contact under complicated conditions. There is obvious deflection angle in wheel-rail roller 3D contact even under small lateral displacement condition, which needs to be corrected in simulation.%为便于研究轮轨接触的几何关系,将轮轨的直线上接触、曲线上接触和轮轮接触3种典型轮轨三维接触几何计算归结为轮轨直线接触平行投影轮廓和轮轨曲线、轮轮接触旋转投影轮廓的二维接触问题.利用轮对的旋转体特性,分别推导出轮对在不同投影下其底部轮廓的计算公式,给出求解步骤以及适合轮轨三维接触计算的二维同步迭代流程.以S1002CN踏面轮对与60 kg·m-1钢轨的三维接触几何关系为例,仿真分析直线、300m半径曲线及轨道轮半径为900mm的滚动试验台的轮轨三维接触几何情况.结果表明:将轮轨接触点相对于轮对底部母线的偏转角作为计算参数,使得基于投影轮廓的轮轨三维接触几何计算方法简单、易用；直线及曲线线路上的轮轨三维接触几何关系相近,当轮对摇头角小于5～10 mrad时还可用轮轨二维几何关系近似；轮对大横移下的接触点偏转角,在一定的摇头角范围内可视为轮对摇头角的线性函数；二维同步迭代能有效实现复杂条件下的轮轨三维接触几何计算；小横移条件下,轮轮三维接触即具有明显的接触点偏转角,仿真时需要修正.
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