【作者】 姚鑫；

【导师】 王建斌；

【作者基本信息】 西南交通大学 ， 车辆工程， 2022， 硕士

【摘要】 轮轨磨耗演变仿真的核心在于在动力学计算中实时更新型面曲线,动力学方程每个积分步均进行轮轨接触几何快速计算是其核心。研究了轮轨接触几何约束方程快速迭代算法,围绕轮对与钢轨的物理约束关系,建立相关约束方程组。首先研究了在不考虑摇头角的情况下,二维的约束方程迭代算法;再考虑摇头角,将该约束方程迭代算法扩展到三维。该算法能够解决不同匹配关系的轮轨型面在不同运动姿态下的轮轨接触几何关系问题。并基于Python平台开发了一套快速、准确计算轮轨接触几何关系的牛顿迭代实时算法,以满足在动力学仿真计算过程中,对型面曲线的实时更新以及计算量小的要求。以该算法为基础,通过单轮对系统的运动仿真,验证了该算法适用于车辆动力学仿真中轮轨匹配关系的实时计算。围绕该算法,做了以下几点工作:(1)基于轮轨型面曲线实时更新的需求,具有变截面轮轨匹配关系的车辆动力学仿真过程中,每次更新型面曲线只会改变部分数据点,采用具备局部支撑特性的三阶非均匀有理B样条曲线描述轮轨型面,局部控制点的变化不会引发全局形状的改变;基于计算过程中对轮轨型面的可导性、平滑度的要求,以接触斑横轴尺寸为高斯平滑窗口对型面和导曲线进行平滑处理,以满足雅可比矩阵数值稳定性要求。(2)为了使算法在全局上的计算量适当,避免在轮缘接触区迭代增量越界振荡,采用阻尼型牛顿迭代算法,选取步长缩放系数为0.5。(3)基于迭代分形图研究了不同区域的无条件收敛稳定域,迭代初值在精确值±2 mm的邻域可保证收敛稳定。根据轮轨接触本身具有连续性的特点,采用以上一接触点为迭代初值,并在接触点跳跃处根据横移速度方向进行调整的方法来满足算法对迭代初值精确度的要求。(4)采用实测的轮轨型面曲线,应用轮轨接触几何约束方程快速迭代算法,计算实测轮轨匹配关系,并与最小距离法的计算结果进行对比,验证算法的有效性;对比两者所需的运行时间,轮轨接触几何约束方程快速迭代算法在效率上具有明显优势;采用不同磨耗程度的踏面,应用轮轨接触几何约束方程快速迭代算法,计算实测轮轨匹配关系,验证算法的可靠性。(5)采用Hertz接触理论分析轮轨接触问题与蠕滑率公式,在Python平台上建立相关运动仿真程序,通过对单轮对系统的运动仿真,验证了轮轨接触几何约束方程快速迭代算法适用于车辆动力学仿真中轮轨匹配关系的实时计算。更多还原

【Abstract】 The core of wheel rail wear evolution simulation is to update the profile curve in real time in the dynamic calculation.The rapid calculation of wheel rail contact geometry in each integral step of the dynamic equation is its core.The fast iterative algorithm of wheel rail contact geometric constraint equation is studied.Based on the physical constraint relationship between the wheelset and the rail,the related constraint equations are established.Firstly,the iterative algorithm of two-dimensional constraint equation is studied without considering the shaking angle;furthermore,considering the shaking angle,the iterative algorithm of the constraint equation is extended to three-dimensional.The algorithm can solve the problem of wheel rail contact geometric relationship of wheel rail profile with different matching relationship under different motion attitude.Based on Python platform,a set of Newton iterative real-time algorithm for fast and accurate calculation of wheel rail contact geometric relationship is developed to meet the requirements of real-time updating of profile curve and small amount of calculation in the process of dynamic wear simulation.Based on this algorithm,through the motion simulation of a single wheelset system,it is verified that the algorithm is also suitable for the real-time calculation of the wheel-rail matching relationship in the vehicle dynamics simulation.The following work has been done around the algorithm:(1)Based on the requirement of real-time update of wheel-rail profile curve,in the process of vehicle dynamics simulation with variable cross-section wheel-rail matching relationship,each update profile curve will only change some data points.Therefore,the third-order non-uniform rational B-spline curve with local support characteristics is used to describe the wheel-rail profile,and the change of the local control point will not cause the change of the global shape.Due to the requirements for the derivability and smoothness of the wheel-rail profile in the calculation process,the profile and guide curve are smoothed with the horizontal axis of the contact spot as the Gaussian smoothing window to meet the numerical stability requirements of the Jacobian matrix.(2)In order to make the global calculation amount of the algorithm appropriate and the iterative increment in the flange contact area will not oscillate beyond the boundary,the Newton iterative method is improved,the damped Newton iterative algorithm is adopted,and the step size scaling coefficient is 0.5.(3)The unconditional convergence stability regions of different regions are studied based on the iterative fractal diagram.The initial geometric parameters falling in the neighborhood with the target point as the center ± 2 mm can ensure the convergence stability.Then,according to the continuity of wheel rail contact itself,the above contact point is used as the initial value of iteration,and the method of adjusting according to the transverse speed direction at the jump of contact point is adopted to meet the accuracy requirements of the algorithm for the initial value of iteration.(4)Using the measured wheel-rail profile curve,the fast iterative algorithm of the wheel-rail contact geometric constraint equation is used to calculate the measured wheel-rail matching relationship.Compared with the calculation results of the minimum distance method,the effectiveness of the algorithm is verified.Comparing the running time of the two,the fast iterative algorithm of the geometric constraint equation of wheel-rail contact has obvious advantages in efficiency.Using treads with different degrees of wear,the fast iterative algorithm of wheel-rail contact geometric constraint equation is applied to calculate the measured wheel-rail matching relationship to verify the reliability of the algorithm.(5)The Hertz contact theory is used to analyze the wheel rail contact problem and the creep rate formula,and the relevant motion simulation program is established on the python platform.Through the motion simulation of a single wheelset system,it is verified that the fast iterative algorithm of the wheel-rail contact geometric constraint equation is also suitable for the real-time calculation of the wheel-rail matching relationship in the vehicle dynamics simulation.更多还原