车轨耦合振动中4种轮轨竖向接触模型的适用性比较分析

Comparative Analysis on Applicability of Four Wheel-Rail Vertical Contact Models for Coupling Vibration of Vehicle-Track System

为进一步简化对竖向轮轨力的计算,在Hertz非线性接触模型的基础上,提出割线线性近似模型和切线线性近似模型,并推导出相应的轮轨竖向接触刚度及其引起的车轨系统附加刚度矩阵和附加轮轨力的表达式。以双块式无砟轨道为例,建立车轨系统的整体动力方程,分别采用Hertz非线性接触模型、轮轨竖向密贴模型、割线线性近似模型和切线线性近似模型,计算和分析车轨系统动力响应、轮轨振动频谱及时间步长的适应条件。结果表明:无论是否考虑轨道不平顺,切线线性近似模型均可替代Hertz非线性接触模型;在分析车体竖向加速度时,4种轮轨竖向接触模型均可用;在分析竖向轮轨力、钢轨竖向位移及轮对竖向加速度时,可采用Hertz非线性接触模型、割线线性近似模型和切线线性近似模型;在分析轮轨接触点处钢轨竖向加速度时,可采用Hertz非线性接触模型和切线线性近似模型;轮轨竖向密贴模型因为假定轮对与钢轨在竖向上始终不分离,所以导致在高频段的计算结果有较大误差;对于轨道不平顺的各个波段,当时间步长低于1ms时,Hertz非线性模型、割线线性近似模型、切线线性近似模型的计算误差均在可以接受的范围内。

To further simplify the calculation of vertical wheel-rail force,the secant linear approximation model and tangent linear approximation model were put forward based on Hertz nonlinear contact model.Meanwhile,the corresponding expressions were deduced for wheel-rail vertical contact stiffness,the induced additional stiffness matrix and additional wheel-rail force of vehicle-track system.The double-block ballastless track was taken for example and the overall dynamic equations of vehicle-track system were established.The dynamic response of vehicle-track system,the frequency spectrum of wheel-rail vibration and the applicability conditions of time step were respectively calculated and compared by Hertz nonlinear contact model,wheel-rail vertical tight contact model,secant linear approximation model and the tangent linear approximation model.Results show that Hertz nonlinear contact model can be replaced by tangent linear approximation model,regardless of whether rail irregularities are considered.Four wheel-rail vertical contact models can all be adopted for analyzing the vertical acceleration of car body.Hertz nonlinear contact model,secant linear approximation model and tangent linear approximation model can be adopted for analyzing vertical wheel-rail force,the vertical displacement of rail and the vertical acceleration of wheelset.Hertz nonlinear contact model and tangent linear approximation model can be adopted for analyzing the vertical acceleration of rail at wheel-rail contact point.The calculation results of wheel-rail vertical tight contact model in high frequency band have larger error because it assumes that wheelset and rail are never separated in vertical direction.For each band of track irregularity,the calculation errors of Hertz nonlinear contact model,secant linear approximation model and tangent linear approximation model are all in an acceptable range when the time step is less than 1ms.