基于分数阶Zener模型的高速铁路扣件动静刚度比限值研究

Research on the limit value of dynamic and static stiffness ratio of high-speed railway fastenings based on fractional Zener model

目前,高速铁路扣件动静刚度比的设计更多的是凭经验进行,且仅针对低频,缺乏可靠的理论基础。基于此,使用能够较好反映黏弹性材料刚度频变特性的分数阶Zener模型,采用编程和Simpack-Simulink联合仿真的方法,首先建立车辆-轨道耦合动力学模型,验证2种方法模拟扣件系统黏弹性特征的正确性和可行性;然后通过修改分数阶Zener模型的松弛时间得到具有不同动静刚度比的扣件模型,以焊缝不平顺与高铁谱作为轨道不平顺激励,分别模拟高铁350 km/h匀速、350 km/h减速和450 km/h减速不同扣件系统动静刚度比条件下列车的运营状态;最后,以动态轮重减载率为限定指标研究不同运营时速下的扣件系统动静刚度比取值范围,讨论扣件静刚度降低对轮重减载率的影响。研究结果表明:列车在减速条件下的动态轮重减载率相较于匀速条件呈现出明显的上升趋势;当列车以350 km/h减速运行时,扣件在过车频率下的动静刚度比不应超过1.7,此时对应的扣件低频(3~5 Hz)动静刚度比为1.34;当列车以450 km/h减速运行时,扣件在过车频率下的动静刚度比建议不超过1.6,此时对应的扣件低频(3~5 Hz)动静刚度比建议不超过1.27;满足钢轨最大位移限值条件下,降低扣件静刚度可为扣件动静刚度比的设计提供更多余量。以上研究可为450 km/h速度运行下的高速铁路轨道刚度设计提供一定的参考。

Currently,the design of dynamic and static stiffness ratio for high-speed railway fastening is mainly based on experience,and only for low frequencies,lacking reliable theoretical basis.To make the design more scientific,a fractional-order Zener model was used,which can better reflect the frequency-dependent stiffness of viscoelastic materials.The vehicle-track coupled dynamic model was first established based on programming and Simpack-Simulink co-simulation to verify the correctness and feasibility of the two methods in simulating the viscoelastic characteristics of the fastening system.Then,by modifying the relaxation time of the fractional order Zener model,the fastener model with different dynamic and static stiffness ratios is obtained.The operation state of the train under the conditions of a constant speed of 350 km/h,deceleration of 350 km/h,and deceleration of 450 km/h is simulated using weld irregularity and the high-speed railway spectrum as excitations for track irregularity.Finally,the range of dynamic and static stiffness ratio values for the fastening system under different operating speeds was studied using the dynamic wheel load reduction rate as the limiting index,and the influence of the reduction of static stiffness on the wheel load reduction rate was discussed.The research results show that the train’s dynamic wheel load reduction rate under deceleration conditions has a significant upward trend compared with that under constant speed conditions.When the train decelerates at 350 km/h,the dynamic and static stiffness ratio of the fastening system at the passing frequency should not exceed 1.7,and the corresponding dynamic and static stiffness ratio at low frequencies(3~5 Hz)is1.34.When the train decelerates at 450 km/h,it is recommended that the dynamic and static stiffness ratio of the fastening system at the passing frequency should not exceed 1.6,and the corresponding dynamic and static stiffness ratio at low frequencies(3~5 Hz)are recommended not to exceed 1.27.Reducing the static stiffness can provide more margin for the design of dynamic and static stiffness ratios while satisfying the maximum displacement limit of the rail.This study provides some reference for the track stiffness design of high-speed railways at 450 km/h.