Maxwell减振器模型载荷数值积分方法及其在高速动车组动力学仿真中应用

doi:10.3901/JME.2025.20.253

机械工程学报 ›› 2025, Vol. 61 ›› Issue (20): 253-262.doi: 10.3901/JME.2025.20.253

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Maxwell减振器模型载荷数值积分方法及其在高速动车组动力学仿真中应用

任君临, 李强, 任尊松, 吴养民

北京交通大学机电学院北京 100044

收稿日期:2024-09-30 修回日期:2025-06-20 发布日期:2025-12-03
作者简介:任君临，男，1996年出生，博士研究生。主要研究方向为车辆结构可靠性。E-mail:21116038@bjtu.edu.cn
任尊松(通信作者)，男，1969年出生，博士，教授，博士研究生导师。主要研究方向为车辆系统动力学及可靠性。E-mail:zsren@bjtu.edu.cn
基金资助:
国家重点研发计划(2022YFB3402901)和国家自然科学基金重点(U2368215)资助项目。

Numerical Integration Methods of Damping Force Calculation in Maxwell Model and Its Application in Real-time Simulation of High-speed Railway Vehicle Dynamics

REN Junlin, LI Qiang, REN Zunsong, WU Yangmin

School of Mechanical, Electrical & Control Engineering, Beijing Jiaotong University, Beijing 100044

Received:2024-09-30 Revised:2025-06-20 Published:2025-12-03

摘要/Abstract

摘要： Maxwell模型是车辆动力学研究常用的一种减振器模型之一。相比于简化模型，Maxwell模型引入串联刚度，因而该模型更为合理。由于Maxwell模型存在阻尼力数值求解困难问题，因此该模型多用于较少自由度的车辆系统动力学理论推导和解析，难以应用于多自由度车辆系统动力学数值仿真研究。首先，提出一种可用于车辆系统动力学仿真计算的Maxwell模型载荷数值积分方法，该方法包括两种数值积分格式，其中一种积分格式是载荷由减振器两端总位移、黏性阻尼位移和速度确定，另一种积分格式是载荷由减振器两端总位移、黏性阻尼位移和速度及加速度确定。其次，通过建立包含弹簧及Maxwell模型的一个单质量系统，采用数值方法获得该系统的自由振动响应，验证Maxwell模型阻尼力数值积分方法的有效性和合理性。最后，利用车辆-轨道系统动力学模型并应用提出的数值积分方法对车辆系统进行动力学仿真计算，获得车辆系统的减振器阻尼力和轮轨接触力，验证Maxwell模型阻尼力数值积分方法在动力学仿真中应用的合理性。结果表明，提出的Maxwell模型载荷数值积分方法，可应用于车辆系统动力学数值研究，且具有优良的数值计算结果准确性。相比于简化模型，采用Maxwell模型获得的仿真结果更为合理。

关键词: Maxwell模型, 阻尼力计算, 数值积分方法, 车辆系统动力学

Abstract: Maxwell model is one kind of damper dynamics model in vehicle dynamics investigation. Compared with the simplification damper model, Maxwell model is more reasonable because of the introduction of a series stiffness in it. However, Maxwell model is generally used to deduce the theoretical dynamics of railway bogie with low degrees of freedom(DOFs). It is hardly employed to implement dynamics simulation of the railway vehicle because of the co-calculation difficulty of the damping force in the model. Two numerical integration methods are presented to achieve the real-time damping force calculation of Maxwell model. One of the numerical integration methods is that the damping force is determined with the total displacement of the damper, displacement and velocity of the viscous damping. Another numerical integration method is that the damping force is decided by the total displacement of the damper, the displacement, velocity and acceleration of the viscous damping. A single mass model with a spring and a damper is developed in which the damper is modeled as a Maxwell model. The simulation results of the free vibrations of the single mass are presented to validate the availability of the numerical integration methods in real-time calculation of the damping force. A vehicle-track system dynamics model is employed to simulate the vehicle dynamics with Maxwell model and simplification model. Damping forces and wheel-rail contact forces of the railway vehicle are presented to validate the application of Maxwell model on the real-time dynamics simulation with the numerical integration methods. The investigation results show that the two numerical integration methods for the damping force calculation in Maxwell model are all available for the vehicle dynamics calculation. The simulation result with Maxwell model is more reliable than that with the simplification model.

Key words: Maxwell model, damping force calculation, numerical integration method, vehicle system dynamics

中图分类号:

U270

任君临, 李强, 任尊松, 吴养民. Maxwell减振器模型载荷数值积分方法及其在高速动车组动力学仿真中应用[J]. 机械工程学报, 2025, 61(20): 253-262.

REN Junlin, LI Qiang, REN Zunsong, WU Yangmin. Numerical Integration Methods of Damping Force Calculation in Maxwell Model and Its Application in Real-time Simulation of High-speed Railway Vehicle Dynamics[J]. Journal of Mechanical Engineering, 2025, 61(20): 253-262.

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Maxwell减振器模型载荷数值积分方法及其在高速动车组动力学仿真中应用

Numerical Integration Methods of Damping Force Calculation in Maxwell Model and Its Application in Real-time Simulation of High-speed Railway Vehicle Dynamics

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