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

doi:10.3901/JME.2025.20.253

Abstract

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

CLC Number:

U270

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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