The coil spring is an important element in the suspension system of railway vehicles, and its structural vibration caused by the mass distribution can deteriorate the dynamic performance of the vehicle. However, the coil spring is usually modelled as a simple linear force element without considering the dynamic characteristics in multibody dynamic simulations of railway vehicles. To integrate the dynamic characteristics of the coil spring into the simulation, three equivalent dynamic models of the coil spring are established by treating the coil spring as multimass spring series, Timoshenko beam, and flexible spring, respectively. The frequency-sweep method is applied to obtain the dynamic response of the proposed models of coil spring, and the accuracy of the models’ results has been compared and verified by the laboratory test. Results show that all of these three equivalent models can reflect the influence of the spring mass distribution on its dynamic responses. Compared with the mass-spring series and beam element equivalent models, the flexible spring model can better reflect the dynamic stiffness and stress of the coil spring changing with the exciting frequency. Thus, the flexible spring model proposed in this paper is more applicable to railway vehicle system dynamics and the fatigue analysis.

中文翻译：

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螺旋弹簧建模方法研究

螺旋弹簧是铁路车辆悬架系统中的重要元素，由质量分布引起的结构振动会降低车辆的动力性能。但是，通常将螺旋弹簧建模为简单的线性力元件，而不考虑铁路车辆多体动力学仿真中的动力学特性。为了将螺旋弹簧的动态特性集成到仿真中，通过将螺旋弹簧分别视为多质量弹簧系列，Timoshenko梁和柔性弹簧，建立了三个等效的螺旋弹簧动力学模型。应用扫频方法获得了所提出的螺旋弹簧模型的动力响应，并通过实验室测试对模型结果的准确性进行了比较和验证。结果表明，所有这三个等效模型都可以反映弹簧质量分布对其动力响应的影响。与质量弹簧系列和梁单元等效模型相比，柔性弹簧模型可以更好地反映螺旋弹簧的动态刚度和应力随激振频率的变化。因此，本文提出的柔性弹簧模型更适用于铁路车辆系统动力学和疲劳分析。