The static stiffness of rubber springs is affected by temperature and prepressure. In this thesis, the relationship between Young’s modulus and temperature of rubber was studied, and the quantitative relationship between them was determined. The approximate formula for calculating the static stiffness of rubber pads was further modified, and the ellipse approximation method and convexity coefficient correction method were proposed. In addition, the influence of temperature on geometric nonlinearity was considered. The formula for calculating nonlinear stiffness includes two variables: temperature and prepressure. The results of tests and theoretical calculations demonstrate that the nonlinear formula can be a good approximation and that it can meet the requirements of engineering applications.
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.
The dynamic mechanical properties of rubber spring have great influence on the vehicle dynamic performance, so the accurate description of the mechanical properties of rubber spring has always been the focus of the train dynamics. Among the mechanical properties of rubber springs, the study of non-hyperelastic properties are the most difficult and complex. Therefore, this paper mainly studies non-hyperelastic forces. Based on the experimental data of rubber springs, an elliptic analysis model is derived to describe the non-hyperelastic properties of rubber springs. On the basis of this model, a modified model based on time change and a modified model based on displacement change are also proposed. The results show that the ellipse analysis model is simple, but the error of calculation is large; the calculation precision of time correction model is high, but the calculation process is complex; the displacement correction model is between the previous two models, with both accuracy and convenience. Compared with other models, the displacement correction model has great advantages, which can improve the accuracy of the calculation of train dynamics. It is suggested to adopt the rubber spring displacement correction model in engineering application.
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