An Investigation into the Modeling Methodology of the Coil Spring

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

Calculation of Nonlinear Stiffness of Rubber Pad under Different Temperatures and Prepressures

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

Mathematical Modelling and Computational Simulation of the Hydraulic Damper during the Orifice-Working Stage for Railway Vehicles

The objective of this paper is to establish an accurate nonlinear mathematical model of the hydraulic damper during the orifice-working stage. A new mathematical model including the submodels of the orifices, hydraulic fluids, pressure chambers, and reservoir chambers is established based on theories of the fluid mechanics, hydropneumatics, and mechanics. Subsequently, a force element based on the established model of the hydraulic damper which contains 56 inputs, 6 force states, and 47 outputs is developed with the FORTRAN language in the secondary development environment of the multibody dynamics software SIMPACK. Using the force element, the damping characteristics of the modified yaw damper with different diameters of the base orifice are calculated under different amplitudes and frequencies of the sine excitation, and then the simulation results are compared with the experimental results which are obtained under the same conditions. Results show that during the orifice-working stage, the new established mathematical model can accurately reproduce the nonlinear static and dynamic characteristics of hydraulic dampers such as the force-displacement characteristic, force-velocity characteristic, fluid shortage, hysteresis effect, and pressure limited effect. Furthermore, it also shows that the nonlinear characteristics of the orifice, air release, cavitation, leakage for high frequencies, and dynamic characteristics of fluid (i.e., the density, bulk modulus, and air/gas content) should be taken seriously during the modelling of the hydraulic damper at the orifice-working stage. The mathematical model proposed in this paper is more applicable to the railway vehicle system dynamics and individual system description of the hydraulic damper

Study of Vertical Characteristics with Changes in Prepressure of Rubber Pad Used by High-Speed EMU

Rubber spring plays an important role in improving train performance, so the study of rubber spring is one of the focuses of train dynamics. The vertical characteristic parameters of rubber spring are affected by prepressure significantly, as a result of varying parameters of static stiffness, dynamic stiffness, periodic energy consumption, damping coefficient, and so on. In order to use the theoretical method to calculate the precise static stiffness and predict the dynamic characteristics and to reduce the workload of the rubber spring performance test, this paper takes the annular rubber pad as an example to study with different prepressures. In this paper, the convexity coefficient correction formula (simply called the CCCF) for static stiffness calculation and the dynamic fiducial conversion coefficient (simply called the DFCC) method based on different prepressures are proposed. Through further analysis, the accuracy of CCCF and DFCC is proved both theoretically and experimentally. The results have shown precise prediction of the variation of prepressure on rubber spring parameters by using CCCF and DFCC and can be used as the reference of accurate vertical dynamic-static characteristics of the rubber spring