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The purpose of this paper is to propose an improved method which can shorten the calculation time and improve the calculation efficiency under the premise of ensuring the calculation accuracy for calculating the response of dynamic systems with periodic time-varying characteristics.

An improved method is proposed based on Runge–Kutta method according to the composition characteristics of the state space matrix and the external load vector formed by the reduction of the dynamic equation of the periodic time-varying system. The recursive scheme of the holistic matrix of the system using the Runge–Kutta method is improved to be the sub-block matrix that is divided into the upper and lower parts to reduce the calculation steps and the occupied computer memory.

The calculation time consumption is reduced to a certain extent about 10–35% by changing the synthesis method of the time-varying matrix of the dynamics system, and the method proposed of paper consumes 43–75% less calculation time in total than the original Runge–Kutta method without affecting the calculation accuracy. When the ode45 command that implements the Runge–Kutta method in the MATLAB software used to solve the system dynamics equation include the time variable which cannot provide its specific analytic function form, so the time variable value corresponding to the solution time needs to be determined by the interpolation method, which causes the calculation efficiency of the ode45 command to be substantially reduced.

The proposed method can be applied to solve dynamic systems with periodic time-varying characteristics, and can consume less calculation time than the original Runge–Kutta method without affecting the calculation accuracy, especially the superiority of the improved method of this paper can be better demonstrated when the degree of freedom of the periodic time-varying dynamics system is greater.

To address the lack of data in this field and determine the relationship between the coefficient of friction and the interference between locomotive wheels and axles, this study evaluates the theoretical relationship between the coefficient of friction and the interference under elastic deformation.

When using numerical analyses to study the mechanical state of the contacting components of the wheels and axle, the interference between the axle parts and the coefficient of friction between the axle parts are two important influencing factors. Currently, as the range of the coefficient of friction between the wheel and axle in interference remains unknown, it is generally considered that the coefficient of friction is only related to the materials of the friction pair; the relationship between the interference and the coefficient of friction is often neglected.

A total of 520 press-fitting experiments were conducted for 130 sets of wheels and axles of the HXD2 locomotive with 4 types of interferences, in order to obtain the relationship between the coefficient of friction between the locomotive wheel and axle and the amount of interference. These results are expected to serve as a reference for selecting the coefficient of friction when designing axle structures with the rolling stock, research on the press-fitting process and evaluations of the fatigue life.

The study provides a basis for the selection of friction coefficient and interference amount in the design of locomotive wheels and axles.

According to relevant research, non-uniform speed has a significant impact on the vehicle-track systems. Up to now, research work on it is still very limited. In this paper, the PEM is adopted to further transform it into a deterministic process to solve the vehicle’s problem of running at a non-uniform speed.

The multi-body vehicle model has 10 degrees of freedom and the track is regarded as a finite long beam supported by lumped sleepers and ballast blocks. They are connected via linear Hertz springs. The vertical track irregularity is a Gaussian stationary process in the space domain. It is transformed into a uniformly modulated nonstationary random process in the time domain with respect to the non-uniform vehicle speed. By solving the equation of motion of the coupled vehicle-track system with the pseudo-excitation method, the pseudo-response and consequently the power spectral density and the standard deviation of the structural response can be obtained.

Two kinds of vehicle braking programs are taken in the numerical example and some beneficial conclusions are drawn.

The pseudo-excitation method (PEM) was used to perform the random vibration analysis of a coupled non-uniform speed vehicle-track system. Transforming the track irregularity into a uniformly modulated nonstationary random process in time domain with respect to the non-uniform vehicle speed was undertaken. The pseudo-response of the coupled system is solved by applying the Newmark algorithm with constant space integral steps. The random vibration transfer mechanism of the coupled system is fully discussed.

The car body stiffness of express freight sliding side covered wagon decreased for the sliding and the resonance vibration based on the flexible car body has affected the dynamics performances. Dynamic loading will cause fatigue cracks and eventually lead to fatigue failure of the car body. This paper aims to investigate the influence of car body flexibility on the evaluation of the failure.

In this paper, the railway vehicles random analysis procedure (RVRAP) is employed to study the fatigue failure of the rigid-flexibility model. Following the analysis process, the rigid-flexibility model is established and four contrastive schemes for simulation analysis are designed. To verify the results, an experimental test using the real car body structure on the vibration test plant is carried out; the RMS of dynamic stress is obtained and compared with the simulation results.

The results show that the flexibility of the car body has a crucial influence on the fatigue life.

The reliability is verified regarding the use of RVRAP at an appropriate stage on the antifatigue design of the vehicle.