Studies On The Numerical Methods For Dynamics Of Coupled Vehicle-track System

The vehicle riding quality, vehicle running safety and the service life of the vehicle and track are significantly influenced by vibration characteristics of the vehicle and track, when the vehicle travels along the track at the high speed. In order to obtain vibration characteristics of the vehicle and track, the core problem to be solved is to accurately obtain actual track irregularities status, random response of the coupled vehicle-track system subjected to track random irregularities, contact status between vehicle and track and so on. The numerical simulation of the coupled vehicle-track system is an effective way to obtain the vibration characteristics of the vehicle and track, and one of the crucial factors in the numerical simulation is numerical algorithm. Based on demand and characteristics of the coupled vehicle-track system, the accurate and efficient numerical methods for dynamics integration of the large scale system, random response analysis, random vibration inverse problem and dynamic contact analysis play a key role in achieving the numerical simulation of the coupled vehicle-track system. In the present PhD thesis, for the problems in dynamics integration method, random response analysis, identification of the power spectral density of track irregularities and dynamic contact between vehicle and track of the coupled vehicle-track system, based on some computational mechanics methodology, such as the precise integration method, symplectic mathematical method, pseudo excitation method, inverse pseudo excitation method and linear complementarity method, the accurate and efficient numerical methods for solution of the dynamic response of the coupled vehicle-track system are proposed. The main work in this PhD thesis can be summarized into the following four aspects:1. A improved precise integration method for coupled vehicle-track system dynamic response including nonlinear wheel-rail contact is proposed. Based on the periodical characteristics of the track and the finite propagation speed of the energy, the computational efficiency of the exponential matrix of the track structure is improved by the modified precise integration method, and the exponential matrix of track structure obtained is sparse, and thus the computational cost of the dynamic response of the track can be reduced. The recurrence formula for the nonlinear normal wheel-rail contact force is obtained by use of the Lagrange interpolation polynomial, and then the dynamic response of the vehicle-track system can be solved without iteration by the modified precise integration method. For three cases, i.e., the smooth rail, the rail corrugation and the irregularity at the rail weld, the dynamic responses of the coupled vehicle-track system are calculated by the Runge-Kutta method, Zhai’s method and the proposed method. Comparison of numerical results from the Runge-Kutta method and Zhai’s method verities that the dynamic response of the coupled vehicle-track system is solve accurately by the proposed method, and the propose method is more efficient than the Runge-Kutta method and Zhai’s method.2. A parallel algorithm based on the pseudo excitation method for nonstationary random vibration of a coupled vehicle-slab track system is proposed. Based on a combination of the computational characteristics of the power spectral density for the pseudo excitation method and the relation between computational frequency point of nonstationary random vibration of the coupled vehicle-slab track system and the number of CPU, a parallel algorithm for nonstationary random vibration of the coupled vehicle-slab track system is proposed. This algorithm characteristics are nonstationary random response calculated independently at each computational point, no data exchange between the different computational point, and almost a linear speedup. The correctness of the proposed method is verified by use of the Monte Carlo method, and then by contrast with the computational time, it is verified that the proposed method is more efficient than the conventional pseudo excitation method. The proposed method is applied to analyse the basic characteristics of nonstationary random vibration of the coupled vehicle-slab track system, and to investigate the effect of vehicle speed and slab track parameter on nonstationary random response of the coupled vehicle-slab track system.3. A symplectic-inverse pseudo excitation method for identification of the power spectral density of track irregularities is proposed. Based on the symplectic mathematical method, the dynamic export stiffness matrix of semi-infinite sub-structural chain is obtained by use of the eigenvectors of the symplectic matrix, and then the computational cost of the coupled vehicle-track system can be reduced. Based on the small-scale coupled vehicle-track system, the power spectral density of track irregularities is conveniently identified by the inverse pseudo excitation method. By contrast with the numerical results, the correctness of the proposed method is verified by the conventional method, and the proposed method is more efficient than the conventional method. The power spectral density of track irregularities obtained accurately by the proposed method is verified through investigation on the effect of the measurement noise, vehicle speed, primary suspension parameters and track irregularities status on the identification accuracy of the power spectral density of track irregularities.4. A linear complementarity method for solution of the coupled vehicle-track system dynamic response including separation between wheel and rail is proposed. The contact problem between vehicle and track is changed into a linear complementarity problem, and the different contact situations between vehicle and track can be described by the uniform mathematical expression. On this basis, a high-performance algorithm for solution of the dynamic contact problem in the coupled vehicle-track system including separation between wheel and rail is proposed by use of a combination of the Generalized-a method and the Lemke algorithm. Compared with the displacement constraint method, the proposed method does not need to update the equivalent stiffness matrix of the coupled vehicle-track system model at each time step, and the same motion equation of the coupled vehicle-track system is adopted at the different wheel-rail contact situations. Compared with Hertz contact method, the numerical result from the proposed method is not affected by the Hertz contact stiffness.