Stability is a key factor for the operation safety of railway vehicles, while current work employs linearized and simplified wheel/rail contact to study the bifurcation mechanism and assess the stability. To study the stability and bifurcation characters under real nonlinear wheel/rail contact, a fully parameterized nonlinear railway vehicle wheelset model is built. In modeling, the geometry nonlinearities of wheel and rail profiles come from field measurements, including the rolling radius, contact angle, and curvatures, etc. Firstly, four flange force models and their effects on the stability bifurcations are compared. It shows that an exponent fitting is more proper than a quintic polynomial one to simulate the flange and works well without changing the Hopf bifurcation type. Then the effects of each term of the nonlinear geometry of wheel/rail contact on the Hopf bifurcation and limit circle bifurcation are discussed. Both the linear term and nonlinear term of rolling radius have a significant influence on Hopf bifurcation and limit point of circle (LPC) bifurcation. The linear critical speed (Hopf bifurcation point) and the nonlinear critical speed (LPC bifurcation point) changes times while within the calculated range of the linear term of the rolling radius. Its nonlinear term changes the bifurcation type and the nonlinear critical speed almost by half. The linear term of the contact angle and the radius of curvature of the wheel and rail profiles should be taken into consideration since they can change both the bifurcation point and type, while the cubic term can be ignored. Furtherly, the field measured wheel profiles for several running mileages are employed to examine the real geometry nonlinearities and the corresponding Hopf bifurcation behavior. The result shows that a larger suspension stiffness would increase the running stability under wheel wear.

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Bifurcation analysis of a railway wheelset with nonlinear wheel–rail contact

To study the vehicle hunting behavior and its coupling with car body vibrations, a simplified lateral-dynamics-intended railway vehicle model is developed. A two-truck vehicle is modeled as a 17 degrees-of-freedom rigid system, into which the car body flexural vibrations of torsion and bending modes are further integrated. The wheel/rail interaction employs a real-time calculation for the Hertzian normal contact, in which the nonlinear curvatures of wheel and rail profiles are presented as functions of wheelset lateral movement and/or yaw rotation. Then the tangential/creep forces are analytically expressed as the Hertzian contact patch geometry, and lead to a continuous and fast calculation compared to a look-up table interpolation. It is shown that the hunting frequencies of the vehicle model and a truck model differ significantly, which verifies the necessity of the whole vehicle model. In the case of low wheel/rail conicity, the hunting frequency increases linearly with vehicle speed, whereas it rises slowly at high speed for a large conicity. Comparison of hunting frequency and damping ratio between various conicities shows that first hunting (car body hunting) may occur when the vehicle is operated at a low speed in a small conicity case, while a second hunting (truck hunting) appears when the vehicle is operated at a high speed in a large conicity case. Stability analysis of linear and nonlinear vehicle models was carried out through coast down method and constant speed simulations. Results tell that the linear one overestimates the lateral vibrating. Whereas the structural vibrations of car body can be ignored in the stability analysis. Compared to existing simplified models for hunting stability study, the proposed simplified vehicle model released limitations in the nonlinear geometries of wheel/rail profiles, and it is suitable for a frequency-domain analysis by deriving the analytical expressions of the normal and tangential wheel/rail contact forces.

Improved lateral-dynamics-intended railway vehicle model involving nonlinear wheel/rail interaction and car body flexibility

Linear stability analysis of a high-speed rail vehicle concerning suspension parameters variation and active control

The dynamic characteristics of the hydraulic damper are time-varying in the complex working environment. To reveal the internal influence mechanism of the boundary conditions on the dynamic performance of the hydraulic damper and take it into account in the multi-body dynamics calculation, the laboratory test of the hydraulic damper is carried out firstly, and it is confirmed that the hydraulic damper has significant frequency-dependent and amplitude-dependent and temperature-dependent characteristics. Then, combining the physical parameter model with the neural network model, an accurate hybrid neural network model of the hydraulic damper is proposed. The physical parameter model considers the damper structure, including orifice, damping valve, rubber joint and the relationship between temperature and viscosity of hydraulic oil. The neural network model describes the personality characteristics of the hydraulic damper, such as oil leakage, the internal friction force and the percentage of entrapped air in oil. Finally, the responses and the dynamic parameters of the hybrid neural network model are calculated and compared with the experimental results by considering various exciting amplitudes and frequencies. The results show that the proposed model can fully simulate the dynamic performance of the hydraulic damper under various operating conditions.

A physical model-neural network coupled modelling methodology of the hydraulic damper for railway vehicles

Ensuring running stability and minimising wheel tread wear are critical factors for enhancing the dynamic performance of high-speed trains. As an efficient method for improving vehicle performances, previous studies on suspension parameter optimisation have not fully considered these two factors. It is essential to pay attention to stability at extreme wheel-rail contact states, and the wheel wear evolution needs to be revealed instead of investigating the wear performance only through an index like wear number. This research aims to investigate the stability/wear Pareto optimisation of bogie suspension parameters for a high-speed passenger train. Stability-related indices are defined as the lateral ride comfort index at low equivalent conicity and the bogie frame acceleration at high conicity. To represent the long-term wheel wear performance, a contact spreading index is proposed and combined with the wear number index. The key suspension parameters are optimised through the genetic algorithm NSGA-II. The obtained Pareto front clearly reveals the relationship between the objective functions. To meet different performance requirements, four distinct matching rules of the suspension parameters are summarised by employing clustering analysis. Finally, the applicability of the parameter matching rules is examined by analysing stability at different equivalent conicities and wheel wear evolution. 

Suspension parameter optimal design to enhance stability and wheel wear in high-speed trains

Yaw damper, widely employed in high-speed railway vehicles, has played an important role in improving the hunting stability. This paper mainly makes a comprehensive analysis on the effect of yaw damper with its series stiffness value on the stability and bifurcation type of the railway bogie. With the prerequisite of the linear critical speed calculated by mathematical method, Center Manifold Theorem is adopted to reduce the dimension of the model to a planar dynamical system. And the symbolic expression associated with yaw damper and its series stiffness to determine bifurcation type at the critical speed is obtained by the method of Normal Form. As a result, the influence of the variation tendency of the yaw damper and series stiffness on the bifurcation type of the bogie is given qualitatively in contrast to different couples. Finally, numerical analysis of corresponding bifurcation diagrams is given to verify the accuracy of the conclusion.

Yong Yan

Papers

Bifurcation analysis of railway bogie with yaw damper