The Rolling Wheel Equations without Magic: A Combined Slip-Stiction Approach by the Udwadia-Kalaba Formulation with Constraints Relaxation for a Smooth Simulation

The Udwadia-Kalaba formulation is proposed to model the dynamics of the rolling wheel. A unified approach that addresses both the slip and the stiction in the contact section is considered. Purely rolling constraints are associated with stiction and are suitably lifted as slip occurs. An extended formulation for the Uwadia-Kalaba equations of motion is introduced for that matter. It resorts to the weighted minimum norm and the weighted semi-least-squares solutions of the constraints equations. This not only allows a bias on constraints, by an appropriate description of weight functions based on friction, it also leads to a smooth activation or deactivation of selected constraints without rewriting the equations of motion or upsetting their numerical integration.

Integration of uniform design and quantum-behaved particle swarm optimization to the robust design for a railway vehicle suspension system under different wheel conicities and wheel rolling radii

This paper proposes a systematic method, integrating the uniform design (UD) of experiments and quantum-behaved particle swarm optimization (QPSO), to solve the problem of a robust design for a railway vehicle suspension system. Based on the new nonlinear creep model derived from combining Hertz contact theory, Kalker's linear theory and a heuristic nonlinear creep model, the modeling and dynamic analysis of a 24 degree-of-freedom railway vehicle system were investigated. The Lyapunov indirect method was used to examine the effects of suspension parameters, wheel conicities and wheel rolling radii on critical hunting speeds. Generally, the critical hunting speeds of a vehicle system resulting from worn wheels with different wheel rolling radii are lower than those of a vehicle system having original wheels without different wheel rolling radii. Because of worn wheels, the critical hunting speed of a running railway vehicle substantially declines over the long term. For safety reasons, it is necessary to design the suspension system parameters to increase the robustness of the system and decrease the sensitive of wheel noises. By applying UD and QPSO, the nominal-the-best signal-to-noise ratio of the system was increased from -48.17 to -34.05 dB. The rate of improvement was 29.31%. This study has demonstrated that the integration of UD and QPSO can successfully reveal the optimal solution of suspension parameters for solving the robust design problem of a railway vehicle suspension system.

Effects of Lateral Motion on the Creep Forces in Wheel/Rail Rolling Contact

The influences of the lateral motion of a single wheelset running on a tangent railway on the creepages and creep forces between wheel and rail are investigated with numerical methods. The effect of the yaw motion of wheelset is neglected in the analysis, and Kalker’s theory of three dimensional elastic bodies in rolling contact is employed to analyze the creep forces in the wheel/rail rolling contact with Non Hertzian form.

Numerical simulation of wheel wear evolution for heavy haul railway

The prediction of the wheel wear is a fundamental problem in heavy haul railway. A numerical methodology is introduced to simulate the wheel wear evolution of heavy haul freight car. The methodology includes the spatial coupling dynamics of vehicle and track, the three-dimensional rolling contact analysis of wheel-rail, the Specht's material wear model, and the strategy for reproducing the actual operation conditions of railway. The freight vehicle is treated as a full 3D rigid multi-body model. Every component is built detailedly and various contact interactions between parts are accurately simulated, taking into account the real clearances. The wheel-rail rolling contact calculation is carried out based on Hertz's theory and Kalker's FASTSIM algorithm. The track model is built based on field measurements. The material loss due to wear is evaluated according to the Specht's model in which the wear coefficient varies with the wear intensity. In order to exactly reproduce the actual operating conditions of railway,dynamic simulations are performed separately for all possible track conditions and running velocities in each iterative step.Dimensionless weight coefficients are introduced that determine the ratios of different cases and are obtained through site survey. For the wheel profile updating, an adaptive step strategy based on the wear depth is introduced, which can effectively improve the reliability and stability of numerical calculation. At last, the wear evolution laws are studied by the numerical model for different wheels of heavy haul freight vehicle running in curves. The results show that the wear of the front wheelset is more serious than that of the rear wheelset for one bogie, and the difference is more obvious for the outer wheels. The wear of the outer wheels is severer than that of the inner wheels. The wear of outer wheels mainly distributes near the flange and the root; while the wear of inner wheels mainly distributes around the nominal rolling circle. For the outer wheel of front wheelset of each bogie, the development of wear is gradually concentrated on the flange and the developing speed increases continually with the increase of traveled distance.