A Hertzian Contact Formulation for the Wheel-Rail Contact Problem in Railway Dynamics

The main difference between railway and other vehicles is that they move on tracks. In conventional rail vehicles, the wheels, assembled in a wheelset, are not free to rotate independently. Hence, their treads are profiled to allow them to negotiate curves without slipping. The accurate prediction of the contact points location between wheel and rail surfaces is fundamental for the accuracy of the dynamic analysis results. A generic contact detection formulation is proposed here in order to determine, online during the dynamic simulation, the coordinates of the multiple contact points between each wheel and rail even for the most general three dimensional motion of the wheelset with respect to the track. The formulation allows the detection of flange contact with lead and lag contact configurations, which are fundamental to evaluate the risk of derailments, to study switches or to investigate the curving performance when dealing with high angles of attack. This methodology is used in conjunction with a general geometric description of the track, which includes the representation of the rails spatial geometry and irregularities. Due to the efficient parameterization, this formulation can be used for any kind of wheel or rail profiles and still be computationally efficient, without requiring the use of lookup tables. The movement of the wheelsets along the rails is characterized by a complex contact with relative motions on the longitudinal and lateral directions and relative rotations of the wheels with respect to the rails. These motions generate tangential creep forces and moments at the wheel-rail interface, especially when the wheelset departs from the center of the tangent track. One of the difficulties of the wheel-rail contact problem arises when the contact point is located in the concave region between the wheel tread and the wheel flange. In this work a Hertzian contact formulation is developed to calculate the contact forces that develop in the wheel-rail interface. The discussion on the benefices and drawbacks of these methodologies is supported by an application to the dynamic analysis of the railway vehicle ML95, which is used by the Lisbon subway company.