Rolling Contract with Friction of a Cylindrical Wheel on a Strip

We establish a model for the rolling motion of an elastic wheel on an elastic strip. It includes carefully formulated (nonlinear) contact conditions for a regularized form of Coulomb's friction. The system resembles a railway aheel on a rail. The rim of the wheel and the strip (the head of the rail) are substituted by three-layer-models deduced from linear elastodynamics for plane deformations. For stationary rolling motion the set of governing (ordinary differential) equations is worked out in detail, nonlinear inside the contact region and linear outside. Numerical solutions to the problem are under investigation and will be published shortly. However, some facts can be read directly from the equations. Different from the common Hertz approach the pressure jumps at the borders of the contact region ; beside the contact length, the longitudinal position and the inclination of the contact surface depend on all loads, on the friction and on the overall dimensions of wheel and strip. A drawback of the present model is that it is based on "linear" elastodynamics.