ABSTRACT
If the goal is to develop general and detailed models of railroad vehicle systems, multibody system algorithms must be modified to include a wheel/rail contact model. Three steps are employed in the computational algorithm used to obtain the numerical solution of the wheel/rail contact problem. The first is the
geometry step
, in which the locations of the points of contact between the wheel and the rail are determined. The second is the
kinematic step
, in which normalized kinematic quantities called creepages that measure the relative velocities between the wheel and the rail at the contact points are determined. In the third step, called the
dynamic
or
kinetic step
, the forces that act on the wheel and the rail as the result of the contact are determined. The accuracy of the numerical solution of the contact problem depends strongly on the accurate prediction of the location of the contact points. The solution for the contact locations requires an accurate representation of the geometry of the wheel and the rail surfaces. This representation can be defined using local surface geometric properties such as the radii of curvature and the tangent and normal vectors to the surfaces. These geometric properties are not only important for determining the contact locations (geometry problem), but they are also important, as described in Chapter 4, in determining the forces that represent the dynamic interaction between the wheel and the rail. Therefore, basic knowledge of differential geometry is necessary to understand the wheel/rail contact problem. In particular, the theories of curves and surfaces are fundamental in the study of the dynamic interaction between the wheel and the rail. This chapter discusses topics in differential geometry that are repeatedly used in this book and that are used in the geometric description of wheel and rail surfaces.
