| Recently there has been a surge of interest in simulation-based approaches to study the dynamics of railroad vehicles. This includes the study of derailment, switching, wheel climbing and curving. Central to these problems is the development of an efficient and robust approach for finding all common normals between rail and wheel surfaces. To accomplish this, signed distance function for wheel and rail surfaces is formed. It is shown that the location of the common normal corresponds to zero of the gradient of signed distance function.;The search for common normals is accomplished in two phases. The first phase is a global search where the wheel parameter space is divided into a number of cells and the rotation of the gradient of signed distance function is computed. If this rotation is nonzero, then one concludes that common normals exist within that cell. Cells with zero gradient rotation are discarded as no common normal exists within them. This process is repeated until cells that contain common normal are small enough. This completes the first phase. The second phase is a local search. In this phase, Newton method and trust region method are used as two alternatives to accurately locate common normals. To implement this approach, the closed-form equation for signed distance function and its first and second derivatives are reported. Subtasks are identified and several alternatives to implement them are tested and their relative merit is reported. Also, the contours of the signed distance function for a rail and wheel surface for several positions of the wheel relative to the rail surface are generated. These contours verify that our algorithm correctly identifies all common normals. |
