Three-Point Contact Study of a Wheelset and Rails

Three-point contact occurs in curving and transfer of a wheelset over switches and turnouts. In this study, an approach is presented that enforces three-point contact between a wheelset and a rail. This is accomplished by placing the wheelset over the track by setting the wheelset position parameters. Then, the location of all common normal are computed. Next, three common normal with shortest length are used to set up the non-penetrating constraint equations in track coordinate system. This led to nine algebraic equations whose Jacobean can be represented by block matrices. A Newton iterate based on these block matrices are used to compute the location of the three contact points. Several numerical examples are presented to verify the accuracy of the approach.