Computation of contact points between the wheel and rail is a fundamental problem in dynamic simulation of trains. To compute these contact points, one needs to locate common normals first. The objective of this study is to develop an efficient method to compute common normals between wheel and rail surface. This is done by devising a method to compute an estimate of location of common normals and then using them as the initial guess to compute them. To generate an estimate of the location of common normal, a local approximation of the rail is constructed. To achieve this, the intersection of the vertical mid-plane of the wheelset with a track curve of a rail is computed and the tangent line at this point is generated. The rail profile is place on the tangent line and is swept along it. The resulting rail is called linearized rail in this study. It is shown that the four nonlinear equations governing the location of the common normal can be reduced to one equation in one unknown. This equation is referred to as reduced equation. A bracketing algorithm is added to identify the intervals within which this reduced equation changes sign. These intervals contain the zero of the reduced function. The zeros of the reduced equation are used to compute an estimate of the common normals. These estimates are used as an initial guess for a Newton iterate to accurately locate all common normals. It is observed that the CPU time to compute all common normals is of the order of mili-second.

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