Multibody System Investigation of Contact Geometry: Application to Deformable and Variable Profile Rails

Modeling the contact problem is a fundamental feature in a variety of multibody system dynamics applications and is of particular importance in the area of railroad vehicle dynamics. An accurate model of the wheel and rail is required in order to develop high fidelity models of vehicle/track interaction scenarios. This may be accomplished through including the dynamic effects of track flexibility and through refinement of the contact surface geometry model. This thesis will present an alternative approach for modeling both of these applications. The first method introduced is an adaption of the finite segment approach to modeling rail flexibility as an alternative to conventional finite element methods. The finite segment approach differs from the finite element approach by concentrating a body's elasticity and inertia between rigid elements rather than distributing them throughout each elastic element. It is first shown that the finite segment method may be integrated with existing rail geometry representation techniques. It is then shown through a comparative numerical analysis that the finite segment method provides reasonable accuracy in the prediction of the deformation of the rail. It is also shown that this method results in fictitious spikes in the contact forces which are not eliminated via model refinement. The second method introduced is an adaption of absolute nodal coordinate formulation (ANCF) thin plate element geometry to modeling contact surfaces. It is shown that existing methods for modeling variable profile contact geometry do not satisfy the continuity requirements of the contact approach employed in this thesis. The most common procedure is direct linear interpolation between profile curves. The low order continuity of this method results in erroneous spikes in the predicted contact forces. A new ANCF thin plate element is introduced after demonstrating that existing ANCF elements do not satisfy the continuity requirements. A railroad vehicle example including variable profile rail is commented on. Here, a comparative numerical analysis shows that the new ANCF thin plate surface model eliminates the erroneous spikes in the predicted contact forces at the cost of a small increases in the computational time required for the simulation.