Three-dimensional contact formulation for assessment of dynamic interaction of pantograph and overhead conductor rail system

Overhead conductor rail (OCR) is an important power supply device in tunnel railway lines. The penalty method is widely adopted to model the dynamic interaction behaviour of the pantograph-OCR system (POCRs), while it is difficult to determine a proper contact stiffness value. This paper proposes a three-dimensional contact formulation for the POCRs based on the Lagrange multiplier method. Accurate contact forces can be obtained easily by this contact formulation without the trouble of determining the contact stiffness. Contact force is defined in the global coordinate system as a three-dimensional vector. Coulomb law of friction is adopted in this paper to describe the tangential contact force, and the train speed is included in the contact formulation. The central finite difference approximation method is utilised, and an iteration procedure is elaborated to calculate the accurate contact force vector. The proposed contact formulation is verified by comparing simulation results with in-line measured data. The maximum statistical relative error of the contact force is only 2.63%. The advantages of the proposed contact formulation are also demonstrated by comparing it with the penalty method.

Automated summary

In this paper, a three-dimensional contact formulation for the pantograph-OCR system (POCRs) based on the Lagrange multiplier method is proposed. The contact forces can be accurately obtained without the need to determine the contact stiffness value. The effectiveness and accuracy of the proposed contact formulation are verified by comparing the simulation results with in-line measured data.