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Finite element implementation of an eigenfunction solution for the contact pressure variation due to wear

James Barber (University of Michigan), Yong Hoon Jang (Yonsei University, Korea), Yuwei Liu (Beijing Institute of Technology)

Contact Mechanics

Tue 9:00 - 10:30

Barus-Holley 163

Wear in sliding systems causes the contact pressure distribution to evolve with time. For example, the contact pressure between newly installed brake pads and the disc in an automotive disc brake will depend on the elasticity of the components and the design of the brake mechanism, but as wear occurs it will tend towards a state such that the distribution of incremental wear is consistent with the kinematics of rigid-body motion. Analytical solutions to evolutionary problems of this class have been obtained by assuming Archard's wear law and an exponential approach to the steady state. This leads to an integral equation for the contact pressure in which the exponential decay rate functions as an eigenvalue. More general solutions can then be written as eigenfunction expansions. In the present paper, we show how this method can be formulated in the context of the finite element method. Static reduction is used to reduce the full stiffness matrix to the N contact nodes, after which the assumption of a separated variable solution with exponential decay in time leads to a linear eigenvalue problem with N eigenvalues and eigenfunctions. A general solution to the transient problem can then be written as an eigenfunction series, with the unknown coefficients being determined from the initial conditions.