A Complementarity Problem–Based Solution Procedure for 2D Steady-State Rolling Contacts with Dry Friction

ABSTRACT

The problem of steady-state rolling contact between two cylinders with dry friction was formulated into standard linear complementarity problems (LCPs) using the explicit physical definition. For normal contacts, the complementarity variables are the normal pressure and the gap. For the tangential contact, the traction distribution and relative slip are the variables obtained by solving the LCP. The frictional behavior is assumed to be governed by the Coulomb friction law, and LCP formulations of both similar elastic (Carter problem) and dissimilar elastic rolling contacts are presented in this work. Good agreement was found between the current LCP approach and publicly available software for both the rolling contact of similar elastic and dissimilar elastic cylinders. Moreover, the surface roughness was taken into account in this article by the verified approach. The results show the initial slope of the traction-relative creepage curve decreases as the surface roughness increases.

KEYWORDS:

• Dry friction
• rolling contact
• linear complementarity problem
• surface roughness

Funding

The first author acknowledges support from the China Scholarship Council (No. 201406280045).