A node-to-surface linear complementarity problem approach for general three-dimensional contact analysis

Contact between two deformable bodies is a complex nonlinear problem especially when rigid-body motion and geometric errors of components are taken into consideration. In this paper, an effective node-to-surface contact scheme, termed as NTS-LCP, is presented to handle three-dimensional quasi-static contact between deformable bodies experiencing prescribed rigid body motion. The scheme is developed on the basis of the finite element modelling and the component substructuring, and formulated as a linear complementarity problem (LCP) for a speedy and robust solution to the gap sizes and contact forces by means of the well-known Lemke algorithm. The proposed scheme is valid for both conforming and non-conforming meshes. The accuracy and efficiency of the proposed scheme were established through two test cases—cam-follower contact and gear-gear contact, and comparisons with the ANSYS benchmark solution and the Hertz contact theory. The proposed scheme, effective and versatile, is successfully implemented in a computer code to investigate the effects of gear tooth modifications and assembly errors on transmission characteristics of spur gears and helical gears. It is anticipated that the results reported in the paper are useful in design of mechanical systems for optimal performance.