Applicability of the Hertz Contact Theory to Rolling Rubber Cylinders Model

Abstract

Hertz contact theory (HCT) is a study of contact stress and deformation which is widely used in many engineering fields. However, there are many limiting conditions for the applications of the HCT, in this paper, the contact model between a plastic cylinder and a rubber cylinder does not fit two limiting conditions: Small deformation and no rigid body motion. By applying three-dimensional finite element models, the deformation and the maximum contact stress of two rotating cylinders have been analyzed. Comparing the simulation results and the theoretical results, the applicability of Hertz contact theory to this model has been discussed. The results show that: In the condition of large deformation, the theoretical results of maximum contact stress fit the actual situation, but the half-width of the contact area does not fit. Under the rolling condition, the theoretical maximum contact stress has a large deviation to simulation result.

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“…Therefore, the results are more reliable at high velocities when the rubber has higher stiffness. Hongyan et al [36] also studied the applicability of the Hertz contact theory to large deformation using finite element methods. They found that the Hertz contact theory can predict the maximum contact stress under large deformation with about 2% error and overestimates the contact length with about 33%, but they did not validate the results with experiments.…”