An elastic–plastic asperity contact model and its application for micro-contact analysis of gear tooth profiles

This paper presents a continuous elastic–plastic asperity contact model with or without the consideration of friction to investigate the micro-contact properties of gear tooth profiles. The model for normal or side contact analysis is established according to Hertz contact theory and the asperity morphology feature, which yields to similar results as obtained from the model proposed by Chang W.R., Etsion I., and Bogy D.B. (CEB model) and the model proposed by Kogut L. and Etsion I. (KE model). More importantly, this model avoids the constant average contact stress as predicted by the CEB model, and the noncontinuous contact stress and deformation within the ultimate strength as given by the KE model. As a application of the present theoretical model in micro-contact analysis of rough tooth profiles, a finite element model (FE model) for elastic–plastic asperity in normal or side contact is established according to the measured surface parameters of a spur gear pair. It is shown that the extreme point of Von Mise stress of the asperities along the normal vector is ascertained by FE model, and that the extreme point is relative to the initial occurrence of the asperities plastic deformation. Compared with the present theoretical model, the similar normal contact stress along the contact radius is attained by FE model. Though the contact stress isogram in the specific plane in normal or side contact of the asperities is a circle or ellipse respectively when the plastic deformation is expanded from the inside of the asperities to their surfaces, it is in line with the distribution of elastic and plastic region of the theoretical model. Compared with CEB model, KE model, and FE model, the consistent results are attained by the present theoretical model in elastic–plastic asperity contact analysis. The results indicate that the theoretical model is applicable to the elastic–plastic asperity contact analysis on the rough surface of a spur gear drive.