Dynamic Model of Variable Speed Process for Herringbone Gears Including Friction Calculated by Variable Friction Coefficient

Abstract

A dynamic model that includes friction and tooth profile error excitation for herringbone gears is proposed for the dynamic analysis of variable speed processes. In this model, the position of the contact line and relative sliding velocity are determined by the angular displacement of the gear pair. The translational and angular displacements are chosen as generalized coordinates to construct the dynamic model. The friction is calculated using a variable friction coefficient. The tooth profile error excitation is assumed to depend on the position along the contact line and to vary with the angular displacement of the driving gear. Thus, the proposed model can be used in the dynamic analysis of the variable speed process of a herringbone gear transmission system. An example acceleration process is numerically simulated using the model proposed in this paper. The dynamics responses are compared with those from the model utilizing a constant friction coefficient and without friction in cases where the profile error excitations are included and ignored.