In this study, a hybrid dynamic model of high-speed thin-rimmed gears is developed. In this model, the translational and angular displacements (including the rigid and vibration displacements) with a total of six degrees-of-freedom (DOFs) are selected as the generalized coordinates for each gear, and the meshing force distributions along the contact line and between the teeth are considered. Thus, the model can be implemented under stationary and nonstationary conditions. The condensed finite element models (FEMs) are developed with the centrifugal and inertia forces for gear bodies. This paper proposes a novel method to couple the lumped-parameter model and condensed finite element model for the hybrid dynamic model system, which considers the variation of the meshing tooth during the gear operation, namely, the variations of the acting point of meshing force. Based on the model, the dynamic analysis of high-speed thin-rimmed gears is conducted under stationary speed and acceleration processes. The effects of the flexible gear body, high speed, and tooth errors on the system dynamics and tooth load distribution are investigated. The analysis results are also compared with the current reference and pure finite element method to validate the proposed model.

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.