Theoretical analysis of nonlinear vibration characteristics of gear pair with shafts

The circumferential vibration of a gear pair is a parametric excitation caused by nonlinear tooth stiffness, which fluctuates with meshing. In addition, the vibration characteristics of the gear pair become complicated owing to the tooth profile error and backlash. It is considered that the circumferential vibration of the gear pair is affected by the torsional vibration of the shafts. It is important to understand quantitatively the vibration characteristics of the gear system considering the shafts. Therefore, the purpose of this research was to clarify the nonlinear vibration characteristics of a gear pair considering the influence of the shafts using theoretical methods. To achieve this objective, calculations were performed using equations of motion in which the circumferential vibration of the gear pair and the torsional vibration of the shafts were coupled. The nonlinear tooth stiffness was represented by a sine wave. The influence of tooth separation was considered by defining a nonlinear function using backlash and the tooth profile error. For the numerical calculations, both stable and unstable periodic solutions were obtained by using the shooting method. The effect of the shafts on the gear system vibration were clarified by comparing the results in the cases in which the shaft was not considered, one shaft was considered, and both shafts were considered.