Nonlinear Dynamic Analysis of a Spiral Bevel Geared System

A nonlinear dynamic model of a spiral bevel gear train mounted on flexible shafts and bearings is proposed in this study. The finite element model of shafts is combined with a three-dimensional discrete mesh model of a spiral bevel gear pair. Bearing flexibilities are as well included in the model. Gear backlash is incorporated into the model in the form of clearance-type displacement functions and clearance nonlinearity and stiffness fluctuations of the bearings are neglected. A time-invariant mesh stiffness is assumed for the gear pair to simplify the dynamic model. Eigenvalue solution is used to predict the natural modes of the system. A multi-term Harmonic Balance Method (HBM) is employed for the solution of resulting equations of motion for periodic steady-state response. The results of HBM are validated by comparing them to the solutions obtained by direct numerical integration. Forced response of the system in the form of dynamic mesh force is studied to demonstrate the effects of static mesh force and backlash amount