Effect of tooth backlash and ball bearing deadband clearance on vibration spectrum in spur gear boxes

Abstract

An analytical model is presented for studying the effect of tooth backlash and ball-bearing deadband clearance (clearance between bearing outer ring and its housing) on vibration spectrum of spur gear boxes. Included in the model are coupled torsional-lateral vibrations of the shafts, time-varying tooth backlash (backlash is a function of operating center distance), mesh stiffness (stiffness is calculated based on the bending, shear, axial, and Hertzian contact strain energies of the tooth that is treated as a cantilever of involute shape), and Hertzian damping at mesh, friction between meshing teeth, and interaction between gear box casing and internals. The bearing–housing reaction forces are calculated with consideration of bearing clearance and system vibrations. The above parameters are accounted for with allowance for number of teeth pairs sharing the load to alternate between one and two. The analysis is applied to a single stage gear box and equations of motion are deduced using Newton’s laws of motion and numerically integrated using Runge–Kutta method. The gear box casing velocities in time domain are transformed into frequency domain (vibration spectrum) using Fast Fourier Transform (FFT). This was done for different values of tooth backlash and bearing clearance and samples of the results are shown. This model provides an analysis procedure for predicting effect of tooth wear (wear affects backlash) and bearing deadband clearance on gear box vibration spectrum.