Effect of Backlash on Vibration Spectrum in Spur Gearboxes Incorporating Sleeve Bearings

Abstract

Abstract An Analytical model is presented to simulate effect of tooth backlash on vibration spectrum of spur gearboxes incorporating sleeve bearings. Included in the model are: elasticity of shafts, friction between meshing teeth, interaction between gearbox casing and internals, and time-varying tooth backlash (backlash is a function of operating center distance), mesh stiffness (stiffness is calculated based on the strain energies of the tooth that is treated as a cantilever beam of involute shape) and Hertzian mesh damping. The bearing forces are calculated with consideration of bearing radial clearance and system vibrations. The analysis is applied to a single stage gearbox and equations of motion are numerically integrated to obtain system reponse in time domain. This response is transformed into frequency domain (vibration spectrum) using Fast Fourier Transform (FFT) algorithm and samples of the results are shown for different values of tooth backlash. The results show that backlash has a pronounced effect on gearbox vibration and study provides an analysis procedure for predicting such effects.