Study of gear pair vibration caused by random manufacturing errors

摘要

The surface quality and manufacturing errors of gear teeth directly affect their noise and vibration during operation. These errors depend on the quality classes of the gears. The errors or deviations from the ideal surface of a gear have a combination of periodic and random patterns. The available research on the random errors applies numeric methods for solving the governing equations, which are not able to apply arbitrary complicated types of input models in terms of frequency content. They require several iterations and long simulation times especially if the studied system has multiple degrees of freedom, e.g., multi-stage gearboxes. In this paper, a new approach is proposed to determine the effect of random manufacturing errors on the vibrations measured on the bearings of mating gears. This approach is based on finding the spectral density of the response using the excitation spectral density and the frequency response function of the transfer path between an excitation point and a measurement point. For that purpose, a dynamic model for a gear pair and bearings is considered, and the governing equations are derived. Then, an expression for the vibration caused by random error is derived based on the frequency response functions of the system. The numerical values of the expression are then compared with the results obtained from Monte Carlo simulation for a range of values of system parameters. Then, different levels of random manufacturing error are investigated, and the effect of system parameters on the resulting vibration is also studied. The results provide insight into designing new gearboxes based on acceptable levels of vibration and in quantifying the contribution of manufacturing errors in the gearbox to machinery vibration.