On the vibration spectrum of high‐speed spur gear boxes

Abstract

An analytical model is presented to simulate the effect of tooth backlash and ball‐bearing radial clearance on the vibration spectrum of high‐speed spur gear boxes. Included in this model are elasticity in bending and torsion of the shafts, friction between meshing teeth, interaction between gear box casing and internals, and time‐varying tooth backlash, mesh stiffness (stiffness is calculated based on the strain energies of the tooth, which is treated as a cantilever beam of involute shape), and Hertzian mesh damping. The bearing loads are calculated with consideration of shaft oscillations and speed, bearing radial clearance, ball centrifugal force, and bearing outer ring oscillations. To demonstrate the model, a single stage gear box is analyzed, and equations of motion are numerically integrated to obtain system response in the time domain. This response is transformed into the frequency domain using a fast Fourier transform (FFT) algorithm and samples of the results are shown for different values of backlash and bearing clearance.