Analytical approximations to damaged gear tooth transmission-error contributions for gear-health monitoring

A generic model of transmission-error contributions arising from gear-tooth damage is developed. Damage is modeled as material removed from tooth-working-surfaces. Regions of modeled tooth damage are of limited size as in pitting damage or are extended to full working surfaces as in tooth-bending-fatigue damage. Results are computed for a wide variety of damage forms and formulated for any collection of teeth experiencing damage. Final results are expressed as transmission-error rotational-harmonic amplitudes arising from damage. Rotational-harmonic regions experiencing significant damage contributions from pitting/spalling damage and from tooth-bending-fatigue damage are delineated. Increases in higher harmonic-number amplitudes arising from transmission-error discontinuities are formulated. The overall model framework can be used to explain and interpret observed features of gear transmission-error spectra arising from gear-tooth damage and to develop new methods of detecting and assessing the severity of such damage.