A mathematical model of static-transmission-error frequency-domain contributions caused by a single generic form of gear-tooth damage is used to explain observed behavior of the average-log-ratio (ALR) gear-damage detection algorithm applied to a case of tooth-bending-fatigue damage. The periodic behavior of rotational-harmonic frequency spectra resulting from tooth damage is explained and experimentally verified. Monotonic increases in ALR contributions in the rotational-harmonic region below the tooth-meshing fundamental harmonic are unambiguously related to increasing gear damage by use of Parseval’s theorem for the discrete Fourier transform. Computation of ALR using rotational-harmonic bands between adjacent tooth-meshing harmonics is suggested for early detection of gear damage. Large high-frequency ALR contributions are explained by transmission-error jump (step) discontinuities caused by large tooth-pair deformations, indicating a severe state of damage.
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