Bending-fatigue damage-detection on notched-tooth spiral-bevel gears using the average-log-ratio, ALR, algorithm

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

“…equation (44) and Figure 7(a), as described above and illustrated by the mesh-attenuation function, equation (41), and Figure 6(a) to (d). Therefore, utilizing ratios of after potential damage to before potential damage of individual rotational-harmonic amplitudes, as described in Hines and Mark 19 and Mark et al., 20 is likely to be useful for detecting and assessing tooth-bending-fatigue damage and tooth-surface pitting/spalling damage, and for distinguishing between bending-fatigue damage and pitting damage.…”

“…This behavior suggests an increase in the transmission-error very-low-order rotational-harmonic amplitudes and also increases in rotational-harmonic “sideband” amplitudes of the tooth-meshing harmonics with increasing damage of contiguous teeth . Moreover, when the combined elastic/plastic deformation of damaged teeth in contact, 8(Figure 5),19(Figure 12) exceeds tip and/or end reliefs of mating gear teeth, the transmission-error discontinuity at tooth-contact initiation and/or termination changes from a discontinuity in slope (discontinuity in first derivative, or higher order derivative 29 ) to a jump (step) discontinuity, which will increase transmission-error high-order rotational-harmonic amplitudes, 30(Figure 7) as can be seen by a comparison of Figure 6(b) and (c). In Appendix 2, it is shown that the coefficient of the high-frequency asymptotic decay is “volume of missing material ÷π 2 ” for all damage models.…”

“…Parseval’s theorem 33 applied to the transmission-error rotational-harmonic spectrum, equation (7), of a gear with N teeth and base pitch Δ is Therefore, excluding the transmission-error tooth-meshing harmonics n = pN , p = 0, ±1, ±2, … , which include intentional tooth modifications and tooth elastic deformations, an approximate linear metric of total gear damage transmission-error contribution is, from equation (53) which relates increasing rotational-harmonic transmission-error amplitudes αζ(n) to increasing damage. 19,30…”

“…which relates increasing rotational-harmonic transmission-error amplitudes ðnÞ to increasing damage. 19,30…”

“…Bending-fatigue damage on gear teeth consists of tooth plastic (permanent) deformation and reduced tooth stiffness due to root cracks. 8,19 All such geometric deviations from tooth-working-surfaces consist of absent material from undamaged working surfaces. Such deviations can take place on only one tooth or on more than one tooth.…”