Frequency-domain assessment of gear-tooth bending-fatigue damage-progression using the average-log-ratio, ALR, algorithm

• Gear-tooth bending-fatigue damage progression is computed by the ALR average-log-ratio algorithm.
• Initial damage is detected by ALR and FM4 algorithms at the same running time.
• High-frequency ALR computations indicate damage-amplitude exceeding tip/end relief of teeth.
• FM4 abruptly increases at same running time as high-frequency ALR abrupt increase.

Frequency-domain (rotational-harmonic) behavior of the average-log-ratio, ALR, gear-damage detection algorithm [MSSP 24 (2010) 2807–2823] [18] is utilized to explain behavior caused by tooth-bending-fatigue damage progression. For spur and helical gears, the strongest bending-fatigue damage contributions are typically found in the rotational-harmonic region below the tooth-meshing fundamental harmonic, where ALR increases almost monotonically with increasing damage. However, when the combined elastic/plastic deformation of a damaged tooth or teeth exceeds tooth tip/root/end relief magnitude, at tooth-contact initiation and/or termination, the lowest-order transmission-error discontinuity is changed from slope discontinuity to step discontinuity, resulting in transmission-error high-frequency (rotational-harmonic n) behavior changing from proportional to 1/n2 to proportional to 1/n, therefore indicating progression to severe damage. Decomposition of the ALR damage-detection metric into rotational-harmonic frequency bands using accelerometer recordings from a notched-tooth spiral-bevel gear test illustrates the above-described behavior, thereby showing increasing stages of damage progression prior to complete gear failure.