The effect of time-varying operating condition on the crack induced impulses and its application to gearbox tooth crack diagnosis

Gearbox tooth crack diagnosis under Time-Varying Operating Conditions (TVOC) is a challenging issue. TVOC induce both Amplitude Modulation (AM) and Frequency Modulation (FM) effects into gearbox vibration signals, which results in difficulties in tooth crack diagnosis. To overcome this problem, the TVOC-induced AM and FM effects on vibration signals of gearboxes with tooth cracks need to be well studied. Many studies have been reported to investigate the influence of TVOC on gearbox vibration signals using dynamic modelling, some of which only focused on healthy gearboxes while others only considered piecewise constant operating conditions, failing to make comprehensive analyses involving both tooth cracks and TVOC. This paper aims to conduct a comprehensive study on how TVOC affect vibration signals of gearboxes with tooth cracks using dynamic simulation. Firstly, gear tooth mesh stiffness is evaluated considering both tooth crack severity progression and operating condition variations, through which gearbox vibration responses are generated under TVOC. A signal analysis procedure is proposed with its focus placed on the Crack Induced Impulses (CII), which are extracted from gearbox vibration signals using the adaptive harmonic decomposition method or its modified version. Envelope analysis is conducted on the CII to study how the CII are affected by TVOC, and a linear dependence of the AM effect of the CII on TVOC is identified. Based on the identified linear dependence, a novel Condition Indicator (CI), which is sensitive to crack growth while insensitive to operating condition variations, is proposed to track tooth crack severity progression under TVOC. The linear dependence of the AM effect of the CII on TVOC and the effectiveness of the proposed CI for tooth crack diagnosis are demonstrated using both simulated gearbox vibration signals and experimental gearbox vibration datasets.