Analysis of vibration signals and detection for multiple tooth cracks in spur gearboxes

Tooth crack diagnosis is important to ensure the reliability of gearboxes. However, most reported studies on tooth crack diagnosis only involved the scenario of one tooth crack in a gearbox, which is not always the case since gearboxes may also suffer from multiple tooth cracks in the industry. To overcome this problem, this study first brings some insights into the vibration characteristics of a spur gearbox with multiple tooth cracks using dynamic modelling. Three scenarios of multiple tooth cracks are considered, including two nonadjacent tooth cracks on the pinion and a healthy gear, two adjacent tooth cracks on the pinion and a healthy gear, and one tooth crack on the pinion and one tooth crack on the gear. Tooth mesh stiffness is analytically evaluated using the potential energy method and is further inserted into the spur gearbox dynamic model to generate vibration responses. Analyses of mesh stiffness and vibration responses are conducted in both time and frequency domains. Besides, a novel method focusing on the crack induced impulses (CII) is proposed to detect the number and locations of multiple tooth cracks. Firstly, the CII are extracted from gearbox vibration signals using a new strategy based on the singular value decomposition. Time synchronous average (TSA) is conducted on the CII to get the TSA signals for both the pinion and the gear. Afterwards, detection of the number and locations of multiple tooth cracks is achieved via analyzing the squared envelopes of the TSA signals for both the pinion and the gear. The obtained insights into vibration characteristics for multiple tooth cracks and the effectiveness of the proposed method for detecting the number and locations of multiple tooth cracks are demonstrated using both simulated gearbox vibration signals and experimental gearbox vibration datasets.