Sensitivities of Transverse and Torsional Vibrations to Gear Tooth Crack Growth: A Numerical and Experimental Comparison

Abstract

Vibration measurement and signal analysis are widely employed techniques for gearbox fault diagnosis in industry, typically including transverse and torsional vibration measurements. A key advantage of torsional vibration compared to transverse vibrations is its simpler frequency spectrum. This is because it is not affected by amplitude modulation caused by the time-varying vibration transmission path. This study investigates the relative sensitivities of transverse and torsional vibrations to progressive local tooth-root crack growth in a fixed-shaft spur gearbox. In addition to the spectral advantages previously associated with torsional measurements, the study examines whether torsional vibration provides a stronger response to crack progression than transverse vibration under a fixed-shaft configuration. To this end, the transverse and torsional vibrations of a gearbox drivetrain are numerically simulated using a lumped-parameter model. The transverse response is represented by pinion acceleration, while the torsional response is characterized by the dynamic torque transmitted through the pinion shaft. The time-varying mesh stiffness of the gears is calculated using the potential energy method for two cases of healthy and faulty gearboxes with a local crack of varying lengths in a tooth. The crack is made at the tooth root, and the system's dynamic response is evaluated as the crack grows up to complete tooth breakage. Various time-domain indicators have been utilized to compare the sensitivity and performance of torsional and transverse vibrations in crack detection. The results reveal higher sensitivity of torsional vibrations to fault progression. The changes in the indicators with crack growth are greater for torsional vibrations than for transverse vibrations. Experimental results further support this increasing trend for torsional vibrations over transverse ones, particularly for cracks exceeding 50%, indicating the advantage of torsional vibrations in detecting faults in fixed-shaft gearboxes.

Conflict of Interest Statement

The authors declare no conflicts of interest.