Spectrum Diagnostics of a Damaged Differential Planetary Gear during Various Operating Conditions

Abstract

Planetary gears are identified as compact alternatives to fixed-axis gear trains and show more complicated dynamical behavior due to the nonlinearity induced by the interaction between backlash and tooth defects. The majority of current publications are based on theoretical models of ideal planetary gears, and therefore cannot simulate the time varying dynamic forces induced by damaged teeth. By utilizing a multi-body dynamics and motion analysis software, this paper presents unpublished vibration spectra and fault indicators of a ubiquitous multi-input industrial differential planetary design that includes tooth damage. Backlash between the sun and planet gears are precisely dimensioned to avoid teeth interference and undercut. The region of point-to-point contact along the involute profile is modeled elastically and accounts for tooth flexibility. Boundary conditions that closely match realistic operation are considered, including component constraints, resistive bearing torques, and direct modification of the software parametric resolution. Torsional vibration induced by backlash and tooth geometry errors is shown to cause teeth separation and double-sided impacts in unloaded and lightly loaded gearing drives. Frequency analyses reveal distinct sideband modulations of the gear mesh along with sub and super harmonics. The sideband components, which comprise a large portion of the vibration, are used as fatigue diagnostics by identifying the location of manufacturing errors. Additionally, a joint time-frequency analysis (JTFA) is applied to transient start-up conditions that illustrates an oscillating spectrum in which contact forces increase during acceleration. To the best of our knowledge no research results have been published in fault detection of planetary gears using JTFA.