Dynamic Modelling of Planetary Gearboxes with Cracked Tooth Using Vibrational Analysis

Planetary gearboxes failure has been a major problem in systems reliability, hence condition monitoring of this component is essential. In order to identify faults, a dynamic model of the gearbox is presented taking into account backlash and tooth cracks. Newtonian equations of motion developed for a planetary gear is solved and modal analysis for solving the lumped parametric differential equations of modelled single stage planetary gearbox is adopted to observe the vibrational responses and to compare with existing literature. This work focuses primarily on the effects of stiffness and damping. The eigenvalue problem has been solved to measure the natural frequencies and amplitude of the system. Parametric studies using stiffness and damping results indicate significant changes in vibrational signals when there is a crack present on tooth. Simulation results also show the relation between increment in backlash and high frequency responses in the resultant vibration.