Time-Varying Meshing Stiffness Calculation and Vibration Analysis for a 16DOF Dynamic Model With Linear Crack Growth in a Pinion

Abstract

A modified mathematical model for simulating gear crack from root with linear growth path in a pinion is developed, in which an improved potential energy method is used to calculate the time-varying meshing stiffnesses of the meshing gear pair while we also take the deformation of gear-body into consideration. The formulas for the meshing stiffness are deduced when the crack grows as the linear growth path in the pinion. A 16DOF dynamic model of a one-stage spur gear system is used to study the response from the system considering time-varying meshing stiffnesses and different levels of crack growing in the pinion. As vibration signals induced by the tooth crack are buried in normal vibration signals which are induced by the normal gear pair in meshing at the early stage of crack growth, the algorithm combined autoregressive modeling method and demodulation method is proposed to process the signals to investigate the response characteristics as the crack grows, and the comparison of the relationship between indicators and the crack levels from different simulation methods are given.