Dynamic modelling and analysis of cracked gear system with tip relief based on proposed variable-angle deformation energy integration method

Due to ignoring the effects of the change of the tooth attachment position caused by the cracks, traditional time vary mesh stiffness (TVMS) calculation models and dynamic simulations for cracked gears will lose their precision in the body crack case. To address this shortcoming, a new analytical TVMS calculation model of cracked gear considering tip relief (TR) is developed based on a proposed variable-angle deformation energy integration method. On this basis, a dynamic model of the gear system for the analysis of fault vibration characteristics is established. The effectiveness and accuracy of the proposed TVMS calculation model are verified by the finite element method. A comprehensive investigation is finally carried out to reveal the effects of the parameters of TR, load and crack on the TVMS and dynamic characteristics of the cracked gears. The study results indicate that the proposed models can meet the accurate TVMS calculation and dynamic simulation for both the tooth- and body-cracked gears, and the influences of the tooth attachment position change caused by the crack cannot be ignored. This study could provide a systematic methodology and meaningful reference for the dynamic modelling, simulation and fault diagnosis of gear systems with crack failures.