Simulation of crack propagation in spur gear tooth for different gear parameter and its influence on mesh stiffness

Abstract

Most of the gear dynamic model relies on the analytical measurement of time varying gear mesh stiffness in the presence of a tooth fault. The variation in gear mesh stiffness reflects the severity of tooth damage. This paper proposes a cumulative reduction index (CRI) which uses a variable crack intersection angle to study the effect of different gear parameters on total time varying mesh stiffness. A linear elastic fracture mechanics based two dimensional FRANC (FRacture ANalysis Code) finite element computer program is used to simulate the crack propagation in a single tooth of spur gear at root level. A total potential energy model and variable crack intersection angle approach is adopted to calculate the percentage change in total mesh stiffness using simulated straight line and predicted crack trajectory information. A low contact ratio spur gear pair has been simulated and the effect of crack path on mesh stiffness has been studied under different gear parameters like pressure angle, fillet radius and backup ratio. The percentage reduction of total mesh stiffness for the simulated straight line and predicted crack path is quantified by CRI. The CRI helps in comparing the percentage variation in mesh stiffness for consecutive crack. From the result obtained, it is observed that the proposed method is able to reflect the effect of different gear parameters with increased deterioration level on total gear mesh stiffness values.