Modal analysis of spur gears for varied teeth root cracks characteristics: finite element analysis (FEA) simulations

Gear failure is considered the main alarming and undesirable event in gearboxes. Usually, cracks happen by fatigue caused due to cyclic loading. Fatigue stress is focused on the teeth root because of the small tooth fillet radius. This causes progressive damage to gear teeth which causes teeth failure, and hence, a damaged gear. This work shows a numerical framework to identify and quantify cracks' existence at the teeth root of spur gears. The problem is numerically analysed through finite element-based simulation with ANSYS by conducting a modal analysis. There are nine cases of gears with different cracks on their tooth; these cracks are varied by their number (single or multiple), Crack Length Percentage (CLP %), and location. The FEA is used to simulate all nine cases to predict the bending natural frequency of teeth and to investigate the effects of the variation of the crack by looking at the natural frequency of the teeth bending as well as the deformation level. Results revealed that the teeth bending natural frequency decreases as the CLP% increases. In addition, the gear stiffness is calculated based on the natural frequency and gear’s mass and it is indicated that the stiffness decreases as the CLP% increases, while the deformation level increase with CLP%.