Determination of the crack propagation effect on the mesh stiffness for a polymer spur gear tooth using the extended finite element method

Polymer spur gears have considerable advantages over transmissions in metallic materials such as lower cost, much less weight and superior resistance to corrosion. As a result of material fatigue, they can be subject to cracks on gear teeth. Most researches are concentrated on the investigation of different field such as the thermal and wear behaviour of the polymer gears and there is a significant drop in the number of research works concerning the crack propagation effect on the mesh stiffness of polymer gears. For this reason, this paper is focused on the study of the mechanical behaviour of a polymer spur gear, with and without faults, under a static condition by using the extended finite element method with cohesive approach in order to identify the crack propagation effect on the mesh stiffness. This numerical method is applied through Abaqus software and it has considerable benefits over other standard methods since crack propagation can be modelled without remeshing. Here, this method is used with a cohesive segment approach based on the traction-separation law. One-tooth pair model is considered in simulations. Then, the total GMS is obtained by the superposition method. As a result, the crack initiation, which can be identified by the reduction of the mesh stiffness, occurs in the fillet radius and it is propagated into the tooth thickness since the backup ratio value is higher than 0.5. Finally, the obtained GMS is injected into a dynamic model of a polymer spur gearbox and dynamic responses are computed in the cases of healthy gearbox and cracked tooth gearbox.