XFEM-Based Simulation of Polymer Gear Pair for Time-Dependent Mesh Stiffness Estimation Considering Viscoelastic Behaviour

The growing popularity of polymer gears in modern mechanical systems is due to their lightweight, self-lubricating characteristics, and excellent vibration and noise damping compared to metallic gears. Nevertheless, the viscoelastic behaviour of polymers under dynamic loading significantly affects gear performance, which has usually been overlooked in conventional elastic studies. This study investigates the evolution of gear mesh stiffness (GMS) and failure behaviour of polymer spur gears over time by integrating viscoelastic material modelling with the extended finite element method (XFEM). The viscoelastic response is defined through the Prony series coefficients obtained from stress relaxation test and implemented in Abaqus using the generalized Maxwell model (GMM). A cohesive zone traction-separation law was used to simulate crack initiation and propagation, allowing mesh-independent crack growth. Additionally, dynamic modelling of a polymer gear pair has been done by employing GMS obtained from XFEM. The response of the dynamic model is experimentally validated. The model effectively predicts the time-dependent GMS degradation and vibration characteristics of cracked polymer gears.