Time Varying Mesh Stiffness Estimation of Cracked Polymer Gear Pair Considering Modified Contact Stiffness with Experimental Validation

Abstract

Purpose: Polymer gears are increasingly used as an alternative to metal gears in power transmission due to their advantages such as lightweight, low noise and vibration. However, crack induced failures remain a critical concern. Vibration signal analysis, governed by time varying mesh stiffness (TVMS), is an effective tool for fault detection. Hertzian contact stiffness (HCS) plays a critical role in TVMS estimation, and several models exist to estimate it. This study proposes a modified Hertzian contact stiffness (MHCS) model and a TVMS estimation model that accounts for pitch point cracks. Methods: The proposed MHCS formulation is incorporated into a TVMS model to estimate the mesh stiffness of cracked polymer gear. Finite Element Method (FEM)simulations are performed to validate the developed model. Further, dynamic modelling of a polymer gear pair has been done by employing proposed TVMS for a cracked gear and the vibration response is experimentally validated. Results: The proposed MHCS model shows improved accuracy in predicting contact stiffness. The results demonstrate that pitch point cracks cause significant fluctuations in TVMS, which are effectively captured by the developed model. The dynamic response analysis reveals distinct vibration signatures corresponding to crack presence, and experimental validation confirms good agreement with the predicted results. Conclusion: The proposed model effectively predicts the mesh stiffness and vibration characteristics of a cracked gear system, providing valuable insights through vibration analysis for detecting tooth cracks. © Springer Nature Singapore Pte Ltd. 2026.