Fatigue lifetime analysis of POM gears for generalized tooth root shapes

The current calculation methods for determining the tooth root load capacity of polymer gears (e.g., VDI 2736) are based on the same assumptions as those for steel gears. However, due to the non-linear material behavior, temperature, and rate dependency of polymers, these predictions are often inaccurate. A previous study employed rate-dependent nonlinear viscoplastic finite element (FE) modelling of polyoxymethylene (POM) to quantify material influences not considered in standard metal gear assumptions. A lifetime model was developed and validated to predict tooth root fracture based on rotational speed for a constant tooth root geometry. In this study, the existing damage model is adapted and validated to include the dependency on notch (tooth root) geometry. The extension of the model to two damage parameters allows for a geometry-independent representation of the nonlinear speed dependency of tooth root breakage. This correlative modelling approach incorporates two independent damage mechanisms inside the material which lead to tooth root breakage failure of the gear. To map these mechanisms, local material states at the crack initiation point are used as damage parameters. Calibration of the bi-parametric damage model with experimental data shows that model predictions fall within the experimental scatter. Further research is ongoing to extend the damage model regarding generalized torque loading conditions.