Bi-parametric damage model for the lifetime prediction of POM gears

Abstract Polymer gears are increasingly being used across various industries; however, existing lifetime prediction methods face significant limitations. The current standard calculation approach, VDI 2736, which is based on assumptions originally developed for steel gears, is not well suited for polymer gears when predicting failure mechanism tooth root fracture. These conventional methods assume rigid body behaviour, linear-elastic material properties, and rotational speed-independent lifetimes, which do not accurately reflect the nonlinear, strain-rate-dependent characteristics of thermoplastic materials. Consequently, their lifetime predictions for polymer gears remain inadequate. To overcome these limitations, a lifetime modelling approach was previously developed to predict tooth root fracture in polymer gears. This approach integrates nonlinear viscoplastic material behaviour and dynamic load effects using finite element (FE) simulations. A key feature of this model is the bi-parametric damage model, which is inspired by the mechanical destruction of molecular bonds and thermal degradation of mechanical properties in polymers. The model relies on local material states at the crack initiation point and has demonstrated the ability to predict the dependency of gear lifetime on rotational speed at a constant torque level, independent of tooth root geometry. This paper presents a theoretical extension of the bi-parametric damage model and validates it against new experimental data. The damage functions of the model are separately calibrated for two distinct torque levels and two different tooth root geometries within a defined rotational speed range. The results demonstrate that the nonlinear dependency of lifetime on rotational speed can be accurately predicted for both torque levels, independent of root geometry, with the experimental scatter band. Furthermore, the study reveals a shift in the maximum lifetime within the tested rotational speed range. As torque decreases, the influence of root geometry on lifetime increases, while the predictive accuracy of the bi-parametric model declines.