Bidimensional fuzzy-based propagation of interdependent uncertainty in pseudo-rigid multibody models of spur gears

In gear analysis, pseudo-rigid multibody models offer a strategic compromise between accuracy and computational efficiency. However, these models are characterized by parameters affected by epistemic uncertainty, which is often neglected. This work proposes a bidimensional fuzzy representation to quantify such uncertainty while explicitly accounting for physical correlations between key parameters, such as joint positions and elastic element values. The approach is applied to both quasi-static and dynamic analyses. In the static case, fuzzy membership levels of static transmission error consistently enclose finite element results across three torque levels, whereas assuming independent uncertainties leads to a misleading overestimation of the output uncertainty. In the dynamic case, the model reveals a progressive widening of the uncertainty band around resonance, linked to nonlinear jump phenomena and dynamic hysteresis. However, experimental results from the literature fall within the fuzzy zero-level envelopes, verifying the model's predictive capabilities. This bidimensional fuzzy framework provides a physically consistent and computationally efficient tool for uncertainty quantification in geartrain simulations. Its generality makes it applicable to other multibody systems with physically linked uncertainties, enhancing simulation interpretability and guiding the need for higher-fidelity modeling.