A Phenomenological Model with Bootstrap-Based Uncertainty Estimation for Friction Coefficient Prediction in Gear Transmissions

This study investigates the correlations between the parameters of the Hysteresis-Attrition-Friction model (HAF), hysteresis (h), attrition (a), and friction coefficient (ν), under different surface conditions and contact pressures. The HAF model, a sigmoidal model developed in-house, provides a novel approach for characterizing tribological behaviour through its three key parameters (h, a, ν). The analysis employed a bootstrapping method to generate numerous parameter samples, allowing for the estimation of joint distributions and the identification of correlations between parameter pairs. The model here is applied to data from experiments conducted using both smooth and rough surface configurations at three distinct contact pressures: 1.2 GPa, 1.6 GPa, and 1.9 GPa. The results revealed a positive correlation between hysteresis and attrition across both surface types, indicating that higher energy dissipation through hysteresis is associated with increased friction. Conversely, negative correlations were found between hysteresis and friction coefficient, and between attrition and friction, suggesting a trade-off between energy dissipation and friction. The bivariate kernel density plots further highlighted these patterns, helping to visualize the complex relationships within the model. The results emphasize the importance of considering surface conditions and pressure when applying the HAF model to predict performance in tribological systems.