Physically Consistent Benchmarking of Analytical and Machine-Learning-Based Friction Models in Cold Forging

Friction modeling in finite element simulations of cold forging is commonly based on analytical formulations ranging from the Coulomb and shear friction laws to advanced models incorporating multiple tribological state variables. However, fundamentally different friction formulations are difficult to compare directly because their parameters refer to different physical quantities. This work presents a systematic benchmark of conventional, extended analytical and machine-learning-based friction models under identical tribological boundary conditions. Sliding compression tests covering a wide range of contact conditions are combined with finite element simulations to establish a time-resolved database of local tribological state variables. To enable a physically consistent comparison independent of the mathematical friction-law formulation, all models are evaluated on the common level of FE-derived frictional shear stress. Conventional friction models exhibit pronounced load-dependent residual structures, while extended analytical formulations reduce but do not eliminate systematic deviations. The neural-network-based formulations introduced in this study, which predict either the coefficient of friction, the friction factor, or the frictional shear stress directly, achieve the highest predictive accuracy, with MAEs of 5.68–6.39 MPa and corresponding WAPE values of 15.12–17.02%. Despite their different internal parameterizations, these models converge toward highly similar frictional shear stress predictions. Explainability analyses further show that similar predictive behavior on the stress level is achieved through formulation-dependent relationships on the parameter level. The results therefore reveal a distinction between stress-level convergence and parameter-level divergence in data-driven friction modeling.