Dimensional Analysis-Based Modeling of Cutting and Thrust Forces in Orthogonal Cutting of AISI 1045 Steel

Abstract

Accurate prediction of cutting forces remains a key challenge in metal machining due to the strong coupling between geometry, material behavior, friction, and thermal effects, which limits the generality of purely empirical models. In this study, physically interpretable models with predictive capability for cutting and thrust forces are developed for orthogonal cutting of AISI 1045 steel using a dimensional analysis framework based on the Buckingham Π theorem. Experimental data collected from the literature are used to construct dimensionless formulations incorporating geometrical, kinematic, mechanical, and thermal parameters. The proposed models are calibrated and evaluated using statistical performance metrics and residual analysis, and subsequently validated against independent experimental datasets not used during model development. A correction factor associated with the tool–chip contact length is optimized during validation to improve predictive accuracy. Results show that both force components can be consistently represented through a reduced set of governing dimensionless groups, providing physically meaningful scaling across a wide range of cutting conditions. The validation results confirm the robustness of the proposed formulation, while also revealing different sensitivities of cutting and thrust forces to contact, thermal, and geometrical effects. A physical interpretation of the dimensionless groups is presented, framing the machining process as a case of severe plastic deformation under high strain rates and strong thermomechanical coupling. The study demonstrates that dimensional analysis offers a physically consistent, scalable, and transferable approach for modeling cutting forces, with potential applicability to other materials and machining configurations.