Semi-analytical modeling of cutting forces in precision turning considering size effects

In precision turning, the cutting thickness is comparable to or even smaller than the tool edge radius, where the size effect caused by the tool edge radius significantly influences the cutting force. Addressing the issue that existing precision cutting force models often overlook the influence of tool geometry on the effective shear layer thickness and the undeformed chip area, which leads to insufficient prediction accuracy, this study investigates the material deformation mechanism. Based on the tool geometry, the geometric mapping relationship between the undeformed chip area and the tool nose radius as well as the tool edge radius under the influence of size effect is elucidated. Subsequently, a semi-analytical model for precision turning force is established, incorporating both shearing and plowing mechanisms. By coupling a modified empirical model of the flank friction force, the model achieves a maximum relative errors of 10.37%, 16.14%, and 9.17% for F _X , F _Y , and F _Z , respectively, with corresponding mean absolute relative errors of 6.15%, 5.28%, and 5.66%, demonstrating accurate prediction of the cutting force under tool wear conditions. Furthermore, based on the developed model, the evolution of material removal mechanisms from plowing to shearing is revealed. The shearing force proportion approaches zero near the minimum chip thickness region, increases to approximately 47% when both the depth of cut and feed rate reach four times the tool edge radius, and exceeds 85% with further increases in cutting parameters, indicating a transition toward shearing-dominated material removal. This research provides technical support for process optimization and quality improvement in precision turning.