Analytical–Mechanistic Model for Determining Local Friction and Normal Forces in Oblique Cutting

Abstract

This paper presents an analytical—mechanistic model for determining local friction and normal force components acting on the rake and flank surfaces during oblique cutting. The proposed formulation integrates the tool geometry by considering both the constructive angles of the cutting tool and the functional angles resulting from the cutting conditions, including cutting speed, feed rate, and depth of cut. The transformation from the oblique cutting coordinate system to the dynamometer reference system is performed using successive rotation matrices based on Euler angles. The model is formulated as a system of three equations with four unknown local force components F,FN,Fα,FNα, which is analytically resolved by combining the measured cutting force components Fx,Fy,Fz with an experimentally determined friction coefficient. The geometric direction parameters derived from the Euler angles enable the decomposition of the measured global forces into local friction and normal force components acting on the active tool surfaces. The model is further extended to functional geometry by accounting for changes in the effective tool orientation under actual cutting conditions. The internal consistency of the proposed formulation is supported through several particular cases, including orthogonal cutting and zero-angle geometry. Experimental validation was carried out using P20 carbide inserts and AISI 1045 steel. The obtained results showed good agreement between the analytically reconstructed force components, the measured cutting forces, and the friction coefficient values identified experimentally, supporting the applicability of the proposed model for local force evaluation in oblique cutting.