Cutting force prediction in end milling of curved surfaces based on oblique cutting model

Abstract

To obtain a superior machined surface quality, predicting cutting force is important for planning and optimizing cutting process before actual machining. This paper established a novel analytical cutting force model for end milling of curved surfaces. Taking the variation of cutter geometry into account, cutting force coefficients were characterized by physical parameters, e.g., the normal friction angle, the normal shear angle, the chip flow angle, and the shear stress. Based on an oblique cutting model, a mathematical relationship of the physical parameters was obtained by the minimum energy principle. A Newton iterative algorithm was utilized to solve the established non-linear equations for calibrating the cutting force coefficients. Taken the variable radial depths of cut into account, a vector method was derived to calculate the equivalent feed rates and the entry/exit angles. After calibrating the cutting force coefficients with performing straight milling tests, two typical curved surfaces were investigated. The one was a circular curved surface with constant radial depth of cut, while the other was a Bezier curved surface with variable radial depth of cut. The predicted cutting forces were compared with experimental results, and a good correlation was obtained.