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Abstract
Tool deflection resulting from cutting forces places a constraint on the achievable precision and productivity in machining. This paper presents an analytical model of machining error, in terms of part form deviation in end milling due to the elastic compliance of cutting tool. Based on the relationship of local cutting forces and chip thickness, the shear loading and bending moment on the tool cross section are presented in terms of cutter angular position. The tool deflection resulting from the bending moment is then established from the principle of virtual work. The resulting deflection of workpiece and machine tool structure is also considered through shear loading analysis. The expression for machining error is derived as a closed-form function of the machining parameters, cutting configuration, material characteristics, and machine receptance. End milling experiments were conducted to verify the analytical model under various cutting conditions. Error maps are presented to illustrate the effects of process conditions on the achievable part accuracy.