CONVOLUTION ANALYSIS OF MILLING FORCE PULSATION

This paper presents the establishment of a closed form expression for the dynamic forces as explicit functions of cutting parameters and too l/workpiece geometry in milling processes. Based on the existing local cutting force model, the generation of total cutting forces is formul ated as the angular domain convolution of three cutting process compon ent functions, namely the elementary cutting function, the chip width density function, and the tooth sequence function. The elemental cutti ng force function is related to the chip formation process in an eleme ntal cutting area and it is characterized by the chip thickness variat ion, and radial cutting configuration. The chip width density function defines the chip width per unit cutter rotation along a cutter flute within the range of axial depth of cut. The tooth sequence function re presents the spacing between flutes as well as their cutting sequence as the cutter rotates. The analysis of cutting forces is extended into the Fourier domain by taking the frequency multiplication of the tran sforms of the three component functions. Fourier series coefficients o f the cutting forces are shown to be explicit algebraic functions of v arious tool parameters and cutting conditions. Numerical simulation re sults are presented in the frequency domain to illustrate the effects of various process parameters. A series of end milling experiments are performed and their results discussed to validate the analytical mode l.