Analysis of milling forces via angular convolution

The measurement of cutting force systems is one of the most frequently used techniques for the monitoring of machining processes. Its wide spread application ranges from tool condition identification, feedback control, cutting system design, to process optimization. To gain fundamental understanding of the force system in machining, this paper presents the work of establishing a closed form expression for the cutting force in end milling as an explicit function of cutting parameters and tool/workpiece geometry. Based on the theoretical local cutting force model, the generation of total cutting forces is formulated as the angular convolution of three uncorrelated cutting process component functions, namely the elemental cutting force function, the chip width density function, and the tooth sequence function. The elemental cutting force function is related to the chip formation process in an elemental cutting area and it is characterized by the chip thickness variation, specific cutting pressure constants, and entry/exit angles. 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 as the function of the angular position of each cutting point. The tooth sequence function represents 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 transforms of the three component functions. Fourier series coefficients of the cutting forces are shown to be algebraic functions of various tool parameters and cutting conditions. Simulation results are presented in the frequency domain to illustrate the effects of process parameters. A series of end milling experiments are performed and their results discussed to validate the analytical model.