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Fourier Analysis of Milling Force for General Helical Cutters via Spacetime Convolution, Part 1: Model Development

Zheng CM and Junz Wang JJ

A space-time convolution approach to analyze the milling force for a general helical cutter is proposed. The single flute cutting force is firstly established through an integrated space-time convolution process. Subsequently, multi-flute milling forces are obtained through convolution integration in time domain (i.e., angular domain). In this convolution force model, convolution theorem does not apply directly and a modified convolution theorem is presented to find the Fourier coefficients of the total milling force for any analytically definable helical cutter. From the Fourier analysis, the magnitudes of higher order Fourier coefficients are shown to drop off quickly. Therefore, the capability to extract a small number of Fourier coefficients as characteristic values of milling forces is an important advantage of this convolution force model. Furthermore, this model provides a convenient means to calculate the Fourier coefficients of the milling forces if the profile of cutter/workpiece can not be analytically definable and only the discrete values of cutter/workpiece profile data are given from scanning. Also, the general effects of cutter geometry and cutting parameters on the spectra characteristics of the milling forces are extracted and discussed. Based on the spectra characteristics, the strategy of selecting cutters for rough and finish machining in slot milling is presented.