Журнал прикладного машиностроения

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Fourier Analysis of Milling Force for General Helical Cutters via Spacetime Convolution, Part 2: Applications for Common Cutters and Model Validation

Zheng CM and Junz Wang JJ

Part 2 of this study illustrates the applications of the frequency domain force model put forth in Part 1 for three common helical cutters: the square, taper, and ball end mills. The respective geometric and boundary functions required for the evaluation of the force spectra are derived by applying differential geometry to these three types of cutters including cutters of constant helix angle and constant helix lead. By virtue of the explict expression of Fourier coefficients of milling force, the differences between cutting forces generated by two cutters with constant helix angle and constant helix lead can be described quantitatively. In slot (or half slot) milling for the taper end mills with a constant helix angle and constant helix lead, the strategy for selecting axial depths of cut to reduce force pulsation is presented respectively. Also derived are the specific expressions for the average forces of these three helical cutters in common cutting configurations. Moreover, as an inverse application, a linear equation is formulated for the identification of six shearing and ploughing cutting constants from the measured average cutting forces for a general helical cutter. The frequency domain force model and the identification of the cutting constants are finally demonstrated and validated through experiments with all three types of milling cutters.