A pole/zero cancellation approach to reducing forced vibration in end milling

An analytical model for the forced vibration in an end milling process is derived and a criterion in selecting cutting parameters to reduce the forced vibration is presented in this paper. The analytic expression for the forced vibration due to the periodic milling force is obtained as the product of the Fourier transform of the milling force and the frequency response function of the structure dynamics. The pole/zero cancellation technique is then employed for reducing the forced vibration. Analysis shows that the suppression of forced vibration can be achieved by choosing cutting parameters so that one of the zeroes of the Fourier transform of the milling process function is near the pole of the structure dynamics. A design equation in terms of cutter geometry, axial depth of cut, spindle speed and structure resonant frequency is derived for the conditions when the forced vibration can be minimized. The presented analysis is illustrated through numerical simulation and verified by experimental results.