Forced vibration analysis in the end milling of a thin plate

An analytical model for the forced vibration of a thin plate in the end milling process along with criteria for selecting cutting conditions to reduce the forced vibration are 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 transform of the structure dynamics. Analysis of the vibration model shows that the plate vibration can be reduced by selecting the cutting parameters so that the zeroes of the frequency transform of the milling process function coincide with the resonant frequencies of the structure. An expression in terms of cutter geometry, axial depth of cut, and major natural frequency of the structure is obtained for the conditions that the forced vibration can be minimized. The presented analysis is verified by vibration measurement of a thin plate in an end milling experiment.