Forced vibration or the steady state vibration in a milling process inevitably occurs due to the periodic excitation of the intermittent cutting engagement of the milling cutter on the work and the structure, and it almost always exist even in the absence of chatter in a stable milling system, leading to dimensional and surface error and premature wear in tool and machine components. In this paper, an analytical model for the forced vibration in an end milling process is derived and criteria in selecting cutting conditions to reduce the forced vibration are presented. 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 structure vibration can be reduced by selecting cutting parameters so that the zeroes of the frequency transform of the milling process function are near the poles of the structure dynamics. A design equation in terms of cutter geometry, axial depth of cut and structure natural frequency is obtained for the conditions when the forced vibration can be minimized. The presented analysis is illustrated through numerical simulation and verified by experimental results.

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