In this paper, a 2D milling stability analysis is reduced to a 1D problem by performing a modal analysis on an oriented transfer function matrix under a given feed direction. The oriented frequency response function (FRF) of the oriented transfer matrix are obtained as explicit functions of the radial immersion and feed direction. At different feed directions in most of the lower immersion range, the process is demonstrated to be the least stable when the modal direction of the directional matrix is oriented at 45° and 225° and in the −45° and 135°, yielding a local minimum critical depth of cut, regardless of up or down cuts. At higher immersion, the worst critical depth of cut is dominated by the lower frequency mode, and becomes a constant, independent of the feed direction at full cut. When the modal direction is oriented along the x or y axes, the process has a local maximum critical depth of cut.

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