| Summary: | 博士 === 國立成功大學 === 機械工程學系 === 105 === In this thesis, the stability analysis for a 2D milling process with general asymmetric dynamics is reduced to a 1D scalar problem by an eigen-analysis approach. Through decomposing the oriented transfer function matrix, the scalar oriented frequency response functions for a regenerative milling chatter is defined and obtained in a closed form expression. The scalar modal characteristic equation is derived to obtain closed form expressions for the stability limit and spindle speed at each possible chatter frequency. This thesis further presents analytical models for determining the forces and tool tip displacement during stable and unstable milling with axis-symmetrical structural dynamics. The trajectory of nominal, static milling forces under both stable and unstable cutting conditions was demonstrated to run clockwise in an elliptical path, with the dynamic forces during chatter running counterclockwise. Both the static and dynamic forces had similar modal directions, pointing to the right and left sides of the x axis for up and down-millings, respectively. Moreover, the oriented FRF concept is adapted to determine the worst spindle speeds and the critical limiting axial depth of cut in explicit, analytic expressions. Finally, formulas for determining the critical depths of cut and asymptotic spindle speed for stable milling processes with process damping are presented. The asymptotic spindle speed of a theoretically infinite stable depth of cut is shown to be proportional to the modal natural frequency, radial ploughing constant and radial immersion angle, but inversely proportional to the shearing related cutting constant and tool diameter. These formulas enable identifying the asymptotic speed, absolute stability limit, and in-process radial ploughing constant from two sets of experimental stability limits without requiring modal parameters. The presented analytical models for the force and displacement trajectories, critical depth of cut and identification of process damping constants are verified by experiments.
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