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The mechanistic and unified mechanics of cutting approaches to the prediction of forces in milling operations are briefly described and compared. The mechanistic approach is shown to depend on milling force coefficients determined from milling tests for each cutter geometry. By contrast the unified mechanics of cutting approach relies on an experimentally determined orthogonal cutting data base (i.e., shear angle, friction coefficient and shear stress), incorporating the tool geometrical variables, and milling models based on a generic oblique cutting analysis. It is shown that the milling force coefficients for all force components and cutter geometrical designs can be predicted from an orthogonal cutting data base and the generic oblique cutting analysis for use in the predictive mechanistic milling models. This method eliminates the need for the experimental calibration of each milling cutter geometry for the mechanistic approach to force prediction and can be applied to more complex cutter designs. This method of milling force coefficient prediction has been experimentally verified when milling Ti6Al4V titanium alloy for a range of chatter, eccentricity and run-out free cutting conditions and cutter geometrical specifications.

A new analytical method of chatter stability prediction in milling is presented. A general formulation for the dynamic milling system is developed by modeling the cutter and workpiece as multi-degree-of-freedom structures. The dynamic interaction between the milling cutter and workpiece is modeled considering the varying dynamics in the axial direction. The dynamic milling forces are governed by a system of periodic differential equations with delay whose stability analysis leads to an analytical relation for chatter stability limit in milling. The model can be used to determine the chatter free axial and radial depth of cuts without resorting to time domain simulations.

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An analytical prediction of stability lobes for milling cutters with variable pitch angles is presented. The method requires cutting constants, number of teeth, and transfer function of cutter mounted on the machine tool as inputs to a chatter stability expression. The stability is formulated by transforming time varying directional cutting constants into time invariant constants. Constant regenerative time delay in uniform cutters is transformed into nonuniform multiple regenerative time delay for variable pitch cutters. The chatter free axial depth of cut is solved from the eigenvalues of stability expression, whereas the spindle speed is identified from regenerative phase delays. The proposed technique has been verified with extensive cutting tests and time domain simulations. The practical use of the analytical solution is demonstrated by an optimal tooth spacing design application which increases the chatter free depth of cuts significantly.

The general formulation for the milling chatter prediction developed in Part I of the paper is applied to common milling systems. Three cases are considered: a workpiece with single-degree-of-freedom, a face milling cutter with two-degree-of-freedom, and peripheral milling of a cantilevered thin web. The general milling stability formulation is further simplified for the less complicated models. For each case, an analytical expression which explicitly relate the chatter limit to the milling conditions and tool-workpiece dynamics are derived. The analytical predictions are compared with numerical and time domain solutions proposed by previous research. It is shown that the proposed method can accurately predict the chatter limits in milling and thus eliminates the time consuming numerical solutions.

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