This research discusses the methodology of developing a symbolic closed form solution that describes the dynamic stability of multi-flute end milling. A solution of this nature facilitates machine tool design, machining parameter planning, process monitoring, diagnostics, and control. This study establishes a compliance feedback model that describes the dynamic behavior of regenerative chatter for multi-flute tool-work interaction. The model formulates the machining dynamics based upon the interconnecting relationship of the tool geometry convolution and the machining system compliance. The tool geometry convolution characterizes the cutting forces as a function of the process parameters and the material properties, while two independent vibratory modules, the mill tool and the workpiece, represent the machining system compliance. The compliance feedback model allows the development of a corresponding characteristic equation. By investigating the roots of the characteristic equation, this research symbolically expresses the stability of the system as a function of the cutting parameters, the tool geometry, the workpiece geometry, and the vibrational characteristics of the machine tool. Machining experimentation examining the fidelity of the regenerative charter model is discussed. The dynamic cutting forces, cutting vibration, and surface finish of the machining process confirm the validity of the analytical prediction.

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