Dynamics and stability of variable-pitch milling

The occurrence of the regenerative chatter phenomenon in the milling process is studied for cutters with non-uniform distribution (called variable-pitch cutters). The dynamic model of the process is developed and is evaluated from stability point of view. The mathematical characterization of the problem falls within a general class of delay differential equations (DDE) with multiple and rationally independent delays. The contribution of this paper is in the adoption of a mathematically novel and very recent paradigm to determine analytically the bounds of the stable versus unstable chatter. The novel paradigm is called the Cluster Treatment of Characteristic Roots, CTCR. The end result of CTCR provides a powerful tool to determine two important aspects of the process: (i) the pitch angle formation (i.e. the geometry) of the tool; (ii) the optimum cutting conditions (i.e. the depth of cut and the spindle speeds). This means that some process parameters as well as design features are considered via this procedure towards a consolidated optimization procedure. A set of case studies is also presented to demonstrate these capabilities.