Stability of Circular Feed End-Milling Compared with That of Linear Feed Equivalent

A new delay differential equation (DDE) which is non-periodic is presented to govern circular feed end-milling. This equation is considered extended or more generalized since special simplifications lead to the classical periodic DDE model for linear feed end-milling and a new periodic DDE model postulated to govern circular end-milling. Stability analysis of both periodic DDE is conducted using a modified full-discretization map and directly compared on the same cutting parameter plane of spindle speed and depth of cut. It is found that stability of regenerative vibration of both periodic mechanical models is identical. This means that curvature has negligible effect on stability thus circular end-milling can almost accurately be represented as straight-line feed end-milling.