A stability problem of milling process is under consideration. A novel analytical tool is presented to assess the optimal cutting parameters which provide a chatter free machining. Chatter instability is broadly studied in the literature. However, the problem of simultaneous optimization of radial and axial depths of cut is kept out of scope. To describe the optimization method a single-degree-of-freedom model of milling process is investigated as well as corresponding equation of motion and function of cutting force. A unified delay-differential equation is proposed. A theorem of asymptotic stability is suggested. Suggested optimization technique allows to create a diagram of radial and axial depth-of-cut dependence.  As shown, there exists an extremum of function of axial and radial depth-of-cut dependence.  

Keywords: chatter, stability, delay-differential equation, oscilations, self-excited vibrations, optimization