Exact region of stability for a linear orthogonal cutting model

In this work, stability of chatter in orthogonal cutting is investigated in order to identify the critical spindle speeds. The process is modeled by a second-order linear delay-differential equation and the characteristic equation is analyzed in formulating the continuous stability boundaries, explicitly for any given range of the spindle speeds. Moreover, a simple algorithm is introduced for checking whether the system is in the stable zone without determining the whole stability diagram. Numerical simulations and comparison with some other methods are presented to justify the theoretical results.