Stability of turning process with a distributed cutting force model

Abstract

Chatter is investigated for a single degree of freedom model of turning process, where the tool is simplified into a cantilever beam, and the modal parameters of the tool can be obtained from the theory of continuous beam. The cutting force is modeled as a force system distributed along the rake face of the tool. And the distributed cutting force combines the Taylor approximation of the cutting force with an exponential shape function. The distributed cutting force model results in a discrete time delay and a continuous time delay in the governing equation of the system, while the conventional cutting force model only involves a discrete time delay. It is shown that the delay terms significantly influence the stability of machining operations, especially at low spindle speeds. The effect of the continuous time delay is further studied in this paper by ignoring the discrete time delay in the governing equations of the system. The semi-discretization technique is used to compute the stability lobe diagrams of turning operations. The sensitivity of stability charts to the shape of force distribution and the ratio of the discrete time delay and the continuous time delay q is analyzed. Turning stability tests are also conducted to verify the accuracy of the distributed cutting force model.