S-domain stability analysis of a turning tool with process damping

This work involved S-domain stability analysis of a turning tool with process damping. Process damping is a phenomenon of dry friction between the tool flank face and workpiece which induces high stability and smoothness at low turning speed. A pair of valid equations for stability analysis of turning with process damping was derived in this work using Laplace transformation method. This work for the first time introduced non-linear feed term in the existing process damping model leading to process damping force of form F-pd (v tau)(alpha) where F-pd processed damping force model in related literature. It is seen that in light of experiments of the related literature, the new proposal can only be valid for low values of a in the neighbourhood of 0.01. MATLAB delay differential equation solver called dde23 was used to simulate the vibration response of turning processes at selected points on the stability diagram of turning with and without process damping. This helped in confirming that stable points in the stability diagram of turning with process damping became unstable points in the stability diagram of turning without process damping. The stability was much higher at low speed of 200rpm than at speed of 4000rpm. Process damping coefficient C-pd of the experiment was estimated at C-pd of 61,000 N/m by comparing experimental depths of cut with theoretical depths of cut of known process damping coefficient.