Position-dependent stability analysis of turning with tool and workpiece compliance

A universal frequency domain approach for studying the dynamics of metal cutting with a flexible workpiece and a compliant tool is derived. The method is used for the identification of the position-dependent stability lobes in turning. It enables a fast, accurate, and systematic stability analysis of turning processes in the parameter space, which is not restricted to simple dynamic models with only a specific number of modes in one spatial direction. In particular, a combination of experimental data for the tool tip dynamics with analytical or numerical data for the workpiece dynamics is possible, which is demonstrated by a concrete example. The effect of the mode interaction between tool and workpiece modes via the cutting process is illustrated. Counterintuitively, the possibility of a process destabilization for an increased workpiece stiffness was observed, which can be explained by the mode interaction. The presented methods and results can be efficiently used for optimizing machine tool development and process planning.