Dynamics and cutting stability of the dynamically loaded worktable subjected to simply supported conditions

This paper aims to explore the dynamic characteristics and cutting stability of a surface grinder. In simulated grinding, the dynamically loaded worktable is described by the Euler-Bernoulli beam theory. In the model, the elastic worktable has both ends simply supported on a movable and massless rigid base. The analysis of the dynamics and stability of the worktable is complex due to the operating worktable being dynamically loaded in variable positions. With the Lagrange energy method combined with the assumed mode expansion method, the system dynamic equations are derived and a state space model for the dynamically loaded worktable subjected to simply supported conditions is developed. In this study, the maximum negative real part of the overall dynamic compliance and the limiting depth of cut are used as indicators to assess the structural static and dynamic performance of the worktable in various positions. The effects of worktable damping, contact stiffness, and damping between the tool and the workpiece on the system performance are studied. Based on the regenerative chatter and stability theory, the 3D stability lobes diagram is analyzed to optimize the maximum depth of cut at the highest available spindle speed. The cutting stability is verified by comparing the results obtained in the time domain analysis with the stability lobe diagram. The procedure illustrated in this study to improve the dynamics performance of a surface grinder can also be implemented in a similar fashion for many machine tool applications.