Dynamics of the truncated conical thin-wall turning process

Dynamics of the rotational truncated conical thin-walled workpieces, which are widely used in predicting stability of turning process, was seldom reported. This article presents a systematical method to study the dynamic behaviors of these kinds of workpieces under the practical clamping conditions of their turning processes. Mathematical derivations, which consider the radius change along the conical direction, are detailed to predict the instantaneous dynamic characteristics of the workpieces by comprehensively considering the influence of rotation factor. The boundary condition of a clamping and free combination, which corresponds to the actual clamping requirement in turning, is well considered in the derivation. The frequencies and modal shapes of the workpiece under different rotating speeds are solved by the generalized differential quadrature algorithm. A series of modal impact tests, conducted with the workpiece under both static and rotating states, are used to confirm the method's accuracy in predicting the in-process dynamic behavior. It is theoretically found that in contrast to the conventional turning processes, this thin-walled workpiece's turning process undergoes clear multi-mode effects, which further significantly influence the process stability. After that, the aforementioned derivations are incorporated into the dynamic governing formulation of the turning process for solving the stability lobe diagrams (SLDs). Finally, actual truncated conical thin-wall turning tests confirm the reasonability of the proposed method, and find that the first three modes dominate the stability of the process but not only the first one.