A Stability Analysis of Turning without Using Tailstock Considering Deflection in the Previous Cycle or Not

In this study, the work-piece without using tailstock was considered as an elastic and deformable body under the external forces generated by the cutting tool. Such work-piece was studied by an Euler-Bernoulli beam, and a second order partial differential equation was established for the lateral forced vibrations. In addition, a model for the cutting tool vibration is also developed in a second order ordinary differential equation formulation. Combining these models permitted system full analysis and discussion of the interactions between work-piece and tool. Not only study the stability analysis of turning with using tailstock considering deflection in the previous cycle or not, but also analyze the difference of both. In chatter mechanism, considering the regenerative chatter, system characteristic equation could be yielded from the Laplace transformation of the dynamic equations. The frequency domain stability analyses and Nyquist Chart implied the governing equations of critical chip width for this case. During the machining process, the slot cutting was discussed. By the simulations, the conclusive results could be obtained in the following: larger the critical chip width would be resulted with various deflection method; the larger the critical chip width would be also resulted with considering lathe deflection in the previous cycle in high spindle speed. And the result obtained from rigid body case will always be the worst.