A stability analysis of turning a tailstock supported flexible work-piece

This paper proposes a new approach to analyze the stability of a cutting process. Previously, most studies have generally assumed the work-piece to be rigid and have, therefore, ignored work-piece deformation. In analyzing, the stability of the cutting process, these studies simply considered the dynamic equation of the tool. However, in practice, the work-piece undergoes deformation as a result of the application of an external force by the cutting tool. This deformation changes the chip thickness and has an effect on the critical chip thickness. Consequently, this study proposes a novel stability analysis method for the turning process in which deformation of the work-piece is considered. The cutting, which takes place in the turning process, is described using partial differential equations, and a set of dynamic equations is developed by considering the interaction between the tool and the work-piece. Having performed Laplace transformation, the stability of the cutting system can be analyzed in terms of the work-piece length, radius, natural frequency, deflection, slenderness ratio, cutting point, and material. The relationship between the critical chip width and the cutter spindle speed is investigated under a range of cutting and work-piece conditions. The analytical results for the current flexible work-piece are compared with those for a rigid work-piece. It is found that the critical chip width of the flexible work-piece is always greater than that of the rigid body.