Time-Varying Characteristics of Bending Deformation of Work-Piece in the Turning Process
Based on the geometrical description of work-pieces cutting process, the time-varying differential equations of deflection curve under two different conditions were obtained using the singular function: one with thimble and one without thimble constraint. Using the Mathcad software, we have solved the time-varying differential equations analytically and have studied the deflection changing of work piece with the position of turning tool and given the distribution characteristic for the time-varying deflection of each section. The results indicate that (1) the deflection of an arbitrary section is time-varying due to the time-varying position of the turning tool and the time-varying inertia moment; (2) for the shaft with thimble constraint, the position of the maximal deflection is not at the section with turning tool; (3) for the shaft without thimble constraint, when the turning tool is at the free end, the deflection at each section of the work-piece is the maximal compared with the other positions of turning tool.