Analytical modeling of a thin-walled cylindrical workpiece during the turning process. Stability analysis of a cutting process

Abstract

The purpose of this work is to develop a mathematical model of the dynamics of turning a thin-walled cylindrical shell. This model uses a finite number of degrees of freedom and takes into account the variability of dynamic compliance. It is then possible to obtain estimates of the boundaries of stability of the continuous cutting process. The model is based on the theory of shells with application of Galerkin’s method in conjunction with the expansion of the displacement field in beam and trigonometric functions. On the basis of the developed model, an algorithm designed for constructing boundaries of stability of turning of the thin-walled cylindrical parts is presented and compared to experimental results. A strategy to define matter removal sequences is proposed.