Increased Stability of Low-Speed Turning Through a Distributed Force and Continuous Delay Model

Abstract

This paper investigates the increased stability behavior commonly observed in low-speed machining. In the past, this improved stability has been attributed to the energy dissipated by the interference between the workpiece and the tool relief face. In this study, an alternative physical explanation is described. In contrast to the conventional approach, which uses a point force acting at the tool tip, the cutting forces are distributed over the tool-chip interface. This approximation results in a second-order delayed integrodifferential equation for the system that involves a short and a discrete delay. A method for determining the stability of the system for an exponential shape function is described, and temporal finite element analysis is used to chart the stability regions. Comparisons are then made between the stability charts of the point force and the distributed force models for continuous and interrupted turning.