Analysis of Workpiece Behavior and Optimization of the Machining Conditions in Milling of a Long Shaft (1st Report)

—Analytical Prediction of the Workpiece Behavior and Possibility of Avoidance of Resonance Occurring—

Abstract

The productivity of circular shafts with a straight groove and/or a plane surface on outside surface of workpiece was much improved by the development of CNC lathe having a milling spindle. However, for milling of shafts with a large length and a small diameter, workpiece deflection induced by cutting forces causes deterioration of surface quality and chatter vibration. This investigation deals with an analysis of workpiece behavior and optimization of the machining conditions for ball-end milling a shaft with a small flexural rigidity in the direction of perpendicular to the shaft axis. In this paper, to apply a previously developed cutting model to milling of shafts, geometric quantities such as contact region between the cutting edge and the workpiece surface, and distribution of undeformed chip thickness along the cutting edge are analyzed. Cutting forces are calculated by using the cutting model and an energy method. Then, the workpiece deflection is analyzed on the basis of calculated results of cutting forces, and the variation of the above quantities with tool rotational angle are compared with experimental results at various tool locations on the workpiece. It is found that both of the cutting forces and the workpiece deflection take each maximum value at a location where the tool axis reaches close to the perpendicular plane passed the axis of the workpiece. Through the comparison of the results obtained by analysis of resonance frequency of the workpiece and that obtained by impact test using impulse hammer it is shown that the possibility of avoiding the occurrence of chatter vibration.