An investigation of stability and pattern formation in reaming

Abstract

One of the important factors affecting the quality of a surface manufactured by reaming is chatter. In this paper, chatter is investigated by means of a numerical linear stability analysis. The trajectory of the centre of the tool is discretized in time and an eigenvalue problem is solved to determine the formation and evolution of patterns on the manufactured surface. The pattern forming process is shown to be unstable under certain circumstances. The unstable patterns lead to a wavy profile of the workpiece, as often observed in practice. In contrast, the stable patterns are shown to disappear during reaming due to the exponential decrease in their magnitude, thus leading to a fixed location for the centre of the tool and a circular final profile of the workpiece. The unstable patterns grow in magnitude until non-linear effects become important and limit their growth. Some of these important non-linear phenomena are analysed. Specifically, the non-linear analysis is based on the limited allowed slope of the profile of the workpiece. Numerical examples for a typical reaming system are presented and the final patterns obtained are shown to be similar to experimental observations.