A model for feed forward control of chatter in end milling

Abstract

High productivity while maintaining the quality of products is one of the main goals of manufacturers. Even though the machining parameters such as spindle speed, feed rate and depth of cuts can be increased in order to increase the production rate, the increase of these parameters leads to machine tool vibration, which degrades the quality of the product. Since the early 1920's machine tool vibration has been extensively studied. Various theoretical models have been proposed to obtain stability domains, which give the critical axial depth of cut for various spindle speeds. More recently a trend to control chatter by varying spindle speed is seen. However, most of those studies were restricted to machining on a lathe. In a more recent work by Fussel and Srinivasan (1989), chatter control by varying spindle speed and feed rate was considered. However, they only considered low spindle speeds of 550rpm for steel. The contribution of this research is the development of a model that enable the identification of unstable regions in end milling for higher spindle speeds in the range of 1000rpm-4000rpm. The stability curves for this speed range were obtained and were validated in the experimental data. Since the force in the speed direction dominates the system dynamics, a single degree of freedom model was sufficient. This simplification did not affect the stability curves considerably as the model was able to predict stability curves accurately. The model is non-linear with time delay. Another contribution of this research was the demonstration that chatter can be controlled by varying the feed rate. The frequency of cutter displacement profiles for unstable regions were studied in order to generate a variable feed rate, which was then used to cancel the displacement profiles. This cancellation was done by introducing a variable feed rate with a phase shift and the same initial amplitude variation. This suppressed the instability and increased the critical depth of cut. Although this increment was only several thousandths of an inch, it demonstrated the viability of variable feed machining.