Stability Analysis of Machining Processes Using Spectral Element Approach

The stability analysis of machining processes is of utmost importance in order to guarantee high removal rates while at the same time maintaining acceptable surface ?nish and tool life. One of the key mechanisms for losing stability in machining is chatter vibration, which is a self-excited vibration due to the surface regeneration effect. This type of chatter occurs due to the variation in the dynamic cutting load between successive tool or workpiece rotations. A common approach to capture this dependency on prior states is to model the machining process using delay differential equations. Since chatter has detrimental effects on the cutting process, the ability to predict the combinations of the cutting process parameters that will result in chatter-free cutting is highly desirable. In this paper we describe how the stability of turning and milling processes can be studied using the spectral element approach. The results show that this approach can successfully predict the chatter-free regime in turning and milling. Further, we describe how recent numerical implementations of the approach to a wider class of delay equations can enable the analysis of more complex and realistic machining models.