Creating a Stability Lobe Diagram

Machine tool chatter causes machining instability, surface roughness, and tool wear in metal cutting processes. A stability lobe diagram based on regenerative chatter theory is an effective tool to predict and control chatter. Stability diagrams can be applied in machining processes to optimize the maximum depth of cut at the highest available spindle speed, thus improving the material removal rate and increasing productivity. A stability lobe diagram is formed by a series of intersected scallop-shaped borderlines of stability. The intersections of the lobes denote the deepest stable cuts at various ranges of spindle speed. These optimum depths of cut have traditionally been found by graphical solution from the stability lobe diagram. The creation of a stability lobe diagram requires lengthy procedures and calculations. Furthermore, discussion of the topic in manufacturing textbooks is still limited. This paper presents a simple method to analytically calculate the approximate optimum depths of cut and determine the corresponding spindle speeds. This method allows machine operators to practically choose cutting parameters, instructors to effectively teach the regenerative chatter theory, and students to easily create stability lobe diagrams and practice optimizing cutting parameters. A procedure is also introduced to use a spreadsheet to analyze machining parameters and construct stability lobe diagrams. The characteristics and limitations of the stability lobe diagram are discussed. Case studies are also provided to illustrate the method and verify the results.