Synthesis of Stability Lobe Diagrams

Chatter vibrations during machining lead to poor workpiece surfaces and increased tool wear. In the worst case, the tools and even the main spindle can be damaged. Nowadays, the surface regeneration is considered to be the main effect causing chatter instabilities. Regenerative chatter is initiated by repetitive tooth engagement where the currently engaged tooth cuts the surface produced by the preceding tooth. In a stability lobe diagram (SLD), the stable and unstable areas are separated by the graph of a critical cutting parameter plotted against the spindle speed. Stability lobe diagrams can be used to optimize machining processes in terms of maximizing material removal rate under stable cutting conditions. These SLDs are computed by time domain simulations. However, this consumes a lot of computational time. Thus, several time efficient algorithms in discrete time as well as frequency domain have been developed in the last decades. This chapter scrutinizes under what conditions different algorithms in frequency domain can be applied. The processes are separated regarding cutting conditions and dynamic behavior so that the most time efficient algorithm can be chosen for each class.