Stability analysis of multi-degree of freedom systems in milling operations: Altintas analytical method vs. chebyshev polynomial approximation-Edición Única

Chatter phenomena, essentially known as forced and self excited (regenerative) vibration, has long been a problem in machining operations. Many approaches trend to predict the limits of stable zones based on predictive machine tool chatter vibration theory derived by Tobias and Fishwick (S. A. Tobias, and W. Fishwick, 1958) and Tlusty (Tlusty, J. and F. Ismail, 1981). Different mechanistic models of exciting forces on the machine tool interface has been developed and compared with experimental data. However, since the dynamic cutting force is strongly influenced by the cutting parameters of the process, a great number of variations can be presented when machining a workpiece in milling operations. The importance of chatter study comes from productivity issues related to machining industry. Since the generated vibration affects the surface finish and dimensional accuracy of the workpiece, tool life and even machine life due to excessive wear, chatter becomes both quality and production issues that affect the cost of productivity of a Company. Thus, solutions to chatter problems have become increasingly important in manufacturing industry. Though chatter is simply a consequence of vibration within a machining system, finding causes for the vibration and developing corrective strategies is the main scope of chatter problems. The analytical method developed by Altintas is one of the most used to compute stability zones in milling operations. In this document, we use the Chebyshev approximation method, and compare the results with those obtained by Altintas (Altintas and Budak, 1998), Stepan (Stepan, et. al. 2002 (a)) and De LaCalle (De LaCalle, 2005). The stability analysis was done for one, two and three degree of freedom systems of milling operations.