This paper is based on previous work of the author and his associates which was published in a series of papers, mainly on those given here as references [2–6], dealing with time domain simulation of chatter in milling, with cutting process damping and with stability lobes. These matters are reevaluated here from the particular point of view of high-speed milling. First, the derivation of limit of stability of chatter in the frequency domain is recapitulated, and lobes of stability explained. These lobes should lead to substantial increases of stability at high speeds of milling. Further, corrections to the results of the simple theory using time domain are presented as they are obtained by time domain simulation which takes into account, in a very realistic way, all the main aspects of milling. It is shown that still, in many instances, high gains of stability are achievable by determining and using a particular spindle speed such that the cutter tooth frequency approaches the frequency of the decisive mode of vibrations as measured on the cutter. The usual modes of vibration of a spindle with a long end mill are discussed, and it is shown how a long end mill stabilizes cutting at medium speeds but becomes a flexible element strongly involved in chatter at higher speeds. In the following section, cutting process damping is discussed which has a very strong stabilizing effect at low speeds but is also partly effective at speeds presently in use. This damping is lost in high-speed milling. Typical cases of high-speed face milling of steel and long end milling of aluminum are discussed and a need of about seven times more stiffness for spindle modes and 14 times more stiffness for the end mill mode derived. The former should be achieved by spindles with larger diameter roller bearings while simultaneously the technology for the design of these spindles running at high speeds must be developed. Present research work shows good promise for this development. For the latter, methods of maximum use of the lobing effect should be developed as well as methods of increasing the damping of the end mill mode.
Convolution-based time-domain simulation for fluidelastic instability in tube arrays
