Prospects for chaos control of machine tool chatter

The authors analyze the nonlinear tool-part dynamics during turning of stainless steel in the nonchatter and chatter regimes, toward the ultimate objective of chatter control. Their previous work analyzed tool acceleration in three dimensions at four spindle speeds. In the present work, the authors analyze the machining power and obtain nonlinear measures of this power. They also calculate the cycle-to-cycle energy for the turning process. Return maps for power cycle times do not reveal fixed points or (un)stable manifolds. Energy return maps do display stable and unstable directions (manifolds) to and from an unstable period-1 orbit, which is the dominant periodicity. Both nonchatter and chatter dynamics have the unusual feature of arriving at the unstable period-1 fixed point and departing from that fixed point of the energy return map in a single step. This unusual feature makes chaos maintenance, based on the well-known Ott-Grebogi-Yorke scheme, a very difficult option for chatter suppression. Alternative control schemes, such as synchronization of the tool-part motion to prerecorded nonchatter dynamics or dynamically damping the period-1 motion, are briefly discussed.