Feedback control of regenerative chatter in high speed machining
Résumé
In this paper, we propose three controllers, namely PDD, NPDD and VPDD to suppress the presence of regenerative chatter in high speed machining. The controllers stand for P-proposal, D-derivative, D-Delay, N-nonlinear and V-variable feedback forces. Higher speeds and feeds that are available today in machine tools provide significant reductions in cycle times and per unit part cost production. In the high speed machine-tool industry, faster, more accurate and fewer unproductive stop times refer to the controlling of regenerative chatter phenomena from taking place in the machining operations. Regenerative chatter usually appears when the machining system cannot sufficiently sustain the energy imposed by the material removal operations at earlier and subsequent periods of spindle rotations. It is a vibration phenomenon that leads to unplanned consequences. The quality of the part to be machined, the structural characteristics of the machine tool and tool life are adversely impacted by presence of regenerative chatter. The equations that can properly describe the influence of regenerative chatter on machining operations are nonlinear delay differential equations. These equations explicitly contain the regenerative chatter effect, which in the classical ordinary differential equations is not accounted for. It is proposed in this paper to establish a mathematical framework for controlling nonlinear regenerative chatter in high speed machining. The mathematical framework is based upon the theoretical concepts of delay dynamical systems which are widely known to establish insightful and practical solutions at infinite dimensional frequencies in function spaces. Regimes of safe high speed machining at low, intermediate and high frequencies will be located in terms of the parameters of the cutting conditions, tool shape and feedback controllers. The essential energy levels that a high speed machine-tool system must encompass for specific machining parameters are established.