Active magnetic bearings provide a new tool for the control of chatter produced in high speed milling. The fundamental mechanism of chatter is the regeneration of waviness and is inherently a problem of state-delay. Complicating the control problem, the dynamics of the cutting process change with tool replacement, feedrate, or type of cut (e.g., down-milling, slotting, etc.), among other factors. Since active magnetic bearings permit the variation of bearing properties during cutting, magnetic bearings can be used to adapt to changes in the dynamics of the cutting process. To achieve high metal removal rates free from chatter, the magnetic bearing control must be tuned for the particular parameters of the cutting condition as well as the delay. This may be achieved via the use of the new control synthesis techniques of implicit gain scheduling.
The approach considered seeks to exploit the important phase information of the cutting process dynamics due to the time delay in synthesis. Toward this end, we have developed a new unified approach to the analysis of time delay systems through the application of scaled small gain concepts to a comparison system that is free of delay. This provides a frequency domain interpretation to previously published delay-independent and delay-dependent results in this field based on Lyapunov-Krasovskii functionals and Lyapunov-Razumikhin functions. This approach allows the use of m-analysis and m-synthesis results for the problems with uncertainty in both the delay and the system model.
