Multi-dimensional time-frequency control of micro-milling instability

Abstract

Micro-milling is inherently unstable and chattering with aberrational tool vibrations. While the time response is bounded, however, micro-milling can become unstably broadband and chaotic in the frequency domain, inadvertently rendering poor tolerance and frequent tool damage. A novel simultaneous time-frequency control theory is applied to negate the various nonlinear dynamic instabilities including tool chatter and tool resonance displayed by a multi-dimensional, time-delayed micro-milling model. The time and frequency responses of the force and vibration of the model agree well with the experimental results published by Jun et al. A multi-variable control scheme is realized by implementing two independent controllers in parallel to follow a target signal representing the desired micro-milling state of stability. The control of unstable cutting at high spindle speeds ranging from 63,000 to 180,000 rpm and different axial depth-of-cuts are investigated using phase portrait, Poincaré section, and instantaneous frequency (IF). The time-frequency control scheme effectively restores dynamic instabilities, including repelling manifold and chaotic response, back to an attracting limit cycle or periodic motion of reduced vibration amplitude and frequency response. The force magnitude of the dynamically unstable cutting process is also reduced to the range of stable cutting.