Delayed feedback based active control of milling operations

Vibrations due to time-delay effects in milling operations is undesirable as it may lead to a poor surface finish on parts, lower cutting productivity, as well as promote tool wear and costly tool failures. In the current study, the authors present a four degree-of-freedom model for a cylindrical end milling operation which includes the dynamics of workpiece. Because of regenerative effects, the model at hand is a time delay system with periodic parametric excitation. Stability diagrams which can be used as a reference in milling operations are obtained and the effects of the dynamics of workpiece on the stability of the system are studied via the semi-discretization method. The result shows that the stable region might shrink due to the added mass and flexibility from the workpiece. Further, to expand the workable region of stable cutting, an linear feedback control strategy using optimal feedback gains of delayed-states is proposed. Simulations are carried out and they show the stable region can be enlarged by the control strategy and the delayed-state feedbacks are an effective means of feedback control variables. The result also indicates that a controller can benefit from delayed feedbacks in a time-delay system by choosing appropriate feedback gains.