Controller design for a magnetically suspended milling spindle based on chatter stability analysis

The chatter stability of a rigid milling spindle levitated by five-axis active magnetic bearings (AMBs) is studied for its chatter free cutting, as the control gains of AMBs vary. The characteristic equation for regenerative chatter loop with a delay element is described by a linear differential-difference equation, accounting for the dynamics of the AMB controllers, the uncut chip thickness equation and the cutting process as well as the rigid spindle dynamics itself. An efficient chatters stability analysis method is, then proposed to predict the stability lobes and chatter frequency in milling. The analytically predicted stability lobes are found to be in good agreement with the lobes generated by other methods available in the literature. Using the proposed method, parametric study is also performed to investigate the influences of the damping and stiffness coefficients of AMBs on the chatter free cutting conditions, as they are allowed to vary within the stable region formed by the AMB-control gains.