A theoretical model for analyzing the dynamic behavior of a misaligned rotor with active magnetic bearings

The dynamic response of a misaligned rotor, mounted in two identical active magnetic bearings (AMBs) was numerically investigated in this work. Three simplified models of current biased radial active magnetic bearings were presented, where four, six and eight electromagnets were powered by the bias current i0 and respective control current. The magnetic forces acting on the rotor, the coil currents and the displacement of the rotor were obtained through an electromagnetic theory. The AMBs’ dynamics support parameters were modelled by linearised direct cross axes stiffness and damping coefficients. These are strongly dependent on the air gap between the stator and the shaft. A spatial model of a misaligned rotor with two degrees of freedom was presented. The motion equations were established for the rotor bearing system and simulated with Newmark method. Simulations results were carried out to survey the dynamic behavior of spatial misaligned rotor mounted in AMBs. The angular misalignment was such that the 2× and 4× running speed components are predominant. Their magnitudes varied with the number of magnets in the bearing and with the air gap between the stator and the shaft.