6. Summary

Magnetic bearings do not wear and have virtually no friction. The consequences of their usually unstable equilibrium of forces have to be corrected by feedback control loops. In general five such loops are required. In each control loop the difference between the displacement measured by a sensor and the desired displacement is converted into a control current through the coils of the magnetic circuit for generating the load-carrying capacity. With a suitable magnetic geometry it is possible to manage with a smaller number of control loops, but this has the disadvantage of reducing the load-carrying capacity and stiffness corresponding to the non-controlled degrees of freedom. This disadvantage can to some extent be overcome by including concentric grooves in the pole pieces. The load-carrying capacity can be calculated fairly easily from Maxwell's equations in vector notation, by expressing the force density at an enclosed surface in terms of the magnetic-flux-density vector. The ratio of the forces in the radial and axial directions of the magnetic bearings investigated, which had grooved pole pieces and one or three control loops, can be calculated from the same equation for the density of forces. The stability of two control methods, one using displacement feedback and the other velocity feedback, is demonstrated with the aid of Nyquist diagrams. The advantage of control with velocity feedback is that less heat is dissipated in the control coils. If a limiting speed is exceeded the magnetically supported rotor is dynamically unstable. This instability is comparable with the 'half-omega whirl' that can occur in hydrodynamic bearings.