Wiesenborn, Robert Kyle (2006-12). Circular sensor array and nonlinear analysis of homopolar magnetic bearings. Master's Thesis. Thesis uri icon


  • Magnetic bearings use variable attractive forces generated by electromagnetic
    control coils to support rotating shafts with low friction and no material wear while
    providing variable stiffness and damping. Rotor deflections are stabilized by position
    feedback control along two axes using non-contacting displacement sensors. These
    sensor signals contain sensor runout error which can be represented by a Fourier series
    composed of harmonics of the spin frequency. While many methods have been
    proposed to compensate for these runout harmonics, most are computationally intensive
    and can destabilize the feedback loop. One attractive alternative is to increase the
    number of displacement sensors and map individual probe voltages to the two
    independent control signals. This approach is implemented using a circular sensor array
    and single weighting gain matrix in the present work. Analysis and simulations show
    that this method eliminates runout harmonics from 2 to n-2 when all sensors in an ideal
    n-sensor array are operational. Sensor failures result in reduced synchronous amplitude
    and increased harmonic amplitudes after failure. These amplitudes are predicted using
    derived expressions and synchronous measurement error can be corrected using an
    adjustment factor for single failures. A prototype 8-sensor array shows substantial
    runout reduction and bandwidth and sensitivity comparable to commercial systems.
    Nonlinear behavior in homopolar magnetic bearings is caused primarily by the
    quadratic relationship between coil currents and magnetic support forces. Governing
    equations for a permanent magnet biased homopolar magnetic bearing are derived using
    magnetic circuit equations and linearized using voltage and position stiffness terms.
    Nonlinear hardening and softening spring behavior is achieved by varying proportional control gain and frequency response is determined for one case using numerical
    integration and a shooting algorithm. Maximum amplitudes and phase reversal for this
    nonlinear system occur at lower frequencies than the linearized system. Rotor
    oscillations exhibit amplitude jumps by cyclic fold bifurcations, creating a region of
    hysteresis where multiple stable equilibrium states exist. One of these equilibrium states
    contains subharmonic frequency components resulting in quasiperiodic rotor motion.
    This nonlinear analysis shows how nonlinear rotor oscillations can be avoided for a wide
    range of operation by careful selection of design parameters and operating conditions.

publication date

  • December 2006