Kang, Kyungdae (2010-12). Nonlinear Dynamics of a Rotor Supported by Homopolar Magnetic Bearings with Saturation. Doctoral Dissertation. Thesis uri icon

abstract

  • An objective in the design of high performance machinery is to minimize weight so magnetic bearings are often designed to operate slightly lower than the magnetic material saturation. Further weight reduction in the bearings requires operation in the nonlinear portion of the B-H curve. This necessitates a more sophisticated analysis at the bearing and rotordynamic system levels during the design stage. This dissertation addresses this problem in a unique manner by developing a fully nonlinear homopolar magnetic bearing model. The nonlinear dynamics of permanent magnet-biased homopolar magnetic bearing (PMB HoMB) system with 2-dof rigid and 4-dof flexible rotor is analyzed. The dynamic behavior of the rotor-bearing system is examined in the feedback control loop that includes low pass filter effects. An analytical magnetization curve model is proposed to predict the nonlinear magnetic force under the influence of the magnetic flux saturation more accurately. The modified Langmuir method with the novel correction terms for the weak flux region is used to curve-fit the experimental magnetization data of Hiperco 50. A new curve fit model of the B-H curve is shown to have significantly better agreement with the measured counterpart than conventional piecewise linear and other models. PMB HoMB characteristics with flux saturation, such as forces depending on the rotor position and bearing stiffness, are compared with these other models. Frequency response curve, bifurcation diagram, Poincare plot, and orbit plot are utilized to demonstrate the effects of the nonlinearities included in the 2-dof rotorbearing system. Due to heavy static loads applied to the rotor, it operates within the magnetic flux saturation region at the bearing clearance. The voltage saturation in the power amplifier of the magnetic bearing introduces lag in the control loop and the response of the heavily loaded 4-dof rotor-bearing system shows that limit cycle stability can be achieved due to the magnetic flux saturation or current saturation in the amplifier; otherwise the system would experience a destructive instability. These simulation results provide the first explanation of this commonly observed limit cycle which is referred to as 'virtual catcher bearings'.
  • An objective in the design of high performance machinery is to minimize weight
    so magnetic bearings are often designed to operate slightly lower than the magnetic
    material saturation. Further weight reduction in the bearings requires operation in the
    nonlinear portion of the B-H curve. This necessitates a more sophisticated analysis at the
    bearing and rotordynamic system levels during the design stage. This dissertation
    addresses this problem in a unique manner by developing a fully nonlinear homopolar
    magnetic bearing model.
    The nonlinear dynamics of permanent magnet-biased homopolar magnetic
    bearing (PMB HoMB) system with 2-dof rigid and 4-dof flexible rotor is analyzed. The
    dynamic behavior of the rotor-bearing system is examined in the feedback control loop
    that includes low pass filter effects.
    An analytical magnetization curve model is proposed to predict the nonlinear
    magnetic force under the influence of the magnetic flux saturation more accurately. The
    modified Langmuir method with the novel correction terms for the weak flux region is used to curve-fit the experimental magnetization data of Hiperco 50. A new curve fit
    model of the B-H curve is shown to have significantly better agreement with the
    measured counterpart than conventional piecewise linear and other models. PMB HoMB
    characteristics with flux saturation, such as forces depending on the rotor position and
    bearing stiffness, are compared with these other models.
    Frequency response curve, bifurcation diagram, Poincare plot, and orbit plot are
    utilized to demonstrate the effects of the nonlinearities included in the 2-dof rotorbearing
    system.
    Due to heavy static loads applied to the rotor, it operates within the magnetic flux
    saturation region at the bearing clearance. The voltage saturation in the power amplifier
    of the magnetic bearing introduces lag in the control loop and the response of the heavily
    loaded 4-dof rotor-bearing system shows that limit cycle stability can be achieved due to
    the magnetic flux saturation or current saturation in the amplifier; otherwise the system
    would experience a destructive instability. These simulation results provide the first
    explanation of this commonly observed limit cycle which is referred to as 'virtual
    catcher bearings'.

publication date

  • December 2010