Homopolar Magnetic Bearing Saturation Effects on Rotating Machinery Vibration

An objective in the design of high performance machinery is to minimize weight so magnetic bearings are often designed to operate slightly lower than their magnetic material saturation. Further weight reduction in the bearings requires operation in the nonlinear portion of the - curve. This necessitates a more sophisticated analysis at the bearing and rotordynamic system levels during the design stage. This paper addresses this problem in a unique manner by developing a fully nonlinear homopolar magnetic bearing model. The nonlinear dynamics of a permanent magnet-biased homopolar magnetic bearing (PMB HoMB) system with a flexible rotor is analyzed. Nonlinear effects due to power amplifier voltage and current saturation and position dependent reluctances are also included in the model. A new curve fit model of the - curve is shown to have significantly better agreement with the measured counterpart than conventional piecewise linear. The modified Langmuir method, with a novel correction terms for the weak flux region, is used to form an analytical model of the experimental magnetization curve of Hiperco 50. High static and dynamic loads applied to the rotor force the magnetic bearing to operate in a flux saturated state. 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. The stable limit cycle prevents the linear model instability, creating what is experimentally observed as a "virtual catcher bearing." To the authors' knowledge this is the first explanation of this commonly observed phenomenon.