1984 IEEE TRANSACTIONS ON MAGNETICS, VOL. 48, NO. 6, JUNE 2012 Homopolar Magnetic Bearing Saturation Effects on Rotating Machinery Vibration Kyungdae Kang and Alan Palazzolo Samsung Techwin Co., LTD, Seongnam-si, Gyeonggi-do 463-400, South Korea Mechanical Engineering, Texas A&M University, College Station, TX 77843 USA 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 por- tion 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. Index Terms—Bearings (mechanical), vibrations. I. INTRODUCTION I N general, magnetic bearings are classified in two groups: heteropolar and homopolar. Heteropolar magnetic bearings (HeMB) designs employ magnetic fields that include both N and S poles around the circumference of the bearing, whereas homopolar magnetic bearings (HoMB) have either all N poles or all S poles. HoMB most often employ permanent magnets to provide the DC bias field. The improvement of efficiency which this provides, and the reduction of eddy currents that result from eliminating complete flux reversals are distinct advantages of HoMB over HeMB. Extensive research has been done in nonlinear dynamics analysis of rotor-active mag- netic bearing (AMB) systems, but there are few publications dealing with the effect of magnetic saturation and amplifier voltage/current saturation on the nonlinear dynamic response of rotor. This is especially true for HoMB designs. Maslen et al. investigated the performance limits of HeMB, such as peak force, slew rate, and displacement sensitivity [1]. He found that peak force limitation is primarily due to the nonlinearity in the magnetization curve of the electromagnet core material and force slew rate limit is caused by the power amplifier voltage limit, which results in phase lag and reduction in both stiffness and damping in the bearing. For PMB HoMB, Lee et al. studied similar performance limits [2], however these two papers do not deal with the effects of saturation on nonlinear dynamic response of a flexible rotor. They instead focus solely on the effect of magnetic core saturation on the maximum static force, Manuscript received June 18, 2011; revised October 27, 2011; accepted De- cember 07, 2011. Date of publication January 05, 2012; date of current version May 18, 2012. Corresponding author: A. Palazzolo (e-mail: a-palazzolo@tamu. edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2012.2182776 and on the power amplifier voltage saturation’s effect on the force slew rate. Chinta investigated the forced response of a two-dof (x-y) rigid rotor supported symmetrically by identical heteropolar magnetic bearings, including imbalance excitation, and a simple bilinear model of magnetic flux saturation [3], [4]. Flux saturation was found to reduce the maximum forces depending on the rotor speed. Steinschaden et al. investigated the dynamics of an active magnetic bearing system for the case of large rotor eccentricities [5]. They modeled the nonlinearities such as magnetic saturation effect, saturation of the amplifier and of the control current, but only present results from the control current limit. These authors restrict application of their approach to light saturation where their bilinear - type model is most suitable and not for the case of heavy saturation, above the starting point of the second linear part of the bilinear - curve. For specific parameter sets, symmetry breaking and quasiperiodic solution result from the effects of current saturation. Analytical (curve fit) models of the magnetization curve have been formed in various way, such as an exponential series [6], rational-fraction approximations [7], [8], and modified expo- nential functions [9]. These approximations are suitable for the magnetization curves with low initial slope, and do not fit to the weak flux region very well. We propose a modified Langmuir method with the cor- rection terms for the weak flux region to form an analytical model of the experimental magnetization curve of Hiperco 50. This improves the prediction of the magnetic force when the bearing is operating dynamically with both weak and high magnetic fluxes. This approach is employed for the nonlinear analysis of a heavily loaded 4-degree-of-freedom (DOF) flex- ible rotor-bearing system. Heavy static and dynamic loads applied to the rotor causes the magnetic bearings to operate within the regions of the magnetic bearing clearance that cause 0018-9464/$31.00 © 2012 IEEE