Abstract
In this article, hybrid factor is proposed for hybrid magnetic bearing. The hybrid factor is defined as the ratio of the force produced by the permanent magnet and the forces produced by the permanent magnet and current in hybrid magnetic bearing. It is deduced from a certain radial hybrid magnetic bearing using its important parameters such as the current stiffness and displacement stiffness at first and then the dynamic model of magnetically suspended rotor system is established. The relationship between structural parameters and control system parameters is analyzed based on the hybrid factor. Some influencing factors of hybrid factor in hybrid magnetic bearing, such as the size of the permanent magnet, length of air gap, and area of the stator poles, are analyzed in this article. It can be concluded that larger hybrid factor can be caused by the smaller power loss according to the definition of hybrid factor mentioned above. Meanwhile, the hybrid factor has a maximum value, which is related to control system parameters such as proportional factor expect for structural parameters. Finally, the design steps of parameters of hybrid magnetic bearing can be concluded.
Highlights
Nowadays, magnetic bearings have been widely used in actuators such as flywheels,[1,2,3] control momentum gyro,[4] turbines,[5] and high-speed machines.[6]
Considering the structural parameters such as outer diameter of the permanent magnet Dpm[1], the length of air gap (d) at the equilibrium position, the area of the stator poles (A), and the proportional coefficient kP can influence the hybrid factor according to equations
The hybrid factor Kpmc is decreased according to equation (9). From these simulation results above, it can be seen that the difference between MATLAB and 3D finite element method (FEM) analysis is mainly the different leakage flux and iron saturation caused by different permanent magnet dimensions, air gap length, the stator poles area, and so on
Summary
Magnetic bearings have been widely used in actuators such as flywheels,[1,2,3] control momentum gyro,[4] turbines,[5] and high-speed machines.[6]. The power loss is small in HMB because the supporting force is produced by the permanent magnet.[12,13,14] the negative displacement stiffness in HMB can cause the instability of the magnetically suspended rotor system. 1: permanent magnet; 2: inner magnetic ring; 3: stator poles; 4: air gap; 5: coil; 6: rotor core stacks; 7: outer magnetic ring. Flux density in the air gap produced by the permanent magnet and current in coil can be derived according to equation (2). When the gravity of rotor is known, equation (8) can be expressed in another form
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