Principle and performance analysis for six‐pole hybrid magnetic bearing with a secondary air gap

In order to reduce the non-linearity of radial suspension forces of the three-pole hybrid magnetic bearing and further reduce the cost and power consumption, an AC six-pole hybrid magnetic bearing with secondary air gaps is proposed. First, the structure and working principle of the AC six-pole hybrid magnetic bearing with secondary air gaps are introduced, and the mathematical model of suspension forces are derived. Second, on the basis of the mathematical model, the linearity and coupling characteristics of the radial suspension forces are analysed, and then the suspension forces are simulated and verified by the finite element method (FEM). Then, the correlation performance indexes are compared with the six-pole hybrid magnetic bearing without secondary air gaps. Finally, an experimental platform is built, and suspension and disturbance tests are carried out. The research results show that the maximum bearing capacity of the six-pole hybrid magnetic bearing with secondary air gaps is 184% of the six-pole hybrid magnetic bearing without secondary air gaps.

In order to reduce the non-linearity of radial suspension forces of the three-pole hybrid magnetic bearing and further reduce the cost and power consumption, an AC six-pole hybrid magnetic bearing with secondary air gaps is proposed. First, the structure and working principle of the AC six-pole hybrid magnetic bearing with secondary air gaps are introduced, and the mathematical model of suspension forces are derived. Second, on the basis of the mathematical model, the linearity and coupling characteristics of the radial suspension forces are analysed, and then the suspension forces are simulated and verified by the finite element method (FEM). Then, the correlation performance indexes are compared with the six-pole hybrid magnetic bearing without secondary air gaps. Finally, an experimental platform is built, and suspension and disturbance tests are carried out. The research results show that the maximum bearing capacity of the six-pole hybrid magnetic bearing with secondary air gaps is 184% of the six-pole hybrid magnetic bearing without secondary air gaps.
Introduction: The friction between the rotor and stator of the traditional mechanical bearing increases the energy loss, and magnetic bearing can solve this problem effectively [1]. Two power amplifiers are required for magnetic bearing with four magnetic poles [2]. Only one three-phase inverter is required for three-pole magnetic bearing in [3], and it will greatly reduce the cost and power consumption of the magnetic bearing system. To overcome the shortcomings of the existing modelling methods, a new mathematical modelling method of suspension force for a centripetal force type-magnetic bearing is proposed in [4].
Although the three-pole magnetic bearing has many advantages, it also increases the overall design difficulty and cost of the system in [5]. A new radial magnetic bearing structure and its working principle are introduced in this manuscript, and a parameter design method is put forward. Compared with the existing magnetic bearing structure, the structure can increase the linear working range and stability margin of the model.

Structure and working principle:
The six-pole hybrid magnetic bearing is mainly composed of a permanent magnet, radial stator, rotor and radial coil as shown in Figure 1.
When the flux flows through the air gaps between the rotor and the magnetic poles of the stator, the corresponding maxwell force is generated. The direction and magnitude of the maxwell force can be controlled by adjusting the direction and magnitude of the flux, and finally, the rotor can be suspended in the balance position. When the bias flux and the control flux are superimposed in the radial air gaps, one of the relative radial air gaps is increased and the other air gap magnetic flux  is decreased, and finally, the controllable radial suspension force can be produced. The suspension force in the radial direction can be obtained by adjusting the control current.
In Figure 2, the F m is the magnetomotive force of the permanent magnet, m is the total flux, A11 , A12 , B11 , B12 , C11 , C12 , A21 , A22 , B21 , B22 , C21 , C22 are the fluxes in the radial direction, respectively, are the magnetic conductance in the radial gaps, N is the total turns of a single radial control coil, i A , i B , i C are the control currents.
Through mathematical modelling of the six-pole hybrid magnetic bearing, the suspension force expression is obtained, and the maximum suspension force in the x-direction is 3B s 2 S r /2μ 0 , (B s is saturation flux, S r is magnetic pole area, μ 0 is air permeability), the maximum suspension force in the y-direction is √ 3B s 2 S r /μ 0 . The six-pole hybrid magnetic bearing has a maximum suspension force determined by the smaller ones in the x-and y-directions; therefore, the maximum suspension force of the six-pole hybrid magnetic bearing is 3B s 2 S r /2μ 0 . Figures 3(a) and (c) shows the magnetic density distribution of the six-pole magnetic bearing with only bias current. In Figure 3(a), the flux flow direction is same as the analysis result, and the magnetic density distribution is uniform in all six directions, which is about half of the saturation magnetic induction intensity 0.4T. The maximum control current in the positive direction of x-axis is introduced into the radial coils. The magnetic density distribution of the six-pole hybrid magnetic bearing is shown in Figures 3(b) and (d). The magnetic flux direction in each pole is the same as the bias flux, so the control flux is only superimposed on the bias flux; the A11 magnetic density is 0.8 T, the A12 density in the air gap is almost zero, and the maximum suspension force in the x-axis is 201 N.

Finite element analysis:
As can be seen in Figure 4(a), the control current and suspension force in the x-direction is linear. In Figure 4(b), the control current and suspension force in the y-direction is linear too. The six-pole structure benefits from the symmetry of its spatial structure. The force-current characteristic curves in the x-and y-axes are symmetric and have good linearity, which verifies the validity of the theoretical analysis.
As can be seen in Figure 5, when the length of secondary air gaps increases, the suspension force in the x-direction increases. When the length of the secondary air gaps is 3 mm, the force in the x-axis is 201 N. When the length of the secondary air gaps is 0 mm, the force of xaxis is 109 N. Therefore, the maximum bearing capacity of the six-pole hybrid magnetic bearing with secondary air gaps is 184% of the six-pole hybrid magnetic bearing without secondary air gaps.

Experiment validation:
Based on the mathematical model of magnetic bearing, the control system of the magnetic bearing is designed and the experimental platform of numerical control magnetic bearing is established as shown in Figure 6. The displacement of the magnetic bearing is detected by the eddy current sensors, the signal is adjusted to the acceptable value of the digital signal processing (DSP) controller through the interface circuit, and the control current is obtained by the DSP controller using the proportion integral derivative (PID) algorithm. The magnetic bearing is stabilised by the inverter.
The relationships between suspension force and control current of the six-pole hybrid magnetic bearing are shown as Figures 7(a) and (b), respectively. There is a little difference between simulation, experimental and calculation results. The experimental results are relatively bigger than the simulation results. The reason is that the air gap becomes smaller and the magnetic conductivity increases due to the rotor eccentricity during the experiment, which makes the maximum suspension force bigger.
Conclusion and discussion: This manuscript introduced the principle and performance analysis for six-pole hybrid magnetic bearing with a secondary air gap. Theoretical research and simulation analysis show that this radial magnetic bearing structure can effectively avoid the coupling of magnetic flux between two radial degrees of freedom and greatly reducing the control difficulty of magnetic bearing rotor offset. Thus, the linear range of the system is increased to improve the operational reliability, which is suitable for high speed and high precision magnetic levitation system. The research results show that the maximum bearing capacity of the six-pole hybrid magnetic bearing with secondary air gaps is 184% of the six-pole hybrid magnetic bearing without secondary air gaps.