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Dynamic characteristics of triaxial active control magnetic bearing with asymmetric structure

  • Atsushi Nakajima EMAIL logo , Katsuhiro Hirata , Noboru Niguchi and Masayuki Kato
Published/Copyright: March 8, 2018
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Open Physics
From the journal Open Physics Volume 16 Issue 1

Abstract

Supporting forces of magnetic bearings are lower than those of mechanical bearings. In order to solve these problems, this paper proposes a new three-axis active control magnetic bearing (3-axis AMB) with an asymmetric structure where its rotor is attracted only in one axial direction due to a negative pressure of fluid. Our proposed 3-axis AMB can generate a large suspension force in one axial direction due to the asymmetric structure. The performances of our proposed 3-axis AMB are computed through 3-D finite element analysis.

Keywords: Magnetic bearings; magnetic levitation; electromagnet; finite element method
PACS: 02.30.Fn; 07.20.Ka; 84.71.Ba; 85.70.Ay

1 Introduction

Magnetic bearings realize a high-speed rotation, long life, low noise and dust-free operation because of their contactless and oil-less constitutions [1,2,3,4,5,6]. Because of these advantages, the magnetic bearings are practically used in turbomachinery and high-speed rotating machines. In order to support the rotating shaft using the magnetic bearings, a five-axis control (three translational axes, and two rotating axes except the rotating axis of the shaft) is needed. Generally, the stiffness of the magnetic bearings is lower than that of the mechanical bearings. Therefore the system tends to become large and the critical rotation speed also tends to decrease. In addition, a flat disk generating thrust forces causes a complicated manufacturing process and decreases the rotation speed limit. Recently, 3-axis AMBs have been proposed in order to increase the critical rotation speed and remove the flat disk [7,8,9,10,11]. However, their supporting forces are not high enough.

In this paper, we propose a new 3-axis AMB with an asymmetric structure for a canned motor where its rotor is attracted only in one axial direction due to a negative pressure of fluid. Our proposed 3-axis AMB can generate a large suspension force in one axial direction due to the asymmetric structure. The performances of our proposed 3-axis AMB are computed through 3-D finite element analysis (3-D FEA), and its effectiveness is verified.

2 Structure and operating principle

2.1 Basic structure

The sectional view of the proposed three-axis magnetic bearing is shown in Figure 1. This magnetic bearing consists of a radial stator, three thrust stators and a rotor. The radial stator is axially sandwiched by the thrust stators z1 and z2, and a non-magnetic material is inserted between the thrust stators z2 and z3. The radial stator with 8 electromagnetic poles is formed by laminated silicon steel sheets, and has 8 radial coils. 2 adjacent radial coils are wound in the opposite direction with each other and are connected in series. Therefore, the radial coils consist of 4 circuits: positive and negative coils (x1, x2) for X-axis, and positive and negative coils (y1, y2) for Y-axis as shown in Figure 2 (a). The thrust coils z1 and z2 are connected in series. The rotor consists of a magnetic material and 2 non-magnetic materials (A, and B) are inserted as shown in Figure 1 (b). The non-magnetic material A leads magnetic fluxes from the rotor to the radial stator as shown in Figure 2 (b). The non-magnetic material B controls magnetic fluxes so that the thrust force due to the thrust stator z2 in the positive direction of Z-axis will not be generated.

Figure 1 New three-axis magnetic bearing with asymmetric structure
Figure 1

New three-axis magnetic bearing with asymmetric structure

Figure 2 Operating principle
Figure 2

Operating principle

2.2 Operating principle

The operating principle of our proposed magnetic bearing is shown in Figure 2. A radial suspension force is generated by the magnetic flux due to the radial coils. A magnetic flux due to one set of excited coils flows through the air gap (Figure 2 (a)). This magnetic flux generates a magnetic attractive force between the stator and the rotor. This magnetic attractive force is used as a radial suspension force.

A positive Z-axis thrust force is generated by the magnetic flux due to the thrust coils z1 and z2. When the coil z1 and coil z2 are excited in the same direction, a magnetic flux flows through the thrust stator, rotor, radial stator and air gap (Figure 2 (b)). This magnetic flux flows through the radial stator so as to avoid the non-magnetic parts in the rotor facing the radial stator. Therefore, a magnetic attractive force is generated by the magnetic flux obliquely flowing between the stator and the rotor. Because the radial magnetic attractive force is cancelled in the circumference, only the axial magnetic attractive force remains. This magnetic attractive force is used as a radial suspension force.

Similarly, a negative Z-axis thrust force is generated by the magnetic flux due to the thrust coil z3. A negative Z-axis thrust force utilizes the magnetic attractive force at the low edge of the rotor.

3 Analyzed results

3.1 Computed result by 3-D FEM

We conducted 3-D FEAs to evaluate a supporting force of the proposed 3-axis AMB, where its specification is shown in Table 1. The analysis condition is shown in Table 2.

Table 1

Analysis specifications

Outer diameter130
StatorInner diameter50.2
Height75
Dimension [mm]Outer diameter49.1
RotorInner diameter29.5
Height67.9
Air gap lengthRadial0.55

Table 2

Analysis specifications

CPUIntel(R) Xeon(R) CPU E5-2609 v2
Number of elements1,064,688
 Number ofnodes181,147

Each bearing force was analyzed by changing the rotor’s X- and Z-axis displacements, X-axis radial current and positive Z-axis thrust current. The influence of the X-axis displacement on the X-axis radial suspension force is shown in Figure 3. In this case, the maximum radial suspension force was about 180 N, and when the rotor moves in the positive direction of X-axis, the radial air gap length decreases and the radial suspension force increases. In addition, it is observed that the rate of the increase of the suspension forces decreases as the current density increases. This is because of magnetic saturations in the stator and the rotor (Figure 4).

Figure 3 Radial suspension force v.s. current density of the radial coil
Figure 3

Radial suspension force v.s. current density of the radial coil

Figure 4 Magnetic flux density when radial coils x1 are excited
Figure 4

Magnetic flux density when radial coils x1 are excited

Table 3. shows the computed suspension forces when each coil is excited independently. The current density of the coils are 12 A/mm2 and the rotor is fixed in an initial position. From Table 3., it is observed that the suspension force in the positive direction of Z-axis is significantly higher than the other forces due to the asymmetric structure.

Table 3

Analysis specifications

Suspension force
Exicitation coil
Direction forceForce [N]
 Radial coil+x179
Thrust coil( +z)+z830
Thrust coil(-z)-z131

3.2 Active control

The controllability of the proposed 3-axis AMB under position control is investigated. A position feedback control system using a PID controller is built to achieve a stable controllability in the X- and Z-axis directions as shown in Figure 5. The suspension forces are determined from the suspension force data table in each axis calculated from 3-D FEA. The maximum allowable displacements of the X- and Z-axis are 0.1 mm and 0.15 mm, respectively, and the maximum current density in the coils is 12 A/mm2.

Figure 5 Position feedback control block diagram
Figure 5

Position feedback control block diagram

In order to verify the controllability of the proposed 3-axis AMB, the displacements in the X- and Z-axis directions were simulated when an external force is applied from 0 to 600 N as shown in Figure 6. In this simulation, the initial positions in the X- and Z-axis directions are 0 and 0.15 mm, respectively.

Figure 6 Simulation result of Z-axis position control
Figure 6

Simulation result of Z-axis position control

The simulated displacement in the X- and Z-axis directions are shown in Figure 6. From Figure 6, the displacement in the X-axis direction is almost 0, and the radial coils are not used. In addition, it is observed that the displacement in the Z-axis direction is converged to 0. In this simulation, the maximum thrust current density was less than 12 A/mm2. From these results, it can be concluded that the proposed 3-axis AMB can generate a sufficient thrust force and is effective for a canned motor.

Next, the position controllability in a steady operation when an instantaneous external force is applied in the X-axis direction is investigated. An external force of 175 N was applied in the negative direction of x-axis. The displacements are shown in Figure 7. A displacement increases in the X-axis due to the external force, however it can be controlled within the allowable displacement. The current density was also within the allowable value. In this time, a displacement also increases in the Z-axis direction, however it can be controlled within the allowable value. This is because the X-axis displacement affected the thrust force due to the magnetic structure.

Figure 7 Controllability when an external force is applied in the X axis
Figure 7

Controllability when an external force is applied in the X axis

Similarly, in a steady state, an external force was applied only in the Z axis. The displacement is shown in Figure 8. In this case the Z-axis displacement can be controlled within the allowable displacement and current density.

Figure 8 Control of Z-axis disturbance
Figure 8

Control of Z-axis disturbance

Finally, external forces were simultaneously applied in the X- and Z-axis. The displacement is shown in Figure 9. The displacement of each axis can be controlled within the allowable displacement and current density.

Figure 9 Controllability when external forces are applied in the X and Z axes
Figure 9

Controllability when external forces are applied in the X and Z axes

From these results, the proposed magnetic bearing can be controlled within the allowable displacement and current density against instantaneous external forces.

4 Conclusion

In this paper, we proposed a new three-axis active control magnetic bearing with an asymmetric structure to increase its thrust force. The operational principle was described and the fundamental suspension force characteristics of the proposed magnetic bearings were evaluated employing 3D-FEM. By arranging non-magnetic material parts in the rotor and controlling the flow of the magnetic flux, it was possible to generate a large thrust force in one direction.

In addition, we verified the controllability of the proposed AMB by conducting a control simulation using a PID control. It was verified that the proposed bearing can control the displacement within the allowable displacement and current density when instantaneous external forces are applied.

In future works, we will perform dynamic analysis coupled with 3-D FEM and simulation. In addition, the computed characteristics will be verified by carrying out measurements on a prototype.

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Received: 2017-11-01
Accepted: 2017-11-12
Published Online: 2018-03-08

© 2018 Atsushi Nakajima et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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https://doi.org/10.1515/phys-2018-0002
Keywords for this article
Magnetic bearings; magnetic levitation; electromagnet; finite element method
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BY-NC-ND 4.0

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