# Development of a Compact Axial Active Magnetic Bearing with a Function of Two-Tilt-Motion Control

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## Abstract

**:**

## 1. Introduction

## 2. Three-Degree-of-Freedom Magnetic Suspension Apparatus

#### 2.1. Mechanical Configuration

#### 2.2. Controller Configuration

- ${z}_{k}$: vertical displacement at each sensor position k (k = 1, 2, 3, 4),
- $\widehat{z}$: displacement of the translational motion along the z axis,
- $\widehat{\alpha}$: angular displacement of the rotational motion around the x axis,
- $\widehat{\beta}$: angular displacement of the rotational motion around the y axis,
- $l$: distance of the sensors from the center of the pole.

- ${\widehat{i}}_{z}$: equivalent control current for the translational motion along the z axis,
- ${\widehat{i}}_{\alpha}$: equivalent control current for the rotational motion around the x axis,
- ${\widehat{i}}_{\beta}$: equivalent control current for the rotational motion around the y axis,
- ${i}_{1}$–${i}_{4}$: coil currents of the upper electromagnet unit,
- ${i}_{5}$–${i}_{8}$: coil currents of the lower electromagnet unit.

## 3. FEM Analysis

## 4. Parameter Identification

- $m$: mass of the floator (kg),
- ${p}_{vz}$: feedback gain of velocity (derivative gain) (As/m),
- ${p}_{dz}$: feedback gain of displacement (proportional gain) (A/m).

- ${\omega}_{0z}$: resonance angular frequency,
- $\zeta $: damping coefficient.

## 5. Design of Controller

- ${p}_{vz}$: velocity feedback gain (As/m),
- ${p}_{dz}$: displacement feedback gain (A/m),
- ${p}_{zz}$: local current integral feedback gain (As).

## 6. Experiments

#### 6.1. Frequency Characteristics

#### 6.2. Inter-Axis Interferences

- ${\omega}_{0z}=30\times 2\pi $ rad/s,
- ${a}_{2z}=2$, ${a}_{1z}=2$.

- ${\omega}_{0\alpha}=20\times 2\pi $ rad/s,
- ${a}_{2\alpha}=2$, ${a}_{1\alpha}=2$,
- ${\omega}_{0\beta}=20\times 2\pi $ rad/s,
- ${a}_{2\beta}=2$, ${a}_{1\beta}=2$.

- 1.27 N
_{0-p}, 0.5 Hz for along the z axis, - 3.76 × 10
^{−3}Nm_{0-p}, 0.75 Hz for around the x axis, - 3.76 × 10
^{−3}Nm_{0-p}, 1.0 Hz for around the y axis.

## 7. Rotation

_{0-p}. In this experiment, the zero power control is applied to the three modes. Figure 15 shows a relation between time and the rotation speed. The floator starts to rotate at 0 s. A black marker is pasted on the side of the floator. A reflective photo interrupter is used for the displacement sensor for measuring the horizontal direction. The output voltage of the photo interrupter generates pulse signal when the reflecting signal is blocked during passing the black marker. The rotation speed is measured from the pulses. Also, the output of the photo interrupter fluctuates due to the motion of the horizontal displacement. Figure 16 shows the output of the displacement sensor for the horizontal direction around 20 s and around 77 s after the rotation starts. The resolution of this measurement is 1 ms. The output signal is fluctuating like a sinusoidal wave due to the unbalance of the floator. The fluctuation of the floator increases as the rotation speed of the floator approached to the critical speed at 77 s. When the rotation speed approaches a critical speed, the floator collides with the horizontal displacement sensor unit. Therefore, the rotational signal is stopped manually at 78 s. The bias magnetic flux generated by the permanent magnet does not fluctuate according to the rotation around the z axis in the fabricated magnetic pole structure. Therefore, the floator can rotate under the zero power control without any special control.

## 8. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 8.**Relation between the displacement of the floator and the attractive force when the equivalent current is applied (analytical results).

**Figure 9.**Relation between the square of resonance angular frequency to the proportional gain (

**a**) in the translational motion along the z axis; (

**b**) in the rotational motion around the x axis; (

**c**) in the rotational motion around the y axis.

**Figure 10.**Block diagram of zero power feedback controller for the translational motion along the z axis.

**Figure 11.**Frequency characteristics of the simulated disturbance to the displacement with the zero power control. (

**a**) Translational motion along the z axis; (

**b**) Rotational motion around the x axis.

**Figure 12.**Step characteristics of equivalent current. (

**a**) Translational motion along the z axis; (

**b**) Rotational motion around the x axis; (

**c**) Rotational motion around the y axis.

**Figure 13.**Step characteristics of the displacement and angles. (

**a**) Displacement along the z axis; (

**b**) Angle around the x axis; (

**c**) Angle around the y axis.

**Figure 16.**Output of horizontal sensor. One pulse per rotation is generated which is used to estimate the rotational speed. (

**a**) 20 seconds after the start of rotation; (

**b**) approaching to the critical speeds.

Parameters | m | k_{sz} | k_{iz} |

Along z axis | 0.408 kg | 11,600 N/m | 6.35 N/A |

Parameters | I | k, _{sα}k_{sβ} | k, _{iα}k_{iβ} |

Around x axis | $0.165\times {10}^{-3}$ kgm^{2} | 1.00 Nm/rad | $2.35\times {10}^{-3}$ Nm/A |

Around y axis | $0.165\times {10}^{-3}$ kgm^{2} | 1.00 Nm/rad | $2.35\times {10}^{-3}$ Nm/A |

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**MDPI and ACS Style**

Ishino, Y.; Mizuno, T.; Takasaki, M.; Hara, M.; Yamaguchi, D. Development of a Compact Axial Active Magnetic Bearing with a Function of Two-Tilt-Motion Control. *Actuators* **2017**, *6*, 14.
https://doi.org/10.3390/act6020014

**AMA Style**

Ishino Y, Mizuno T, Takasaki M, Hara M, Yamaguchi D. Development of a Compact Axial Active Magnetic Bearing with a Function of Two-Tilt-Motion Control. *Actuators*. 2017; 6(2):14.
https://doi.org/10.3390/act6020014

**Chicago/Turabian Style**

Ishino, Yuji, Takeshi Mizuno, Masaya Takasaki, Masayuki Hara, and Daisuke Yamaguchi. 2017. "Development of a Compact Axial Active Magnetic Bearing with a Function of Two-Tilt-Motion Control" *Actuators* 6, no. 2: 14.
https://doi.org/10.3390/act6020014