# Three-Axis Inductive Displacement Sensor Using Phase-Sensitive Digital Signal Processing for Industrial Magnetic Bearing Applications

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## Abstract

**:**

## 1. Introduction

## 2. Three-Axis Inductive Displacement Sensor

#### 2.1. Requirement Specification

#### 2.2. Measurement Principle

#### 2.3. Electromagnetic Design

#### 2.4. Phase Sensitive Signal Processing

## 3. Experimental Results

#### 3.1. Static Accuracy and Linearity

#### 3.2. Dynamic Performance

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 2.**Effect of measurement coil stray series resistance on the linearity of the inductive measurement bridge output based on an analytical model of the electromagnetic circuit. Output error (lower figure) calculated as deviation from the best straight-line fit (dashed line) over the measurement range (grey area).

**Figure 3.**Mechanical dimensions of the displacement sensor and the winding scheme for all three measurement axes.

**Figure 5.**Cross-section of the sensor at poles corresponding to axial measurements. Numbers denote the following parts: 1—axial sensor stator stack, 2—radial sensor stator stack, 4—non-magnetic aluminium holding parts, 3—laminated rotor part.

**Figure 6.**Inductive differential three-axis rotor displacement sensor. Laminated stator stacks with windings (

**left**) and laminated rotor sensing surface with non-magnetic aluminium surroundings installed on electrical machine rotor (

**right**).

**Figure 7.**Measurement setup with a 350 kW, 15,000 r/min industrial high-speed induction machine and interface electronics for the displacement sensor.

**Figure 8.**Magnitude response and phase delay of the digital low-pass filters filtering the measurement signal during demodulation. Filtering consists of a 10-sample moving average filter combined with a 3rd-order low-pass IIR filter operated at 100 kHz sampling frequency. The filtering results in a 4 kHz −3 dB cut-off frequency with 87 µs phase delay at the cut-off frequency.

**Figure 9.**Static sensor linearity measurement on a manual three-axis linear stage. Measurement points (blue) and deviation points (orange) from the best straight-line fit (red). The grey area corresponds to the specified linear measurement range. The best straight-line fit corresponds to a radial gain of −2870 µm/pu and axial gain of −12,950 µm/pu. The maximum deviation from the best straight-line fit (DSL) throughout the linear measurement range is 7 µm for radial axes and 2 µm for the axial axis.

**Figure 10.**Measured noise level when the machine’s rotor is lying statically on the safety bearings. Frequency domain fast Fourier transform (FFT) consists of 32,768 samples at 20 kHz sampling frequency.

**Figure 11.**Rotor displacement measurement signals from two inductive displacement sensors placed at each end of the machine while the rotor is levitated and rotating at 1200 r/min.

**Figure 12.**Rotor displacement measurement signals fed to the rotor position controller of the magnetic bearing system from two inductive displacement sensors while the rotor is levitated and rotating at 1200 r/min. Note: The difference from the measurement signals presented in Figure 11 is the removal from the controller input of harmonic content synchronous to the rotational frequency.

Parameter | Value |
---|---|

Measurement range (radial/axial) | ±300 µm/±600 µm |

Air gap, d | 1 mm |

Non-linearity (deviation from line of best fit) | <8% (full scale) |

Frequency response range | 0–3 kHz (−3 dB) |

Noise | <0.1% (p-p, full scale) |

Signal-to-noise ratio (SNR) | >60 dB |

Effective number of bits (ENOB) | >10 bits |

Sampling frequency | >60 kHz |

(−20 dB suppression at Nyquist frequency) |

Parameter | Value |
---|---|

Number of turns per pole, n (radial/axial) | 35/25 |

Inductance per pole pair, L (radial/axial) | 208 µH/53 µH |

Excitation voltage | 10.3 V |

Excitation frequency | 10 kHz |

Stator/rotor sheet material | SURA M270-35A (0.35 mm) |

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**MDPI and ACS Style**

Sillanpää, T.; Smirnov, A.; Jaatinen, P.; Vuojolainen, J.; Nevaranta, N.; Jastrzebski, R.; Pyrhönen, O. Three-Axis Inductive Displacement Sensor Using Phase-Sensitive Digital Signal Processing for Industrial Magnetic Bearing Applications. *Actuators* **2021**, *10*, 115.
https://doi.org/10.3390/act10060115

**AMA Style**

Sillanpää T, Smirnov A, Jaatinen P, Vuojolainen J, Nevaranta N, Jastrzebski R, Pyrhönen O. Three-Axis Inductive Displacement Sensor Using Phase-Sensitive Digital Signal Processing for Industrial Magnetic Bearing Applications. *Actuators*. 2021; 10(6):115.
https://doi.org/10.3390/act10060115

**Chicago/Turabian Style**

Sillanpää, Teemu, Alexander Smirnov, Pekko Jaatinen, Jouni Vuojolainen, Niko Nevaranta, Rafal Jastrzebski, and Olli Pyrhönen. 2021. "Three-Axis Inductive Displacement Sensor Using Phase-Sensitive Digital Signal Processing for Industrial Magnetic Bearing Applications" *Actuators* 10, no. 6: 115.
https://doi.org/10.3390/act10060115