# A Novel Permanent Magnetic Angular Acceleration Sensor

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## Abstract

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^{−2}). Finally, the angular acceleration of the actual rotating system has been tested, using both a single-phase asynchronous motor and a step motor. Experimental result confirms the operating principle of the sensor and indicates that the sensor has good practicability.

## 1. Introduction

^{2}with a resolution of 1 r/s

^{2}in a 250 Hz bandwidth. Besides, a six-degree-of-freedom (6-DOF) piezo-resistive accelerometer has been designed by Amarasinghe, which is capable of measuring three components of the angular acceleration on three orthogonal axes at a frequency bandwidth of 300 Hz [17]. Wolfaardt proposed a novel micro-fluidic channel angular accelerometer [18], whose sensor consists of micro-machined spiral channels. It is fabricated on multiple wafers and can be used to construct a spiral-helix fluid column which generates high pressure during angular acceleration around the sensitive axis. In addition, a method for determining the instantaneous angular acceleration of the crankshaft by a magnetic encoder has been presented. This method is based on accurate determination of the measured angular speed and precise values of time when leading edges of individual magnetic teeth pass through the magnetic sensor [19]. Li has proposed a novel micro-electromechanical system (MEMS) pendulum angular accelerometer with electrostatic actuator feedback [20]. Compared with the other MEMS angular accelerometers, the proof pendulum with optimized moment of inertia improves sensitivity and resolution. Moreover, a fiber Bragg grating based angular accelerometer (FBGAA) imposed by an oscillating plate has also been proposed for angular acceleration measurement [21]. A novel wireless thermal convection angular accelerometer without movable parts and grooved cavity has been developed [22], which can be further integrated with an active RFID tag on the same flexible substrate. A novel prototype transducer, which is based on eddy current induction within a moving conductor slab in the presence of permanent magnets, has been developed by Restivo for relative angular acceleration measurement [23]. The contact-less operating principle can be readily applicable to the measurement of linear or angular relative acceleration. A concept of a fiber optic sensor, which consists of a light source, a fiber coil, and a two-beam interferometer, has also been described by Schloeffel for angular acceleration measurement [24].

## 2. Mechanical Structure of the Sensor

## 3. Operating Principle of the Sensor

_{P}generated by the permanent magnetics is shown in Figure 5. It forms a closed loop by passing through the outer stator, air and the inner stator. The copper sleeve is used here to guarantee Ф

_{P}will pass through the air. Assuming symmetrical magnetic circuit, according to the Ohm’s law and Kirchhoff’s voltage law of magnetic circuit theorem, Ф

_{P}can be expressed as:

_{P}: The magnetomotive force generated by the permanent magnets; R

_{mP}: The reluctance of magnetic circuit Ф

_{P}; H

_{P}: The strength of the magnetic field in the permanent magnets; l

_{P}: The effective thickness of permanent magnets.

_{P}counterclockwise at a speed of n (unit: r/min), generating the electromotive force which is given by:

_{e}is the structure constant of the cup-shaped rotor.

_{R}can be determined using the right-hand rule as shown in Figure 6.

_{R}, the current in the cup-shaped rotor i

_{R}is given by:

_{m}: The reluctance of magnetic circuit Ф; N

_{R}: The effective number of bars of the cup-shaped rotor.

_{o}is the total number of effective coils of the output winding.

## 4. FEM Modeling and Simulation of the Sensor

Component | Material | Inner Diameter | Outer Diameter | Thickness |
---|---|---|---|---|

copper sleeve | Brasses | 30 mm | 35 mm | 5 mm |

permanent magnet | XG240/46 | 22 mm | 28 mm | 4 mm |

Outer stator | DW540_50 | 22 mm | 30 mm | |

Cup-shaped rotor | silicon manganese bronze | 21 mm | 21.5 mm | 0.5 mm |

Inner stator | DW540_50 | 10 mm | 20.5 mm | |

Output winding | Copper-75C | 5 mm |

_{P}(shown in Figure 8) and the density cloud distribution of Ф

_{P}(shown in Figure 9).

_{P}distribution is consistent with that in Figure 5, and there is no flux crossed with the output winding. According to Figure 9, the magnetic circuits are not saturated.

_{m}, we have constant i

_{R}generated by the electromotive force e

_{R}. Let i

_{R}= 0.5 A, the simulation results obtained are shown in Figure 13.

_{m}. With a constant angular velocity, the induced voltage of angular acceleration sensor is zero, which confirms the operating principle of the angular acceleration sensor.

_{R}generated by the electromotive force is given by:

_{m}= 0.5 A, the simulation results obtained are shown in Figure 14.

## 5. Calibration and Angular Acceleration Testing Experiments

#### 5.1. The Composition and Principle of the Calibration Equipment

_{n}are the damping ratio coefficient and the intrinsic oscillation angular frequency of the calibration system, respectively.

_{0}is the initial amplitude of the pivot angle, ${\mathrm{\omega}}_{d}={\mathrm{\omega}}_{n}\sqrt{1-{\mathrm{\xi}}^{2}}$ is the damped oscillation angular frequency and the damping ratio is $\mathrm{\xi}{\mathrm{\omega}}_{n}=\mathrm{\beta}$.

_{0}is the amplitude of the initial angle and θ

_{N}is the amplitude of the Nth cycle, yielding

#### 5.2. The Calibration Experiment Results

^{−2}).

The peak voltage of the PMAA sensor (V) | 0.28 | 0.25 | 0.22 | 0.20 | 0.17 |

The peak voltage of angle sensor (V) | 1.68 | 1.44 | 1.28 | 1.12 | 1.04 |

The time corresponding peak (s) | 0.11 | 0.60 | 1.13 | 1.65 | 2.14 |

Oscillation period t/(s) | (0.49 + 0.53 + 0.52 + 0.49)/4 = 0.5075 | ||||

Angle values (rad) | 2.11 | 1.809 | 1.608 | 1.407 | 1.307 |

System damping ratio coefficient β | (ln(2.11 ÷ 1.307)) ÷ 4 ÷ 0.5075 = 0.2359 | ||||

Angular acceleration value (rad/s^{2}) | 322.4 | 276.4 | 245.7 | 215 | 199.7 |

Sensitivity coefficient (mV/(rad/s^{2)}) | 0.87 | 0.90 | 0.89 | 0.93 | 0.85 |

#### 5.3. Single-Phase Asynchronous Motor Angular Acceleration Testing

_{N}= 120 W, U

_{N}= 220 V, I

_{N}= 1 A, and n

_{N}= 1450 r/min. The cup-shaped rotor of sensor is connected with the rotating system coaxially. As shown in Figure 18, different components are labeled as (13) single-phase asynchronous motor, (14) coupling, (15) angular acceleration sensor and (16) digital oscilloscope. The induced voltage of angular acceleration sensor output winding are shown in Figure 19.

#### 5.4. Step Motor Angular Acceleration Testing

#### 5.5. Practicability Improvements of Angular Acceleration Sensor

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Zhao, H.; Feng, H. A Novel Permanent Magnetic Angular Acceleration Sensor. *Sensors* **2015**, *15*, 16136-16152.
https://doi.org/10.3390/s150716136

**AMA Style**

Zhao H, Feng H. A Novel Permanent Magnetic Angular Acceleration Sensor. *Sensors*. 2015; 15(7):16136-16152.
https://doi.org/10.3390/s150716136

**Chicago/Turabian Style**

Zhao, Hao, and Hao Feng. 2015. "A Novel Permanent Magnetic Angular Acceleration Sensor" *Sensors* 15, no. 7: 16136-16152.
https://doi.org/10.3390/s150716136