# A Novel Method for Reducing the Lift-Off Effect in Coercivity Measurement through Auxiliary Inductance Data

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Coercivity Measurements Based on Pulse Excitation

#### 2.1. Principle and Components

#### 2.2. System Description

## 3. Methodology

#### 3.1. Inductance Measurement

#### 3.2. Relationship Extrapolation

## 4. Coercivity Correction

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Kikuchi, H.; Ara, K.; Kamada, Y.; Kobayashi, S. Effect of Microstructure Changes on Barkhausen Noise Properties and Hysteresis Loop in Cold Rolled Low Carbon Steel. IEEE Trans. Magn.
**2009**, 45, 2744–2747. [Google Scholar] [CrossRef] - Liu, J. Magnetic characterisation of microstructural feature distribution in P9 and T22 steels by major and minor BH loop measurements. J. Magn. Magn. Mater.
**2016**, 401, 579–592. [Google Scholar] [CrossRef] - Rumiche, F.; Indacochea, J.; Wang, M. Assessment of the Effect of Microstructure on the Magnetic Behavior of Structural Carbon Steels Using an Electromagnetic Sensor. J. Mater. Eng. Perform.
**2008**, 17, 586–593. [Google Scholar] [CrossRef] - Kikuchi, H.; Sugai, K.; Murakami, T.; Matsumura, K. Dependence of Coercivity and Barkhausen Noise Signal on Martensitic Stainless Steel with and without Quench. In Studies in Applied Electromagnetics and Mechanics; Tian, G., Gao, B., Eds.; IOS Press: Amsterdam, The Netherlands, 2020; Available online: http://ebooks.iospress.nl/doi/10.3233/SAEM200027 (accessed on 20 July 2023).
- Mitra, A.; Mohapatra, J.; Swaminathan, J.; Ghosh, M.; Panda, A.; Ghosh, R. Magnetic evaluation of creep in modified 9Cr–1Mo steel. Scr. Mater.
**2007**, 57, 813–816. [Google Scholar] - Wang, Q.; Cong, G.; Lyu, Y.; Yu, W. A new Cr25Ni35Nb alloy critical failure time prediction method based on coercive force magnetic signature. J. Magn. Magn. Mater.
**2022**, 549, 168809. [Google Scholar] [CrossRef] - Stupakov, O. Local Non-contact Evaluation of the ac Magnetic Hysteresis Parameters of Electrical Steels by the Barkhausen Noise Technique. J. Nondestruct. Eval.
**2013**, 32, 405–412. [Google Scholar] - Tomas, I.; Kadlecova, J.; Vertesy, G. Measurement of Flat Samples With Rough Surfaces by Magnetic Adaptive Testing. IEEE Trans. Magn.
**2012**, 48, 1441–1444. [Google Scholar] [CrossRef] - Matyuk, V.F.; Goncharenko, S.A.; Hartmann, H.; Reichelt, H. Modern State of Nondestructive Testing of Mechanical Properties and Stamping Ability of Steel Sheets in a Manufacturing Technological Flow. Russ. J. Nondestruct. Test.
**2003**, 39, 347–380. [Google Scholar] [CrossRef] - Mazaheri-Tehrani, E.; Faiz, J. Airgap and stray magnetic flux monitoring techniques for fault diagnosis of electrical machines: An overview. IET Electr. Power Appl.
**2022**, 16, 277–299. [Google Scholar] [CrossRef] - Bida, G.V. The effect of a gap between the poles of an attachable electromagnet and a tested component on coercimeter readings and methods for decreasing it (Review). Russ. J. Nondestruct. Test.
**2010**, 46, 836–853. [Google Scholar] - Balakrishnan, A.; Joines, W.T. Air-Gap Reluctance and Inductance Calculations for Magnetic Circuits Using a Schwarz–Christoffel Transformation. IEEE Trans. Power Electron.
**1997**, 12, 654–663. [Google Scholar] [CrossRef] - Stupakov, O.; Perevertov, O.; Stoyka, V.; Wood, R. Correlation Between Hysteresis and Barkhausen Noise Parameters of Electrical Steels. IEEE Trans. Magn.
**2010**, 46, 517–520. [Google Scholar] [CrossRef] - Lenz, J.; Edelstein, S. Magnetic sensors and their applications. IEEE Sens. J.
**2006**, 6, 631–649. [Google Scholar] [CrossRef] - Lenz, J. A review of magnetic sensors. Proc. IEEE
**1990**, 78, 973–989. [Google Scholar] [CrossRef] - Ramsden, E. Integrated Sensors: Linear and Digital Devices. In HallEffect Sensors: Theory and Applications; Elsevier: Oxford, UK, 2006. [Google Scholar]
- Zhu, W.; Yin, W.; Peyton, A.; Ploegaert, H. Modelling and experimental study of an electromagnetic sensor with an Hshaped ferrite core used for monitoring the hot transformation of steel in an industrial environment. NDT E Int.
**2011**, 44, 547–552. [Google Scholar] [CrossRef]

**Figure 6.**Measured inductances and fitting curves for sample A at frequencies of 1, 200, and 500 kHz.

**Table 1.**Goodness of fit for Figure 6.

Fit Curve | 1 kHz | 200 kHz | 500 kHz |
---|---|---|---|

Sum-of-squares error | 0.0418 | 0.0078 | 0.0028 |

Root-mean-square error (RMSE) | 0.0511 | 0.0220 | 0.0132 |

Test Sample | Sample A | Sample B | Sample C |
---|---|---|---|

Coercivity (A/cm) | 4.8 | 7.2 | 56.0 |

Size (mm × mm × mm) | 80 × 25 × 8 | 81 × 25 × 8 | 81 × 27 × 8 |

**Table 3.**Goodness of fit for Figure 7.

Fit Curve | Sample A | Sample B | Sample C |
---|---|---|---|

Sum-of-squares error | 0.0028 | 0.0061 | 0.2383 |

Root-mean-square error (RMSE) | 0.0132 | 0.0195 | 0.1220 |

Coefficients | a | b | c | d |
---|---|---|---|---|

Sample A | −3.268 × 10${}^{7}$ | 2.077 × 10${}^{6}$ | −4.425 × 10${}^{4}$ | 3.203 × 10${}^{2}$ |

Sample B | −5.857 × 10${}^{7}$ | 3.792 × 10${}^{6}$ | −8.226 × 10${}^{4}$ | 6.048 × 10${}^{2}$ |

Sample C | −6.171 × 10${}^{8}$ | 3.948 × 10${}^{7}$ | −8.433 × 10${}^{5}$ | 6.069 × 10${}^{3}$ |

Test Sample | Sample D | Sample E | Sample F |
---|---|---|---|

Coercivity (A/cm) | 7.5 | 58.9 | 15.6 |

Mean Predicted Coercivity (A/cm) | 7.93 | 58.01 | 16.38 |

Mean Prediction Error | 5.17% | 2.66% | 5.01% |

Max Prediction Error | 9.33% | 7.47% | 9.62% |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lyu, R.; Meng, T.; Shao, Y.; Salas Avila, J.R.; Yin, W.
A Novel Method for Reducing the Lift-Off Effect in Coercivity Measurement through Auxiliary Inductance Data. *NDT* **2023**, *1*, 35-45.
https://doi.org/10.3390/ndt1010004

**AMA Style**

Lyu R, Meng T, Shao Y, Salas Avila JR, Yin W.
A Novel Method for Reducing the Lift-Off Effect in Coercivity Measurement through Auxiliary Inductance Data. *NDT*. 2023; 1(1):35-45.
https://doi.org/10.3390/ndt1010004

**Chicago/Turabian Style**

Lyu, Ruilin, Tian Meng, Yuchun Shao, Jorge Ricardo Salas Avila, and Wuliang Yin.
2023. "A Novel Method for Reducing the Lift-Off Effect in Coercivity Measurement through Auxiliary Inductance Data" *NDT* 1, no. 1: 35-45.
https://doi.org/10.3390/ndt1010004