# Comparison of Inspecting Non-Ferromagnetic and Ferromagnetic Metals Using Velocity Induced Eddy Current Probe

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Velocity Induced Eddy Current Method

**v**above the specimen surface. This problem can be considered from another perspective due to the relativity of motion. It can be viewed (in a coordinate system that is fixed with respect to the magnet) as a specimen that moves with velocity −

**v**with the magnet at rest. Then, the eddy current generated by the magnet array can be expressed as:

**J**is the induced eddy current density, σ is the electrical conductivity of the specimen, and

**B**is the magnetic flux density. At low speed, when the secondary field can be ignored,

**B**represents the magnetic field produced by the magnets

**B**

_{M}. The minus sign is due to the definition of the direction of velocity.

**B**

_{M}and the magnetic field produced by the eddy currents created in the specimen

**B**

_{EC}. Eddy currents have a stable path when there is no defect, and the Hall sensor picks up a constant magnetic field. The presence of a defect perturbs the eddy currents’ path, and further changes the magnetic field picked up by the Hall sensor.

## 3. Experimental Tests

#### 3.1. Experimental Setup

^{2}, and a maximum speed of 9 m/s.

#### 3.2. Inspection of Aluminum Plates

#### 3.3. Inspection of Steel Plates

## 4. Finite Element Simulations

#### 4.1. Finite Element Model

#### 4.2. Aluminum Plates

#### 4.3. Steel Plates

**J**= σ

**E**, the diffusion equation for current density can be expressed as:

## 5. Conclusions

- The velocity induced eddy current probe can detect cracks in aluminum plates. The velocity induced eddy current inside the aluminum plate is approximately proportional to the speed of the moving magnet. The inspection signal amplitude increases with crack depth and probe speed.
- The velocity induced eddy current probe can detect cracks in steel plates. The experimental results show that the signal amplitude does not increase linearly with probe speed, which means that the signal is not caused by eddy current. Two effects, namely the eddy current effect and direct magnetic field perturbation, exist when inspecting steel plates. The simulation results show that the signals obtained with and without eddy currents have almost the same amplitude, which means that the direct magnetic field perturbation is responsible for the crack detection in steel plates.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Mix, P.E. Introduction to Nondestructive Testing: A Training Guide, 2nd ed.; John Wiley & Sons Inc.: Hoboken, NJ, USA, 2005. [Google Scholar]
- Rao, B.P.B. Practical Eddy Current Testing; Alpha Science International Limited: Oxford, UK, 2006. [Google Scholar]
- Pasadas, D.J.; Ribeiro, A.L.; Ramos, H.G.; Rocha, T.J. Inspection of Cracks in Aluminum Multilayer Structures Using Planar ECT Probe and Inversion Problem. IEEE Trans. Instrum. Meas.
**2017**, 66, 920–927. [Google Scholar] [CrossRef] - He, Y.; Luo, F.; Pan, M.; Weng, F.; Hu, X.; Gao, J.; Liu, B. Pulsed eddy current technique for defect detection in aircraft riveted structures. NDT E Int.
**2010**, 43, 176–181. [Google Scholar] [CrossRef] - Tian, G.Y.; Sophian, A.; Taylor, D.; Rudlin, J. Multiple sensors on pulsed eddy-current detection for 3-D subsurface crack assessment. IEEE Sens. J.
**2005**, 5, 90–96. [Google Scholar] [CrossRef] - Ribeiro, A.L.; Ramos, H.G. Inductive probe for flaw detection in non-magnetic metallic plates using eddy currents. In Proceedings of the Instrumentation and Measurement Technology Conference, Victoria, BC, Canada, 12–15 May 2008. [Google Scholar]
- Rocha, T.J.; Ramos, H.G.; Ribeiro, A.L.; Pasadas, D.J. Magnetic sensors assessment in velocity induced eddy current testing. Sens. Actuator A Phys.
**2015**, 228, 55–61. [Google Scholar] [CrossRef] - Feng, B.; Kang, Y.; Sun, Y. Theoretical Analysis and Numerical Simulation of the Feasibility of Inspecting Nonferromagnetic Conductors by an MFL Testing Apparatus. Res. Nondestruct. Eval.
**2016**, 27, 100–111. [Google Scholar] [CrossRef] - Weise, K.; Schmidt, R.; Carlstedt, M.; Ziolkowski, M.; Brauer, H.; Toepfer, H. Optimal magnet design for Lorentz force eddy-current testing. IEEE Trans. Magn.
**2015**, 51, 1–15. [Google Scholar] [CrossRef] - Mandayam, S.; Udpa, L.; Udpa, S.S.; Lord, W.I.S.U. Signal processing for in-line inspection of gas transmission pipelines. Res. Nondestruct. Eval.
**1996**, 8, 233–247. [Google Scholar] [CrossRef] - Park, G.S.; Park, S.H. Analysis of the velocity-induced eddy current in MFL type NDT. IEEE Trans. Magn.
**2004**, 40, 663–666. [Google Scholar] [CrossRef] - Feng, B.; Kang, Y.; Sun, Y.; Yang, Y.; Yan, X. Influence of motion induced eddy current on the magnetization of steel pipe and MFL signal. Int. J. Appl. Electromagn. Mech.
**2016**, 52, 357–362. [Google Scholar] [CrossRef] - Li, Y.; Tian, G.Y.; Ward, S. Numerical simulation on magnetic flux leakage evaluation at high speed. NDT E Int.
**2006**, 39, 367–373. [Google Scholar] [CrossRef] - Wu, J.; Sun, Y.; Feng, B.; Kang, Y. The effect of motion-induced eddy current on circumferential magnetization in MFL testing for a steel pipe. IEEE Trans. Magn.
**2017**, 53, 1–6. [Google Scholar] [CrossRef] - Rocha, T.J. Velocity Induced Eddy Current Testing. Ph.D. Thesis, Instituto Superior Técnico, Lisbon, Portugal, 2017. [Google Scholar]
- Rocha, T.J.; Ramos, H.G.; Ribeiro, A.L.; Pasadas, D.J.; Angani, C.S. Studies to optimize the probe response for velocity induced eddy current testing in aluminium. Measurement
**2015**, 67, 108–115. [Google Scholar] [CrossRef] - Rocha, T.J.; Ramos, H.G.; Ribeiro, A.L.; Pasadas, D.J. Evaluation of subsurface defects using diffusion of motion-induced eddy currents. IEEE Trans. Instrum. Meas.
**2016**, 65, 1182–1187. [Google Scholar] [CrossRef] - Uhlig, R.P.; Zec, M.; Ziolkowski, M.; Brauer, H.; Thess, A. Lorentz force sigmometry: A contactless method for electrical conductivity measurements. J. Appl. Phys.
**2012**, 111, 094914. [Google Scholar] [CrossRef] [Green Version] - Petković, B.; Haueisen, J.; Zec, M.; Uhlig, R.P.; Brauer, H.; Ziolkowski, M. Lorentz force evaluation: A new approximation method for defect reconstruction. NDT E Int.
**2013**, 59, 57–67. [Google Scholar] [CrossRef] - Sun, Y.; Kang, Y.; Qiu, C. A new NDT method based on permanent magnetic field perturbation. NDT E Int.
**2011**, 44, 1–7. [Google Scholar] [CrossRef] - Aguila-Muñoz, J.; Espina-Hernández, J.H.; Pérez-Benítez, J.A.; Caleyo, F.; Hallen, J.M. A magnetic perturbation GMR-based probe for the nondestructive evaluation of surface cracks in ferromagnetic steels. NDT E Int.
**2016**, 79, 132–141. [Google Scholar] [CrossRef]

**Figure 1.**Schematic diagram of experimental setup: (

**a**) Top view of probe structure; (

**b**) Side view of inspection system.

**Figure 6.**Distribution of velocity induced eddy currents in an aluminum plate for different probe speeds: (

**a**) 1 m/s; (

**b**) 2 m/s; (

**c**) 4 m/s; (

**d**) 6 m/s.

**Figure 9.**Distribution of velocity induced eddy currents in a steel plate for different probe speeds: (

**a**) 1 m/s; (

**b**) 2 m/s; (

**c**) 4 m/s; (

**d**) 6 m/s.

Speed | Amplitude |
---|---|

1 m/s | 3.7 mT |

2 m/s | 3.8 mT |

4 m/s | 3.9 mT |

6 m/s | 4.0 mT |

Without eddy current | 3.6 mT |

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**MDPI and ACS Style**

Feng, B.; Ribeiro, A.L.; Rocha, T.J.; Ramos, H.G.
Comparison of Inspecting Non-Ferromagnetic and Ferromagnetic Metals Using Velocity Induced Eddy Current Probe. *Sensors* **2018**, *18*, 3199.
https://doi.org/10.3390/s18103199

**AMA Style**

Feng B, Ribeiro AL, Rocha TJ, Ramos HG.
Comparison of Inspecting Non-Ferromagnetic and Ferromagnetic Metals Using Velocity Induced Eddy Current Probe. *Sensors*. 2018; 18(10):3199.
https://doi.org/10.3390/s18103199

**Chicago/Turabian Style**

Feng, Bo, Artur L. Ribeiro, Tiago J. Rocha, and Helena G. Ramos.
2018. "Comparison of Inspecting Non-Ferromagnetic and Ferromagnetic Metals Using Velocity Induced Eddy Current Probe" *Sensors* 18, no. 10: 3199.
https://doi.org/10.3390/s18103199