# Residual Magnetic Field Non-Destructive Testing of Gantry Cranes

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### RMF Methods

- ${B}_{p}$ is the induction component perpendicular to the metal surface;
- ${\mu}_{0}=2\pi \ast {10}^{-7}$ is the air magnetic permeability.

- tangential component ${H}_{p\left(x\right)}$;
- normal component ${H}_{p\left(y\right)}$.

- $r=\left[x-l,y\right]$ is a vector, a variable related to the element surface;
- $\rho $ is a function defining the boundary condition presenting the distribution of the magnetic charge density on the specimen surface, which depends directly on the dislocation density and indirectly on the stress;
- x, y are the coordinates of the point on the tested element surface;
- l is the dislocation length;
- b is the dislocation width.

- ${K}_{in}$ is the RMF gradient;
- $\left|\Delta {H}_{p}\right|$ is the absolute value of the difference in ${H}_{p}$ between two control points located at equal distances ${l}_{k}$ on both sides of the line ${H}_{p}$ = 0.

- $\Delta M\left({H}_{0}\right)$ is the rise in magnetization under the influence of a weak magnetic field;
- $\Delta {M}^{\sigma}\left[{H}_{0};\sigma \left(x,\alpha \right)\right]$ is the rise in magnetization under the influence of elastic stresses in the presence of a weak magnetic field.

## 3. Results of the RMF Scanning

- $Hp\left(x\right)$ is the RMF intensity value in the point where the gradient was determined;
- ${H}_{p}\left(x+a\right)$ is the RFM intensity value for the next measuring point;
- a is the distance between consecutive points on the measuring line.

## 4. Validation and Numerical Simulation

## 5. Conclusions

- The RMF technique enabled the effective location of stress concentration zones in the analyzed crane beam by determining the gradient of the RMF tangential component.
- The experimental verification using the X-ray diffraction method confirmed the stress concentration zones in the beam.
- Creating a relational database of magnetograms of the ferromagnetic structure from the beginning of its operation seems to be an interesting addition to standard magnetic diagnostic methods.
- Combining different methods and measurement techniques, for example a fiber optic beam deflection measurement system using the FEM method which implements boundary conditions from optical fiber measurements, with residual magnetic field techniques can significantly contribute to the identification of stress concentration zones.

## Funding

## Conflicts of Interest

## References

- Shannon, R.W.F.; Braithwaite, J.C.; Morgan, L.L. Flux-leakage vehicles pass tests for pipeline inspection. Oil Gas J.
**1988**, 32. [Google Scholar] [CrossRef] - Fu, M.L.; Bao, S.; Zhao, Z.Y.; Gu, Y.B. Effect of sample size on the residual magnetic field of ferromagnetic steel subjected to tensile stress. Non-Destr. Test. Cond. Monit.
**2018**, 60, 90–94. [Google Scholar] [CrossRef] - Bao, S.; Fu, M.L.; Lou, H.J.; Bai, S.Z. Defect identification in ferromagnetic steel based on residual magnetic field measurements. J. Magn. Magn. Mater.
**2017**, 441, 590–597. [Google Scholar] [CrossRef] - Yao, L.K.; Wang, Z.D.; Deng, B. Experimental research on metal magnetic memory method. Exp. Mech.
**2012**, 3, 305–314. [Google Scholar] [CrossRef] - Wang, Z.D.; Yao, K.; Ding, K.Q. Quantitative study of metal magnetic memory signal versus local stress concentration. NDT E Int.
**2010**, 6, 513–518. [Google Scholar] [CrossRef] - Wang, Z.D.; Yao, K.; Ding, K.Q. Theoretical studies of metal magnetic memory technique on magnetic flux leakage signals. NDT E Int.
**2010**, 43, 354–359. [Google Scholar] [CrossRef] - Juraszek, J. Innovative Non–destructive Testing Methods Monography; ATH, Univ. of Bielsko-Biala: Bielsko-Biała, Poland, 2013. [Google Scholar]
- Ren, S.K.; Song, K.; Ren, J.L. Influence of environmental magnetic field on stress magnetism effect for 20 steel ferromagnetic specimen. Insight
**2009**, 51, 672–675. [Google Scholar] [CrossRef] - Wilson, J.W.; Tian, G.Y.; Barrans, S. Residual magnetic field sensing for stress measurement. Sens. Actuators A
**2007**, 135, 381–387. [Google Scholar] [CrossRef] - Yao, K.; Deng, B.; Wang, Z.D. Numerical studies to signal characteristics with the metal magnetic memory-effect in plastically deformed samples. NDT E Int.
**2012**, 47, 7–17. [Google Scholar] [CrossRef] - Juraszek, J. Hoisting machine brake linkage strain analysis. Arch. Min. Sci.
**2018**, 63, 583–597. [Google Scholar] - Shi, C.L.; Dong, S.Y.; Xu, B.S.; Peng, H. Stress concentration degree affects spontaneous magnetic signals of ferromagnetic steel under dynamic tension load. NDT E Int.
**2010**, 43, 8–12. [Google Scholar] - Dong, L.H.; Xu, B.S.; Dong, S.Y.; Chen, Q.Z.; Wang, D. Stress dependence of the spontaneous stray field signals of ferromagnetic steel. NDT E Int.
**2009**, 42, 323–327. [Google Scholar] [CrossRef] - Guo, P.J.; Chen, X.D.; Guan, W.H.; Cheng, H.Y.; Jiang, H. Effect of tensile stress on the variation of magnetic field of low-alloy steel. J. Magn. Magn. Mater.
**2011**, 23, 2474–2477. [Google Scholar] - Shui, G.S.; Li, C.W.; Yao, K. Non-destructive evaluation of the damage of ferromagnetic steel using metal magnetic memory and nonlinear ultrasonic method. Int. J. Appl. Electromagn. Mech.
**2015**, 47, 1023–1038. [Google Scholar] [CrossRef] - Yi, S.C.; Wei, W.; Su, S.Q. Bending experimental study on metal magnetic memory signal based on von Mises yield criterion. Int. J. Appl. Electromagn. Mech.
**2015**, 49, 547–556. [Google Scholar] [CrossRef] - Chen, H.L.; Wang, C.L.; Zuo, X.Z. Research on methods of defect classification based on metal magnetic memory. NDT E Int.
**2017**, 92, 82–87. [Google Scholar] [CrossRef]

© 2019 by the author. 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Juraszek, J.
Residual Magnetic Field Non-Destructive Testing of Gantry Cranes. *Materials* **2019**, *12*, 564.
https://doi.org/10.3390/ma12040564

**AMA Style**

Juraszek J.
Residual Magnetic Field Non-Destructive Testing of Gantry Cranes. *Materials*. 2019; 12(4):564.
https://doi.org/10.3390/ma12040564

**Chicago/Turabian Style**

Juraszek, Janusz.
2019. "Residual Magnetic Field Non-Destructive Testing of Gantry Cranes" *Materials* 12, no. 4: 564.
https://doi.org/10.3390/ma12040564