# Influence of Magnetostriction Induced by the Periodic Permanent Magnet Electromagnetic Acoustic Transducer (PPM EMAT) on Steel

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Ferromagnetic Properties of 1018 Steel

#### 2.2. SH Wave EMATs

#### 2.2.1. PPM EMAT

#### 2.2.2. MS-EMAT

#### 2.3. Magnetostriction within the PPM EMAT

#### 2.4. PPM EMAT Magnetostriction Model

**S″**in the principal coordinate system (x”-y”-z”) is [23] (p. 27)

#### Magnetostriction Model Implementation Procedure

#### 2.5. Finite Element Modeling of Entire NDT System to Determine Magnetostriction Empirical Factors

#### 2.6. Experimental Setup

- MS-EMAT magnet liftoff = 4.45 mm; associated average static magnetic field ${H}_{ot}$ = 1084 A/m.
- MS-EMAT magnet liftoff = 8.92 mm; associated average static magnetic field ${H}_{ot}$ = 797 A/m.
- MS-EMAT magnet liftoff = 23.68 mm; associated average static magnetic field ${H}_{ot}$ = 437 A/m.

- PPM EMAT transmitter to PPM EMAT receiver (PPM-to-PPM)
- MS-EMAT transmitter to PPM EMAT receiver (MS-to-PPM)
- one MS-EMAT transmitter to MS-EMAT receiver (MS-to-MS) experiment

## 3. Results

#### 3.1. Magnetostriction in the Receiver

#### 3.2. Magnetostriction Model Optimization

#### 3.3. MS-to-PPM Simulation and Experimental Data

#### 3.4. Magnetostriction within the PPM EMAT Transmitter (PPM-to-PPM EMAT)

## 4. Discussion

- With a 27% reduction in the static field strength, the MS-EMAT’s signal amplitude decreases by 11%, while a Lorentz-only PPM EMAT’s signal amplitude decreases by 18%.
- With a 24% reduction in the dynamic field strength, the MS-EMAT’s signal amplitude decreases by 7.6%, while a Lorentz-only PPM EMAT’s signal amplitude decreases by 24%.
- With a 27% reduction in the static field strength and 24% reduction in the dynamic field strength, the MS-EMAT’s signal amplitude decreases by 17%, while a Lorentz-only PPM EMAT’s signal amplitude decreases by 38% without movement. If the known magnetostrictive effect is now added, the PPM-to-PPM assembly moved from its original position along the wavelength direction will experience a signal reduction of 58%, while the MS-EMAT’s signal loss remains at 17%.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Periodic Permanent Magnet (PPM) EMAT 3D Diagram; (

**b**) Cross-section of PPM EMAT at Surface.

**Figure 2.**(

**a**) Magnetostrictive (MS) EMAT 3D Diagram; (

**b**) Top View of the Magnetostriction within the Plate.

**Figure 4.**(

**a**) Component Breakdown of the Static Field; (

**b**) Dynamic Field Angle $\alpha $ Definition.

**Figure 8.**Overhead View and Dimensions of each EMAT Configuration. (

**a**) Racetrack coil (PPM with Magnets Removed); (

**b**) PPM EMAT; (

**c**) Meander coil in the MS-EMAT transmitter. “Lifted” portions of coils are sufficiently distant from the test plate that they do not participate in the transduction mechanism.

**Figure 11.**Experimental MS-to-MS and MS-to-PPM Receiver Voltage on Steel Plate. Both MS-EMAT transmitter and receiver have a magnet liftoff of 8.92 mm. The input current to the transmitter in both tests is the same waveform with a maximum of 35.1 A.

**Figure 12.**Optimized ${d}_{6y}^{MS}$ Coefficient Values vs. Maximum Simulated Dynamic Field within the Steel Plate (Theory curve). Experimental Voltage divided by Maximum Simulated Dynamic Field vs. Maximum Simulated Dynamic Field (Experiment points).

**Figure 13.**Simulated and Experimental MS-to-PPM Maximum Receiver Voltage on Steel Plate vs. Input Current for three values of Static Field.

**Figure 14.**Simulated (either Lorentz only or combined Lorentz and magnetostriction) and Experimental PPM-to-PPM Maximum Receiver Voltage on Steel Plate vs. Input Current.

**Figure 15.**Reduction in the theoretical Lorentz-only PPM-to-PPM Maximum Receiver Voltage due to Magnetostriction vs. PPM EMAT Transmitter Gap/Magnet Width Ratio.

${\mathit{f}}_{\mathit{H}\mathit{o}\mathit{t}}$ | ${\mathit{f}}_{\mathit{\alpha}}$ | ${\mathit{f}}_{\mathit{\gamma}}$ | ${\mathit{f}}_{\mathit{\u03f5}}$ |
---|---|---|---|

$-4.3102\times {10}^{-4}\mathrm{m}/\mathrm{A}$ | $0.98501$ | $10.061$ | $0.31732$ |

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**MDPI and ACS Style**

Sun, C.Z.; Sinclair, A.; Filleter, T.
Influence of Magnetostriction Induced by the Periodic Permanent Magnet Electromagnetic Acoustic Transducer (PPM EMAT) on Steel. *Sensors* **2021**, *21*, 7700.
https://doi.org/10.3390/s21227700

**AMA Style**

Sun CZ, Sinclair A, Filleter T.
Influence of Magnetostriction Induced by the Periodic Permanent Magnet Electromagnetic Acoustic Transducer (PPM EMAT) on Steel. *Sensors*. 2021; 21(22):7700.
https://doi.org/10.3390/s21227700

**Chicago/Turabian Style**

Sun, Cong Zhu, Anthony Sinclair, and Tobin Filleter.
2021. "Influence of Magnetostriction Induced by the Periodic Permanent Magnet Electromagnetic Acoustic Transducer (PPM EMAT) on Steel" *Sensors* 21, no. 22: 7700.
https://doi.org/10.3390/s21227700