## 4 Experimental Parameter Design
### Coil Experimental Parameters  
Meander coils of EMATs are generally used to excite Lamb waves. According to the coherent principle, the coil's interval is designed for odd multiples of half the guided wavelength. The frequency of the current in the excitation coil is 220 kHz, and the frequency of the Lamb wave is 440 kHz in the steel. In the experiment, 1 mm thick Q235 steel plates were used as the detected material. According to the spectrum characteristic of Lamb, the lamb frequency thickness product of the 1 mm thick steel plate is 0.44 MHz\(\cdot\)mm, and the phase velocity of the steel plate is 1.56 km/s. The enameled wire with a wire diameter \(D\) of 1 mm was used to make the coil, and the center-to-center spacing of the meander coil was designed to be 1.77 mm. Besides, the spacing d of the separator is 0.77 mm, as shown in Figure 9.  
Figure 8: The characteristics of the received current in the excitation coil. (**a**) Time domain diagram of current; (**b**) frequency domain diagram of current.  
The current in the coil is a pulse impulse current, which is similar to short-circuit current. Therefore, the thermal and dynamic stabilities of the impact state need to be checked to verify its reliability. The purpose of thermal stability verification is to ensure that the coil will not be burned by the current thermal effect in a large current. The minimum cross-sectional area of the conductor determined by thermal stability is \(S_{min}\):  
\[S_{min}=\frac{1}{C_{h}}\sqrt{Q_{\mathrm{k}}K_{f}}. \tag{13}\]  
\(C_{h}\) is the thermal stability coefficient. In this experiment, \(C_{h}\) is 186, \(Q_{\mathrm{k}}\) is the short-circuit current thermal effect, and \(K_{f}\) is the skin effect coefficient, which is 1.02.  
From Figure 8a, the pulse current duration is 25 \(\upmu\)s, the current amplitude is 1700 A. The RMS current is calculated to be 506 A, and the calculated short-circuit thermal effect \(Q_{\mathrm{k}}\) is 2.3409 A\({}^{2}\)-s. Therefore, \(S_{min}\) is 8.307 \(\times\) 10\({}^{-3}\) mm\({}^{2}\). Whereas, the cross-sectional area of the copper wire with a radius of 0.5 mm is 0.785 mm\({}^{2}\). It is much larger than the minimum cross-sectional area of the conductor's thermal stability, so the thermal stability requirement is met.  
The purpose of dynamic stability verification is to ensure that the coil structure will not be destroyed by the action of electromotive force in a large current. The limitation of the conductor's mechanical properties is determined by the dynamic stability verification Equation (14):  
\[\sigma=\frac{f_{\mathrm{ph}}L^{2}}{10W}. \tag{14}\]  
The \(f_{\mathrm{ph}}\) is the electromotive force on the conductor of unit length, \(L\) is the line spacing, and \(W\) is the interface coefficient of the conductor perpendicular to the direction of the force. In the experiment, 3D printing technology PVC material was used to make the skeleton, and the coil was embedded in it to fix. The withstand stress of PVC material can be up to 50 MPa, which is much greater than the theoretical calculated stress and pressure of the wire. Therefore, the structure meets the requirements of safety and reliability.