Sub-MHz EMAR for Non-Contact Thickness Measurement: How Ultrasonic Wave Directivity Affects Accuracy

Abstract

Electromagnetic acoustic resonance (EMAR) is a well-established non-contact method for ultrasonic thickness measurement, typically operated at frequencies above 1 MHz using an electromagnetic acoustic transducer (EMAT). This study successfully extends EMAR into the sub-MHz range, allowing supply voltages below 60 V and thus offering safer and more cost-effective operation. Experiments were conducted on copper blocks approximately 20 mm thick, where a relative thickness accuracy of better than 0.2% is obtained. Regarding this result, the research identifies a critical design principle: Stable thickness resonances and subsequently accurate thickness measurement are achieved when the ratio of ultrasonic wavelength to EMAT track width (λ/w) falls below 1. This minimizes the excitation and interactions with structural eigenmodes, ensuring consistent measurement reliability. To support this, the study introduces a system-based model to simulate the EMAR method. The model provides detailed insights into how wave propagation affects the accuracy of EMAR measurements. Experimental results align well with the simulation outcome and confirm the feasibility of EMAR in the sub-MHz regime without compromising precision. These findings highlight the potential of low-voltage EMAR as a safer, cost-effective, and highly accurate approach for industrial ultrasonic thickness measurements.

Keywords: EMAR limitations; EMAR simulation; electromagnetic acoustic resonance; electromagnetic acoustic transducer; thickness gauging.

Figure 1

Illustration of EMAT operating methods. (a) Pulse-echo method: A short pulse is emitted and caught again by the EMAT. By measuring the ToF of the wave packet, the thickness is estimated. (b) EMAR method: A standing wave is implied beneath the EMAT, where the thickness can be estimated from the resonance frequency.

Figure 2

(a) Top view of racetrack coil configuration used for the EMAT. Each track spans a width of $6.32$ mm. The red dotted square marks the area where the magnets are positioned. (b) 2D-Illustration of Lorentz force generation. A cross-section of the EMAT, including the racetrack coil and magnets on top, which provide the constant magnetic flux density, is shown. The color indicates the magnetic flux density $\overrightarrow{B}$ in y-direction.

Figure 3

Depiction of EMAR working principle. The EMAT impresses a wave along the thickness of the specimen, which is reflected back to the top. When the timing is exact, the reflected wave is constructively interfering with another impressed wave from the EMAT.

Figure 4

Test specimens used in this work. Two copper blocks are taken for the study. One has a thickness of $20.08$ mm and the other one $19.82$ mm, respectively. Those thickness values were determined with a caliper ( 10 μm resolution).

Figure 5

2D-FE model. The EMAT is centered on top of the 20 mm copper sample. It consists of the racetrack coil and stacked NdFeB magnets magnetically shorted on top with an iron bar. The EMAT is lifted off by $0.12$ mm from the copper surface. The surrounding domain is air.

Figure 6

Convolution output at the first and 16th resonance, representing the amplitude of the copper particle velocity within the ultrasonic wave. Although the resonance condition is met, no significant constructive interference is seen for the first resonance frequency. For the 16th resonance frequency, the output adds up nicely every time the wave returns from the bottom surface until the end of the excitation.

Figure 7

Computed EMAR resonances given by the simulated step response and further computation.

Figure 8

Simulated standing wave motion inside the copper block in terms of velocity in x-direction at 15.85 μs. (a) First resonance frequency. (b) 16th resonance frequency.

Figure 9

Schematic illustration of the measurement setup. The input stage provides the high current for driving the EMAT. The commonly used decoupling network allows for the EMAT to be used as transmitter and receiver. The received EMAT voltage is amplified and stored within the data acquisition block. The last part is considered the EMAT itself.

Figure 10

Measurement setup used in laboratory environment. 1: Power amplifier with power supply; 2: Current probe; 3: Amplifier for the measured EMAT signal and power supply; 4: Picoscope (Signal generator and data acquisition); 5: Pre-amplifier and power supply; 6: EMAT on copper block; 7: Decoupling network.

Figure 11

Measured current amplitude during the EMAT excitation and corresponding calculated voltage provided by the power amplifier.

Figure 12

(a) Exemplary unfiltered output from the signal amplifier at excitation frequency of 658 kHz. (b) Zoom into the bandpass filtered EMAT time signals for excitation frequencies of 655 kHz and 658 kHz within the 500 μs evaluation window.

Figure 13

Measured EMAR spectrum in the frequency range from 40 kHz up to 1 MHz. In blue, the spectrum for the $20.08$ mm block is shown and in red the spectrum for the $19.82$ mm block is depicted. Furthermore, the predicted resonance frequencies for each thickness are included.

Figure 14

Measured resonance peak at the vicinity of the 11th resonance frequency. From the Gaussian fit, the resonance frequency of the peak is estimated (dashed black line). Also plotted is the predicted resonance frequency (black).

Figure 15

Estimated thickness from n evaluated resonance frequencies from measurement and simulation.

Figure 16

Absolute value of the relative deviation from the true thickness value for the measurements on the $20.08$ mm and $19.82$ mm copper block and for the simulation of the 20 mm block.

Figure 17

Ratio of wavelength $\lambda$ over track width w versus the estimated resonance frequencies for the $20.08$ mm and $19.82$ mm copper block.