# Study on Molybdenum-Rhenium Alloy Ultrasonic Resonance Temperature Sensor
## 3 Results
### Calibration Experiment  
After completing the construction of the temperature measurement system, the ultrasonic resonant temperature sensor with the same parameters as the simulation model was prepared, and its design parameters are shown in Table 2 below. In order to verify the performance, the assembled sensor was placed in the calibration furnace for static calibration experiments [30]. Before the calibration experiment, the temperature range of the calibration furnace was set from room temperature to 1800 \({}^{\circ}\)C, and the temperature was kept for 5-10 min after every 100 \({}^{\circ}\)C rise to make sure that the temperature field in the furnace was uniform, that the sensor maintained a stable working state, and that the temperature-frequency relationship curve of the sensor was obtained. During the process of temperature increase/decrease, the intrinsic frequency of the resonator changes according to the temperature change. The resonance phenomenon in the echo waveform was observed by adjusting the frequency meter, and data acquisition was performed. The resonance waveforms at different temperatures are shown in Figure 8. The resonance waveform amplitude gradually decreases with the increase in temperature, and there is a cross-zero phenomenon. The temperature-resonant frequency relationship curves obtained by polynomial fitting during the temperature increase/decrease process are shown in Figures 9 and 10. The experiments show that when the molybdenum-rhenium alloy is used as the sensitive element for temperature measurement, a nonlinear relationship between frequency and temperature is presented. When the temperature changes in the range of room temperature to 1800 \({}^{\circ}\)C, the physical properties of the waveguide rods change accordingly, affecting the acoustic-wave-propagation speed. As the temperature increases, the propagation speed of sound waves in the medium gradually slows down, resulting in a lower resonator frequency. The average resonance frequency at room temperature is 341.8 kHz when \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sensor** & **Length \(L\)** & **Cone Face** & **Diameter \(d_{1}\)** & **Diameter \(d_{2}\)** & **Cone Length \(L_{1}\)** & **Resonator Length \(L_{2}\)** \\ \hline Parameters/mm & 1000 & 0.83 & 2 & 9.5 & 19 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Ultrasonic resonant temperature-sensor design parameters. Figure 7: Acoustic pressure propagation in the resonator: (**a**) 342 kHz, (**b**) 309 kHz. warming up, while it decreases to 310.37 kHz at 1800 \({}^{\circ}\)C; the average resonance frequency at 1800 \({}^{\circ}\)C is 309 kHz when cooling down. Based on the relationship between the change of the resonance frequency and the change of the temperature, the average sensitivities are calculated to be 17.66 Hz/\({}^{\circ}\)C and 18.43 Hz/\({}^{\circ}\)C, respectively. Figure 8: Resonance waveforms at different temperatures. Figure 9: Temperature–frequency curve during temperature rise. By analyzing the frequency dispersion curves in Figure 5, it can be seen that in the frequency range of (300-400) kHz, the propagation velocity of acoustic waves in the waveguide changes due to the physical properties of the material, which exhibits an obvious dispersion effect and affects the frequency change. Further combined with the experimental results in Figures 9 and 10, it can be seen that under different temperature conditions, the change of propagation velocity within the waveguide also varies with temperature, which affects the operating frequency of the resonator, resulting in a slightly smaller value of the resonant frequency at each temperature in the practical test. Based on the resonance frequencies corresponding to different temperatures, a polynomial fitting was used to establish the functional relationship between the average resonance frequency of the resonator during a temperature rise and fall and the measured ambient temperature as follows:  
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