# Investigation on Eddy Current Sensor in Tension Measurement at a Resonant Frequency
## 4 Experimental Results and Discussion
### Sensor Performance at the Resonant Frequency  
#### 4.2.1 Impedance Magnitude  
As mentioned previously, the solenoid coil produces a circumferential current field into the test specimen, which creates an induced magnetic field that opposes the primary magnetic field. According to the variations of the impedance magnitude and phase, the eddy current sensor can detect the change of magnetic field caused by the external tension. Experimental analysis of the eddy current sensor was achieved by comparing the impedance magnitude signatures, as shown in Figure 9.  
From Figure 9, it can be observed that the peak value of the impedance at the resonant frequency decreased with the increase of the external tension. Thus, the external tension of ferromagnetic materials specimen can be detected by measuring the peak value of sensor impedance. The experimental data were fitted and linear relationship between the peak value of impedance and the external tension was obtained. To reduce experimental error, the peak value of impedance was extracted in Figure 10 by averaging the six experimental results. The statistics of the repetitive experiments are listed in Table 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Inductance** & **Resistance** & **Capacitance** \\ \hline Values & 176.5 \(\mathrm{\SIUnitSymbolMicro}\)H & 1.8 ohms & 182.9 pF \\ \hline \hline \end{tabular}
\end{table}
Table 1: Inductor–resistor–capacitor (LRC) parameters.  
Figure 8: Resonant frequency shift with different external capacitances.  
Table 2 demonstrates that the coefficient of variation is around 0.14% in the loading and unloading processes, which means that the variation among the different repetitive experiments is small and sensor performance is repeatable. Hence, these variations among repetitive experiments will not affect the usability of such a system where the mean values are used to draw conclusions. As seen from Figure 10, the peak value of impedance varies with the increasing tension in a good linearity with the linear regression equation \(y=-2.771x+1608.619\) and a correlation coefficient of \(R^{2}=0.991\) in Figure 9a,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Statistics**} & \multicolumn{1}{c}{**Mean Value**} & \multicolumn{1}{c}{**Variance**} & \multicolumn{1}{c}{**Coefficient of Variation (\%)**} \\ \hline \multirow{2}{*}{0 kN} & loading & 1610 & 2.27 & 0.14 \\  & unloading & 1607 & 1.53 & 0.10 \\ \hline \multirow{2}{*}{3 kN} & loading & 1600 & 1.49 & 0.09 \\  & unloading & 1596 & 1.07 & 0.07 \\ \hline \multirow{2}{*}{6 kN} & loading & 1590 & 0.94 & 0.06 \\  & unloading & 1588 & 1.11 & 0.07 \\ \hline \multirow{2}{*}{9 kN} & loading & 1583 & 1.07 & 0.07 \\  & unloading & 1580 & 0.90 & 0.06 \\ \hline \multirow{2}{*}{12 kN} & loading & 1577 & 1.57 & 0.10 \\  & unloading & 1575 & 0.94 & 0.06 \\ \hline \multirow{2}{*}{15 kN} & loading & 1567 & 1.70 & 0.11 \\  & unloading & 1567 & 1.70 & 0.11 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistics of the repetitive experiments.  
Figure 10: Fitted results between the impedance magnitude and the external tension in the (**a**) loading and (**b**) unloading processes.  
Figure 9: Impedance magnitude analysis of eddy current sensor in the (**a**) loading and (**b**) unloading processes.  
and the unloading process can be described with the linear regression equation \(y=-2.581x+1604.857\) and a correlation coefficient of \(R^{2}=0.986\) in Figure 9b. Therefore, the results indicate the existence of a good linear relationship between the peak value of sensor impedance and the external tension.