# Bol Looseness Detection Based on Piezoelectric Impedance Frequency Shift
## 3 The Experimental Setup and Process
### Experimental Processes  
In the experiment, the tensile force is set from zero to the maximum nominal preload. In each step of steady-state load, the piezoelectric impedance of the PZT patch is captured by the WK6500B impedance analyzer ([PERSON], West Sussex, UK).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Density & \(\rho\) & 7800 kg/m\({}^{3}\) \\ Piezolectric constant & \(d_{31}\) & \(150\times 10^{-12}\) C/N \\ Dielectric constant & \(\varepsilon_{31}^{T}\) & \(1.3\times 10^{-8}\) F/m \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of PZT.  
Figure 1: Schematic diagram of the bolt clamp.  
Figure 2: Testing device.  
Before the experiments, a proper sweep frequency band should be chosen to identify the frequency of interest. In this paper, the preliminary sweep frequency range is set from 2 KHz to 5 MHz, and the piezoelectric admittance signature was acquired by the impedance analyzer. It is found that the susceptance (the imaginary part of admittance) [37] changes more regularly with frequency, as shown in Figure 3. In Figure 3, there exists a peak in the susceptance plot for both M16 and M12 bolts. The peak frequencies for M16 and M12 are about 3.92 MHz and 4.12 MHz, respectively. In the subsequent refining sweep frequency analysis, these peak frequencies are chosen as the specified frequencies, and the sweep frequency bandwidths are around these frequencies. For a tested bolt, the specified peak frequencies were measured under no-preload and rated preload, respectively. Then the sweep frequency band is started at a point before the non-preload peak frequency and ended at a point behind the rated-preload peak frequency for the experiments.  
Figure 4a shows the conductance (the real part of admittance) plot with sweep frequency from 3.91 MHz to 3.932 MHz of the M16 bolt under different bolt preload. The peak frequency (resonance frequency of a certain order) is about 3.93 MHz without a preload and it is selected as the specified frequency for tracking its shift. As the bolt preload increases, the specified peak frequencies shift to the left side, which means it decrease. Based on this discovery, the specified frequency is chosen as an indicator to characterize the bolt preload. For the susceptance of admittance signature, it also has such a trend, as shown in Figure 4b, and the amplitude of the susceptance is larger than that of the conductance [37]. This is different from the previous studies that most of them used the conductance to establish the damage index, and in this approach the imaginary part of admittance can also be used as a feature parameter of bolt preload. For the decrease of the frequency as the increase of the bolt preload, it is mainly due to the sensing region of the piezoelectric transducer is focused on the bolt head in such high scanning frequency band. The stress status of the bolt head (a state of compressive stress) changed with the increase of the bolt preload, and that cause the piezoelectric transducer also in a compressive state. Since the resonance of the piezoelectric transducer is mainly affected by its mechanical and physical properties, but not the electrical properties, the compressive stress state causes the mechanical and physical properties of the PZT transducer to change and thus leads to the decrease of the frequency [39; 40].  
Figure 3: Susceptance changes with frequency of (**a**) M16; and (**b**) M12 bolts.