# Piezoelectric Sensor with a Helical Structure on the Thread Core
## 4 Results
### Output Voltage of the Sensor According to Bending Input Variation  
We investigated the sensing response of the piezoelectric sensor with variations in \(\Phi_{0}\). Flexural loadings with varying \(\Phi_{0}\) at the nominal frequencies of 0.8, 1.2, 2, and 3 Hz were applied to the piezoelectric sensor. Specifically, \(\Phi_{0}\) was increased from \(1.5^{\circ}\) to \(30^{\circ}\), and each experiment was repeated five times. We utilized the average value of the peak-to-peak voltages, \(V_{0}\), from the repetitive experiments. Figure 5 shows \(\Phi_{0}\) with respect to \(V_{0}\). Therein, the plotted values are not nominal, but measured. We conducted the power fitting of \(\Phi_{0}\) according to \(V_{0}\), at \(f=1.2\) Hz, to study the \(\Phi_{0}\)-\(V_{0}\) relation of the piezoelectric sensor; that is,  
\[\Phi_{0}=\psi V_{0}^{\eta} \tag{1}\]  
where \(\psi\) and \(\eta\) indicate the gain and exponent of the \(\Phi_{0}\)-\(V_{0}\) relation, respectively. The fitted \(\Phi_{0}\)-\(V_{0}\) relation for the sensor had \(\psi\) of 2.47 and \(\eta\) of 1.29 and was consistent with the experimental result with an R-squared value of 0.998. Based on the fitted result, the bending angle applied to the sensor could be predicted by observing the peak-to-peak voltage of the piezoelectric sensor with good precision. To study the sensitivity and resolution of the proposed sensor, we linearly fitted \(\Phi_{0}\) having a range from \(5^{\circ}\) to \(29^{\circ}\) according to \(V_{0}\). The fitted result showed high resemblance to the experimental result with an R-squared value of 0.9931. Herein, the piezoelectric sensor had a sensitivity of 4.874\({}^{\circ}\)/V. Additionally, considering the ADC (analog-to-digital converter) of the DAQ board (\(\pm\) 10V range and 16 bit channel), the sensor had a resolution of \(1.5\times 10^{-3}\).  
Figure 4: **(a)** Flexural loading applied to the sensor and **(b)** voltage output of the piezoelectric sensor. The red solid lines and dotted lines represent the bending angle and sine-fitted bending angle, respectively. The blue solid lines and dotted lines represent the voltage output and sine-fitted result of the piezoelectric sensor, respectively.  
We additionally investigated the sensing response of the sensor according to various operating frequencies. Flexural loadings were applied with the operating frequencies ranging from 0.8 Hz to 3 Hz at \(\Phi_{0}\) of 10\({}^{\circ}\), 20\({}^{\circ}\), and 29\({}^{\circ}\). Figure 6 shows the peak-to-peak output voltage according to the operating frequency. The peak-to-peak voltage outputs remained approximately constant with a maximum difference of 14% according to the frequency shift. Specifically, when flexural loadings having a frequency of 0.8 Hz were applied to the sensor, the peak-to-peak voltage output of the sensor had a smaller amplitude than when flexural loadings having higher frequencies were applied. We note that the difference of peak-to-peak voltage was due to the larger internal impedance of the sensor at a lower frequency, which resulted in a more imperfect open-circuit condition.