# Research on Hybrid Vibration Sensor for Measuring Downhole Drilling Tool Vibrational Frequencies
## 3 Experiments
### Sensing Performance Experiments  
The sensor measures the vibration frequency through the TENG unit and the PENG unit. We tested the output signals of the sensor at different vibration frequencies, and then captured portions of the signal waveform, as shown in Figure 8. From the perspective of waveform frequency, for both the TENG unit and the PENG unit, the frequencies of their output voltage and current signals increase with the increase in vibration frequency. This is consistent with the working principle we analyzed, confirming that the sensor can measure vibration frequency. From the perspective of waveform peak values, as the input vibration frequency increases, the voltage of the TENG unit remains essentially unchanged, while the current shows an increasing trend. Conversely, both the voltage and current of the PENG unit show an increasing trend. During drilling operations, the vibration frequency of downhole drilling tools is typically related to the rotation speed of the drill bit and usually remains within 10 Hz. However, in cases of uneven formation distribution, high-frequency vibration signals may also occur. Figure 9 shows the experimental results of the HDV-TENG sensing performance experiments. HDV-TENG can measure vibration within the vibration frequency of 1-200k Hz and output stable waveform. Therefore, the frequency measurement range of the sensor can meet the requirements of actual working conditions. For the TENG unit, as the vibration frequency increases, the peak output voltage remains generally stable, with only a very slight increasing trend. When the vibration frequency is 10 Hz, the output voltage reaches approximately 15.6 V. For the PENG unit, the peak output voltage also increases with the increase in frequency, and when the frequency is 200k Hz, the output voltage reaches about 54 V. During the experimental process, we also observed deviations in the measurement results due to factors such as the structural design of the sensor and  
Figure 8: Output signal test of sensor. (**a**) Output voltage signal of TENG at different vibration frequencies; (**b**) output current signal of TENG at different vibration frequencies; (**c**) output voltage signal of PENG at different vibration frequencies; (**d**) output current signal of PENG at different vibration frequencies. uneven vibrations. Therefore, we evaluated the measurement accuracy of the sensor. The accuracy of vibration frequency measurement is expressed by deviation:  
\[Deviation=\frac{f1-f2}{f2}\times 100\%\]  
Among them, \(f1\): measured frequency; \(f2\): actual vibration frequency. The frequency is measured by TENG at the low frequency of 1 to 10 Hz, and its output voltage keeps steady with the increase in frequency, as shown in Figure 9a. Statistical calculation of the deviation of vibration frequency measurement at different frequencies shows that the deviation of HDV-TENG measurement at the frequency of 1 to 10 Hz is less than 5%, which meets the requirements of downhole working conditions, as shown in Figure 9b. The frequency measurement is carried out by PENG at medium and high frequencies of 10 to 200k Hz; the output voltage increases with the increase in frequency, and the change relationship is shown in Figure 9c. The measurement of PENG also adopts the deviation index. Through statistical calculation, it can be seen that the deviation of the measurement frequency of 10 to 200k Hz is less than 10%, while the vibration frequency does not exceed 10k Hz in the downhole condition, and the corresponding deviation is less than 9%, which meets the downhole measurement accuracy requirements. as shown in Figure 9d. In conclusion, within the frequency range of 1 to 10 Hz, due to the smaller measurement deviation of TENG compared to PENG, we utilized the signal from the TENG component as the sensing signal. However, after the vibration frequency exceeded 10 Hz, the measurement deviation of the TENG component gradually increased, surpassing that of PENG, and its output voltage was also smaller than that of PENG.