# Research on Hybrid Vibration Sensor for Measuring Downhole Drilling Tool Vibrational Frequencies
## 2 Structure and Principle
### Working Principle of HDV-TENG  
Figure 2a shows a cross-sectional view of the HDV-TENG, which supplements the structure of the HDV-TENG. During the working process of the drill pipe, the TENG, PENG, and EMG work together. The working principle is shown in Figures 3-5; the floating block vibrates with the vibration of the drill pipe under the action of magnetic force, and the cylindrical protrusions on the suspension block contact and rub the copper electrodes to form an independent layer working mode. The physical photo and SEM image of the PTFE material in the TENG component are shown in Figure 2b.  
Figure 1: Schematic diagram of HDV-TENG structure. (**a**) Schematic diagram of drilling and installation of HDV-TENG; (**b**) schematic diagram of HDV-TENG structure.  
Figure 2: HDV-TENG working principle. (**a**) HDV-TENG cross-section; (**b**) physical photos and SEM pictures of PTFE.  
During the rising process, the surface of the upper copper electrode generates positive induced charges, and the lower copper electrode generates negative induced charges due to the passage. The current direction at this time is calibrated to be positive, and the output is positive. For the pulse wave, when the floating block descends, oppositely induced charges are generated on the surfaces of the two copper electrodes. The current direction is calibrated to be negative at this time, and a negative pulse wave is output; the charge transfer is shown in Figure 3 I-IV. The current output equation for the TENG part is [41]  
\[RA\frac{d\sigma_{I}(z,t)}{dt}=z\sigma_{c}/\varepsilon_{0}-\sigma_{I}(z,t)[d_{1} /\varepsilon_{1}+d_{2}/\varepsilon_{2}+z/\varepsilon_{0}]\]  
Among them, \(\sigma_{I}\) is the variation of free electrons in the electrode over time, and \(\sigma_{c}\) represents the surface charge density of the friction material.  
Figure 4: PENG working principle.  
Figure 3: TENG working principle.  
The vertical vibration of the floating block acts on the bottom magnet in magnet group 2 through the magnetic force, so that the piezoelectric ceramic sheet is deformed by force, and opposite charges are induced on the surface of the piezoelectric ceramic sheet, resulting in a potential difference, and the calibration output current is positive. After the upward vibration magnetic force is weakened, the deformation of the piezoelectric ceramic sheet recovers, the potential difference decays to 0, the current also becomes 0, and a positive pulse wave is output, the charge transfer is shown in Figure 4 I-IV. The current output equation for the PENG part is [42]  
\[RA\frac{d\sigma}{dt}=z[\sigma_{p}(z)-\sigma(t)]/\varepsilon\]  
Among them, \(A\) is the electrode area, and \(z\) is a function of time \(t\).  
During the vibrating process of the floating block, the copper coil cuts the magnetic field lines between the magnet groups 1 and 2 to induce electromotive force, leading to generating voltage and current, and the current changes are shown in Figure 5 I-IV.  
The acquisition of vibration frequency is realized by two parts, including TENG and PENG, corresponding to the vibration measurement of low frequency and medium-high frequency, respectively. The measurement method obtains the real-time vibration frequency by calculating the number of pulse waves per unit time. In comparison to TENG and PENG, the output power of the EMG part is higher; thus, the collection of vibration energy is mainly achieved by the EMG part. The functions of each part of the sensor, as shown in Figure 6, indicate that the TENG part is responsible for measuring low-frequency vibrations, the PENG part is responsible for measuring high-frequency vibrations, and the EMG part implements the power generation function of the sensor.  
Figure 5: EMG working principle.