# Measurement and Analysis of Downhole Drill String Vibration Signal
## 3 Result Analysis  
### Time Domain Analysis of Vibration Signal  
In the entire igneous rock drilling, the downhole collapse and block falling accidents frequently occurred, especially at the depths of 4700-4720 m and 4740-4750 m. The drilling parameters are shown in Table 4. Therefore, a representative time-domain signal was selected for analysis in the two segments of drilling vibration signals. To study the vibration of the downhole drilling tool during these two sections of drilling, we intercepted the time-domain signal analysis with a higher proportion in the two segments of signals. The signal types shown in Figures 5 and 6 both account for more than 40% of the vibration signals in the 4700-4720-m and 4740-4750-m segments, respectively. We analyzed its characteristics in the time domain. The three-axis acceleration signals in the signal shown in Figure 5 all exhibit periodic fluctuations in the time domain, and the fluctuation laws are the same. Tangential acceleration and radial acceleration fluctuated sharply above and below the 0 value, but the amplitude of the radial acceleration value in the negative direction was greater than the amplitude in the positive direction. The axial acceleration fluctuated around 1 g. The vibration amplitude of radial acceleration and tangential acceleration was basically about 7 g, and the amplitude of axial acceleration was 2 g. It was found that the tangential acceleration was less affected by the speed change than the radial acceleration from Equations (1) and (2), indicating that the lateral vibration of the drill string in the downhole was more severe than the axial vibration. In the intercepted signal segment, the tangential acceleration and radial acceleration were close to 0 g simultaneously after a wave packet of signal appeared. This may have been due to factors such as bending or shrinkage of the borehole wall when the drill string moved downhole, and friction with the borehole wall inevitably occurs. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Depth** **(m)** & **WOB** **(kN)** & **Rotating Speed** **(RFM)** & **Torque** **(kN\(\cdot\)m)** & **Fluid Inlet** **Temperature** (°C) & **Fluid Outlet** **Temperature** (°C) & **Pump Volume** **(SPM)** \\ \hline
4700–4720 & 30–68 & 43–49 & 11–14 & 46 & 55 & 150 \\
4740–4750 & \(-\)1.3–84 & 43–49 & 8–15 & 44 & 52 & 120 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Drilling parameters of vibration data collection section. Figure 4: Schematic diagram of drill string vibration pattern. When the friction is large enough, the drill string stops rotating due to excessive resistance. At this time, the downhole torque will gradually accumulate. When the torque is accumulated enough to overcome the frictional resistance torque, the drill string will be released instantly, thus forming a viscous phase and a slip phase. When the axial acceleration is gradually close to 1 g and continues for a period of time, and when the values of radial acceleration and tangential acceleration tend to 0 g, it indicates that the rotation of the drill string gradually stops and is stable in a stagnant state. It can be seen from the alternating appearance of wave packets in the time domain signal. At this time, the drill string was in a state of 'rotation-stagnation-rotation', which is also consistent with the movement characteristics of stick-slip vibration. It shows that the vibration represented by this type of signal in igneous rock drilling is stick-slip vibration. In the time interval of 20-30 s in Figure 5, the radial acceleration gradually converged from \(-4\) g to 0 g, indicating that the centripetal force experienced by the sensor gradually decreased to 0, and, at the same time, that the drill string rotation speed gradually decreased to 0. This process lasted about 7 s. In Figure 5, the tangential acceleration also gradually decreased from the peak value to 0 g. This shows that the torsional vibration and lateral vibration of the drill string gradually decreased until it stops.