# Measurement and Analysis of Downhole Drill String Vibration Signal
## 3 Result Analysis
### Time Domain Analysis of Vibration Signal
However, after about 3 s of stagnation, the radial acceleration and tangential acceleration increased to their peak values in a dominant manner, indicating that the drill string was rotating again. Axial acceleration also has a similar changing law. The difference is that the stable value of axial acceleration when it tends to stagnate is 1 g, which is consistent with the gravitational acceleration in a vertical well. It can be seen that the period of stick-slip vibration under this working condition was 10 s, in which the viscous phase was 7 s and the slip phase was 3 s.  
In Figure 6, the three-axis acceleration is disorderly. The radial acceleration fluctuated from 2 g up and down, the fluctuation range was large, and the overall range of change reached 50 g. The fluctuation center of the tangential acceleration was slightly less than 2 g, and the overall fluctuation amplitude was roughly equal to the radial acceleration. It can be seen from Equations (1) and (2) that radial acceleration is more sensitive to changes in speed, while tangential acceleration is more representative of lateral vibration. The axial vibration acceleration fluctuation center was approximately 1 g, which was approximately equal to the gravitational acceleration in a vertical well. From the overall change of the time-domain signal, it can be seen that the degree of lateral vibration and torsional vibration of the drill string was more severe than the axial vibration, but the vibration mode cannot be judged only from the time-domain signal. Figure 5: Timing chart of drilling signals intercepted from 4700 m to 4720 m.  
Peak value, mean value, and root mean square calculation methods are as follows:  
\[X_{p}=\max\{\,|x_{i}|\} \tag{4}\]  
Mean value:  
\[\overline{X}=\frac{1}{N}\underset{i=1}{\overset{N}{\underset{i=1}{\sum}}}x_{i} \tag{5}\]  
Root mean square:  
\[X_{rms}=\sqrt{\frac{1}{N}\underset{i=1}{\overset{N}{\underset{i=1}{\sum}}}x_{i }^{2}} \tag{6}\]  
In the peak curve of Figure 7, the changes of radial acceleration and tangential acceleration are highly similar. The maximum radial acceleration peak is 5.73 g, the maximum tangential acceleration peak is 4.50 g, and the axial acceleration peak fluctuates slightly above 2 g. This shows that the lateral vibration of the drill string during this period was relatively strong, accompanied by weaker axial vibration. The root mean square value of acceleration can reflect the vibration energy of the drill string. Figure 7 shows that, in the viscous phase, the root mean square of the radial acceleration and the tangential acceleration are both at a low level. The maximum value of the root mean square value of radial acceleration reached 1.83 g, the maximum value of root mean square value of tangential acceleration reached 1.57 g, and the root mean square value of axial acceleration fluctuated with a very small amplitude around 1 g. This shows that the drill string had the largest lateral impact energy on the borehole wall in the process of stick-slip vibration, followed by torsional vibration energy, and axial vibration was the smallest. From the mean value curve in Figure 7, the value of tangential acceleration was the smallest, the mean value of tangential acceleration fluctuated slightly above and below 0.7 g, and the maximum value did not exceed 1 g. The mean value of radial acceleration varied greatly, the maximum value reached 1.7 g, and the minimum value of the mean value in the viscous phase was not much different from the average level of the mean value of tangential acceleration. The average value of axial acceleration fluctuated slightly above and below 1 g. This shows that  
Figure 8: The peak value, root mean square value, and mean value curve of the time domain signal intercepted from the 4740–4750-m section according to a time window with a length 100 of signal points. the mean value of tangential acceleration is related to lateral vibration.