# Measurement and Analysis of Downhole Drill String Vibration Signal
## 3 Result Analysis
### Time Domain Analysis of Vibration Signal
The regular wave crests in the radial acceleration are related to the centripetal force generated by the high rotational speed of the drill string during slippage, which indicates that the average value of the radial acceleration can directly reflect the torsional movement of the drill string. The average curve in Figure 7 shows that the torsional vibration of the drill string was relatively strong, and the axial vibration was weak. Moreover, it can be judged that the inclination angle was small, according to the average value of the axial acceleration being stable around 1 g.  
Figure 8 shows the peak, root mean square, and mean curve of the drill signal intercepted from 4740 m to 4750 m in a time window with a length of 100 signal points. It can be seen from the peak curve in Figure 8 that the peak curves of radial acceleration and tangential acceleration are chaotic and have a high degree of coincidence. The maximum value in the radial acceleration peak curve was 28 g, the maximum value in the tangential acceleration peak curve was 37 g, and the maximum value in the axial acceleration peak curve was 11.32 g. This indicates that the lateral vibration of the drill string was relatively severe, it may have had a relatively severe impact on the well wall, and the degree of axial vibration was weaker than that of lateral vibration. In the root mean square curve of Figure 7, the maximum value of radial acceleration was 4.96 g, the maximum value of tangential acceleration was 4.99 g, and the root mean square value of axial acceleration fluctuated up and down at the center of fluctuation slightly greater than 1 g. It can be known from the analysis of stick-slip vibration in the previous article that the change of speed has a great influence on radial acceleration; so, radial acceleration can reflect the intensity of torsional vibration. Rotation speed has little effect on tangential acceleration; so, tangential acceleration can reflect the severity of lateral vibration. It shows that in this segment of the signal, the torsional vibration of the drill string was as severe as the lateral vibration, and the axial vibration was the weakest. In the mean curve in Figure 8, the fluctuation center of tangential acceleration is slightly less than 1 g, the fluctuation center of radial acceleration is about 1.8 g, and the fluctuation center of axial acceleration is 1 g. This shows that the torsional vibration and lateral vibration of the drill string occurred at the same time. The torsional vibration was relatively strong, followed by the lateral vibration, and the axial vibration was the weakest; the coupling formed a whirl motion. From the small amplitude fluctuation of the axial vibration up and down 1 g, it can be seen that the inclination angle of the well in this section was very small. This is also consistent with the on-site situation. The effects of stick-slip and whirl are shown in Figure 9.  
Figure 9: Schematic diagram of stick-slip and whirl. Through the statistical analysis of the signal in the time domain, the method for judging the vibration mode of the drill string was preliminarily proposed, as shown in Table 5.