# Measurement and Analysis of Downhole Drill String Vibration Signal
## 3 Result Analysis
### Frequency Analysis of Vibration Signal
#### 3.2.2. Whirl  
Field logging data indicated that the wall of the well was severely dropped in the igneous rock drilling process, indicating that the drill string may have laterally vibrated and collided with the wall of the well. When the lateral vibration and torsional vibration of the downhole drill string are coupled, the motion state of the drill string changes to whirl. Whirl is a motion in which the drill string undergoes both revolution and rotation. The time-frequency analysis of the whirl vibration signal in Figure 6 was performed. Figure 15 is a spectrum diagram of the whirl time-domain signal drawn by the fast Fourier method (FFT). The amplitude of the three-axis acceleration was not high, but the frequency of the tangential acceleration spectrum was relatively rich. In addition, both tangential acceleration and axial acceleration had a dominant frequency of 155.5 Hz, while  
Figure 14: Time-frequency diagram of axial acceleration of stick-slip vibration. Figure 13: Time-frequency diagram of tangential acceleration of stick-slip vibration. the dominant frequency of 155.5 Hz in radial acceleration was not obvious. It can be seen from the frequency spectrum that the lateral vibration occurring in the movement of the drill string was very likely to have coupled vibration with the axial vibration. We extracted the frequency between 0-0.5 Hz in the spectrum for analysis, as shown in Figure 15. All three-axis acceleration signals had a dominant frequency of 0.05341 Hz, which is very likely to be related to the natural frequency of the drilling tool. Figures 16-19 are time-frequency diagrams obtained by analyzing the whirl signal using short-time Fourier transform (DFT). It can be seen from Figures 16 and 17 that the radial acceleration frequency distribution of the drill string presented a disorderly shape in a short period of time. Additionally, the frequency was basically below 200 Hz. However, in the entire time interval, the energy spectrum density changed with a period of slightly less than 20 s. This cycle was also basically consistent with the main frequency of 0.05341 Hz in Figure 16. It can be seen from Figure 18 that the tangential acceleration frequency distribution was irregular, but the two main frequencies of 145.7 Hz and 155.5 Hz always existed, and there was a peak of energy spectral density approximately every 20 s. As shown in Figure 16, the frequency distribution of the axial vibration acceleration signal was similar to that of the tangential acceleration signal. There is always a dominant frequency of 155.5 Hz, and the change law of the energy spectral density was similar to that of the tangential acceleration. To sum up, it can be seen that during the drilling of igneous rock, the drill string motion whirled and it was accompanied by slight axial vibration. acceleration was particularly obvious. During the 4740-4750-m drilling process, whirl accounted for about 50% of the total drilling time. Through the time-frequency analysis of the signal (Table 6), it was found that the frequencies that play a major role in the occurrence of stick-slip vibration are 0.1221 Hz, 145.9 Hz, and 155.9 Hz. Among them, 0.1221 Hz is consistent with the period of stick-slip vibration, and 0.3967 Hz is approximately three times the frequency of 1.221 Hz. When the flow of drilling fluid is stable, the impact frequency of the torsional impactor is 50 Hz. Additionally, 145.9 Hz and 155.9 Hz are close to the triple frequency of the torsional impactor. The remaining high-frequency signals are most likely to be the coupling vibration frequency of the torsional impactor and the jar or the coupling vibration frequency of the drill bit and the jar 0.05341 Hz plays a major role in the occurrence of whirl, and this frequency is close to the whirl period. The effects of 145.9 Hz and 155.9 Hz were weaker than 0.05341 Hz, and the two main frequencies of 145.9 Hz and 155.9 Hz did not appear in  
Figure 16: Time-frequency diagram of radial acceleration of whirl.