# Measurement and Analysis of Downhole Drill String Vibration Signal
## 2 Principle and Method of Drill String Vibration Measurement  
### Principle of Drill String Vibration Measurement  
The downhole drilling tool assembly used in this vibration data collection is shown in Figure 1. In order to reduce the impact of the jar and the torsion device on the vibration measurement signal, the vibration measurement equipment was installed 32 m above the drill bit, 30.25 m from the lower torsion impactor, and 99 m from the upper jar. The vibration measurement equipment was connected with the torsion impact device and the jar by drill collars. The dimensions of the main downhole drilling tools are shown in Table 1.  
In deep or ultra-deep well drilling, the borehole environment is harsh. Downhole measuring instruments need to work in high-temperature and high-pressure environments. Therefore, a reliable and effective measuring device is a prerequisite for analyzing drill string vibration. This research group developed a vibration measurement equipment based on the investigation of the current development status of existing measurement equipment. The purpose of this equipment is to install the three-axis acceleration sensor radially eccentrically on the measuring sub body. The specific principle is shown in Figure 2. The sensor was installed on the measuring sub body with a certain eccentricity \(R\). It started to move with the rotation of the drill string and collected the composite signal of the revolution and rotation of the drill string. The specific parameters of the acquisition sensor are shown in Table 2.  
Figure 1: Schematic diagram of installation of drilling tool assembly and vibration measuring equipment. Figure 2: Schematic diagram of field installation of vibration measuring equipment. **(a)**, \(c\) represents the center of the drill string, \(S\) is an orthogonal three-axis acceleration sensor, \(A\) is the cross section of the column, \(r\) is the radius of the drill string, \(X\) measures the acceleration of drill string tangential vibration, \(Y\) measures the radial vibration acceleration of the drill string, and \(Z\) measures the axial vibration acceleration of the drill string. **(b)** shows the sensor installation method on site. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number** & **Name** & **Length (m)** & **Diameter (in)** \\ \hline
1 & DC & 18 & 8 \\
2 & Vibration Impactor & 9 & 8 \\
3 & DC & 99 & 8 \\
4 & Vibration Measuring Equipment & 0.45 & 8 \\
5 & DC & 30 & \(8\times 1+9\times 2\) \\
6 & Torsion Impactor & 0.75 & 9.6 \\
7 & PDC Bit & - & 13 \\ \hline \hline \end{tabular} Note: The table only describes the main tool size in the drill tool assembly, which does not include the specific parameters of the adapter.  
\end{table} 
Table 1: Drill tool assembly size. The three-axis acceleration sensor was eccentrically installed on the body of the drill string vibration measurement equipment. The three orthogonal axes of the accelerometer respectively measure the axial vibration acceleration of the drill string, the radial vibration acceleration of the measuring point where the sensor on the drill string is pointing to the axis of the drill string, and the tangential acceleration of the sensor on the motion trajectory. The designed completion depth of the logging well is 8054 m, and igneous rock was encountered in the Permian well at a depth of 4565-5020 m. In the process of drilling into the igneous rock, the borehole wall collapsed and blocks frequently occurred. Therefore, this vibration measurement mainly collected vibration data with a depth of 4565-5020 m. The measurement equipment setting parameters and downhole environment are shown in Table 3. After the igneous rock drilling data acquisition was completed, the vibration measurement equipment stored the signal in real time. As the drilling tool was replaced and brought to the ground, the collected data are shown in Figure 3.