# Measurement and Analysis of Downhole Drill String Vibration Signal
## 1 Introduction  
In the process of oil field development and oil and gas reservoir exploration, drilling is a project with high-cost and high-risk characteristics. Researchers have discovered one of the factors affecting the low drilling efficiency when the harmful vibration of the drill string occurs downhole [1, 2, 3, 4, 5, 6, 7], which is also one of the reasons for the increase in drilling costs [8, 9, 10]. In order to control drilling costs and improve drilling efficiency, drill string vibration has become a long-term focus of researchers in the drilling industry [11, 12]. The vibration of the drill string downhole can generally be divided into four patterns: longitudinal vibration, transverse vibration, torsional vibration, and whirl [13]. When the drill string vibrates longitudinally, the drill bit will repeatedly jump off the bottom of the well, causing great damage to the PDC bit [14, 15]. [PERSON] et al. established a model to cause downhole drilling tool damage mainly due to lateral vibration [16]. Torsional vibration is inevitable during the drilling process. [PERSON] et al. found that when the frequency of torsional vibration reaches above 50 Hz, torsional vibration can cause fatigue damage to the drilling tool [17]. When the severity of torsional vibration increases until the rotation of the drill string can be stagnated, the torsional vibration is transformed into a more harmful stick-slip vibration [5, 18]. Whirl is a kind of bending vibration caused by the eccentricity of drill string rotation, and it is also an important reason for downhole drilling tool failure [18, 19, 20]. In order to study the vibration of downhole drilling tools, since the 1970s, researchers have established mathematical models to study the vibration of downhole drilling tools [21; 22]. However, in actual drilling operations, due to the presence of drilling fluid in the borehole, the vibration of the drill string is complicated and difficult to quantify [23; 24]. Therefore, another focus of drill string vibration research is on dynamic measurement. At present, most petroleum service companies use measurement acceleration to achieve dynamic measurement of downhole drilling tools [1] and have developed a drill string vibration measurement and analysis system that can be put on the market [25; 26; 27]. As early as 1993, Baker Hughes developed a ground measurement system for drill string vibration mounted on kelly [28], and later developed a near-bit measurement tool with eccentric accelerometers [13]. Hallibutton developed a vibration measurement tool DDS with a three-axis accelerometer eccentrically mounted in 1998 [13]. In order to solve the problem of real-time signal viewing, Schlumberger developed a vibration measurement system that uses a mud pulse system to transmit signals in real time. The system installs an orthogonal, three-axis accelerometer on the axis of the measurement device [29; 30; 31]. APS company independently developed a drill string vibration measurement system DVMS [32] that installs a three-axis accelerometer radially along the radius of the measuring device. Among the three existing acceleration sensor installation methods, the acceleration sensor installation method of the storage drill string vibration measurement equipment in this article is the same as that of Baker Hughes and Hallibutton, which belong to the eccentric installation method of the acceleration sensor. The research group used this measuring device to collect the near-bit drill string vibration signal during the drilling of an oil well. We intercepted the drilling signal of the igneous rock section. We analyzed the drill string vibration pattern reflected by the vibration signal through the peak value, average value, and root mean square value of the signal. Additionally, through fast Fourier transform [33] and short-time Fourier transform [34] methods, we analyzed the time-frequency characteristics of vibration signals.