Drill string vibration is a widely studied topic. This paper developed a real-time measurement system near the drilling bit and extracted the lateral vibration, longitudinal vibration time series of bottom rotating drill string. In order to reconstruct the phase space, we estimated the delay time with mutual information and calculated the embedding dimension through Cao’s method. Finally, the chaotic characterization of the system is analyzed by calculating the correlation dimension and the largest Lyapunov exponent. The results show that such system can exhibit positive finite-time Lyapunov exponents and a clear convergence toward the correlation dimension, which is a strong indicator for the chaotic behavior of the system. It is expected that the new dynamics found in this paper could be of potential implication to the control methods of the drill string vibration. 1. Introduction In oil and gas drilling engineering, the well is created by drilling a hole 5 to 50 inches (127.0？mm to 914.4？mm) in diameter into the earth with a drilling rig that rotates a drill string with a bit attached. In the process, severe drill string vibration is a major contributor to downhole tool failure. It may also cause hole damage and increase the need for more frequent rig repair. Typically, the drilling string vibration can be divided into three types or modes: lateral, longitudinal, and torsional. The destructive nature of each type of vibration is different. Lateral and longitudinal vibrations of the drill string have been undertaken extensive research since it proposed from mid-1960s, The main reason that caused the fatigue failure of the bottomhole assembly (BHA) [2] was considered to be the vibration of the drill string. Many studies of the drill string focused on the determination of natural frequencies [3, 4], bending stress calculation [5, 6], stability analysis [7], lateral displacement prediction [8], and so forth. Spanos et al. [9] established the finite element model of drill string lateral vibration and analyzed nonlinear random vibration. Chunjie and Tie [10] obtained the natural frequency of drill string longitudinal vibration from a finite element model. Vibrations of all three types (lateral, longitudinal, and torsional) may occur during rotary drilling and are coupled. Single vibration model cannot well describe the dynamics of BHA; furthermore, to establish a precise bottom hole kinetic theory model is difficult to achieve because of the underground complex situation. Additionally, the process of drill bit break rocks is a nonlinear process which is
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