Investigation of drill string dynamics using probabilistic methods

The object of research is a drill string. The work is directed to the study of the drill string dynamics and its influence on the rock, which is drilled using probabilistic methods. It is shown that the nature of the vibrations of the top of the drill string and the downhole signals are different and have a stationary random character. It is proved that the process at the output of the drill string, taking into account random disturbances, is narrow-band (quasi-harmonic) or close to it. It is found that the energy composition of the spectrum sections and the appearance of resonance peaks and their displacement is directly determined by the physical and mechanical properties of the rocks being drilled, as one of the factors that determines the vibration state of the drill string. Graphs of the spectral density of the power of pitting vibrations are given, showing their amplification at frequencies of 30–40 Hz as the hardness of the rocks being drilled increases. The maximum of the power density bending curve shifts towards low frequencies. There is a «mutual convergence» of the maxima of the power spectral density of the oscillations of the top and bottom of the drill string. It is shown that an important feature of drill string vibrations in the process of drilling with ball bits is that the intensity of vibrations of the top of the drill string passes with frequencies close to low frequencies, and the vibrations of the bottom of the string – to high frequencies. It is determined that the process at the output of the drill string, taking into account random disturbances, is narrow-band (quasi-harmonic) or close to it. As a result, the assumption of a narrow band at the output of the system, which is the basis of theoretical research, is justified. It is proven that the drill string, as a system with liquid filling under pressure, is more stable compared to a hollow structure. The washing liquid, in this case, plays the role of a dynamic absorber.