Theoretical study on fatigue damage of sonic standing wave resonant drill-string

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To achieve high-speed and undisturbed core drilling, the standing wave vibration of the drill string in a sonic drill is excited by a high-frequency inertial vibrator; the resulting high alternating stress cycle in the drill string can easily cause fatigue damage. In order to minimize the fatigue failure of drill-string at the stage of its design, it is necessary to assess the fatigue damage caused by alternating stress to guide engineering practice. In this paper, based on one-dimensional wave theory, we analyse the standing wave vibration in a drill-string excited by a sonic vibrator, and theoretically prove that the dynamic resonant stress of a drill-string is the key factor influencing the fatigue damage. By using the Palmgren–Miner fatigue damage rule, we establish a theoretical formula for the cumulative fatigue damage of a variable-length standing wave vibration drill string and reveal the fatigue damage mechanism of the variable-length resonant drill string. Furthermore, the effects of sonic drill systems and process parameters on the damage are quantified. It was found that by an appropriate choice of a drill-pipe length, the fatigue damage can be reduced whilst the axial stress concentration factor (aSCF) kσ on threaded connections can significantly increase it. At the fundamental frequency of the resonant sonic drilling, the maximum fatigue damage point, xf, is located approximately la/2 above the drill bit, not exceeding the theoretical sonic standing wave starting length, la, and unrelated to the hole depth. This study promotes the theoretical understanding and exploration of variable-length standing wave oscillators.