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

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) $k_{\sigma }$ on threaded connections can significantly increase it. At the fundamental frequency of the resonant sonic drilling, the maximum fatigue damage point, $x_f$, is located approximately $l_a/2$ above the drill bit, not exceeding the theoretical sonic standing wave starting length, $l_a$, and unrelated to the hole depth. This study promotes the theoretical understanding and exploration of variable-length standing wave oscillators.