A phenomenological model for percussive drilling systems is proposed in this paper to explain the experimentally demonstrated existence of an optimal weight-on-bit (WOB), for which the rate of penetration (ROP) is maximized. Several hypotheses have been previously proposed to explain this universal characteristic of percussive drilling, including increased wear of the bit, reduced indexing, and poor cleaning of debris under excessive WOB. Motivated by experimental evidence, we instead consider an increase of the pseudo-stiffness of the bit-rock interface (BRI) with increasing WOB, and investigate its effect on the impact energy transmitted to the rock. The 1D model approximates the dynamics underlying the drilling process by assuming that the impact of the hammer generates a longitudinal wave in the bit. It is shown that the BRI pseudo-stiffness influences the incident wave and associated energy transmitted from the bit to the rock. As a consequence, the drilling efficiency is affected by the dependence of the BRI stiffness on the WOB. The model indicates that there exist optimal conditions for the energy transfer from the bit to the rock in terms of the impedance ratio and the BRI stiffness/WOB. Thus it confirms that there is a sweet spot as seen in practice, which suggests that the root cause of the existence of a sweet spot in the ROP-WOB relationship lies in the nature of the BRI laws, rather than with issues related to bit indexing, bit wear, and/or cleaning of the debris.

中文翻译：

---

钻压对冲击钻井性能的影响

本文提出了冲击钻井系统的现象学模型，以解释实验证明的最佳钻压 (WOB) 的存在，在该模型中钻速 (ROP) 最大化。先前已经提出了几种假设来解释冲击钻探的这种普遍特征，包括钻头磨损增加、分度减少以及在过度钻压下碎屑清洁不良。受实验证据的启发，我们考虑随着钻压增加而增加钻头-岩石界面（BRI）的伪刚度，并研究其对传递到岩石的冲击能量的影响。一维模型通过假设锤子的冲击在钻头中产生纵波来近似钻孔过程的动力学。结果表明，BRI 伪刚度会影响从钻头传输到岩石的入射波和相关能量。因此，钻井效率受 BRI 刚度对 WOB 的影响。该模型表明，就阻抗比和 BRI 刚度/WOB 而言，存在从钻头到岩石的能量传递的最佳条件。因此，它证实了在实践中看到的最佳点，这表明 ROP-WOB 关系中存在最佳点的根本原因在于 BRI 法律的性质，而不是与位索引相关的问题、钻头磨损和/或清理碎屑。BRI 刚度对钻压的依赖性影响钻井效率。该模型表明，就阻抗比和 BRI 刚度/WOB 而言，存在从钻头到岩石的能量传递的最佳条件。因此，它证实了在实践中看到的最佳点，这表明 ROP-WOB 关系中存在最佳点的根本原因在于 BRI 法律的性质，而不是与位索引相关的问题、钻头磨损和/或清理碎屑。BRI 刚度对钻压的依赖性影响钻井效率。该模型表明，就阻抗比和 BRI 刚度/WOB 而言，存在从钻头到岩石的能量传递的最佳条件。因此，它证实了在实践中看到的最佳点，这表明 ROP-WOB 关系中存在最佳点的根本原因在于 BRI 法律的性质，而不是与位索引相关的问题、钻头磨损和/或清理碎屑。