Influence of a waveform on the bit-rock impact response considering reflected waves in a drill rod

Percussive drilling is considered an efficient approach for penetrating hard formations. Understanding the responses and mechanical properties of rocks while being impacted and crushed by rock drills is essential for further improving their penetration efficiencies. This paper examines the consecutive impacts between the drill bit and rock, which are induced by the waves reflected in the drill rod after an initial hammer impact. Firstly, the loading and unloading principle for consecutive impacts is proposed. Based on this principle and onedimensional (1-D) longitudinal wave propagation, a 1-D bit-rock interaction dynamics model is subsequently established. This model considers switches between the states of impact and separation, to instantly predict rock responses. Selecting marble as a representative material, the findings from the 1-D theoretical model and threedimensional (3-D) Finite Element Method (FEM) simulations indicate that the number of repeated crushing impacts, which substantially contribute to the final penetration displacement, increases as the wavelength or the baseline level of fc (dimensionless crushing threshold force) in a rock decreases. fc is related to the loading rate, and its baseline level diminishes with decreasing impact energy (waveform amplitude). Due to the increases in fc and loading stiffness for short waves, the overall increasing trend of the final penetration displacement with decreasing wavelength weakens. A suitably-short wave with a high dimensionless exponential growth rate r or a long wave with approximately a unit of r can lead to a relatively-high final penetration displacement. In addition, we find that the dynamic loading and unloading stiffness and crushing threshold force have specific relationships with the penetration displacement and rock loading rate.