## 2 Description of the RC-DTH Air Hammer
### Impact Process of the RC-DTH Air Hammer  
The initial position of the piston within the RC-DTH (Reverse Circulation-Down-The-Hole) air hammer is situated at the base of the cylinder, subject to the persistent influence of gravitational force. The pivotal structural parameters that dictate the design of the piston for the RC-DTH hammer are identified and denoted as \(R_{1}\), \(F_{1}\), \(R_{2}\), and \(F_{2}\). \(R_{1}\) represents the intake stroke of the lower chamber and is a crucial parameter that defines the valve stroke of the RC-DTH hammer's piston structure. \(F_{1}\) denotes the intake stroke of the upper chamber. \(F_{2}\) refers to the outgassing stroke of the upper chamber. \(R_{2}\) represents the exit stroke of the lower chamber. Figure 3 illustrates the single impact cycle of the piston within the RC-DTH (Reverse Circulation-Down-The-Hole) air hammer, detailing the successive stages comprising a full operational cycle. The compressed gas is channeled into the flow channel of the central pipe from the drill pipe, entering via the upper joint. The upper portion of the central pipe serves as the gas inlet, while the lower portion acts as the gas outlet. During the ascending phase, as the piston is at the starting position (stroke length \(L\) equals zero), air begins to flow into the lower chamber through the inlet, traversing the passage within this chamber. Upon reaching \(L=R_{1}\), the lower chamber is isolated from the inlet, sealing it off, and the high-pressure air within commences expansion. As \(L\) advances to \(F_{2}\), the upper chamber is sealed. Upon reaching \(L=F_{1}\), air is introduced to the upper chamber through its dedicated flow path. Simultaneously, the piston's velocity diminishes due to the combined effects of pressure within the upper chamber and the ongoing expansion in the lower chamber. When \(L=R_{2}\), the lower chamber reconnects to the outlet, facilitating a rapid decline in the work performed by internal expansion. At the stroke \(L=L_{\rm s}\) (intake cessation point), the upper chamber is sealed, and the piston decelerates to a stop, marking the onset of its return stroke. The flow channel dynamics during the return process are consistent with  
Figure 2: Two types of RC-DTH air hammers marked as follows: (**a**) outflow piston; (**b**) internal flow piston. those during the ascending process. Upon returning to its starting position, the piston finishes a complete cycle of impact. Through a comparative analysis of the internal and external flow piston structures and utilizing the mathematical model of the piston valve stroke, this study introduces a Type B internal RC-DTH air hammer piston design, as depicted in Figure 4. In contrast to the GQ89 RC-DTH air hammer, which utilizes an outflow piston structure, the Type B model theoretically offers several advantages as follows: It maximizes the compression surface area of both the upper and lower chambers while minimizing the structural requirements to accommodate the outer cylinder. The adoption of a central gas supply method effectively minimizes fluid flow losses and addresses potential structural strength deficiencies in the fitting components. Furthermore, the Type B model streamlines the piston structure design, resulting in reduced mass and enhanced efficiency in converting the internal energy of compressed air into usable work. The detailed parameters for the GQ89 and the Type B RC-DTH air hammer are presented in Table 1. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & **Outer** & **Piston** & **Rated Gas** & \multicolumn{3}{c}{**Gas Distribution Stroke/mm**} \\  & **Diameter/mm** & **Mass/kg** & **Pressure/MPa** & \(\mathbf{R_{1}}\) & \(\mathbf{F_{2}}\) & \(\mathbf{F_{1}}\) & \(\mathbf{R_{1}}\) \\ \hline GQ89 & 89 & 6.5 & 0.6–1.2 & 45.5 & 40 & 68 & 80 \\ Type B & 95 & 5 & 0.6–1.2 & 45 & 57 & 60 & 82 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Partial structural parameters of the GQ89 and the type B RC-DTH air hammer. Figure 3: Impact process of the RC-DTH air hammer.