## 1 Introduction  
The drilling technique with a down-the-hole (DTH) air hammer is commonly utilized in both surface and underground mining operations [1, 2, 3]. This method is favored due to its numerous benefits, including enhanced penetration rates when drilling through hard rock, the creation of more precise and straight boreholes, and the outstanding ability to drill without drilling fluids [4, 5, 6, 7]. However, the traditional drilling method with down-the-hole (DTH) air hammers is a significant generator of respirable dust, which results in the increasing exposure of drilling crews and equipment to that dust [8]. Previous studies predominantly reveal that chronic exposure to high quantities of respirable coal dust can cause pneumoconiosis and silicosis in workers [9]. Hence, minimizing dust generation during the drilling process, particularly when employing the DTH air hammer drilling technique, is crucial for improving the workplace environment [10, 11]. Figure 1 depicts a typical RC-DTH air hammer drilling system, consisting of a flexible discharging tube, a double-passage swivel, a goose neck tube, a flexible air input tube, dual-wall drill pipes, a hollow-through DTH air hammer, and an RC drill bit [12; 13]. Compressed air is injected into the system through the flexible air input tube, which then flows through the double-passage swivel and the annular gap of the dual-wall drill pipes before reaching the RC-DTH air hammer [14; 15]. This drives the piston in the RC-DTH air hammer to perform reciprocating impact motions [16; 17]. Finally, the compressed air is discharged to the bottom of the drill hole through the specially structured RC drill bit, which concentrates the cuttings at the bottom of the central channel to achieve reverse circulation and continuous drilling and sampling [18; 19; 20]. Since the drill cuttings are concentrated in the central channel and dealt with by a cyclone dust collector, this method can ensure the cleanliness of the construction site [21; 22; 23]. Meanwhile, this method can quickly drill holes with diameters ranging from 89 mm to 1.8 m without contamination from the walls of the hole, unlike the normal rotary percussion drilling method [24; 25]. As the key tool of the RC-DTH air hammer drilling method, the performance of the RC-DTH air hammer is closely related to the drill rate [26]. Most prior research in the domain of RC-DTH air hammer drilling has predominantly focused on enhancing the functionality of the reverse circulation drill bit to boost the bit's reverse circulation efficiency by improving the structural design [27; 28]. In contrast, the performance of the RC-DTH air hammer itself has received comparatively little scholarly attention [29; 30; 31]. The drilling speed of the RC-DTH air hammer is significantly influenced by its impact performance [32]. To enable this drilling method to be applicable in more challenging scenarios, it is essential to continuously enhance its impact energy, frequency, and power output [33]. The piston of the RC-DTH air hammer is the primary source of impact energy and is regarded as the key component that dictates the hammer's impact performance [34]. Consequently, extensive scientific  
Figure 1: Schematic of the hollow-through DTH air hammer drilling system marked as follows: 1—flexible discharging tube; 2—double-passage swivel; 3—goose neck tube; 4—flexible air input tube; 5—dual-wall drill pipe; 6—check valve; 7—inner tube of the hammer; 8—inner cylinder; 9—piston; 10—sleeve; 11—drill bit. research has been conducted on the design and optimization of the piston structure for the RC-DTH air hammer, employing methods such as theoretical analysis and experimental validation [35; 36; 37]. [PERSON] and [PERSON] [38] developed a nonlinear dynamic model to assess the performance of the DTH hammer, investigating the optimal solutions for impact power, energy, frequency, efficiency, and mass flow. [PERSON] et al.