## 1 Introduction  
### Research Background  
As a kind of clean and renewable energy, the development and utilization of geothermal energy has attracted widespread attention in the context of the current global energy structure transformation and environmental protection [1; 2; 3]. As a critical technology to obtain geothermal energy, the efficiency and cost of geothermal drilling are directly related to the economy of geothermal projects [4; 5; 6; 7].  
Air DTH hammer drilling (vibratory percussion drilling) has proven to be an efficient geothermal drilling technique (see Figure 1 for its flow chart).  
Most of the commonly used DTH hammer drills are center-exhaust-type single-piston drilling hamsters (valve drilling hammers and valveless drilling hammers), and the early engineering applications are mostly valve DTH hammers. At present, the most used is the valveless drill hammer, which was invented by [PERSON] in the early 1950s; its main feature is to cancel the upper and lower cavity of the valve plate and directly use the hammer piston structure itself for gas distribution. The internal gas distribution structure of this kind of drill hammer is more complex, and the processing requirements are slightly higher, but the effect of removing rock powder is better, so it can reduce the wear of the drill bit and improve the drilling efficiency. It is widely used in the construction process, and the drill hammer used in this paper is exactly of this kind.  
The working principle of the air DTH hammer drill: when drilling, the air compressor to the power system of the drilling hammer continuously delivers high-pressure air into the cylinder as well as the upper and lower cylinders of the piston and the cylinder position (see Figure 2 for its flow chart), so as to achieve the high-pressure gas impact of the impactor piston for high-frequency reciprocating movement; this has an effect on how the drill works. At the same time, the low-speed rotation of the drill provides torque for the drill bit. Under the combined action of impact work and rotary torque, the drill bit has a continuous pulsating impact on the rock at the bottom of the hole until the generated volume is broken. At this time, the high-pressure air will work through the annular gap between the drill pipe and the hole wall, carried by the high-pressure air and discharged out of the hole, to avoid repeated rock fragmentation, with high drilling efficiency. In addition, the high-pressure air flow after work on the one hand can play the role of slag removal, while on the other hand it can cool the drill, so that the heat generated during the contact with the rock is blown away. The rock-breaking process of the DTH hammer drill is completed under the combined action of weight on the bit, impact force, and rotary force. In the process of drilling, the impactor is subjected to the reciprocating action of piston, which exerts axial force on the bit and produces axial speed. At the same time, the head of the impactor is connected with the external torsional structure to apply torque and generate rotary force. From the perspective of rock crushing, the axial speed is used to break rock, and the rotary force changes the position in which rocks are broken, so that the drill can impact and grind the new rock face again, play the role of an auxiliary rock breaker, and finally achieve the purpose of jointly breaking rock.  
Figure 1: Drilling process flow chart of an air DTH hammer.