## 6 Conclusions  
(1) In view of the stick-slip phenomenon during drilling, a new type of torsional impactor is proposed, which can provide circumferential torque, generate circumferential torsional impact vibration, and reduce stick-slip of drill string. The torsion impactor of the new structure is a pure mechanical structure with a simple structure, convenient processing, low-cost manufacturing, and no electronic components or rubber parts, allowing the torsional impactor designed here to work in high-temperature (about 300 \({}^{\circ}\)C) environments. Under the same input, parts with different structural parameters can be selected to adjust to different outputs. The impact direction is consistent with the rotary direction of the bit, which is beneficial to the bit shear rock breaking.  
(2) According to the structure and working principle of the newly designed torque impactor, the relationship between the impact frequency, impact force, impact torque, and related parameters is theoretically analyzed. The results show that the impact frequency \(f\) is directly proportional to the transmission shaft speed \(V_{\mathrm{z}}\) and the number of \(n\) of the installation of the torque impact generator. The impact force \(F\) is directly proportional to the sine value of the impact angle \(\alpha\) (i.e., sin\(\alpha\)), the hammer mass \(m\), the hammer speed (i.e., transmission shaft rotation speed) \(V_{\mathrm{z}}\), and the hammer rotation radius \(r\) and is inversely proportional to the action time \(\Delta t\) of the impact hammer and the anvil. The impact torque \(M\) is directly proportional to impact force \(F\) and the impact hammer rotation radius \(r\); in other words, all of the parameters affecting the impact force \(F\) may affect the impact torque. Under the condition that the other parameters remain unchanged, the impact torque \(M\) is directly proportional to the square of the impact hammer's rotation radius \(r\), indicating that increasing the impact hammer rotation radius \(r\) is the most conducive to increasing the impact torque \(M\).  
(3) According to the analysis results that indicate the parameters of the drill collar and drill bit, the outer diameter parameters of the torsional impactor were selected, and the other related structure and performance parameters of the torsional impactor were obtained through the calculation and analysis of an example. This article lays a foundation for further theoretical research and experimental research on the torsional impactor and provides a reference for the design and testing of the torsional impactor discussed here.  
Conceptualization, X.T. and Z.C.; methodology, L.D.; formal analysis, C.X.; investigation, Y.W.; writing--original draft preparation, X.T. and Z.C.; writing--review and editing, Z.C. and S.T.; supervision, L.D.; project administration, C.X. and Y.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 41972327, and the Open Project of Shandong Provincial Lunar Geology and Exploration Institute, grant number LNY2020-Z07.  
Exclude this statement.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Name (Unit)** & **Parameter Value** \\ \hline Outside diameter of torsion impactor \(D\) (mm) & 203 \\ The rotation speed of transmission shaft \(V_{Z}\) (rot/min) & 500 \\ Installation logarithm of torsional impactor \(n\) & 3 \\ Impact hammer mass \(m\) (kg) & 6 \\ Impact angle \(\alpha\) (\({}^{\circ}\)) & 45 \\ Rotary radius of impact hammer \(r\) (mm) & 60 \\ Impact frequency \(f\) (Hz) & 25 \\ impact force \(F\) (N) & 13,320 \\ Impact torque \(M\) (N\(\cdot\)m) & 1598 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters related to structure and performance of torsional impactor.