## 5 Case Study  
A torsion impactor is a downhole auxiliary rock breaking tool that is used to connect the drill bit and the drill collar. In order to ensure a normal connection between the drill bit and the drill collar, it is necessary to consult relevant industry standards and to determine the outer diameter and joint thread parameters of the tool. According to the type of drill collar and drill bit, the main parameters of other parts can be designed, and the torsional impact performance can analyzed, with a torsional impactor with an outer diameter \(D\) is 203 mm being used as an example.  
With the outer diameter of torsion impactor being designed as 203 mm, the inner diameter \(d\) and outer diameter \(D_{1}\) of the drill collar are selected to be 71.4 mm and 203.2 mm, respectively, while the corresponding outer diameter of drill collar selected as \(D_{2}\) is 311 mm for drilling operations with a torsional impactor. According to the structure of the torsional impactor shown in Figure 1, turbine model 195 was selected. As shown in Table 1. The model 195 turbine has a working speed of 430-560 rot/min and a working torque of 3200-5600 N\(\cdot\)m.  
According to the analysis in Section 3.1, the impact frequency of the torsion impactor designed in this paper is mainly related to the rotation speed of the turbine rotor and the pairs of the torque impact generator. According to the turbine model speed range that was selected, the turbine speed \(V_{z}\) is set as 500 rot/min. Approximately 2-4 pairs of torsional impact generators can be installed as required. Here, the installation logarithm is three pairs. It can be seen from Formula (1) that the impact frequency \(f\) of the torsional impact generator is 25 Hz.  
According to the analysis in Section 3.2, the impact force \(F\) of the torsion impactor that was designed in this paper is mainly related to the impact hammer mass \(m\), the impact hammer speed \(V_{z}\) (i.e., the speed at which the turbine rotor drives the transmission shaft), the impact angle \(\alpha\), and the impact hammer rotation radius \(r\). According to the selected turbine model, the impact hammer speed \(V_{z}\) is 500 rot/min, as above. According to the structure and limited space of the torsional impact generating device, the mass of the impact hammer is taken as \(m\) is 6 kg; in order to ensure that there is enough axial force to ensure that the impact hammer moves axially after impacting the anvil, the impact angle \(\alpha\) should be taken as 45\({}^{\circ}\); according to the outer diameter of the torsion impactor, the structure of the torsion generator and the value range of the rotary radius \(r\) of the impact hammer as well as the rotary radius \(r\) of the impact hammer is taken as 60 mm, and the impact force \(F\) is about 13,320 N, according to the calculation of Formula (4).  
According to the analysis in Section 3.3, the impact torque \(M\) of the torsion impactor designed in this paper is mainly related to the impact force \(F\) and the rotation radius \(r\) of the impact hammer, so the parameters related to the impact force are all related to the impact torque. According to the above impact force calculation results of 13,319.88 N and the radius of gyration \(r\) of the hammer of 60 mm, it can be calculated that the impact torque \(M\) is 1598 N\(\cdot\)m, as per formula (5).  
To sum up, the related parameters of the structure and performance of the torsional impactor are all shown in Table 2.