## 3 Simulation and Optimization of the Joint
### Effect of the Connection Status  
The connection state of the drill pipe joint is an important factor affecting the thread stress distribution. Because the thread has a certain taper, it can be tightened to a greater extent, which will deform the threads and achieve an interference fit, which cannot be achieved by other threads. After the joints are connected, it is necessary to continue tightening at a certain angle to produce an interference fit, achieve sealing and prevent tripping. In this study, the magnitude of the interference of the joint tightened by one turn is 0.099 mm. After trial and error, it is finally determined that the maximum tightening angle is eight degrees, and the pretightening angle actually applied in the simulation is one to eight degrees.  
Figure 13 shows the stress distribution in the joint when the pretightening angle is five degrees. Unlike the tensile load, the pretightening angle primarily affects the stress distribution in the joint shoulder. Figure 14 shows a line graph of the average stress in each thread for different pretightening angles. The results show that when the pretightening angle is small, the stress in the thread is relatively uniform. As the tightening angle increases, the thread stress becomes more concentrated at both ends, whereas the thread stress remains lower in the central portion. The results in Figures 11 and 14 are due to stress concentrations caused by the relief notch near the inner-shoulder face. There are relief notches near the inner-shoulder face of the pin and box joints. Therefore, the equivalent stress in the thread presents the following distribution characteristics: high stress at the two ends and low stress in the middle. This shows that the thread near the inner face is the weak point of the joint, which is consistent with previous research results.  
Figure 12: Stress distribution on the thread contact surface under a tensile load of 100 kN: (**a**) contact surface stress and (**b**) cross-sectional stress distribution.  
Under different pretightening angles, the maximum and minimum axial displacements of the threaded surface, the outer-shoulder surface and the inner-shoulder surface of the box joint are obtained, the results of which are shown in Figure 15. Through an analysis, the maximum displacement of the inner shoulder and the outer shoulder is their interference. The interference of the thread surface is in the opposite direction of the axial displacement, so the absolute value of the minimum axial displacement is the interference.  
Figure 15 shows that when the pretightening angle is less than 3.6 degrees, the interference of the outer-shoulder surface is higher than the interference of the thread surface. As the pretightening angle increases, the interference of the thread surface gradually exceeds the interference of the outer-shoulder surface. From these results, it can be inferred that the thread surface is more likely to deform than the shoulder surfaces at both ends. This difference in deformability produces a thread stress that exhibits the distribution characteristics described above.  
Figure 14: Relationship between the average equivalent thread stress and the pretightening angle.  
Figure 13: Thread stress nephograms with a pretightening angle of five degrees: (a) pin joint and (b) box joint.