## 4 All-Metal Screw Rod Motor Modelling
### Influence of Drilling Fluid Pressure  
To obtain the deformation of the all-metal screw motor stator under operating conditions, a finite element numerical calculation of its model was performed in this study. Since the displacement of the stator was mainly radial, the overall 1/10 th scale was used as the research object for the mesh division as well as the calculation, accounting for the accuracy. Without considering the effect of temperature on the deformation of the all-metal screw motor under actual working conditions, the force condition of the all-metal screw motor, the drilling fluid density was 1.1 g/cm\({}^{3}\), g was taken as 9.8 m/s\({}^{2}\), and the stator internal pressure was taken as 20 MPa, and the simulations were conducted for ultra-deep well depths of 9000-13,000 m. According to the variation in drilling fluid pressure with depth, uniform loads of 110 MPa, 120 MPa, 130 MPa, 140 MPa and 150 MPa were applied to the inner cavity of the motor stator, and its displacement and stress clouds were obtained by using the finite element software Abaqus, as shown in Figures 9 and 10. Figure 9: Displacement cloud diagrams of motor stator at 110–150 MPa. As shown in Figures 9 and 10, the displacement cloud diagrams of the all-metal screw motor stator and the Von Mises stress cloud diagrams under the action of different internal pressures at different burial depths show a certain regular pattern. The diagrams have approximately the same pattern and a more uniform deformation overall, with an approximately circular periodic distribution of both displacement and stress. The maximum displacement of the all-metal screw motor stator convex part was the small diameter of the stator, and the maximum stresses were distributed in the inner diameter depression part of the stator, which is the large diameter of the stator. Under 110 MPa internal pressure, the maximum deformation occurred in the convex part of the stator, which was the part where the stator and rotor were in direct contact, and the displacement reached 0.01073 mm. Compared with the part where the stator and rotor were in direct contact, the displacement in the stator inlet was relatively small, and the maximum value of Mises stress was 144.79 MPa under 110 MPa internal pressure, which was located at the large diameter of the inner concave part of the stator. From 110 MPa to 150 MPa, the corresponding maximum displacement as well as the maximum Mises stress statistics  
Figure 10: Stress cloud diagrams of motor stator at 110–150 MPa. are shown in Table 2. In Table 2, the maximum stator displacement is in the range of 0.010-0.015 mm, and the maximum Mises stress is in the range of 140-200 MPa under different internal pressures. From Figure 11, with increasing internal pressure, its displacement also increased, but the overall increase was small, at approximately 0.001 mm, which also confirmed the stability of the all-metal screw motor made of 40 CrNiMo in a high-pressure environment and showed that the motor was suitable for operation in high-pressure environments deep in the ground. To better describe the deformation of the inner wall of the stator, a right-angle coordinate system was established in the model with the center of the circle as the midpoint, and a circular path was defined by using the define path function of Abaqus; 2000 points were taken on this path. Afterwards, the displacement magnitude on this path was obtained, and the radial displacement curves corresponding to different angles of the circumference were obtained by converting the circumference into angles, as shown in Figure 12. This curve shows that the stator displacement curve of the all-metal screw motor was undulating but flat and smooth, with the smallest displacement at the depression and the largest displacement at the bulge, showing a certain periodicity. The stator inner diameter decreased from a small diameter to a large diameter and then increased to a small diameter, which was very consistent with the stator configuration.