## 4 All-Metal Screw Rod Motor Modelling
### Analysis of Motor Stator Deformation under the Fluid Disturbance Effect  
To better study the temperature field effect caused by fluid disturbance in the all-metal screw motor, the deformation of the screw motor stator was analyzed under fluid heat exchange conditions; the inner chamber of the stator with the surface heat transfer  
Figure 14: Change in clearance after heating.  
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Clearance (mm)**} & **Minimum Variation of** & **Maximum Variation** & **Clearance after** & **Relative Variation** \\  & **Stator Inner Surface (mm)** & **of Rotor Surface (mm)** & **Heating (mm)** & **Ratio of Clearance (\%)** \\ \hline
0.02 & 0.189644 & 0.22476 & \(-\)0.01512 & 175.58 \\
0.04 & 0.189773 & 0.22476 & 0.005013 & 87.4675 \\
0.06 & 0.189903 & 0.22476 & 0.025143 & 58.095 \\
0.08 & 0.190028 & 0.22476 & 0.045268 & 43.415 \\
0.1 & 0.190153 & 0.2 coefficient of the transported oil was 20 W/(m\({}^{2}\)\({}^{\circ}\)C), the initial ambient temperature was taken as 20 \({}^{\circ}\)C, and the deformation at the heat flow temperature of 290-410 \({}^{\circ}\)C is shown in the following figure:  
It is clear from Figure 15 that the maximum displacement of the all-metal screw motor stator was positively correlated with the ambient temperature of the inner cavity under the effect of the temperature field caused by fluid disturbance. Additionally, the displacement caused by the heat of fluid disturbance was negligible compared to the effect of clearance due to downhole ambient temperature on the amount of clearance under the initial installation of the screw motor. Therefore, the effect of temperature was only considered in this study for the variation in the stator-rotor clearance value of the all-metal screw motor under the effect of a high ambient temperature downhole.  
Deformation Characteristics of Spiral Motor Stator under the Joint Influence of Temperature and Pressure  
In the previous section, the deformation of the stator of an all-metal screw motor was studied in a high-pressure environment and in a high-temperature environment. However, under actual working conditions, the joint influence of temperature-pressure conditions on the deformation of the metal stator and rotor should be taken into full consideration.  
Therefore, the analysis of the deformation of the stator of the all-metal screw motor under the joint influence of temperature and pressure is of great significance to guide the selection of the fit clearance and the design of the configuration parameters of the all-metal screw motor.  
To more truly reflect the extreme environment of high temperature and pressure during the drilling of ultra deep wells, the effects from the joint influence of temperature and pressure were studied for all-metal screw motors. The temperature and pressure settings and parameter settings were the same as above. Considering the actual working conditions and the simplicity of the calculation, the outer wall of the stator was completely constrained, and the two end faces were symmetrically constrained. The obtained cloud  
Figure 15: Thermal displacement consideration of the fluid disturbance effect.  
greater amount after joint influence compared to the direct effect of internal pressure. Moreover, as the drilling depth continued to increase, the amount of stator displacement increase caused by the joint influence also continued to increase. It is evident that the temperature would have a great influence on all-metal screw motor drilling tools in deep underground environments of ultra-deep wells, and special attention should be focused on the influence of the temperature of deep underground environments on the performance of the all-metal screw motor.  
Figure 17: Stress under temperature–pressure joint influence.