## 6 Conclusions  
In this paper, a three-dimensional finite element model of an all-metal screw motor applicable to the extremely high-temperature and high-pressure drilling environment of an ultra-deep well was established, and the structural design and working principle of the all-metal screw motor were clarified. The mechanism of the effects of temperature as well as pressure on the deformation of the all-metal screw motor was studied by way of finite element numerical calculations, and the variation in clearance values of the all-metal screw motor under the action of ambient temperature was investigated, with the following conclusions:  
1. Under the action of the internal pressure of the drilling fluid, the overall deformation of the all-metal screw motor was relatively uniform, and both displacement and stress were distributed periodically along the circumference, where the largest displacement was located in the convex part of the motor stator, that is, the small diameter of the stator, with a maximum displacement of 0.01073 mm under 110 MPa internal pressure. The maximum stress was distributed at the depression of the inner diameter of the stator. At the large diameter of the stator, the Mises stress reached 144.792 MPa under the action of 110 MPa internal pressure. 2. The deformation of the all-metal screw motor was greater under ambient temperature than under internal pressure. For the metal stator-rotor clearance model of 0.02 mm, the fit clearance reached \(-0.01512\) mm, and the relative rate of change in the clearance reached \(175.58\%\) when the stator-rotor was overfilled due to expansion. As the initial clearance value continued to increase, the relative rate of change in the clearance after its expansion decreased. When the initial clearance was 0.1 mm, the relative rate of change was 34.607%, and when the initial clearance was 0.2 mm, the relative rate of change was only 16.9%, at which point the relative rate of change curve leveled off and there was basically no change. Therefore, to ensure that the stator and rotor of the all-metal screw motor can maintain engagement operation in high-temperature environments of ultra-deep wells, the minimum fit clearance of the stator and rotor of the all-metal screw motor should be greater than 0.2 mm. 3. Considering the all-metal screw motor stator deformation caused by the nonuniform temperature field under the effect of fluid disturbance, the maximum stator displacement was positively correlated with the ambient temperature of the inner cavity. Additionally, the displacement caused by the heat of fluid disturbance was very small compared to the effect of the downhole ambient temperature on the amount of clearance for the initial installation of the screw motor. Figure 18: Analysis of change in stator displacement after joint influence. * The deformation of the stator of the all-metal screw motor under the effect of temperature-pressure joint influence was greater than that under the effect of internal pressure alone. Under the environment of 110 MPa and 290 \({}^{\circ}\)C, the deformation of the all-metal screw motor stator reached 0.175406 mm, which was much larger compared to the displacement of 0.01073 under 110 MPa internal pressure alone. Temperature clearly has a greater impact than pressure on all-metal screw motors. As the drilling depth continued to increase, the amount of increase in stator displacement caused by the joint influence also continued to increase. Therefore, special attention should be given to the effect of ambient temperature on the performance of all-metal screw motors deep underground. Overall, the metal screw motor designed in this study is expected to have good performance and stability with minimal deformation in the high-temperature and high-pressure environment of 10,000 m ultra-deep wells. Conceptualization, X.F. and C.Z. ; Methodology, X.F. and C.Z. ; Software, X.F. ; Validation, X.Y. ; Formal analysis, L.C. ; Investigation, C.L. ; Resources, L.C. ; Data curation, J.L. ; Writing--original draft, X.F.