# Research on Key Technologies of 260 \({}^{\circ}\)C/210 MPa Ultra-Deep Logging Equipment
## 3 Research on Key Technologies of Ultra-High-Temperature and High-Pressure Logging
### 260 \({}^{\circ}\)C/210 MPa Ultra-High-Temperature-and-Pressure Mechanical Structure  
The existing domestic logging instruments are generally rated for 175 \({}^{\circ}\)C/140 MPa and 230 \({}^{\circ}\)C/170 MPa. Instruments meeting the 260 \({}^{\circ}\)C/210 MPa specifications are used mostly in the overall design and core component testing stages, and there are currently no industry standards for validation in a high-temperature and high-pressure environment exceeding 260 \({}^{\circ}\)C/210 MPa. Below, we will present the design of the pressure-bearing outer casing components and universal parts that meet the 260 \({}^{\circ}\)C/210 MPa requirements through theoretical calculations.  
Design parameters: outer diameter--92 mm, inner diameter--60 mm, material--TC18, yield strength at 260 \({}^{\circ}\)C (\(\sigma_{0,2}\))--820 MPa.  
The Thick-Walled Cylinder Pressure Calculation Formula is as follows:  
The stress in each direction at any point on the pressure-bearing structure of a thick-walled cylinder is:  
\[\text{Radial stress}\;\sigma_{\tau}=-\frac{{{Pr}_{2}^{2}}}{{{r}_{2}^{2}-{r}_{1 }^{2}}}(1-\frac{{{r}_{1}^{2}}}{{{r}^{2}}}) \tag{1}\]  
\[\text{Hoop stress}\;\sigma_{\tau}=-\frac{{{Pr}_{2}^{2}}}{{{r}_{2}^{2}-{r}_{1 }^{2}}}(1+\frac{{{r}_{1}^{2}}}{{{r}_{2}^{2}}}) \tag{2}\]  
\[\text{Axial stress}\;\sigma_{z}=-\frac{{{Pr}_{2}^{2}}}{{{r}_{2}^{2}-{r}_{1}^{ 2}}} \tag{3}\]  
In the formula, \(P\) is the external environmental pressure, MPa; \(r\) is the radius of the pressure point, mm; \(r_{1}\) is the radius of the inner hole of the instrument, mm; \(r_{2}\) is the inner radius of the outer surface of the instrument, mm [12]. \(\sigma_{\tau}\) is the Radial stress at the bearing point, MPa; \(\sigma_{\tau}\) is the Radial stress at the bearing point, MPa; \(\sigma_{z}\) is the Radial stress at the bearing point, MPa;  
When \(r=r_{1}\), the stresses reach their maximum values. By substituting \(r=r_{1}\), \(k=\frac{r_{1}}{r_{2}}\) into the above formula and simplifying, we obtain:  
\[\sigma_{1}=\sigma_{r}=0 \tag{4}\]  
\[\sigma_{2}=\sigma_{\tau}=-\frac{{2P}}{{1-k^{2}}} \tag{5}\]  
\[\sigma_{3}=\sigma_{z}=-\frac{{P}}{{1-k^{2}}} \tag{6}\]  
According to the mechanics of materials and the fourth strength theory, the maximum combined stress on the inner wall is [12]:  
\[\sigma_{\text{s}}=\frac{{1}}{{\sqrt{2}}}\sqrt{{{{\left({\sigma_{1}-\sigma_{2} }\right)}^{2}}+{{\left({\sigma_{2}-\sigma_{3}}\right)}^{2}}+{{\left({\sigma_{3 }-\sigma_{1}}\right)}^{2}}}} \tag{7}\]  
\[\text{Allowable stress}\;{{\left[{\sigma}\right]}={\sigma_{0.2}}/{n}} \tag{8}\]  
In the formula, \(n\) is the safety factor [12]. The pressure safety factor \(n\) of logging instruments is generally \(\geq\)1.25.  
Substituting the design parameters into Equations (4)-(7), we obtain: \(\sigma_{\rm s}\) = 635 (MPa) The Allowable stress of the material is: [\(\sigma\)] = 820/1.25 = 656 (MPa) For \(\sigma_{\rm s}\) < [\(\sigma\)], the instrument's pressure-bearing outer casing structure and material parameters are reasonable.  
The pressure-bearing outer casing components were processed and successfully passed the pressure testing at 230 \({}^{\circ}\)C/180 MPa. The next step is to prepare for pressure testing in an environment of 260 \({}^{\circ}\)C/210 MPa.