# Evaluation of Gasket Surface Contact Stress Uniformity Based on Gray-Level Co-Occurrence Matrix
## 3 Test and Analysis of Test Results
### Evaluation of Stress Distribution in Different Inner Radii of Compression Rods  
In the gasket test rig, the compression rod transfers the pressure from the top surface of the water cooling plate to the surface of the compression plate. Since there are also heating plates and insulation layers on the inner side the compression rod, the inner radius \(r_{1}\) of the compression rods ranges from 75 mm to 95 mm.  
Before the test, we set other parameters for the model; that is, the height of the compression plate was 50 mm. For the calculation model corresponding to each group of compression rods, we set the inner radius \(r_{2}\) to 85, 90, 95, 100, and 105 mm, and conducted finite element calculations.  
The cloud map presented in rainbow colors more clearly reveals the basic distribution of stress without other tools. We take the cloud map of the group with \(r_{1}=85\) mm, \(r_{2}=105\) mm as an example. As can be seen from Figure 4, the stress on the surface increased from the inner side of the gasket to the outer side. The variation hardly occurs along the circumference direction but mainly in the radial direction. There is no sudden variation along the radial direction, and the difference value between two color areas is within 4 MPa, which presents relatively uniform variation.  
To compare the angular second moment and entropy of different groups, an artificially created uneven situation was simulated and is shown in Figure 5b. The stress is concentrated in the middle ring area of the gasket, which represents the deflection angle of the flange after a long test time. The comparison of the characteristic parameters of two groups is shown in Figure 6.  
\begin{table}
\begin{tabular}{c c c} \hline
**Contact Body 1** & **Contact Body 2** & **Contact Relationship** \\ \hline Lower surface of water cooling plate & Upper surface of compression rod & Binding contact \\ Lower surface of compression rod & Upper surface of compression plate & Binding contact \\ Lower surface of compression plate & Upper surface of gasket & Frictional contact \\ \hline \end{tabular}
\end{table}
Table 1: Contact relationships of the gasket test rig during compression.  
Figure 4: Cloud map (\(r_{1}=85\) mm, \(r_{2}=105\) mm) in rainbow colors.  
Figure 5: (**a**) Relatively uniform cloud map (group 1). (**b**) Non-uniform cloud map (group 2).  
Figure 6: Histogram of entropy and angular second moment of group 1 and group 2.  
The angular second moment curve of \(r_{2}\) = 85 mm is above the whole curve. The groups of \(r_{1}\) = 100 mm, \(r_{2}\) = 75 mm and 85 mm are larger than the group of \(r_{2}\) = 85 mm, and the other four groups of compression conditions are smaller than the group of \(r_{2}\) = 85 mm. Under the five compression conditions, the entropy with a compression radius of 105 mm is basically at the top of all curves, reaching the maximum value of 3.085 when the inner radius of the compression rod is 90 mm, followed by the inner radius of 85 mm, which is slightly smaller than the entropy when the inner radius of the compression rod is 90 mm. The entropy curves of \(r_{2}\) = 85 mm and 90 mm are below other curves.  
According to the evaluation standard, the smaller the angular second moment is, the greater the entropy value is, and the better the uniformity of stress distribution is. The following test conclusions are drawn: the compression rod with an inner radius of 90 mm has the best effect on the uniformity of contact stress distribution on the gasket surface, while the compression rod with an inner radius of 75 mm has the worst effect on the uniformity of contact stress distribution on the gasket surface.  
Figure 10: Entropy curve of different compression rod inner radius.  
Figure 9: Angular second moment curve of different compression rod inner radius.