# Pattern and Analysis of Corrugation-Sand Retaining Seals for
## 4 Simulation Research
### Results and Analysis
#### 4.5.1 Main Seal  
The contact pressure cloud diagram is shown in Figure 7a. The contact pressure at the main seal protrusion is the largest, the contact state is stable, the pressure gradually decreases to both sides; there is no fault, sudden change, and no leakage. The maximum pressure value is 18 MPa, greater than the fluid pressure, and has a sealing effect. As shown in Figure 7b, because the force of the rubber is not easy to analyze, the reaction force of the bearing support is used instead of the load on the sealing ring to analyze, and solve the contact area by command to get the seal gap width.  
As shown in Figure 8, when the change value of the calculation result is less than the set allowable deviation value, the number of grid cells will no longer have a significant impact on the calculation result. When the number of grid cells reaches 6000, and the number of nodes reaches 27,000, the upper and lower deviation of the calculation results  
Figure 6: Load application: (**a**) Precompression loading, and (**b**) Schematic diagram of fluid pressure boundary.  
Figure 7: Leakage calculation: (**a**) Contact pressure cloud diagram, and (**b**) Bearing support reaction force.  
shall not exceed 5%, which meets the calculation requirements. At this time, the average size of grid cells is 0.375 mm.  
set,last! selects the final step of the computation iteration  
cmsel,s,pressure! Selects all nodes in the lower half of pressure by name  
cmsel,a,pressure?! Co\(-\)select all nodes in the lower half of pressure2 by name  
esln,s,1! Select the element attached to the node  
esel,r,type,cid1! Reselect only contact elements of type \"cid_1\"  
etable,estat,cont,stat! Save the list of selected cells  
esel,s,etab,estat,3! select contact section  
etable,c_area,VOLU! Select the contact element area  
ssum! Add area  
get,t_area,ssum,0,item,c_area! Store the result in t_area  
my_area=t_area/4.84! Find the seal gap width and output the result to my_area  
Calculation of leakage is carried out through the MATLAB platform. The following is the code of the leak calculation function:  
function [s] = LLJS(L,W); %L is the sealing gap width M, W is the radial load N/M  
L = L/1000; % conversion unit is M  
P1 = 11 \(\times\) 10\({}^{6}\);% internal pressure  
P2 = 10 \(\times\) 10\({}^{6}\);% external pressure  
k = 0.5; % exposure loss proportion  
A = 0.2 \(\times\) 10\({}^{-3}\); % amplitude M  
v = 220 \(\times\) 10\({}^{-6}\); % kinematic viscosity M2/S  
rho = 930;% density KG/M3  
eta = v * rho; % dynamic viscosity N*S/M2  
nRotation = 80; % rotation speed/min  
D = 55 \(\times\) 10\({}^{-3}\); % diameter M  
N = 36; % number of cycles  
V = nRotation * pi() * D/60; % linear velocity M/S  
W = W * N/D/pi(0;  
h = sqrt(0.1602 * eta * V * L^2/W);  
f = @(x) sin(2* N * x/D)./(A^2 * (sin(2 * N * x/D)).^2 + 1).^0.5;  
s = (1 - k)/2 * N * A * h * V * integral(@(x)f(x),0,pi(0));  
g = (1 + k'3) * h^3 * D * pi0 * (P1 - P2)/12/eta/L;  
s = (s + g) * rho * 10 \(\times\) 10\({}^{6}\); % conversion unit is mg  
s = s * 3600; % one hour leakage mg/h  
end  
When used, the result can be calculated by calling the LLJS (L,W) function in the command pane. For example, in the example shown above, the width L of the sealing gap in the axial direction is 2.14 mm, the radial load of the sealing ring W is 374.21 N, the leakage is calculated through the function, and the calculation result is 5.04 mg/h.  
Figure 8: Grid independence verification: (**a**) Influence of mesh number on the result of maximum contact pressure, and (**b**) Influence of mesh number on maximum Mises stress results.