# Analysis of boundary conditions of flange

## Does flange need 3D contact analysis?

Flange is the most common component in pressure vessel. If a flange needs to analyze its stress and evaluate its safety, what kind of model and boundary conditions should be adopted? Is it necessary to build a pair of flange, gasket, bolt and nut, and use three-dimensional model for contact analysis?

My opinion is: in general, if it’s just flange analysis, it’s unnecessary to do 3D contact analysis. The plane model used in flange analysis not only has less calculation, but also has more accurate calculation.
The water method in the code is an axisymmetric model. It is easy to obtain the boundary conditions of flange by using axisymmetric method and load application method in the code.

When we use the conventional waters method to calculate the flange, do we use the bolt load under the operating condition?

Our flange is often pre tightening state control.
The bolt force WM calculated by the medium pressure, the relevant gasket parameters m, y and the effective width b of the gasket is only used to determine the minimum bolt cross-sectional area under the design state. If it is used as the actual bolt installation preload, it can not guarantee the sealing requirements of the flange joint, and it is likely to leak.
In addition, when the gasket is compressed, it is tight outside and loose inside. The PF at the gasket is 2mpc, so the equivalent force is not evenly distributed. Moreover, the internal pressure, gasket load PF and bolt force Pb cannot be balanced.

Therefore, using this kind of boundary condition, the calculated flange can be found that the stress of the flange part is relatively low, and the calculation results of the analysis can not be used to evaluate the flange body.

The two methods of load application are compared:

• The bolt stress in operation state is adopted. The maximum stress is at the connection between small end and flange, and the maximum stress value is 52.29mpa.
• Compared with the previous results of 219.15mpa, it is very small.
• From the calculation of SW6, the stress of flange is very large, and there is not much margin. Therefore, the result is 52.29mpa, it is not credible that the bolt load of bolt preload has not been considered to control the flange thickness.

## Introduction of WRC 538

So how should boundary conditions be imposed?
We can get some inspiration from WRC 538 determination of pressure boundary joint assembly bolt loads. In wrc538, the selection principle of bolt load is listed, and Y is recommended % SY bolt load above to calculate the flange.
The bolt load above is only to X % SY, far less than the actual compression load of the gasket. WRC uses elastoplastic analysis to calculate the maximum allowable bolt load of flange.
When checking, the Mo calculation formula in Appendix 2 of ASME VIII I is replaced by a new formula for the bolt load Mo under operation condition. The new formula is as follows: σB refer to ASME PCC – 1 appendix o, maximum 40 %~ seventy % The minimum yield strength is 20 %~ forty % The yield strength of the bolt at room temperature. Because the safety factor of bolt allowable stress for yield strength is 4, that is 25% yield strength, which is almost the flange stress under the condition of bolt full strength.
Therefore, the recommended bolt load of WRC538 is much greater than the bolt load under operation condition, and also greater than the bolt load recommended by waters method.
So we should at least use mo of waters method to calculate bolt load.
The method of WRC538 is to use elastic-plastic analysis to calculate the maximum allowable bolt load under the ultimate bearing capacity of flange. But we usually only use the elastic analysis method to calculate the flange stress. Therefore, the Mo in the specification is generally used for bolt load moment instead of the Mo improved by WRC538. Bolt load Fb = Mo / LG.
The boundary conditions of wrc538 are in Section 5 (1) ~ 12). By analyzing the boundary conditions of WRC 538 one by one, we can obtain the necessary boundary conditions for elastic analysis. Compared with 1) to 12) of the specification, the calculation flow and boundary conditions are applied as follows:

1) The axisymmetric model of a single flange is established, including half of the gasket model.
2) The model of gasket is established. The gasket adopts effective inner and outer diameter, and the inner and outer rings do not need to be established.

3) In WRC538, the flange adopts plane axisymmetric element, the bolt adopts plane stress element, and the gasket adopts gkax4n gasket element. (the specification uses ABAQUS software, and the unit name may be different.) Observation of deformation shows that the gasket is pressed more tightly, and the reaction force at the gasket is not evenly distributed. The same method can be used in ANSYS, and the gasket element can be 2D gasket element: inter192 or inter193
In order to simplify the application, the flange and bolt adopt the plane axisymmetric element, and the gasket can use the plane element instead of the gasket element, but the value of the elastic modulus is taken according to the gasket, and the value can refer to the “pressure vessel design Manual-4th.”  In ANSYS, it can be input in material properties. 5) The gasket unit is bound with the flange unit. If the gasket adopts the plane element, this can be ignored.
6) The cross section of the nut is the cross section of the standard hexagon nut.
7) Generally speaking, the contact between flange and nut is rough friction, without the ability of lateral friction movement and separation after contact.
In order to avoid non-linear contact non convergence, flange and nut can be considered as binding.
8) The width of the bolt of plane strain element is 3 / 4 of the actual bolt diameter.
9) 11) and 13) are the contents of elastic-plastic loading and evaluation, and the elastic analysis can be ignored.
12) The anisotropic elastic material is used to model the bolt hole area of flange.
Because the bolt hole area is not the failure area, the equivalent elastic modulus is used. The translation is: ## Simplified boundary conditions

The above boundary conditions for elastic analysis obtained from the analysis of WRC538 are relatively complicated.
Most of the time, we only need to check the flange strength according to the waters method, so the boundary conditions can continue to be simplified as follows: The plane axisymmetric element is used as a whole. The elastic modulus of the gasket and the equivalent elastic model of the bolt hole area are used in the gasket part.

• The displacement constraint uy is used at the gasket = 0；
• Internal pressure PC is used on the inner surface of flange nozzle;
• The equivalent pressure PE is adopted at the end face of nozzle;
• Pb = Mo / LG, applied to the bolt hole or nut area.

Using the above boundary conditions, it is in line with the assumption of waters, the concept is clear, and it is very convenient to load.
After the analysis results are obtained, they can be matched with the conventional calculation and evaluated.
The stiffness of flange can be determined by the deflection angle of flange ring. The deflection angle formed by the outermost and innermost XY displacement of flange can be measured if it is less than 0 . three ° Then the stiffness is qualified.
In our analysis, we often encounter the situation that the flange is guaranteed and does not need FEA to calculate the flange.
For example, for the pipe flange with hole reinforcement, such as the equipment flange and so on, it can be considered not to build the flange when modeling, so as to avoid the complex flange boundary condition loading. In particular, to avoid the flange to apply the wrong load, but it is used as a large reinforcing ring, exerting a non conservative influence on the opening reinforcement.
Of course, if the flange calculation passes, the flange is established for the integrity of the model. It is also possible to use equivalent pressure for flange.
For example, in case 5.2.1 of ASME ptb-3, the internal pressure equivalent pressure exerted by flange sealing surface. ## Summary

• The loading method of WRC538 can inspire us to make an equivalent elastic boundary condition.
• The simplified model is used to analyze the flange, which can match the calculation results of the flange in waters method.
• If the strength of the flange itself is not concerned in the calculation, such as opening reinforcement, the modeling of the flange can be omitted or the equivalent pressure can be used. If the influence of flange is considered, Mo of waters method should be used at least, and ASME PCC should be used if necessary – 1 to calculate mo.

Source: China Flange Manufacturer – Yaang Pipe Industry (www.steeljrv.com)

(Yaang Pipe Industry is a leading manufacturer and supplier of nickel alloy and stainless steel products, including Super Duplex Stainless Steel Flanges, Stainless Steel Flanges, Stainless Steel Pipe Fittings, Stainless Steel Pipe. Yaang products are widely used in Shipbuilding, Nuclear power, Marine engineering, Petroleum, Chemical, Mining, Sewage treatment, Natural gas and Pressure vessels and other industries.) 