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# Analysis on design and calculation method of pressed loose flange

A pressed loose flange made of stainless steel was described, including commonly-used design methods ( e. g. Waters) for non-standard flanges and the feasibility of applying this method to calculate the pressed loose flange in the design; and its theoretical calculation was discussed.

The European and American pressed flanges are manufactured according to DIN 2642 and DIN 2576 standards. In foreign countries, pressed flanges are mainly used in dyeing machines, and TC in Germany is one of the first companies to use this flange. In China, dyeing machine manufacturers in many areas have already requested the use of pressed flanges, but because of the lack of design basis for this kind of non-standard flanges in China (GB150 is based on the flat plate theory), this request for use has not been approved.
From the Bach method proposed by Bach in Germany in 1891 to the new EN1591 standard in 2009, the design calculation method of flanges has undergone more than 100 years of development and evolution. The design calculation theory can be divided into 3 stages according to time: the method based on material mechanics, the method based on elastic analysis and the analysis method based on plastic limit. The Waters method is the most representative and widely used flange design method based on elastic analysis. The American ASME, China’s GB150, British BS, Japanese JIS and French CODAP standards are based on the Waters method.

## 1. Introduction of Waters method

Waters method since 1937 by Taylor and Waters, many scholars have conducted in-depth research on it, giving advice and a number of modifications and improvements to it. Waters pointed out that “‘flange design’ actually consists of three parts: gasket design, bolt design, and flange design, and is performed sequentially; failure in any one of these steps directly affects the subsequent steps, and the design results can vary widely.” [1].
Waters method is established on the basis of online elastic plate and shell theory of non-standard flange design calculation method, whether it is internal pressure flange or external pressure flange, in addition to the flange moment calculation formula is different, according to the flange ring and cylinder (or including tapered neck) connected to the degree of solidity, the various types of flanges are distinguished as a whole (including necked) flange and live set (including necked) flange, any flange is close to these two [2]. The basic idea of the Waters method is that, based on the elastic analysis, the maximum stress in the flange is calculated based on the gasket coefficient m and the sealing specific pressure y, under the condition that the forces in the flange are determined, and the maximum stress in the flange is calculated by The maximum stress in the flange is calculated based on the gasket coefficient m and the sealing specific pressure y.

### 1.1 Basic assumptions

The assumptions in the derivation of the Waters method can be summarized as follows:

• a. The flange remains elastic at the design temperature and does not undergo creep or plastic deformation. This assumption ensures that the stresses and strains generated in the flange are within the elastic range.
• b. The bolt load W, gasket load HG and hydrostatic axial forces HD and HT are all known.
• c. The bolt load and force arm are derived as assumed, and the product of the bolt load and force arm is the external moment applied to the flange, which is used as the equivalent force couple on the inner and outer diameters of the flange ring instead.
• d. The radial displacement of the large end of the tapered neck is assumed to be zero due to the interruption of displacement at its connection with the ring plate at its inner surface as the middle surface of the shell and tapered neck.
• e. The deflection and deformation of the flange ring are very small, the radial displacement of the annular shape center can be neglected, and the elongation of its neutral surface due to bending can be neglected [2-4].

### 1.2 Mechanical calculation model and calculation processing method

After Waters’ simplification and assumptions, the calculation model is shown in Figure 1.

Fig. 1 Sketch of flange force
Waters divided the flange (no matter flat welding flange or long neck butt welding flange) into three parts: shell, tapered neck and flange ring for stress analysis.
Shell stress analysis calculation processing method: semi-infinite length cylindrical shell, along the edge (X1 = 0) by the uniform distribution of bending moment M0 and shear force Q0 action.
Calculation method for stress analysis of tapered neck: cylindrical shell with linear variable thickness, with uniformly distributed bending moment and shear force along the edge at the small end of X2=0, and uniformly distributed bending moment and shear force at the large end of X2=h.
The computational treatment of the flange ring stress analysis: the ring-shaped thin plate, in which the inner and outer rings act as a uniform force W0, constituting a moment (where W1 is the sum of the uniform force W0, M0 is the flange design moment) in addition to the role of the uniform bending moment along the inner circumference, the value of X1.

### 1.3 Evaluation

For different flange forms Waters method has different calculation results, literature [5] pointed out that: the calculation error increases with the increase of diameter. For a diameter of 1219 mm, the underestimation is about 10%; while for larger diameters, the underestimation is up to 30%. For flanges with diameters over 1524 mm in the pressure range of 1.138 to 2.172 MPa, a more accurate calculation method should be used in flange design.
Ignore the influence of temperature and leakage level, easily lead to high sealing level can not meet the requirements of use, sealing level of low material waste. 11 of EN13445.3 (based on Taylor-Waters method) on the method will be limited to the design range of internal and external pressure flange. Users who wish to consider thermal cycling, control leakage, or flanges subjected to other additional loads should use the alternative method provided in Appendix G of the standard (i.e., the EN1591-1 method) [6].
The Watesr method omits the discontinuous stress caused by the radial action of the pressure load on the flange and the “direct film stress” caused by the internal pressure on the cylinder and conical neck, which is called “pressure expansion effect”. This is considered to be the main reason why the Watesr method underestimates the flange stress [4].
The Waters method does not take into account the degree of bolt hole sparseness, the longitudinal bending stress of the tapered neck of the flange connection under load, and the working condition of the flange in the elasto-plastic state, which makes the calculation results less accurate. In the literature [6], it is pointed out that the stresses in the flange calculated by Waters are 1/3 smaller than those obtained by FEA, and the deflection is half.
Nevertheless, the Waters method has withstood a large number of practical applications throughout the world for more than half a century and has been proven to give satisfactory design results in design situations [7].

## 2. Stainless Steel pressed flanges

Like other flange connections, pressed flanges are flange bolting systems. Stamped flange assembly is composed of flange, flanged short section, gasket, bolt, nut and spring washer (Figure 2), the flange of stamped flange is not a flat surface, but a combination of depression, projection and peripheral flanges. The unique structure of the flange and flanged short section (especially the flange) of the stamped flange is significantly different from the traditional loose-fitting flange, thus forming the unique advantages of the stamped flange.

Figure 2 Stamping flange assembly
Punching flange is a new type of non-standard pipe flange, compared with the traditional pipe flange, its unique structure, simple processing technology, raw material consumption and comprehensive cost significantly reduced, the large-scale promotion and application will produce significant economic benefits.

## 3. The feasibility of using Waters method to calculate the pressed flange

Through the above analysis, it can be seen that the Waters method, on the basis of elastic analysis, divides the flange into three parts: cylinder, tapered neck and flange ring, which correspond to the three models of cylindrical shell, linear variable thickness cylindrical shell and annular flat plate for calculation. The heterogeneous structure of the pressed flange obviously cannot be applied to the Waters’ calculation model, especially for the flange with non-flat structure, and the flat plate theory calculation method involved in the Waters’ method cannot be used. Therefore, it is not feasible to use Waters’ method for non-standard flange verification method for theoretical calculation of pressed flanges.

## 4. Conclusion

The unique structure of the pressed flange makes it impossible to use the traditional non-standard flange design calculation method (Waters method) for theoretical calculation. The author proposes three theoretical calculation ideas for the pressed loose flange and conducts a comparative analysis:

• a. Calculation based on the theory of moment on the basis of elastic mechanics;
• b. Calculation by conceiving the pressure flange as a cantilever beam along the circumference (based on the Bach method);
• c. The non-flat flange in the stamped flange assembly is equated to a flat plate of a certain thickness using the moment theory, and then calibrated according to the conventional flat non-standard flange (referred to as the equivalence calculation method).

Method a is theoretically feasible, but the process is too complicated, lack of practical use; method b, although greatly simplifies the calculation, but has the same drawbacks as the Bach method, that is, the method only calculates the radial bending stress, ignoring the larger circumferential stress, the calculation results are small, can be considered by adding a safety factor to reduce the error, but through a large number of experiments and simulation analysis, the workload is large; Method c proposes a new way of calculating the pressed flange, although the maximum stress location and the maximum stress value may be different before and after equivalence, but it is verified by finite element and experiment, which is a new direction for theoretical calculation of non-flat flange.

Authors:Huanhuan Zhang,Haiqing Zhu

Source: Network Arrangement – China : www.epowermetals.com

(Yaang Pipe Industry is a leading manufacturer and supplier of nickel alloy and stainless stainless steel products, including Super Duplex Stainless Stainless Steel Flanges, Stainless Stainless Steel Flanges, Stainless Stainless Steel Pipe Fittings, Stainless 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.)

Reference:

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