Bolted flange connection structure of flange design

There are many forms of removable sealing devices for pressure vessels, such as threaded connection, socket connection and bolt flange connection in medium and low pressure vessels, among which bolt flange connection with simple structure and convenient assembly is the most common.
Bolted flange connection is mainly composed of flange, bolt and gasket, as shown in Figure 1.

Figure 1 Bolted flange link structure
The bolt has two functions: one is to provide pre tightening force to realize initial sealing and maintain the sealing during operation; The second is to change the bolted flange connection into a detachable connection.
The gasket is installed between the two flanges to prevent leakage of the container. There are bolt holes in the flange to accommodate the bolts. The bolt force, gasket reaction force and the pressure load acting on the middle surface of the cylinder are not in the same straight line. The flange will be bent and deformed under the action of bending moment.
The general purpose of bolted flange connection design is to determine the safe and economic flange and bolt size for the known gasket characteristics, so that the leakage rate of the joint is within the allowable range of process and environment, and the stress in the joint is within the allowable range of materials, that is, to ensure confidentiality and structural integrity.
The following mainly introduces the sealing principle of sealing device, factors affecting sealing, classification and selection principle of sealing structure, strength calculation of sealing structure, etc.

Sealing mechanism and classification

Sealing mechanism

The following takes the bolted flange connection structure as an example to illustrate its sealing mechanism.
There are two ways for fluid leakage at the sealing port:

  • The first is “penetration leakage”, that is, the penetration leakage through the capillary tube of the gasket material body, which is mainly related to the structure and material properties of the gasket, in addition to the influence of the fluid state properties such as medium pressure, temperature, viscosity and molecular structure. The “penetration leakage” can be avoided by adding some fillers to the permeable gasket material or combined with the impermeable material;
  • The second is “interface leakage”, that is, the leakage between the gasket and the compression surface. The leakage is mainly related to the interface gap size. The pressing surface refers to the contact surface between the upper and lower flanges and the gasket. The uneven gap and insufficient pressing force on the pressing surface are the direct causes of “interface leakage”. “Interface leakage” is the main way of flange seal failure.

The basic method to prevent fluid leakage is to increase the fluid flow resistance at the sealing port. When the resistance of the medium passing through the sealing port is greater than the medium pressure difference on both sides of the sealing port, the medium will be sealed. The resistance of the medium through the sealing port is realized by the specific pressure applied to the pressing surface. The greater the sealing specific pressure acting on the pressing surface, the greater the resistance of the medium through the sealing port, which is more conducive to sealing. The whole working process of bolted flange connection can be described by pre tightening condition, pre tightening condition and operating condition.
Figure 2 (a) shows the working condition without preloading. Enlarge the micro size of the contact between the upper and lower flange pressing surfaces and the gasket, and you can see that their surfaces are uneven, which is the channel of fluid leakage. Figure 2 (b) shows the preloading condition.

Figure 2 Sealing mechanism diagram
Tighten the bolts, and the bolt force acts on the gasket through the flange pressing surface. As the material of the gasket is non-metallic, non-ferrous metal or mild steel, its strength and hardness are much lower than that of the steel flange. Therefore, when the compression force on the unit area of the gasket surface reaches a certain value, the gasket will produce elastic or yield deformation, fill the original unevenness at the upper and lower compression surfaces, block the channel of fluid leakage, and form the initial sealing condition.
When the initial sealing condition is formed, the minimum pressing force on the unit area of the gasket is called “gasket specific pressure”, expressed in Y, and the unit is MPa. Under the pre tightening condition, if the compression force on the unit area of the gasket is less than the specific pressure y, the medium will leak.
Figure 2 (c) shows the operating conditions. At this time, when the medium is introduced, with the rise of medium pressure, on the one hand, the axial force caused by the internal pressure of the medium will promote the separation of the compression surfaces of the upper and lower flanges, the compression amount formed by the gasket under the preloading condition will be reduced, and the sealing specific pressure on the compression surface will be reduced; On the other hand, the elastic compression deformation part of the gasket during pre tightening produces rebound, and the rebound amount of compression deformation compensates for the separation of the compression surface caused by bolt elongation, so that the sealing specific pressure acting on the compression surface can still maintain a certain value to maintain the sealing performance.
The compressive stress that must be applied to the gasket to ensure the sealing performance of the flange in the operating state is called the operating seal specific pressure. The operating seal specific pressure is often expressed as m times of the calculated pressure of the medium. Here m is called “gasket coefficient”, dimensionless.

Seal classification

According to the different methods to obtain the seal specific pressure, the pressure vessel seal can be divided into forced seal and self tightening seal. Forced sealing is to forcibly squeeze the sealing element to achieve sealing by completely relying on the force of the connector (such as the preload of tightening the connecting bolt), so a large preload is required, which is about 1.1 ~ 1.6 times of the axial force generated by the working pressure; The self tightening seal mainly depends on the medium pressure inside the container to compress the sealing elements to achieve sealing. The higher the medium pressure, the more reliable the seal is,
Therefore, the preload required for sealing is small, usually less than 20% of the axial force generated by the working pressure. According to the main deformation form of the sealing element, the self tightening seal can be divided into axial self tightening seal and radial self tightening seal. The sealing performance of the former mainly depends on the axial stiffness of the sealing element being less than that of the connected part; The latter is mainly realized by the fact that the radial stiffness of the sealing element is less than that of the connected part.
In addition, there is a semi self tightening seal. According to the classification principle, its sealing structure belongs to non self tightening forced seal, but it also has certain self tightening performance, such as double cone sealing structure in high-pressure vessel sealing.
According to the pressure of the sealed medium, the pressure vessel seal can be divided into medium and low pressure seal and high pressure seal. The bolt flange connection structure is the most commonly used medium and low pressure seal. It is widely used in the connection between the opening nozzle of the container and the head and the cylinder. It is a forced seal.

Main factors affecting sealing performance

The factors affecting the sealing performance are related to the sealing structure. Now take the bolt flange connection structure as an example.

Bolt preload

Bolt preload is an important factor affecting sealing. The preload must compress the gasket to achieve the initial seal. Properly increasing the bolt preload can increase the sealing capacity of the gasket, because increasing the preload can keep a large contact surface specific pressure of the gasket under normal working conditions.
However, the preload should not be too large, otherwise the gasket will yield as a whole and lose its resilience, or even extrude or crush the gasket. In addition, the preload shall act on the gasket as evenly as possible. Generally, measures such as reducing the bolt diameter and increasing the number of bolts are taken to improve the sealing performance.

Gasket performance

Gasket is an important component in sealing structure, and its deformation ability and rebound ability are the necessary conditions for forming sealing. The sealing gasket with large deformation capacity is easy to fill the gap on the compression surface, and the preload is not too large; The sealing gasket with large resilience can adapt to the fluctuation of operating pressure and temperature. Because the gasket is in direct contact with the medium, it should also have the properties of adapting to the temperature, pressure and corrosion of the medium.

Quality of pressing surface

The pressing surface, also known as the sealing surface, is in direct contact with the gasket. The shape and roughness of the pressing surface shall match the gasket. Generally speaking, the quality requirements of the pressing surface when using metal gasket are higher than those when using non-metal gasket. The pressing surface shall be free of knife marks and scratches; At the same time, in order to evenly press the gasket, ensure the flatness of the pressing surface and the perpendicularity between the pressing surface and the central axis of the flange.

Flange stiffness

Excessive warping deformation due to insufficient flange stiffness (as shown in Figure 3) is often one of the main reasons for seal failure of bolted flange connection in actual production. The flange with large stiffness has small deformation, which can evenly transfer the bolt preload to the gasket, so as to improve the sealing performance of the flange.

The flange stiffness is related to many factors. Appropriately increasing the thickness of the flange ring, reducing the diameter of the bolt center circle and increasing the outer diameter of the flange ring can improve the flange stiffness. The bending capacity of the flange can be significantly improved by using the flange with neck or increasing the size of the cone neck. However, increasing the flange stiffness without principle will make the flange bulky and increase the cost.

Figure 3 Warpage deformation of flange

Operating conditions

It mainly refers to the influence of pressure, temperature and physical and chemical properties of medium on sealing performance. The influence of operating conditions on the seal is very complex. The influence of simple pressure and medium on the seal is not significant, but under the combined action of temperature, especially the fluctuating high temperature, it will seriously affect the seal performance, and even make the seal completely invalid due to fatigue. Because at high temperature, the medium has low viscosity, high permeability and easy leakage; The corrosion of the medium on the gasket and flange intensifies, increasing the possibility of leakage; Flanges, bolts and gaskets will produce large high-temperature creep and stress relaxation, resulting in seal failure; Some non-metallic gaskets will also accelerate aging, deterioration and even burn out.
In short, there are many factors affecting the sealing performance of bolted flange connection. In the sealing design, it should be comprehensively considered according to the specific working conditions.

Bolted flange connection design

Structure type and standard of flange

There are many Classification methods for flanges. For example, according to the width of flange contact surface, it can be divided into wide face flange and narrow face flange. The contact surface of the flange within the circumference of the bolt hole is called “narrow face flange”; The contact surface of the flange extending to the outside of the bolt center circle is called “wide face flange”. According to the application, it can be divided into container flange and pipe flange. Correspondingly, flange standards also include container flange and pipe flange.

Flange structure type

The basic structural form of flange can be divided into loose flange, integral flange and arbitrary flange according to the integrity of cylinder, flange ring and cone neck, as shown in Figure 4.
① Loose flange refers to the structure in which the flange is not directly fixed on the shell or cannot bear the bolt load as a whole with the shell, such as looper flange, threaded flange, lap joint flange, etc. these flanges can be with or without neck, as shown in Fig. 4 (a) ~ (c).
The looper flange is a typical loose flange. The torque of the flange is completely borne by the flange ring itself, and there is no additional bending stress on the equipment or pipeline. Therefore, it is suitable for non-ferrous metal and stainless steel equipment or pipelines, and the flange can be made of carbon steel to save precious metals. However, the flange has small stiffness and thick thickness, which is generally only suitable for occasions with low pressure.
② Integral flange is a flat welding flange that forged or cast the flange and the shell into a whole or through full penetration, as shown in Figure 4 (d)~(f) As shown in. This structure can ensure that the shell and the flange are stressed at the same time, so that the thickness of the flange can be appropriately reduced, but a large stress will be generated on the shell. The neck flange can improve the connection stiffness between the flange and the shell, and is suitable for important occasions with high pressure and temperature.

③ From the structural point of view, this kind of flange is integrated with the shell, but the rigidity is between the integral flange and the loose flange between flanges, see Fig. 4 (g) ~ (I).

Fig. 4 Structural type of flange

Flange standard

In order to simplify calculation, reduce cost and increase interchangeability, countries all over the world have formulated a series of flange standards. In actual use, standard flanges shall be selected as far as possible. Only when large diameter, special working parameters and structural forms are used, they need to be designed by themselves.
The flange standard is based on two sets of standards: Branch flange and vessel flange. The connection dimensions of pipe flange and vessel flange with the same nominal diameter and nominal pressure are different, and they cannot be applied to each other.
The main parameters of flange selection are nominal pressure and nominal diameter.
① Nominal diameter is the standardized size series of vessels and pipes, expressed in DN. For a container, it refers to the inner diameter of the container (except for a container with a tube as a cylinder); For pipes or fittings, nominal diameter refers to the nominal diameter, which is a value close to the inner diameter. For steel pipes with the same nominal diameter, the outer diameter is the same. Because the thickness changes, the inner diameter also changes. For example, DN100 seamless steel pipe has ϕ108×4, ϕ108×4.5, ϕ108×5 and other specifications. The nominal diameter of vessels and pipes shall be selected according to the series specified in national standards.
② Nominal pressure is the standardized pressure grade of pressure vessel or pipeline, that is, the working pressure is divided into several pressure grades according to the standardization requirements. It refers to the maximum working pressure at the specified temperature, which is also a standardized pressure value.
When selecting parts for vessel design, the nominal pressure close to the design pressure and slightly higher than the design pressure shall be selected. When the design temperature of container parts rises and affects the strength limit of metal materials, parts shall be selected according to the higher nominal pressure.
There are two series of international nominal pressure Classes, namely PN series and Class series. Some countries such as Europe use PN series to represent the nominal pressure grade, such as PN25. PN40, etc; The United States and other countries are accustomed to using Class series to represent the nominal pressure grade, such as Class150, Class600, etc. It should be noted that PN and Class are symbols used to represent the nominal pressure Class series, and they are dimensionless.
The nominal pressure grades of PN series include 2.5, 6.0, 10, 16, 25, 40, 63, 100, 160, 250, etc; The nominal pressure Classes commonly used in Class series include Class150, Class300, Class600, Class900, Class1500, Class2500, etc.

The numbers after PN and Class do not represent the actual working pressure that the flange can bear. For a given PN or Class flange, the maximum allowable working pressure should be checked in the pressure temperature rating of the corresponding flange standard according to the flange material and working temperature. See table 4-10 for the corresponding relationship between PN series and Class series.

Table 4-10 The corresponding relationship between PN series and Class series

PN 20 50 110 150 260 420
Class 150 300 600 900 1500 2500

③ Vessel flange standard Chinese pressure vessel flange standard is Nb / T47020 ~ 47027 pressure vessel flanges, gaskets and fasteners. The standard gives the Classification, technical conditions, structural forms and dimensions of type a flat welding flange, type B flat welding flange and long neck butt welding flange, as well as relevant gasket and bolt forms. The nominal pressure range is 0.25 ~ 6.4Mpa and the nominal diameter is 300 ~ 3000mm.

④ The standard of pipe flange is ASME / ANSI B16 5 pipe flanges and accessories, ASME / ANSI B16.47 large diameter steel flange is represented by the standard, and the PN series pipe flange is represented by EN1092.1 ~ 1092.4. In the same series, the pipe flange standards of various countries can basically match each other (referring to the connection size and sealing surface size), but the two series cannot match each other. The obvious distinguishing sign is that the nominal pressure grade is different.
At present, there are many pipe flange standards in China, mainly including national standard GB / T9112 ~ 9125 steel pipe flange, mechanical industry standard JB / T74 ~ 86.2 pipeline flange and chemical industry standard HG / T20592 ~ 20635 steel pipe flange, gasket and fastener (including PN series and Class Series), etc. Considering the wide range of application and complete variety of materials of HG / T20592 ~ 20635 pipe flange standard series, it is recommended to give priority to the standard when selecting pipe flange.
⑤ The selection of standard flange shall be based on the nominal diameter, nominal pressure, working temperature, working medium characteristics and flange material of vessel or pipeline.
The nominal pressure of vessel flange is based on the maximum working pressure of 16Mn or Q345R at 200 ℃. Therefore, when the flange material and working temperature are different, the maximum working pressure will decrease or increase.
Whether it is vessel flange standard or pipe flange standard, there will be a pressure temperature rating table. When selecting a standard flange, first check the maximum allowable working pressure of a flange in the pressure temperature rating table of the standard according to the design temperature and material (or material category) of the flange, so that the maximum allowable working pressure is greater than the design pressure of the flange, and then take the nominal pressure corresponding to the maximum allowable working pressure as the pressure grade of the selected standard flange.
For example, PN25. For long neck butt welding flange (Nb / T47023), the maximum allowable working pressure is 2.5MPa when the design temperature is – 20 ~ 200 ℃, but when the design temperature is 400 ℃, its maximum allowable working pressure will only be 1.93mpa; If the flange material is 20 steel, the maximum allowable working pressure at – 20 ~ 200 ℃ is only 1.81Mpa, and if the design temperature rises to 400 ℃, the maximum allowable working pressure will be reduced to 1.26MPa.

Selection of flange sealing surface and gasket

There are two key problems to be solved in the design of bolted flange connection: one is to ensure that the connection is “tight without leakage”; Second, the flange shall have sufficient strength to avoid damage due to stress. In practical application, bolted flange connections are rarely damaged due to insufficient strength, and most of them leak due to poor sealing performance. Therefore, sealing design is an important link in bolted flange connection, and the sealing performance is related to the compression surface and gasket. The following mainly introduces the selection of flange pressing surface and gasket.

Selection of flange pressing surface

The pressing surface shall be selected mainly according to the process conditions, sealing diameter and gasket. The commonly used pressing surface forms include full plane [Fig. 5 (a)], convex surface [Fig. 5 (b)], concave convex surface [Fig. 5 (c)], tenon and groove surface [Fig. 5 (d)] and ring connecting surface (or T-groove) [Fig. 5 (E)], among which convex surface, concave convex surface and tenon and groove surface are the most commonly used.

Fig. 5 Form of pressing surface

The protruding surface has the advantages of simple structure, convenient processing, easy loading and unloading, and easy anti-corrosion lining. The pressing surface can be made smooth,
You can also open 2 ~ 4 strips on the compression surface with a width of x 0.8mm deep x 0.4mm circumferential groove with triangular cross section. This raised surface with groove can effectively prevent non-metallic gasket from being squeezed out of the pressing surface, so it is more suitable for a wide range of occasions.
Generally, the completely smooth raised surface is only suitable for occasions with nominal pressure ≤ 2.5MPa. After grooved, the container flange can be up to 6.4Mpa, and the pipe flange can even be up to 25 ~ 42MPa. However, with the increase of nominal pressure, the applicable nominal diameter decreases accordingly.
The concave convex pressing surface is easy to align during installation, and can effectively prevent the gasket from being squeezed out of the pressing surface. It is suitable for nominal pressure
Vessel flange and pipe flange with force ≤ 6.4Mpa.
The pressing surface of the tenon groove is composed of a tenon surface and a groove surface, and the gasket is placed in the groove. Because the gasket is narrow and blocked by the groove surface, it will not be squeezed out of the compression surface, and is less scoured and corroded by the medium. The required bolt force is relatively small, but the structure is complex and it is difficult to replace the gasket. It is only suitable for important occasions such as flammable, explosive and highly toxic media.

Gasket selection

Gasket is the core of bolted flange connection. The sealing effect mainly depends on the sealing performance of gasket. During the design, the structural form, material and size of the gasket shall be selected mainly according to the medium characteristics, pressure, temperature and the shape of the pressing surface, and the factors such as price, convenience of manufacturing and replacement shall be taken into account.
The basic requirements are that the gasket materials do not pollute the working medium, are corrosion-resistant, have good deformation ability and resilience, and are not easy to deteriorate, harden or soften at the working temperature. For media commonly used in chemical, petroleum, light industry, food and other production, refer to table 4-11 for gasket selection.

Table 4-11 Gasket selection table

Brief introduction of non-standard flange design method

Waters method

The failure modes of bolted flange connection structure include strength failure and seal failure, and the seal failure is the main failure mode in the two kinds of failure. However, due to the strength failure of structures and the difficulties encountered in the study of design methods based on seal failure, national codes and standards have mainly adopted the strength design method based on elastic analysis for a long time, and the most widely used is the waters method (or Taylor forge method).
The mechanical model of waters method is to divide the flange structure into three parts: shell, cone neck and flange ring (see Figure 4-27)

Figure 4-27 Water method stress analysis model
The body and cone neck are subjected to pressure, and the flange ring is subjected to pressure, gasket reaction force and bolt force. According to the deformation coordination equation of the three parts at the connection, the edge force and edge torque are obtained, and then the stresses of the shell, cone neck and flange ring under external load, edge force and edge torque are calculated respectively. The following assumptions are made in the derivation of waters method:

  • ⅰ. The flange ring and shell (or connecting pipe) are in elastic state, that is, there is no yield or creep;
  • ⅱ. The external torque acting on the flange is approximately considered to be replaced by a couple composed of forces acting uniformly on the inner and outer circumference of the flange ring;
  • ⅲ. The flange ring is regarded as a ring or ring plate with rectangular section. Under the action of external torque, the deformation of rectangular section only rotates the cross section by a certain angle θ, The section of the flange does not have any distortion and bending;
  • ⅳ. The influence of bolt hole is omitted and the flange is regarded as a solid ring or ring plate;
  • ⅴ. The flange ring and shell are only affected by the torque caused by the bolt force, and the stress directly caused by the internal pressure (or external pressure) of the medium on the flange ring or shell is ignored.

When using the waters method to analyze the flange structure, it is also assumed that in order to achieve the purpose of sealing, the gasket reaction force must reach a certain value under the preload and operating conditions of the flange. The gasket reaction force per unit area required under preload condition is y, while the gasket reaction force per unit area required under operating condition is expressed in 2MP.
Where p is the calculated pressure and M is a dimensionless constant. Y and m are called gasket constants. These two parameters are only related to the selected gasket and have nothing to do with the service conditions such as pressure, temperature and medium. The values of Y and m of some common gaskets are given in Chinese pressure vessel standard GB150.
The following steps shall be followed for flange design according to waters method.
(1) Selected flange structure
The flange form, sealing surface form, gasket type and size and the structural size of most flanges shall be determined according to the pressure, temperature and medium hazard given by the process operation conditions.
After the flange form is determined according to the operating conditions, the inner diameter, outer diameter and cone neck height of the flange can refer to the standard flange with similar nominal diameter.
Gasket is the core of bolted flange connection. The sealing effect mainly depends on the sealing performance of gasket. During the design, the structural form, material and size of the gasket shall be selected mainly according to the medium characteristics, pressure, temperature and the shape of the pressing surface, and the factors such as price, convenience of manufacturing and replacement shall be taken into account.
The basic requirements are that the gasket materials do not pollute the working medium, are corrosion-resistant, have good deformation ability and resilience, and are not easy to deteriorate, harden or soften at the working temperature.
(2) Bolt design
Calculate the bolt load according to the pressing force required for sealing, select appropriate bolt materials, calculate the bolt diameter and number, determine the bolt size according to the thread and bolt standards, and finally check the bolt spacing.
① The gasket pressing force can be calculated by knowing the performance (m, y) of gasket material and the calculated sealing width of gasket.
The pressing force required for the gasket under constant diameter and pressure.
The pressing force required during pre tightening is calculated according to formula (4-60)

  • Fa=πDGby (4-60)

In the formula:

  • Fa — Minimum gasket pressing force required under pre tightening state, N;
  • B — effective sealing width of gasket, mm;
  • DG — calculated diameter of center circle of gasket pressing force, mm;
  • When the basic sealing width Bo ≤ 6.4mm, DG is equal to the average diameter of gasket contact;
  • When the basic sealing width Bo > 6.4mm, DG is equal to the outer diameter of gasket contact minus 2B;
  • y — gasket specific pressure, found from table 4-9, MPa.

The pressing force required during operation is caused by the specific pressure of the operating seal. Since the original definition m is taken as 2 times, and the pressing load on the effective contact area of the gasket is equal to m times of the operating pressure, the specific pressure of the operating seal shall be 2mpc during calculation, then

  • Fp=2πDGbmpc (4-61)

In the formula:

  • Fp – the minimum gasket pressing force required under the operating state, N;
  • m – Gasket coefficient, obtained from table 4-9;
  • pc — calculated pressure, MPa.

It should be noted that the gasket width used to calculate the contact area in equations (4-60) and (4-61) is not the actual width of the gasket, but a part of it, that is, the basic sealing width Bo. Its size is related to the shape of the pressing surface, as shown in table 4-12. In the width range of Bo, the specific pressure y is regarded as uniform distribution.
When the gasket is wide, the flange deflects due to the bolt load and internal pressure, so the outer side of the gasket is pressed tighter than the inner side. Therefore, in the actual calculation, the gasket width is smaller than Bo, which is called effective sealing width B. its relationship with the basic sealing width Bo is as follows:

  • When Bo ≤ 6.4mm, B = Bo;
  • When Bo > 6.4mm, B = 2.53bo.

Table 4-12 Gasket seal basic width bo

① When the depth of sawtooth does not exceed 0.4mm and the tooth pitch does not exceed 0.8mm, the pressing surface shape of 1B or 1D shall be adopted.
② Calculation of bolt load under the pre tightening state, the minimum bolt load required is equal to the pressing force required to ensure the initial sealing of the gasket, so it can be calculated according to formula (4-62), i.e

In the formula, WA – Minimum bolt load required under pre tightening state, n.
The minimum bolt load required in the operating state consists of two parts: the axial force generated by the medium and the gasket pressing force required to keep the gasket sealed, i.e

In the formula, WP – Minimum bolt load required under operating state, n.
③ In bolt design, generally, bolts and nuts shall be made of different materials or the same material, but different heat treatment conditions make them have different hardness. The hardness of bolt material shall be more than 30hb higher than that of nut.
In order to ensure reliable sealing during pre tightening and operation, the cross-sectional area of bolts under two working conditions shall be calculated respectively, and the larger one shall be selected as the required cross-sectional area, so as to determine the diameter and number of bolts.
In the pre tightening state, calculated at normal temperature, the required cross-sectional area Aa of the bolt is

In the formula: [σ] b — allowable stress of bolt material at normal temperature, MPa.
Under the operating state, the cross-sectional area Ap required by the bolt is calculated according to the bolt design temperature

In the formula: [σ] tb — allowable stress of bolt material at design temperature, MPa.
The required bolt cross-sectional area am is the larger of Aa and Ap. The diameter and number of bolts can be determined by am

In the formula:
  • do– root diameter of thread or minimum section diameter of bolt, mm;
  • N — number of bolts.

During design, do and N are interrelated unknowns. Generally, first assume the number of bolts n (n should be an even number, preferably a multiple of 4) according to experience or reference to relevant standards, calculate the bolt root diameter do, and then round do into the thread root diameter according to the bolt standard, so that the actual bolt cross-sectional area is not less than am. Small diameter bolts are easy to break when tightened, so the nominal diameter of bolts shall not be less than M12.
When determining the number of bolts, we should not only consider the tightness of bolt flange connection, but also consider the convenience of installation. There are many bolts, the gasket is stressed evenly and the sealing effect is good. However, due to too many bolts and smaller bolt spacing, the wrench may not be able to be put down, resulting in difficulty in assembly and disassembly.
The center distance L (= π dB / N) of two bolt holes on the flange ring shall be in the range of (3.5 ~ 4) dB. If the bolt spacing is too large, additional flange bending moment will be caused between the bolt holes, and uneven stress on the gasket will reduce the tightness. Therefore, the maximum bolt spacing shall not exceed the value determined by equation (4-67)

In the formula:
  • dB – nominal diameter of bolt, mm;
  • δf — effective thickness of flange, mm.

The minimum radial dimension La and le of flange and the minimum value of bolt spacing L (are selected according to table 4-13).

  • Group a data is applicable to the structure of necked flange shown in figure (a);
  • Group B data is applicable to the welded flange structure shown in figure (b).

(3) Flange moment calculation
As with bolt design, pre tightening and operation conditions shall also be considered in calculating the torque on the flange. In the pre tightening condition, only the torque generated by the gasket reaction force and bolt force acts on the flange. At this time, considering the uncertainty of pre tightening torque during bolt assembly, the bolt force specified in the standard is

The resulting torque is
  • Ma=WLG(4-69)

In the formula:

  • Am – required bolt cross-sectional area, mm2;
  • Ab — actual bolt sectional area, mm2;
  • LG — distance from bolt center to gasket force application point, mm.

The flange torque MP under operating conditions can be obtained by taking torque from the bolt center by the pressure acting on the cylinder and flange ring and the gasket reaction acting on the sealing surface. Then, take the flange design torque as:

(4) Stress calculation and verification
The edge force and edge torque acting between the shell, cone neck and flange ring can be obtained through the deformation coordination of the three and expressed by the flange design torque mo. in this way, the stress at the large and small ends of the cone neck and the stress in the flange ring can be calculated.
In the design of pressure vessel, the flange connection structure should not only avoid its strength failure, but also avoid its sealing loss effective. Therefore, the strength condition specified in the flange design in the pressure vessel standard actually limits the stress in the flange ring to limit the flange deformation at the same time.
Considering that the maximum stress in the flange ring forms a linear relationship with the flange deformation, although when the stress at a certain point in the flange ring reaches the yield strength, the stress level in other parts of the flange ring is still at a very low level, that is, the flange ring still has sufficient bearing strength, in order to control the torsional deformation of the flange ring to meet certain sealing requirements.

Since the waters method was introduced into its boiler and pressure vessel design code by ASME in 1940, it has been China GB150.3. UK pd5500, France codap2000, Japan JIS B8265, EU EN13445.3 and other pressure vessel codes or standards.
Although there has been no substantial change in this method for more than half a century, it is still the most widely accepted flange design method in the world. Practice shows that most flanges designed according to this method have no obvious leakage accidents due to design problems. However, in practice, it is found that this method has the following problems, resulting in the leakage of a few bolt flange joints designed according to the specification.

  • ⅰ. Waters method uses gasket coefficient m and gasket specific pressure y to simplify flange design calculation, but it fails to truly reflect the sealing behavior of gasket. M and y are based on experience and some tests. There is no theoretical basis. The leakage rate of flange joint cannot be predicted based on the gasket stress determined by these coefficients. These data have hardly changed since entering ASME Design Code, let alone give corresponding data for alternative asbestos materials and new gaskets.
  • ⅱ. Waters method can not obtain the bolt load required for actual sealing. The bolt load calculated by waters method is only used to determine the size of bolts and flanges, which is inconsistent with the actual bolt load required during installation, and the latter is often much greater than the former. This may not ensure that the sealing requirements can be met under all variable working conditions due to insufficient bolt load, or the flange and bolt may yield due to excessive bolt load, and the gasket may be over compressed to cause insufficient rebound or collapse, resulting in leakage.
  • ⅲ. The waters method does not consider the mechanical interaction between gasket bolt flange under hydrostatic pressure, the change of bolt load caused by different thermal expansion of bolt and flange during temperature transient, and the influence of creep / relaxation of various component materials at high temperature. These factors will lead to leakage of bolted flanged joints in case of temperature transient and pressure fluctuation.

In view of the above problems, ASME has made some improvements in the design method of waters flange in recent years. This is mainly reflected in: increasing the requirements for flange stiffness check, stipulating that the angle of rotation of integral flange and loose flange shall be less than or equal to 0.3 ° and 0.2 ° respectively, so as to control its leakage by limiting the angle of rotation of flange; Considering that the leakage of most bolted flange joints is due to installation problems, the provisions of asmepcc-1 installation guide for bolted flange connections at pressure boundary shall be followed when adding installation flanges, including the selection method of installation bolt load, non design factors to reduce flange joint leakage, etc. For practical problems such as installation, high temperature and flange rotation not considered in the design, ASME VIII – 1 has long given interpretation and suggestions in non regulatory appendix s.

Design method based on leakage rate

In the flange failure cases of normal design, the failure due to insufficient strength is rare, while the leakage failure is not rare. Therefore, the flange design should not only meet the strength failure design criteria, but also meet the leakage failure design criteria. The designer needs to determine an allowable leakage rate, and take the leakage rate of the design flange joint not exceeding the allowable leakage rate as the leakage failure criterion.
Since the 1970s, flange design methods based on leakage rate have appeared in the world, and some have been incorporated into pressure vessel or pressure pipeline design codes or standards. Among these methods, there are two most representative ones, namely, the flange design method proposed by the American pressure vessel Research Committee (PVRC) (hereinafter referred to as “PVRC method”) and the flange design method proposed by the European Standards Committee (CEN) (hereinafter referred to as “en method”).
(1) PVRC method
Since the 1970s, PVRC has been committed to the research on the sealing design method of bolted flange joints for a long time.
PVRC believes that all flange joints will leak. The purpose of flange design is to make the designed bolted flange joint not exceed the allowable leakage rate of sealing fluid under all load conditions.
The most remarkable feature of PVRC method is the introduction of the concept of tightness and the establishment of the correlation between fluid pressure and leakage rate. In this method, the leakage failure criterion of bolted flange joint is defined as five tightness levels, each tightness level corresponds to a certain level of mass leakage rate, and the mass leakage rate of adjacent tightness levels is two orders of magnitude different. For example, T2 is the standard level, and the mass leakage rate per unit gasket diameter is 2×10-3mg / (mm · s); T3 grade is compact grade, and its mass leakage rate is 2×10-5mg / (mm · s).
During flange design, the tightness grade shall be selected first, so that the designed joint leakage rate does not exceed the allowable leakage rate under the tightness grade. This means that a higher tightness grade requires larger bolts and thicker flanges, and which tightness grade is selected as the sealing criterion of the design flange depends on the process conditions, operating conditions, ecological and environmental protection requirements of the designed equipment. For example, class T2 is applicable to general sealing requirements, while class T5 is used in important occasions such as nuclear power and aerospace.
Another feature of PVRC method is that a new gasket design parameter is established based on the test data, that is, the gasket design parameters (a, GB, GS) obtained by correlating the double logarithm relationship between tightness and gasket stress are used to replace m and y. These new gasket design parameters are derived from a large number of test data conducted by PVRC on past and new gaskets, and are related to the allowable leakage rate corresponding to the tightness level.
PVRC method shall first select the tightness grade, calculate the minimum gasket stress and bolt load that meet the design tightness requirements under preload and operating conditions according to the gasket design parameters, and then check the flange strength and stiffness according to the same steps and methods of waters method.
In engineering application, PVRC method still faces many problems. For example, how to determine the appropriate tightness; The designed tightness is not equal to the actual leakage level. Therefore, this method has not yet entered the ASME code and needs further verification, improvement and improvement.
(2) EN method
Since the 1990s, cen has absorbed some PVRC research results while carrying out a series of research on flange design methods. In 2001, en1591-1 design rules for flanges and their joints – circular flange connections with gaskets – Part 1: calculation method (latest version 2013) and en1591-2 design rules for flanges and their joints – circular flange connections with gaskets – Part 2: Gasket parameters (latest version 2008), namely en method, were promulgated. In 2002, en method entered Part 3 of EN13445 non direct contact flame pressure vessels as its non prescriptive appendix G.
The en method also reformed the gasket design basis. Similar to PVRC method, en method divides the allowable leakage rate into three tightness levels, and develops new Gasket parameters based on leakage rate, including minimum installation gasket stress, maximum installation gasket stress, minimum working gasket stress, maximum working gasket stress, unloading resilience modulus, creep coefficient and axial thermal expansion coefficient.
Compared with the gasket parameters proposed by PVRC method, these Gasket parameters directly and comprehensively characterize the mechanical and sealing behavior of the gasket. At the same time, cen issued en13555 gasket coefficients and test methods for flanges and their joints – design rules for circular flange connections with gaskets (latest version, 2013) as the standard method for testing these Gasket parameters.
Another obvious feature of en method is that the bolted flange connection is analyzed as a system, considering its strength and sealing requirements in the whole process of installation and service. The mechanical interaction between gasket bolt flange and its influence on sealing performance are fully considered. On the premise of meeting the sealing requirements under various load conditions, the bolt interaction in actual installation is considered, and the bolt preload required for flange joint assembly is determined more carefully.
In addition to pressure load, the en method also considers the influence of axial thermal expansion difference caused by temperature transient on bolt load and gasket stress, as well as the influence of applied bending moment and axial force. In addition, the en method uses the limit load method to check the flange strength.
Compared with waters method and PVRC method, en method has more comprehensive consideration in design criteria, parameter selection, calculation method and failure evaluation, more accurate calculation, more reasonable results and more in line with the actual situation of bolted flanged joints. Therefore, it is more and more accepted by EU countries.
Because more factors are considered in en method, the calculation process needs multiple iterative operations, which generally needs to be completed by computer program. Therefore, en method is especially suitable for the following occasions: the flange bears thermal cycle load, and its influence is the main; The specified tightening method shall be adopted to control the bolt load; The presence of large additional loads or seals is particularly important.
To sum up, flange design methods can be divided into two categories. One is to take structural integrity as the basic design criterion, which controls the bolt and flange stress within its allowable range, that is, to meet the strength failure design criterion, while the seal gives an indirect guarantee by improving the bolt bearing capacity or (and) controlling the flange ring deformation, such as the waters method; The other is compatible with structural integrity and sealing, considering the two design criteria of strength failure and leakage failure, which is close to the actual situation, such as en method and PVRC method.
For the specific calculation process of PVRC method and en method, readers can refer to literature.

High pressure seal design

Due to the high pressure, the weight of the high-pressure sealing device accounts for about 10% ~ 30% of the total weight of the container, while the cost accounts for 15% ~ 40% of the total cost. Its design is an important part of the high-pressure container design.
(1) Basic characteristics of high pressure seal
There are many structural types of high-pressure sealing devices, but they all have the following characteristics.

  • ① Generally, metal sealing elements are used. The sealing specific pressure required on the high-pressure sealing contact surface is very high, and non-metallic sealing elements can not achieve such a large sealing specific pressure. The common materials of metal sealing elements are annealed aluminum, annealed red copper and mild steel.
  • ② Due to the high pressure of narrow face or line contact seal, a large preload is often required to make the sealing element achieve sufficient sealing specific pressure. Reducing the contact area between the sealing element and the sealing surface can greatly reduce the preload and reduce the diameter of the bolt, so as to reduce the structural size of the whole flange and the sealing head. Sometimes even line contact sealing is used.
  • ③ Self tightening or semi self tightening seals shall be adopted as far as possible, and the operating pressure shall be used to compress the sealing elements to realize self tightening seal. The pre tightening bolt only provides the force required for the initial seal. The higher the pressure, the more reliable the seal is, so it is more reliable and compact than the forced seal.

(2) Structural form of high pressure seal
There are many structural forms of high-pressure seal. What kind of seal structure is adopted is the central problem of high-pressure seal structure design.
Several common structural forms are introduced below.

① The structural form of flat gasket is shown in Figure 4-28. It is a forced seal. The seal between the cylinder end and the flat cover depends on the pre tightening effect of the main bolt to make the metal flat gasket produce a certain plastic deformation and fill the uneven parts of the compression surface, so as to achieve the purpose of sealing.

Figure 4-28 Flat gasket sealing structure

The structure is similar to the bolted flange connection structure commonly used in medium and low pressure vessels, except that the wide surface non-metallic gasket is changed to the narrow surface metal flat gasket. Flat gasket materials are usually annealed aluminum, annealed red copper or #10 steel.
This sealing structure is generally only applicable to small and medium-sized high-pressure vessels with temperature no more than 200 ℃ and inner diameter no more than 1000mm. The utility model has the advantages of simple structure and reliable sealing when the pressure is not high and the diameter is small. However, its main bolt diameter is too large, so it is not suitable for occasions with large temperature and pressure fluctuations.

② There are three structural forms of kazari seal: external thread, internal thread and improved kazari seal. Figure 4-29 shows the structural diagram of external thread kazari seal. The kazari seal is a forced seal, which is characterized by using the compression ring and pre tightening bolt to compress the triangular gasket to ensure the seal, so it is convenient for loading and unloading and has small pre tightening force during installation.

Figure 4-29 External thread kazari sealing structure

The axial force generated by the medium is borne by the threaded sleeve, and large-diameter main bolts are not required. This sealing structure is suitable for large diameter and high pressure range, but the machining accuracy of serrated thread is high and the cost is high.

③ Double cone seal is a semi self tightening seal structure with radial self tightening effect, which retains the main bolt, as shown in Figure 4-30. In the pre tightening state, tighten the main bolts to make the soft metal gaskets lined on the two conical surfaces of the double cone ring contact and compact the conical surfaces on the flat cover and the end of the cylinder, resulting in sufficient pre tightening sealing specific pressure of the soft metal gaskets on the two conical surfaces; At the same time, the double cone ring itself produces radial contraction, so that the gap G between its inner cylindrical surface and the outer cylindrical surface of the flat cover projection disappears and abuts on the head projection.

Figure 4-30 Double cone sealing structure

In order to ensure the pre tightening seal, the specific pressure on the two conical surfaces shall reach the pre tightening seal specific pressure required by the soft metal gasket. When the internal pressure increases, the flat cover tends to lift up, so that the specific pressure applied on the two conical surfaces and achieved during preloading tends to decrease; The double cone ring rebounds due to the radial contraction during preloading, so that a part of the specific pressure continues to be retained on the two cone surfaces; Under the action of medium pressure, the inner cylindrical surface of double cone ring expands outward, resulting in the further increase of specific pressure on the two conical surfaces. In order to maintain good sealing, the specific pressure on the two conical surfaces must be greater than the operating sealing specific pressure required by the soft metal gasket.
In this structure, the biconical ring can be made of materials such as 20, 25, 35, 16Mn, 20MnMo, 15CrMo and 0Cr18Ni9. Both sealing surfaces are provided with semicircular grooves and lined with soft metal pads, such as annealed aluminum or annealed red copper. It is very important to reasonably design the size of biconical ring, make it have appropriate rigidity and maintain appropriate rebound self tightening force.
When the section size is too large, the rigidity of the double cone ring is also too large. Not only the bolt force required for the compression elastic deformation of the double cone ring during pre tightening is too large, but also the medium pressure makes its radial expansion force insufficient and the self tightening force is small. On the contrary, the rigidity is insufficient, and the elastic resilience is also insufficient during operation, which affects the self tightening force. The research shows that the double cone ring designed with the following dimensional data has better sealing effect.
The double cone seal has the advantages of simple structure, reliable sealing, low machining accuracy and easy manufacture. It can be used for containers with large diameter, high pressure and temperature. In the case of pressure and temperature fluctuations, the sealing performance is also good.

④ Wood seal this is the earliest self tightening seal structure, as shown in Figure 4-31. The retaining bolt is screwed into the top cover through the retaining ring. In the pre tightening state, tighten the holding down bolts to generate a pre tight sealing force between the pressure pad, the top cover and the end of the cylinder.

Fig. 4-31 sealing structure of wood

When the internal pressure acts, the sealing force between them increases rapidly with the increase of pressure and the upward jacking of the top cover. At the same time, part or even all of the load of the retaining bolt and retaining ring is removed. Therefore, wood seal belongs to axial self tightening seal.
The structure is designed as line contact seal between the medium pressure pad and the top cover. There is a slight included angle between the pressure pad and the sealing surface contacting the end of the cylinder( β= 5 °), and the other sealing surface in contact with the spherical part of the end cover is made into an inclined plane with a large inclination angle( α= 30°~35°)。
Wood seal has no main bolt connection, reliable sealing, fast opening speed, and the pressure pad can be used for many times; The installation error of top cover shall be
The demand is not high; In the case of temperature and pressure fluctuations, the sealing performance is still good. However, it has complex structure, high assembly requirements and occupies more high-voltage space.
In addition, there are high-pressure sealing structures such as “C” ring seal, metal “O” ring seal, triangular gasket seal, octagonal gasket seal, “B” ring seal and wedge gasket self tightening seal (n.e.c).
⑤ High pressure pipeline sealing, like container sealing, is required to have the characteristics of good sealing performance, easy manufacture, simple and reasonable structure, convenient installation and maintenance, etc. In addition, the pipeline seal has its special features: ○ I the load borne by the pipeline often bears other additional external loads or bending moments in addition to the internal pressure. For example, when the pipeline is installed on site, there is often forced connection, which will produce a large additional bending moment or shear force; ○ II the influence of temperature fluctuation is also great because the pipeline continues for a long time and the thermal expansion value is large; ○ III the number of disassembly and assembly of pipe joint is more than that of container, and the sealing structure of pipe is required to be more convenient for disassembly and assembly.
There are many forms of high-pressure pipeline sealing, including forced type and self tightening type. The forced seal is mainly flat gasket seal, while the self tightening seal mostly adopts radial self tightening seal. The following describes a lens self tightening high-pressure pipeline sealing structure which is widely used.
The lens seal structure is shown in figure 4-32, and the pipe end is processed into β= The 20 ° conical surface is used as the sealing surface, and the lens gasket has two spherical surfaces. When pre tightening, tighten the bolts to form a line contact seal between the lens spherical surface and the conical surface at the pipe end. Therefore, the pressing force per unit area is large, so that there is sufficient elastic deformation and local plastic deformation between the lens gasket and the conical surface at the pipe end.

After boosting, the lens pad expands radially to produce self tightening effect, making the sealing surface fit more closely. The high-temperature lens pad is often processed into the structure shown in Fig. 4-32 (b). This lens pad has an inner annular cavity. When subjected to internal pressure, the internal medium pressure acts on the annular cavity of the lens pad, making the lens pad expand outward and fit more closely with the sealing surface, making the sealing effect better. At the same time, it has a certain elasticity, which can compensate for the impact of false sealing caused by temperature fluctuation.

Figure 4-32 lens seal of high pressure pipeline

With this sealing structure, the pipeline and flange are connected with threads instead of welding, so it is especially suitable for the connection of high-strength alloy steel pipes that are not suitable for welding.
(3) Measures to improve high pressure sealing performance
In order to improve the sealing performance of high pressure, the following three technical measures are often taken.
① Improving the sealing contact surface is to improve the sealing performance of the sealing element by improving the contact condition of the sealing surface on the premise of maintaining the original mechanical properties and resilience of the sealing element. Common methods are: ○ I electroplating or spraying soft metal and plastic on the sealing surface to improve the wear resistance of the sealing surface,
Protect the sealing surface from scratch, reduce the sealing specific pressure required to achieve sealing and reduce the preload, such as silver plating on the surface of hollow metal “O” ring; ○ II soft metal or non-metal thin gaskets are lined between the sealing contact surfaces, such as annealed aluminum or annealed red copper on the double cone sealing surface; ○ III. the sealing surface shall be inlaid with soft metal wire or non-metallic material.

② The improved gasket structure adopts the sealing element composed of elastic parts and plastic cushions, which depends on the elastic parts to obtain good rebound ability and necessary sealing specific pressure, and depends on the plastic cushion to obtain good sealing contact surface. Figure 4-33 shows the combined “B” ring for UHP polyethylene reactor, which is characterized by inserting soft materials into the “B” ring to improve the low-pressure sealing performance of the “B” ring.

Figure 4-33 Combined “B” ring

During operation, the soft material and interference fit are used to establish the initial seal to realize the low-pressure seal (below 60MPa). When the pressure continues to rise, the contact specific pressure between the “B” ring and the sealing surface also rises, forming the seal under high pressure.
The structure can also reduce the interference of “B” ring and is easy to install.

③ Welded sealing elements are used. When the container or pipeline contains flammable, explosive and highly toxic media, or is in high temperature, high pressure and frequent temperature and pressure fluctuations, and the sealing is required to be completely sealed, the welded sealing element structure can be used, as shown in figure 4-34.

Figure 4-34 Welded gasket sealing structure

Different forms of seal welding elements are welded on the two flange surfaces, and then the outer edge of the seal welding element is welded during assembly. This method can also be used when the inside of the container or pipeline is clean and there is no need to replace the internals.
(4) Bolt load calculation
Bolt load is the basis of the design of main bolt, cylinder end and top cover. The most basic flat gasket seal and double cone seal structure are analyzed below. Refer to the literature for the calculation method of main bolt load of wood seal, kazari seal and other high-pressure seals.
① The flat gasket sealing principle is the same as that of medium and low pressure vessels, and the sealing force is provided by the main bolt. It is necessary to ensure that the gasket can be plastically deformed during pre tightening (reaching the pre tightening specific pressure y) and that there is still sufficient sealing specific pressure (i.e. MPC) during operation. However, the high-pressure flat gasket adopts narrow metal gasket.
② According to the sealing principle of double cone ring, the main bolt load wa under pre tightening state and the main bolt load WP under operation state are calculated for double cone seal, and the main bolt is designed according to wa and WP.
ⅰ. Main bolt load wa under pre tightening state. During pre tightening, ensure that the soft metal gasket on the sealing surface reaches the initial sealing conditions, and make the double cone ring produce radial elastic compression to eliminate the radial gap between the double cone ring and the flat cover.

In order to achieve the initial preload seal, the normal pressing force W0=πDGby must be applied on the biconical sealing surface. During pre tightening, the double cone ring shrinks and has a relative sliding trend with the top cover, so that the double cone ring is affected by the friction FM. The direction of the friction is shown in Figure 4-35, and its size is Fm =W0tanρ=πDGbytanρ. FM and W0 are vector synthesized and then decomposed to the vertical direction, which is the load W1 that must be provided by the main bolt during pre tightening, i.e

Figure 4-35 Geometry of biconical ring and force analysis during preloading

The axial component FC of the rebound force of the biconical ring is caused by the deformation rebound force in the ring. The condition of resilience is that the biconical ring is always compressed. The greater the compression, the greater the resilience of the ring. The maximum rebound force VR is


Source: Network Arrangement – China Pipe Flange Manufacturer – Yaang Pipe Industry Co., Limited (

(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.)

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