Development of ultra high pressure valve bellows

At present, there is no unified design method for the bellows of ultra-high pressure valve in China. The initial design of the bellows of 42 MPa (2500 lb) valve based on the finite element method can reduce the cost and cycle of research and development. Through the engineering test, it is proved that the finite element method has practical significance for the design and development of bellows. The design method of bellows involves the whole process from material selection to bellows parameter determination and finalization, which is universal for the design of bellows of ultra-high pressure valves.

Metal bellows is a kind of elastic element with regular wave shape. As a metal elastic element, it not only has the high temperature and high pressure resistance of metal materials, but also has the tensile and compression properties of some non-metal materials. Based on this excellent physical properties, it is widely used in heat exchange, nuclear power, aerospace and other fields.

Bellows as the key parts of the valve, its performance directly affects the quality and safety performance of the valve. At present, we have mature design and production experience for valve bellows with nominal pressure of 26mpa (1500Lb) and below. According to different series of valve models, we have matching bellows models. But most of the valve bellows with nominal pressure above 26mpa (1500Lb) generally need professional design and production of bellows according to the working conditions of products. Based on the production demand of valve bellows with nominal pressure of 42MPa (2500lb) given by a valve enterprise, a design scheme of high pressure resistant bellows is proposed.

Selection of bellows materials

According to the application environment of valve bellows, the assessment objectives of bellows design parameters are put forward. The specific design parameters are shown in Table 1. The elongation of corrugated tube blank is generally required to be no less than 30%. When the elongation of corrugated tube blank is small, it will bring difficulties to the forming process, and it often needs heat treatment and secondary forming.
Table 1 design parameters of bellows

Parameter Numerical value
Design pressure / MPa 42 (external pressure)
Design temperature /  38
Bellows length / mm ≤105
Nominal displacement / mm -10/3.4
Inner diameter / mm 29
Outer diameter / mm 44

The mechanical property parameters and anti pitting equivalent pre values of bellows blank materials are shown in Table 2, among which the listed materials are commonly used for manufacturing bellows. Because there are many corrugated tube forming materials, there are also some tube blank materials used in special working conditions, such as 321, Incoloy825, TA2, etc. MONEL400 and C276 are mainly used in the environment with strong corrosion resistance such as chlorine and chloride. The yield strength and tensile strength of 300 series stainless steel are low, and the external pressure strength of bellows is high, so Inconel625 material is selected as the bellows material. The nominal thickness of Inconel625 is 0.2mm, 0.25mm and 0.3mm. Using Inconel625 tube blank with 0.3mm wall thickness to process the tube blank under external pressure of 42MPa can reduce the number of layers of bellows, reduce the manufacturing difficulty and processing cost of bellows.
Table 2 mechanical properties and pre values of materials commonly used in bellows production

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Simulation calculation

The quality of mesh generation directly affects the accuracy and speed of calculation. The results show that the convergence time can be reduced by using hexahedral mesh to divide the model, and the calculation accuracy is higher when the number of grid layers in the thickness direction of single-layer billet is not less than 3. Due to the large deformation of the geometry in the strength and fatigue simulation calculation of bellows, when using the progressive mechanical method for shape inspection, attention should be paid to the inspection and repair of the failed mesh. When the mesh is divided, dropping the middle nodes can reduce the linearity of the element and increase the stability of the simulation. Fig. 1 is the grid diagram of bellows in strength calculation.

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Figure 1 grid division diagram
Considering the small inner diameter, high forming pressure and high wave of bellows, it is more reasonable to consider work hardening for material yield strength. The material nonlinearity is treated by bilinear isotropic strengthening model. The material parameters of Inconel 625 are shown in Table 3. The strain fatigue parameters of Inconel625 are shown in Table 4.
Table 3 material parameters of Inconel625

Parameter Numerical value
Yield strength / MPa 600
Poisson’s ratio 0.31
Modulus of elasticity / GPA 205
Plastic modulus / MPa 1500

Table 4 strain fatigue parameters of Inconel625

Parameter Numerical value
Fatigue strength coefficient 2264
Fatigue strength index -0.14
Fatigue ductility coefficient 0.97
Fatigue ductility exponent -0.59
Cycle enhancement index 601.1
Strain hardening index 0.11

The forming pressure of the bellows described in this paper is high, the gap between the tube blank and the casing is small, and the working environment pressure of the bellows is 42MPa, so it can be considered that the normal displacement between the layers does not occur during the operation of the bellows. The interlayer contact of bellows is set as no separation. The coordination of solid contact surface is constrained by penalty function contact algorithm. The default value of normal contact stiffness is 10. Because there are more detection points in the Gauss integral point detection method and the node detection method, the Gauss integral point detection method is adopted in the contact detection method.
Generally, domestic bellows enterprises mainly refer to American Standard EJMA for bellows design, but the service environment of valve bellows is external pressure condition, which is beyond the scope of the standard. At present, high pressure bellows are mainly designed by engineering test method. Although this method can solve the engineering problems, it will lead to more tests and increase the R & D cost and R & D cycle. In view of the successful application of finite element method in bellows design, this paper uses finite element method to design bellows. In order to reduce the amount of calculation, 1 / 4 single wave model is selected for simulation. In order to reduce the development cost, the wave distance of the bellows is designed with the existing mold, and the thickness of the mold is 6 mm. Due to the large external pressure on the bellows, according to the previous design experience, the strength of the single wave 5-layer billet is calculated. Fig. 2 ~ Fig. 4 show the stress nephogram of bellows when the pressure is 14MPa, 17Mpa and 30MPa, respectively, and the stress is greater than 600MPa.

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Figure 2 stress nephogram of bellows (14MPa)

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Fig. 3 stress nephogram of bellows (17Mpa)

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Fig. 4 stress nephogram of bellows (30MPa)
According to the stress nephogram in Fig. 2 ~ Fig. 4, it can be seen that when the external pressure of the bellows is 14MPa, the plastic deformation of local elements has occurred. With the continuous increase of the pressure, the plastic deformation of the bellows becomes more and more. In engineering, the criterion for judging the plane instability of bellows is that the change rate of wave distance before and after the pressure test is not more than 15%, which means that the strength test is qualified. The main reason for the great change of the wave distance of the bellows in the simulation calculation is that most of the elements enter the plastic deformation. Fig. 5 is a graph of the maximum displacement and pressure of the element. When the pressure is greater than 32 MPa, the displacement of the bellows element increases significantly. This is too different from the strength requirement of 42MPa, so the strength of 5-layer bellows can not meet the use requirements.

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Figure 5 maximum displacement and pressure curve of unit (5-layer pipe)
In order to enhance the strength of the bellows, the maximum displacement and pressure curve of the unit obtained from the simulation calculation of the 6-layer bellows is shown in Figure 6, in which the abrupt change point of the curve slope is close to 40MPa. Therefore, the 6-layer bellows can be referred to for product design.

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Figure 6 maximum displacement and pressure curve of unit (6-layer pipe)
According to the limitation of bellows length, the final type of bellows is qd44x29x0.3x6x17. Fatigue tool, the fatigue design module of workbench, can well carry out uniaxial fatigue analysis. In this paper, this module is used to calculate the fatigue of bellows, and the cloud diagram of fatigue life is obtained (Fig. 7).

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Figure 7 cloud chart of bellows fatigue life
The simulation results show that the fatigue life of the bellows is more than 12000 times.

Experimental verification

The test and verification of new products is an important link in the research and development work. The main test and assessment indexes of valve bellows with nominal pressure of 42MPa (2500lb) are strength and service life. According to the design parameters of bellows, the strength test and fatigue test are carried out. When the external pressure of bellows is 42MPa, the change rate of wave distance is 13.2%, and the failure times of fatigue test is 5783. The strength of bellows meets the design requirements of products.


For the design of ultra-high pressure valve bellows, the finite element method can be used for design guidance, and the use of this method can save the design cycle and research and development cost. According to the definition of plane instability of valve bellows in engineering application, the curvature change of the maximum displacement and pressure curve of the element can be used to predict the plane instability pressure value in the finite element calculation. This method is simple and practical. The simulation calculation error of bellows life is large, but it is in the same order of magnitude with the actual life value, which has guiding significance for life design.
Authors: Zhang quanhou, song Linhong, Zhang Wenliang, Yu Xianglin, Wang Xue

Source: China Valve Bellows 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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