Design of Bellows
The theoretical basis of metal bellows design is plate and shell theory, material mechanics, and computational mathematics. There are many parameters for the design of the bellows. Due to the different uses of the bellows in the system, the emphasis of its design calculations is different. For example, bellows are used for force balancing components, which require the effective area of the bellows to be constant or change little within the working range. For measuring components, the elastic characteristics of the bellows are required to be linear; for vacuum switch tubes as vacuum seals The vacuum tightness, axial displacement and fatigue life of the bellows are required; for the valve as a seal, the bellows should have a certain pressure resistance, corrosion resistance, temperature resistance, working displacement and fatigue life. According to the structural characteristics of the corrugated pipe, the corrugated pipe can be regarded as a ring shell, a flat cone shell or a ring plate. The design and calculation of the bellows is the design and calculation of a circular shell, a flat cone shell or a ring plate.
The calculated parameters are stiffness, stress, effective area, instability, allowable displacement, pressure resistance, and service life.
Pressure resistance
Pressure resistance is an important parameter for bellows performance. At normal temperature, the maximum static pressure that the bellows can withstand without plastic deformation on the waveform is the maximum pressure resistance of the bellows. Under normal circumstances, the bellows works under a certain pressure (internal or external pressure). Therefore, it must withstand this pressure during the entire work process without plastic deformation.
The pressure resistance of the bellows actually belongs to the strength category of the bellows. The key of calculation is stress analysis, that is, the stress on the wall of the bellows is analyzed. As long as the stress at the maximum stress point on the wall of the bellows does not exceed the yield strength of the material, the pressure on the bellows will not reach its pressure resistance.
The same bellows is more stable under external pressure than under internal pressure when the other working conditions are the same. Therefore, the maximum pressure resistance under external pressure is higher than that under internal pressure.
When the two ends of the bellows are fixed, if a sufficient pressure is passed into the inner cavity of the bellows, the bellows of the bellows may be damaged by blasting. When the bellows starts to burst, the pressure value inside the bellows is called the burst pressure. Burst pressure is a parameter characterizing the maximum compressive strength of the bellows. During the entire working process of the bellows, its working pressure is far less than the burst pressure, otherwise the bellows will be broken and damaged.
When the corrugation length is less than or equal to the outer diameter, the calculation result is very close to the actual burst pressure; the actual burst pressure of a slender corrugated pipe is much lower. The burst pressure is about 3 to 10 times the allowable working pressure.
stability
When both ends of the bellows are restricted, if the pressure inside the bellows increases to a certain critical value, the bellows will cause instability.
Allowable displacement
For a bellows working in a compressed state, its maximum compression displacement is: the maximum displacement value that can be generated when the bellows compresses until the bellows contact each other under pressure, which is also called the maximum allowable displacement of the structure, which is equal to The difference between the free length of the bellows and the maximum compression length.
The maximum displacement that can be obtained without the plastic deformation of the bellows is called the allowable displacement of the bellows.
The bellows will have residual deformation during actual work. The residual deformation is also called permanent deformation or plastic deformation. The bellows is deformed under the action of force or pressure. When the force or pressure is removed, the phenomenon that the bellows does not return to its original state is called Residual deformation. Residual deformation is usually expressed by the amount that the bellows does not restore the original position, also known as zero offset.
The relationship between bellows displacement and zero displacement, whether it is tensile or compressive displacement, in the initial stage of bellows displacement, its residual deformation is very small, which is generally less than the allowable zero position specified in the bellows standard Offset value. However, when the tensile (or compression) displacement gradually increases beyond a certain displacement value, it will cause a sudden increase in the zero offset value, which indicates that the bellows has a relatively large residual deformation, and after that. If the displacement is further increased, the residual deformation will increase significantly. Therefore, the bellows should generally not exceed this displacement, otherwise it will seriously reduce its accuracy, stability, reliability and service life.
The allowable compressive displacement of the bellows when it is working in a compressed state is larger than the allowable tensile displacement of the bellows when it is working in the stretched state. Therefore, the bellows should be designed to work in the compressed state as much as possible. Through experiments, it is found that, in general, the permissible compression displacement of the bellows of the same material and the same specification is 1.5 times the permissible tensile displacement.
The allowable displacement is related to the geometric parameters and material properties of the bellows. In general, the allowable displacement of the bellows is proportional to the yield strength of the material and the square of the outer diameter, but inversely proportional to the elastic modulus of the material and the wall thickness of the bellows. At the same time, the relative wave depth and wave thickness also have some influence on it.
life
The life of the bellows is the shortest working period or number of cycles that can ensure normal work when used under working conditions. The elastic sealing system composed of bellows often works under the conditions of bearing a large number of cycles of variable loads and large displacements, so determining the service life of the bellows is of great significance. Because the role of the bellows is different, the requirements for its service life are also different.
(1) When the bellows is used to compensate for positional deviations caused by installation in the piping system, its service life requirement is only a few times.
(2) The bellows is used in a thermostat with a high switching frequency, and its life must reach 10,000 times to meet the requirements for use.
(3) When a bellows is used as a vacuum switch as a vacuum seal, its life must reach 30,000 times to ensure normal operation.
It can be seen from the above three use cases that due to different conditions of use, the service life required by the bellows varies greatly. The life of the corrugated tube is related to the fatigue characteristics of the selected material, and also depends on the residual stress of the formed corrugated tube, the stress concentration and the surface quality of the corrugated tube. In addition, the service life is related to the working conditions of the bellows. For example: the displacement, pressure, temperature, working medium, vibration conditions, frequency range, shock conditions, etc. of the bellows during operation.
In the working process of the bellows, its life depends mainly on the maximum stress generated during the working process. In order to reduce the stress, it is generally realized by reducing the working displacement of the bellows and reducing the working pressure. The general design stipulates that the working displacement of the bellows should be less than half of its allowable displacement, and its working pressure should be less than half of the pressure resistance of the bellows.
The test of the produced corrugated pipe proves that if the corrugated pipe works according to the above specifications, its basic service life can reach about 50,000 times.
Depending on the nature of the working pressure, the allowable displacement of the bellows is different. Generally, when the bellows only bears the axial load (tension or pressure), its allowable displacement can be selected between 10% ~ 40% of the effective length of the bellows; When the bellows is subjected to lateral concentrated force, torsional moment or comprehensive force, the allowable displacement of the bellows should be appropriately reduced.
The application of multi-layer bellows can reduce the stress caused by stiffness and deformation, which can greatly increase the life of the bellows.
When the bellows is operated under the same conditions and different working pressure properties (constant or alternating load), its service life will be different. Obviously, the life of the bellows is shorter when working under alternating loads than when working under constant loads.
