The bellows expansion joint (compensator) is an expansion joint made from a metal bellows. It can expand and contract along the axis and also allows for some bending. Figure 2 [Bellows Expansion Joint] shows a common axial-type bellows expansion joint, used for axial length compensation in pipelines. To prevent exceeding the allowable compensation amount, protective rods or rings are set at both ends of the bellows, and guide brackets are installed at both ends of the connecting pipes. Additionally, there are angle-type and lateral-type expansion joints, which can be used to compensate for the angular and lateral deformation of pipelines. The advantages of these expansion joints include space and material savings, ease of standardization and mass production. However, the downside is their shorter lifespan. Bellows expansion joints are generally used on pipelines with moderate temperatures and pressures and shorter lengths. With the advancement of bellows production technology, the application scope of these expansion joints is expanding.

The bellows compensator is assembled from bellows and compensators. It is crucial to take proper measures before the bellows compensator is put into operation to ensure its long service life.
The structural characteristics of the bellows compensator illustrate that their radial stiffness is significantly higher than that of the stock, whereas their axial stiffness is much lower. Under conditions of high load, although their strength is sufficient and there is excess radial stiffness, the axial stiffness may not meet the usage requirements. In Chapter 3, Section 3.4, we have analyzed the stability of the bellows: instability is a precursor to failure. From the critical load formula of the bellows, it can be observed that there are three methods to improve the stability of the bellows: 1) Increase the wall thickness of the tube; 2) Decrease the ratio of the outer diameter to the inner diameter; 3) Reduce the effective number of bellows and increase their slenderness ratio.

However, excessively increasing the wall thickness and reducing the ratio of outer diameter to inner diameter results in increased rigidity but decreased flexibility, which is not in line with the relevant regulations for thin-walled corrugated compensators; overly reducing the effective number of corrugations and expanding the slender ratio makes it unable to meet certain compensation requirements. Consequently, we are forced to consider external factors, such as using internal liners, external sleeves, valley reinforcement rings, or composite structures to enhance the stability of the corrugated tubes used as compensators.
Compensators utilizing either an inner sleeve or outer sheath structure typically do not need to bear lateral or angular displacements due to their minimal radial gaps; they are generally used solely for axial pipeline compensation. For bellows compensators with a valley-reinforced ring structure, the compensating amounts for axial, lateral, and angular displacements must be calculated based on their specific geometric dimensions.