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Bellows Design

The bellows is the flexible element of the expansion joint. It must be strong enough circumferentially to withstand the pressure and flexible enough longitudinally to accept the deflections for which it was designed, and as repetitively as necessary with a minimum resistance. This strength with flexibility is a unique design problem that is not often found in other components in industrial equipment.

Most engineered structures are designed to inhibit deflection when acted upon by outside forces. Since the bellows must accept deflections repetitively, and deflections result in stresses, these stresses must be kept as low as possible so that the repeated deflections will not result in premature fatigue failures. Reducing bending stress resulting from a given deflection is easily achieved by simply reducing the thickness of the bending member, which in the case of the bellows, is the convolution. However, in order to withstand the pressure, the convolution, which is also a pressure vessel, must have a thickness great enough that the pressure induced membrane stresses are equal to or less than the allowable stress levels of the materials at the design temperatures. This conflicting need for thickness for pressure and thinness for flexibility is the unique design problem faced by the expansion joint designer.

Bellows are not springs, in that most of their deflections produce bending stresses in excess of the materials’ yield strength. Understanding how various materials perform and their capabilities in this “plastic” deformation region requires years of experience and design equations based upon this empirical understanding.

That bellows routinely operate “plastically” should not be a cause for concern, since most of the materials from which bellows are made share similar highly ductile characteristics. In particular, the endurance limit of these materials, which can be loosely described as the stress at which failure will occur at ten million cycles of repeated stressing, is nearly the same as their yield stress, or the point at which permanent deformation will occur. A bellows which is required to withstand 3000 cycles of a given deflection and pressure, and which ultimately fails after 10,000 cycles, has certainly demonstrated more than acceptable performance. However, it has experienced, during each and every cycle, bending stresses far in excess of the endurance limit and therefore the yield stress, and once deflected, would not have returned on their own to their original undeflected length or shape, as a spring is expected to do. In other words, they would have “taken a set.”

Most bellows fail by circumferential cracking resulting from cyclic bending stresses, or fatigue. Since the best design is a compromise, or balance, between pressure strength and flexibility considerations, it can be concluded that their designs have had lower margins of safety regarding fatigue than they had regarding pressure strength. The years of experience of the engineers who developed these bellows assures that the designs contained in this catalog and those offered to satisfy customer specifications, will have the performance reliability which yields trouble free, safe use.

Occasionally, a bellows will appear to develop a fatigue crack prematurely, i.e., after being subjected to fewer cycles than analysis indicates they should. These premature failures usually are the result of one or more of the following causes:

  • Insufficient margin of safety in the design permitting acceptance of a unit manufactured within a portion of the dimensional tolerance range to yield a part which will not satisfy the design. Metallic bellows bending stresses are extremely sensitive to changes in some dimensions, such as the thickness and the height of the convolution. These dimensional characteristics often affect the various bending stresses by the square or cube of their differences. An understanding of these dimensional factors and how they can be controlled during design and manufacture is the key to preventing this cause of early failure. A poorly manufactured bellows, or one that is made to the “wrong” side of the dimensional tolerances will disappoint the best design and analysis.
  • Insufficient margin of safety regarding stability under pressure. Squirm, described in more detail below, is a characteristic of all bellows subjected to internal pressure. Each bellows has a critical pressure at which the convolution side walls begin to deform or the actual bellows shape begins to change. These deformations cause the bellows to accept the imposed deflections differently than they are normally expected to and they can no longer perform according to the design equations. The critical pressure is a function of the bellow’s shape and actually can change during deflection. If the basic design is close to its stability limit, the beginnings of instability may not be visible to the eye, but the higher than expected bending stresses will occur during each cycle. Stresses are higher particularly at convolutions near its attachments where the flexible element transitions to the highly rigid end connection.