|
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.
|