Tom Peterson

August 11, 2003

Revised September 3, 2003 (Adding twist of extended bellows, pp 6-8)

# Tevatron Beam Tube Bellows Torque Test Report

Abstract.

A stock Tevatron beam tube bellows was twisted in a fixture in order to
study the effect of torsion on the bellows. Realignment of connected
Tevatron magnets in the tunnel may require relative magnet-to-magnet
rolls of up to 8 milliradians; the question was whether the beam tube
bellows could take such a twist without damage, especially without
leaking. The result was that twist on a new bellows is elastic up to
about 5 mr, after which the bellows begins to take on a "helical"
deformation which involves some local yielding of the bellows
convolutions in tension. Extension of the bellows results in easier
deformation into the helical pattern. Repeated twists to 8 mr and some
twisting up to as much as 30 mr did not cause any vacuum leaks in the
bellows. It appears that 8 mr of twist is safe for the beam tube
bellows. In order to keep a safety factor of at least 2, as a
conservative limit, Beams Division agreed to limit twist to 4 mr.

Test apparatus.

A Tevatron beam tube bellows subassembly (stock and drawing \#
MB-103839) was removed from stock and welded to a fixture (designed by
Hans Jostlein and modified by Tom Peterson and Danny Massengill) for a
twist test. One end of the bellows assembly is bolted to its mating
flange just like at a magnet interconnect, while the other end is welded
to a plate. We added a heavy-walled pipe with a nut welded on the end
which rests in a cradle and serves as a point where we apply torque to
the bellows assembly. A torque wrench was used to provide a measured
amount of torque. Bellows extension was 0.915 inches. The two dial
indicators allow measurement of twist.

![](media/image1.jpeg){width="2.9305555555555554in"
height="1.961111111111111in"}![](media/image2.jpeg){width="2.9305555555555554in"
height="1.9472222222222222in"}

Data.

Data were taken with torque values just up to the point of deforming the
bellows. The table below summarizes the data taken on August 6 (by Tom
Peterson and Danny Massengill).

![](media/image3.wmf)

The following plot shows angular displacement as a function of torque up
to the point of the bellows instability.

![](media/image4.wmf)

One can see from the above plot that, although we saw the bellows jump
to a helical shape between 70 and 80 ft-lb, the twist may not have been
completely linear with torque at even lower levels. Nevertheless, after
each of the above plotted points the twist returned to zero with zero
torque; these were elastic deformations.

When we tried 80 ft-lb, the bellows jumped to a helical shape,
displacement jumped to something large, we estimated over 40 mils (over
8 mr), and torque required for that displacement dropped. At this point
we stopped; the bellows remained slightly deformed.

Below is the table of data from the August 7, 2003, bellows twist tests,
taken by Tom Peterson. I did more reverse cycling since the bellows had
been deformed clockwise yesterday and might not show the same stiffness
in each direction.

![](media/image5.wmf)

Below is a plot of these data.

![](media/image6.wmf)

Note in the above plot that the bellows is stiffer in the
counterclockwise (negative torque) direction up to the point (like
yesterday in the clockwise direction) at about 5 mr where the bellows
jumps to the helical configuration. Once it takes on that shape,
subsequent twists to the same angle require less torque, as can be seen
by comparing the data in the clockwise (positive torque) direction with
yesterday's data. For example, yesterday it took 50 ft-lb to get 3 mr,
today 50 ft-lb gave us 6 mr clockwise (positive torque direction).

The photo below shows the bellows twisted at 8 mr. There is some
permanent deformation, but mostly the appearance is of local spreading
and compaction of the convolutions in an elastic manner. It looks ugly,
but as you will see if you try twisting it yourself, the stresses and
forces involved do not seem large. You can see that if a failure
occurred, it would likely be a weld tearing in a combination of tension
and shear, as opposed to simple shear.

![](media/image7.jpeg){width="5.55625in" height="3.6902777777777778in"}

Below is the bellows after it has been deformed but torque is removed.

![](media/image8.jpeg){width="5.55625in" height="3.7006944444444443in"}

Analysis of the bellows as if it were a cylinder (ignoring the helical
deformation, which makes twist easier) does indicate that 70 ft-lb
should be close to the yield point of a 5 mil thick cylinder, 3.5 inches
in diameter. Thus, the jump to a helical configuration allows twisting
beyond what would otherwise be possible.

Conclusion for first sets of tests (all 0.915 inches bellows extension):
although the bellows deforms into a helical pattern at about 8 mr of
twist the first time and retains some deformation after that, repeated 8
mr of twist does not appear to be a problem for these bellows with this
extension.

Twist of extended beam tube bellows.

The same beam tube bellows was tested at two different amounts of
extension (as measured from first to last bellows convolution).

![](media/image9.wmf)

The plot above shows the greater twist at 50 ft-lb with larger bellows
extension.

The plot below shows more data for twist versus extension. The time
sequence is important: tests of twist versus extension were begun at 50
ft-lb and 0.85 inches. The next extension, at 1.3 inches, showed more
twist for the same torque. Then at 1.4 inches even more twist, but the
twist was so large that the bellows were very deformed. The helical
deformation makes the bellows more flexible in twist, so at 1.1 inches
the twist was also very large. At that point I stopped doing 50 ft-lb;
there was too much deformation and twist was beyond that of interest for
Tevatron realignment. However, one can conclude that the bellows deforms
more easily into the helical form at longer extensions. Inelastic
deformation is easier with more extension.

At 30 ft-lb the bellows returns to its initial position, so twist is
elastic, and in that case it really does look like twist is independent
of extension. Elastic deformation looks independent of extension.

![](media/image10.wmf)

![](media/image11.jpeg){width="5.93125in" height="3.9625in"}

The above photo shows the bellows after the above tests, no torque on
the bellows. The test apparatus is shown below.

![](media/image12.jpeg){width="5.930555555555555in"
height="3.953472222222222in"}