**ACC39 Piping Mechanical Loads**

**EDMS \#** **D00000001199141**

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  Prepared by: T. Peterson                              Date: 15 Sep 2008

                                                        

                                                        
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TABLE OF CONTENTS

[SCOPE 3](#scope)

[PIPING CONFIGURATION 3](#piping-configuration)

[ANALYSIS OF AXIAL AND LATERAL LOADING ON PIPING AND SUPPORTS
7](#analysis-of-axial-and-lateral-loading-on-piping-and-supports)

[LATERAL ELASTIC PIPE INSTABILITY 9](#lateral-elastic-pipe-instability)

[CONCLUSIONS 13](#conclusions)

[REFERENCES 13](#references)

# SCOPE

This document describes the anticipated maximum mechanical loads on the
piping and internal support structure for the 3.9 GHz cryomodule, ACC39.
ACC39 will be installed in FLASH between ACC1 and the Endcap. One can
see in Figure 1 that ACC1 and the Endcap are cooled by a separate branch
of piping from the TTF feedbox. Thus, ACC39 will be at the end of a very
short cryogenic "string" with one other cryomodule.

![](media/image2.png){width="5.9840277777777775in"
height="3.1152777777777776in"}

Figure 1 -- TTF2 flow schematic (particle beam goes left to right)

# PIPING CONFIGURATION 

Piping configuration details are presented in the ACC39 INTERFACES
document and in the Piping Engineering Note, so will not be presented
again in complete detail here. Figures 2 and 3 illustrate the piping
interconnects in FLASH. Figures 4 and 5 illustrate the piping within
ACC39. Figure 6 illustrates the interconnects on the Cryomodule Test
Bench (CMTB).

![](media/image3.jpeg){width="5.990277777777778in"
height="5.200694444444444in"}

Figure 2 -- ACC39 cryomodule with FLASH interconnect piping

![](media/image4.jpeg){width="5.990277777777778in"
height="5.200694444444444in"}

Figure 3 -- ACC39 cryomodule, close-up view of FLASH interconnect piping

Figures 2 and 3 result from combining our ACC39 solid model with solid
model information from DESY on the cryomodule piping interconnects.

![](media/image5.png){width="5.092361111111111in"
height="5.249305555555556in"}

Figure 4 -- ACC39 cryomodule piping

![](media/image6.png){width="5.63125in" height="3.0in"}

Figure 5 -- Another view of ACC39 piping

![](media/image7.jpeg){width="5.990277777777778in"
height="5.200694444444444in"}

Figure 6 -- ACC39 cryomodule with CMTB interconnect piping

# ANALYSIS OF AXIAL AND LATERAL LOADING ON PIPING AND SUPPORTS

Piping loads could come from two different sources, unbalanced loads due
to the combination of pressure and an asymmetric pipe configuration
(Figure 7), and mechanical end loads on the pipes due to offsets and
bellows spring constants.

![](media/image8.jpeg){width="5.997222222222222in"
height="1.3493055555555555in"}**Figure 7 -- Piping load with bellows**

The first issue, unbalanced forces due to internal pressure and
asymmetric piping with bellows, does not arise in either FLASH or CMTB,
since the piping is symmetric. Pipes are open at each end of the
cryomodule, there are no offsets of one end relative to another,
interconnects at each end are the same, and end box piping is
self-supported, not anchored axially or radially to ACC39 piping (See
e-mail from Detlef Sellmann in References, but we need to confirm that
no bellows constraints are different at the turnaround box end compared
to ACC1 end).

For the second issue, bellows spring rates with offsets at the
interconnects, again we refer to the e-mail from Sellmann, which
provides bellows spring constants. Suppose the entire cryomodule is
offset in one direction from either ACC1 or the Endcap. Neglecting the
ability of the vacuum connection to take the offset and forces on the
vacuum vessel, consider the sum of the forces in the internal piping,
which is ultimately taken on the support posts. Consider two cases,
axial and lateral offset.

Summing all the interconnect bellows lateral spring constants: 200
N/mm + 3.03 N/mm + 4 x 8.05 N/mm + 4.91 N/mm + 1.61 N/mm = **241.8
N/mm**, dominated by the 168 mm low pressure gas pipe. The distance to
the bellows from the support post can be (depending on the pipe) as much
as approximately the distance between support posts. So the reaction
load at the near support post to a lateral offset load would be
multiplied by two, due to the lever arm. Thus, the lateral load on the
support post would be very conservatively (less than) 480 N/mm of
interconnect offset.

The support posts very conservatively carry a 6 G lateral load with the
mass being half the 2000 lb cold mass (1/2 x 2000 lbf = 4450 Newtons,
Reference: G10 Cold Post Loading, D. Mitchell, 9 Nov 07). Comparing the
total inner pipe spring rate with the 6 G maximum specified lateral
load, we have 4450/480 = 9.3 mm offset. So with a 9.3 mm offset, we
would approximately reach the equivalent of a 6 G lateral load on the
near support post. This offset is much higher than the expected 1 mm
maximum offset. Also, for reference, Sellmann mentions a 500 N limit for
lateral loading for the accelerator cryomodules. Lateral loading of the
piping assembly due to interconnect tolerances will not be a problem.

Now consider axial loads. The sum of the spring constants is: 60 N/mm +
4.8 N/mm + 4 x 14.2 N/mm + 13.9 N/mm + 6.54 N/mm = **142.0 N/mm**. This
axial load would be carried only by the one, fixed post. Again, this
post is conservatively rated (with a large safety factor) for 4450 N
lateral load (half the cold mass at 6 G). Comparing the axial spring
rate with allowable load, we have 4450/142 = 31 mm axial offset. This is
larger than any realistic offset. For comparison, thermal contractions
total about 10 mm. Axial loading of the piping assembly due to
interconnect tolerances will not be a problem.

# LATERAL ELASTIC PIPE INSTABILITY

At a bellows at the end of a cantilevered pipe, lateral displacement
force is proportional to lateral displacement and to internal pressure.
(See Figure 8.)

![](media/image9.png){width="5.860416666666667in"
height="3.6770833333333335in"}

**Figure 8 -- Lateral offset at a bellows resulting in offsetting force
due to internal pressure. (Figure from P. Mazur, personal communication,
for a magnet test stand. But concept applies to any interconnect with
bellows.)**

If the restoring spring constant of the piping system in which the
bellows is installed is less than the constant relating lateral
displacement force to lateral displacement (a "negative spring
constant") at a given pressure, the system is transversely, elastically
unstable at that pressure. Relatively light pipe supports near the
bellows can prevent this instability by adding stiffness.

Referring to Figure 8, F(P) = PAsin(Qmax) where F(P) is the lateral
force as a function of pressure, P is pressure in the system (vacuum
outside), A is bellows areas, and Qmax is the maximum angle of displaced
convolutions.

Qmax = 3Y/(2(L+X)), where X, Y, and L are shown in Figure 8. For small
angles, F(P)/Y = 3 PA/(2(L+X)). Instability occurs when F(P)/Y exceeds
the restoring spring constant, determined by bellows and pipe stiffness.

The excel spreadsheet shown in Figure 13 contains calculations of
cantilever pipe stiffness and offsetting force versus displacement. The
worst cases are the 70 K pipes due to the 18 bar MAWP and length. (See
Figures 9 - 12.) Pipe cantilever stiffness is calculated as if the pipe
were supported only by the first two clamps to the thermal shield, and
those are both rotationally free. Hence, the cantilever length and
support spacing are both required and shown in the figures.

![](media/image10.jpeg){width="5.992361111111111in" height="2.775in"}

**Figure 9. The cantilevered end of the 70 K shield return pipe at
ACC-1.**

![](media/image11.jpeg){width="5.992361111111111in" height="2.8875in"}

**Figure 10. The cantilevered end of the 70 K shield return pipe at the
endcap.**

![](media/image12.jpeg){width="5.999305555555556in"
height="2.6569444444444446in"}

**Figure 11. The cantilevered end of the 70 K shield forward pipe at
ACC-1.**

![](media/image13.jpeg){width="5.99375in" height="2.4006944444444445in"}

**Figure 12. The cantilevered end of the 70 K shield forward pipe at the
endcap.**

Assuming identical bellows at the endcap as at the interconnect with
ACC-1 (bellows dimensions picked off the JT file model at the ACC-1
interconnect), the worst-case predicted stiffness of the pipe is 356
N/mm, for the 70 K forward pipe at the endcap. This should be compared
with an offsetting force as a function of displacement of 69 N/mm. Thus,
the pipe is stable with a margin of safety of about 5. This does not
take into account the restoring spring constant of the bellows itself
(8.05 N/mm) and the constraint of a "clamshell" around the bellows.

![](media/image14.pct)

**Figure 13 -- Calculated cantilevered pipe stiffness and offsetting
force**

**(Displacement forces are identical at each end due to the presence of
identical bellows. Forces are very small for the low pressure lines, so
only one 5 K line is shown for illustration purposes.)**

# CONCLUSIONS

The piping for ACC39 experiences maximum loads which are safely less
than support structure strength. A lateral offset of every pipe of 9 mm
in the same direction, much more than the quoted alignment tolerance of
about 1 mm (e-mail from Sellmann), will still be within safe stress
limits for the internal support structure. With an axial offset of 30
mm, again much larger than any practical offset, we would reach the
support post allowable stresses. Piping is stable with internal pressure
with a margin of safety of about 5 in the worst case.

# REFERENCES 

"Technical Specification for Cryomodule ACC39 Interfaces to the DESY
Cryo Module Test Bench (CMTB) and TTF/FLASH", by P. Pfund and C. Grimm,
EDMS \# D00000001134281, draft-j, June 18, 2008.

"3.9GHz Cryomodule Piping Engineering Note," by D. Olis, EDMS \#
D00000001134181, June 13, 2008.

"G10 Cold Post Loading," by D. Mitchell, 9 Nov 07

The e-mail exchange with Detlef Sellmann quoting piping bellows spring
rates is quoted here:

> **From:** detlef.sellmann@desy.de
>
> **Subject:** **Re: \[Fwd: 3.9 GHz cryomodule questions\]**
>
> **Date:** February 8, 2008 8:53:01 AM CST
>
> **To:** tommy@fnal.gov
>
> **Cc:** Bernd.Petersen@desy.de, claudia.engling@desy.de,
> kay.jensch@desy.de, sellmann@desy.de
>
> Hello Tom,
>
> the 3,9 GHz module will be connected to the process pipes of ACC1 and
> the endcap by identical bellows.
>
> 30 mbar low pressure pipe:  168,3x2 mm,  ax. springrate 60 N/mm
>
> lat. springrate 200 N/mm
>
> two phase pipe: 76,1x2 mm,   ax. springrate 4,8 N/mm
>
> lat. springrate 3,03 N/mm
>
> 40 K supply, : 60,3x2,77 ax. springrate 14,2 N/mm
>
> 80 K return, lat. springrate 8,05 N/mm
>
> 4,5 K supply,
>
> 4,5 K return
>
> 1,8 K supply : 48,3x1,65 ax. Springrate 13,9 N/mm
>
> lat. springrate 4,91 N/mm
>
> warm up pipe : 42,2x1,65 mm ax. springrate 6,54 N/mm
>
> lat. springrate 1,61 N/mm
>
> The bellows are equipped with outer guidance to prevent bulging, but
> there is enough clearance to allow for thermal shrinkage and tolerance
> in position. So the longitudinal forces in the process pipes will be
> balanced. The radial load on the cold mass of the module (all process
> pipes and shields) due to tolerances in position, is not larger than
>
> 500 N (the limit for the accelerator modules). The largest part of
> this value would be expected for the DN 150 bellow with the by far
> largest springrate (200 N/mm). The tolerances are less than 1 mm.
>
> If you need further information, don´t hesitate to contact me
>
> Best regards, and have a nice weekend
>
> Detlef
>
> Thomas J. Peterson wrote:
>
> Hello Detlef,
>
> Thank you very much for this information and for all the conflat
>  flange files.  I once again have my German-English dictionary on my
>  desk!
>
> Regarding the connections from ACC1 and the Endcap to this 3.9 GHz
>  cryomodule, we would like to understand what forces, if any, the
> pipes  might see due to unbalanced pressure or mechanical loads.  For
>  example, if the endcap connects to the 3.9 GHz cryomodule pipes via
>  braided flex hose or bellows with axial constraints, perhaps the
>  cryomodule pipes would see some axial load due to pressure.  Or,
>  perhaps there is a thermal contraction in the endcap which places
> some  small axial or radial load on a pipe.
>
> I do not expect any problem, since this cryomodule structure is
>  essentially the same as 1.3 GHz cryomodules like ACC1.
>
> These questions might be more easily answered with some sketches or
>  drawings. We may just start by exchanging e-mails with attachments
>  such as PDF files.  I could arrange for a Webex meeting if that would
>  be useful.
>
> Thank you and kind regards,
>
> Tom