Structural Analysis of the CCL & SCL BPM Electrode to Feed Through
Connection

SNS Technical Note

By

Jim O'Hara

7/30/2001

Introduction

This report details the analysis done to design the connection between
the vacuum feed through and the BPM electrode. The type of connection
used depends upon the contact pressure between the electrode signal pin
and the vacuum feed through center pin. Brookhaven National Laboratory
developed this type of connection for use on the RHIC project.
Deflecting the BPM electrode by compressing the signal pin inward as the
vacuum feed through is installed generates contact pressure. The spring
force of the deflected electrode maintains the contact pressure between
the signal pin and the feed through. Figure 1 is a section cut through
the SCL BPM showing how this contact takes place. The desired end
product will have the BPM electrodes inner surface flush with inner
diameter of the up and down stream bore tube. In order to accomplish
this, the electrode must be deflected outward during the fabrication
process. The purpose of this analysis is to determine how much
deflection is required to insure the connection will be made correctly.

Figure 1, section cut through the SCL BPM

# Description of the SCL BPM analysis

The finite analysis model utilizes the electrode part of the BPM
assembly. A load is applied to the end of the electrode, while the
opposite end is constrained from moving. The stress and deflection are
reported. The desired result is to determine how far the electrode
should be deflected during the brazing operation. The electrode will be
held in a deflected position during brazing. The heat of the brazing
operation will relieve the stress induced by the deflection such that
the electrode will come out of the furnace with a permanent set. The
idea is that once the signal pin and vacuum feed through are installed,
the electrode will be forced back into the proper position. The
resulting stress in the electrode will maintain the necessary contact
pressure between the signal pin and the electrode.

[Material properties]{.underline}

The material used for the BPM electrode is AISI 304 stainless steel. The
properties used in the analysis are as follows:

![](media/image1.png){width="4.147222222222222in"
height="3.4069444444444446in"}

Figure 2, Material Properties

# Constraints and Loads

One end of the electrode is held fixed and a load is applied to the end
of the electrode. The first load case uses a one pound load, and the
second uses a 13.7 pound load to produce a .008 inch deflection at the
end of the electrode. There are two different loads on two different
electrodes. One pushes the electrode in and the other pulls it out. This
was done to see if the direction of curvature of the electrode caused
any difference in the amount of deflection produced (it didn't).

![](media/image2.png){width="3.30625in" height="2.8020833333333335in"}

Figure3, Applied loads and Constraints

# Results

First load case, 1 lbf load applied at the end of the electrode.

The displacement caused by the 1 lbf load is .00058 inches. Figure 4
shows an exaggerated view of this displacement.

![](media/image3.png){width="4.479861111111111in" height="3.25in"}

Figure 4, deflection caused by 1 lbf load applied at the end of the
electrode.

The stress in the electrode is shown in figure 5. The peak stress is
located at the base of the electrode having a value of 1552 psi. AISI
304 L stainless steel has a yield strength of 30,000 psi. It is desired
to develop as strong a spring force as possible to act against the feed
through center pin without causing the electrode to yield. Staying
within the elastic range (linear range) of the stainless means that the
maximum deflection should be about .011 inches. In order to be close to
the maximum value but not exceed the yield strength a deflection of .008
inches was chosen.

![](media/image4.png){width="4.0in" height="3.15625in"}

Figure 5, stress caused by 1 lbf load.

A second load case was run using a deflecting load of 13.866 lbf to
cause a .008 inch deflection at the end of the electrode. Figure 6,
shows a plot of the stress caused by this load. The value of the stress
at .008 inch deflection is 21,520 psi.

![](media/image5.png){width="3.9194444444444443in"
height="3.1041666666666665in"}

Figure 6, stress when electrode is deflected .008 inches.

Another model was created as a quality check of the first one. The
second model used the same geometry but by decreasing the average
element size from 3.95 to 2.27 a finer mesh was created. The finer mesh
increased the number of elements from 12548 to 46151, thereby increasing
the number of nodes from 25019 to 83732. The deflection caused by the
13.866 lbf force caused a .00814 inch deflection. For a 235% increase in
the number of nodes, the deflection increases by 1.8%.

The next item to look at is whether or not the threaded connection
between the brazing fixturing an the electrode is strong enough to
handle the approximately 15 lbf required to produce the desired
deflection. Attached as an appendix to this document is an excerpt from
a Mathcad file that calculates the maximum force produced by a #5-40
stainless steel screw (596 lbf) and the necessary amount of thread
engagement to prevent thread stripping (0.099 inch). The threaded length
in the end of the electrode is 0.222 inch.

# Conclusions

Further increasing the number of nodes will not significantly change the
results of the analysis. The nominal deflection of the SCL BPM electrode
will be specified to be 0.008 inches requiring approximately 13.7 lbf.
The threaded connection possesses adequate strength to produce the 0.008
inch deflection. There is enough thread engagement to prevent stripping
during the brazing process.

# Description of the CCL BPM analysis

The finite analysis model of the CCL BPM is essentially the same as the
previous model of the SCL BPM, only the geometry is different. The
electrode part of the BPM assembly is analyzed. A load is applied to the
end of the electrode, while the opposite end is constrained from moving.
The stress and deflection are reported. Figure 7 shows the geometry of
the CCL BPM.

![](media/image6.png){width="3.372916666666667in" height="4.1875in"}

Figure 7, CCL BPM assembly

[Material properties]{.underline}

The material used for the CCL BPM electrode is the same as that for the
SCL, AISI 304 stainless steel. See Figure 2 for specific property
values.

# Constraints and Loads

One end of the electrode is held fixed and a load is applied to the end
of the electrode. The first load case uses a one pound load, and the
second uses a 3 pound load to produce a .008 inch deflection at the end
of the electrode. Figure 8 illustrates the loads and constraints.

![](media/image7.png){width="3.8131944444444446in"
height="3.1041666666666665in"}

Figure 8, Applied loads and Constraints

# Results

First load case, 1 lbf load applied at the end of the electrode.

The displacement caused by the 1 lbf load is .00266 inches. Figure 9
shows an exaggerated view of this displacement.

![](media/image8.png){width="4.0in" height="2.9791666666666665in"}

Figure 9, 1 lbf causes 0.0027 inch deflection

The stress developed due to the 1 lbf is 5,827 psi and is shown in
figure 10.

![](media/image9.png){width="3.90625in" height="3.1041666666666665in"}

Figure 10, stress in CCL BPM with 1 lbf load

Using the same 0.008 inch deflection as the SCL BPM would produce
approximately 17, 480 psi. This corresponds to about a 3 lbf load. The
next load case illustrates the deflection and stress results for the 3
lbf load. There is room to increase the deflection if the 3 lbf load
does not create adequate contact pressure.

![](media/image10.png){width="4.30625in" height="3.2395833333333335in"}

Figure 11, 0.008 inch deflection of CCL BPM due to a 3 lbf load

![](media/image11.png){width="3.839583333333333in"
height="3.1041666666666665in"}

Figure 12, 17,480 psi von mises stress due to 3 lbf load

The CCL BPM has the same threaded connection as the SCL BPM. The maximum
thread engagement available for the CCL BPM is 0.134 inches. This is
greater than the 0.099 inch required to prevent thread stripping.
Attached as an appendix to this document is an excerpt from a Mathcad
file that calculates the maximum force produced by a #5-40 stainless
steel screw (596 lbf) and the necessary amount of thread engagement to
prevent thread stripping (0.099 inch).

A quality check on the model was done similar to that done for the SCL
BPM. The first model had an average element size of .08 inches, 13473
elements having 25467 nodes, resulting in a 0.00799 inch deflection. The
verification mesh was .058 inch element size, 25149 elements, 25467
nodes, resulting in a 0.00805 inch deflection. An 80.5% increase in
nodes resulted in a 0.06% increase in deflection.

# Conclusions

Further increasing the number of nodes will not significantly change the
results of the analysis. The nominal deflection of the CCL BPM electrode
will be specified to be 0.008 inches, requiring approximately 3 lbf. The
threaded connection possesses adequate strength to produce the .008 inch
deflection. There is enough thread engagement to prevent stripping
during the brazing process.

APPENDIX A -- Threaded connection analysis

Mathcad file: *mechanical design\\bolt_engagement.mcd*

![](media/image12.wmf)