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13_030303_CLN_01.doc

***TO: DISTRIBUTION***

***FROM: C NEUMEYER***

***SUBJECT: TF FLAG JOINT FORCES AND LOAD PATHS***

This memo provides rough estimates of in-plane forces on the TF flags
and evaluates the various load paths. It is intended to provide guidance
for the initial sizing of the various mechanical components of the
joint. Finite element analysis presently underway will provide more
accurate information for finalizing the design.

*Forces and Load Paths*

A schematic of a inner tier flag associated with an outer layer turn is
shown in the following figure.

![](media/image2.jpeg){width="5.990972222222222in"
height="4.757638888888889in"}

A description of the forces and load paths is as follows:

F~em1~: Vertical EM force generated on the flag. Assumed to include
JxB~t~ contribution from both flag halves, along with attractive force
between the flags in the two tiers. Inner flag half assumed to carry 3x
current of outer flag half. Force on each conductor assumed equal to
Jx(B~self~/2 + B~ext~). Here B~self~ is the self-field and B~ext~ is the
field produced by the other conductors, including those from both the 24
and 12 turn tiers. The effective radius at which the force is applied is
that where the field is at its average value along the length in
question.

F~em2~: Vertical EM force generated on linkage between flags and outer
legs, consisting of solid connectors on either side of a flexible link.
Total force across link is shared between inner and outer leg
assemblies. Here it is assumed that force generated up to midpoint of
omega in flexible link is applied to inner leg assembly. Distance from
flag end to midpoint of omega is assumed to be 6". Again, forces are
based on Jx(B~self~/2 + B~ext~), and the effective radius at which the
force is applied is that where the field is at its average value along
the length in question.

F1, F2, F3, F4: These are the inward radial forces generated by the
tension in the thru-bolts.

F5: This is an additional inward radial force generated by a proposed
jack-screw arrangement which acts between the flag end and the hub disk.

F6: This is a downward force provided by the hub assembly via the flag
insulation, shim, hub disk, torque collar, wet lay-up, and TF ground and
turn insulation, all in series. It resists the vertical forces on the
flag as well as rotation of the flag about point X.

F7: This is an upward force provided by the hub assembly which resists
rotation of the flag about point X.

F8: This is an inward radial force which resists rotation of the flag
about point X. It acts through the flexible link.

F9: This is a downward vertical force which resists the vertical EM
forces on the flag via the frictional connection between the flag and
the inner leg conductor as well as shear of the bolts and/or pins
connected across the joint.

The EM forces on the flags and links at 6kG (71.2kA/turn) are given in
the following table.

**Summary of Forces and Moments at 6kG**

+-----------------------+----------+-----------------+-----------------+
|                       | F~v      | dR from point   | Moment          |
|                       | ertical~ | of application  |                 |
|                       |          | to flag inboard | w.r.t. point X  |
|                       | (lbs)    | edge            |                 |
|                       |          |                 | (in-lbs)        |
|                       |          | (in)            |                 |
+-----------------------+----------+-----------------+-----------------+
| Inner Tier Flag       | 7380     | 4.3             | 31719           |
+-----------------------+----------+-----------------+-----------------+
| Inner Tier Link       | 1855     | 13.8            | 25652           |
+-----------------------+----------+-----------------+-----------------+
| Outer Tier Flag       | 1845     | 4.3             | 7930            |
+-----------------------+----------+-----------------+-----------------+
| Outer Tier Link       | 464      | 13.8            | 6413            |
+-----------------------+----------+-----------------+-----------------+
| Total from All Turns  | 249324   |                 |                 |
+-----------------------+----------+-----------------+-----------------+

Clearly the forces on the inner tier (associated with the 24 turn outer
layer) are much higher than the outer tier.

*Reaction of Applied Moments*

Because of the relatively high elasticity of the load paths associated
with F6, F7, and F8 they are discounted in the following discussion.
This is a worst case scenario for the bolted joint load path.

The applied moment on the flag is equal to
F~em1~\*dR~em1~+F~em2~\*dR~em2~. Assuming that F6, F7, and F8 do not
react against this moment it must be taken by F1, F2, F3, F4, and F5.

Let F5 be an input variable. Assume that the relative values of F1, F2,
F3, and F4 vary in proportion to their vertical distance z to point X.
This is based on the idea that, as the flag rotates through an angle
about point X, the elastic deformation of the bolts will be \~ zthe
associated force will be in proportion to z.

With these assumptions the values of the thru-bolt forces required to
counteract the applied moment can be estimated. Then the total tension
on the bolts is equal to the preload plus the additional force required
to react the moment.

The preload must be chosen such that, under full EM load, adequate
contact pressure is maintained. Given this requirement, the required
thru-bolt preload and peak force in the highest stressed bolt (the one
which supplies F1) can be estimated based on the assumption that the
radial force acting against the preload is equal to the applied moment
divided by the half height of the flag.

The following table shows the forces and stresses corresponding to the
case where an average contact force of 10000 lbs, equivalent to a
contact pressure of approximately 1000/5in^2^=2ksi, is maintained under
all conditions. An F5 force of 5000 lbs applied at a distance of 6"
below point X. For this case the required bolt preload is 2584 lbs.

**Inner Tier Forces and Reactions with 5000 lb. End-jack**

  --------------------------------------- ---------------- ---------------
  ∑Applied Moments                        57371.7          in-lbs

  dZF1                                    4.750            in

  dZF2                                    3.500            in

  dZF3                                    2.125            in

  dZF4                                    0.875            in

  dZF5                                    6.000            in

  F5                                      5000.0           lbs

  F1                                      3242.8           lbs

  F2                                      2389.4           lbs

  F3                                      1450.7           lbs

  F4                                      597.4            lbs

  Bolt Preload                            2584.2           lbs

  Ftot1                                   5827.0           lbs

  Ftot2                                   4973.7           lbs

  Ftot3                                   4035.0           lbs

  Ftot4                                   3181.6           lbs

  ∑Fr                                     10000.0          lbs
  --------------------------------------- ---------------- ---------------

The following curve shows the required bolt preload, and the peak force
(in bolt 1) as a function of end-jack force F5.

![](media/image3.pct){width="4.571527777777778in"
height="2.772222222222222in"}

The following table and curve show the results for the outer tier which
experiences considerably less force.

**Outer Tier Forces and Reactions with 0 lb. End-jack**

  --------------------------------------- ---------------- ---------------
  Fem1                                    1844.9           lbs

  dRem1                                   4.3              in

  Fem2                                    463.7            lbs

  dRem2                                   13.8             in

  ∑Applied Moments                        14342.9          in-lbs

  F5                                      0.0              lbs

  F1                                      1699.2           lbs

  F2                                      1252.1           lbs

  F3                                      760.2            lbs

  F4                                      313.0            lbs

  ∑Reaction Moments                       14342.9          in-lbs

  Bolt Preload                            2833.6           lbs

  Ftot1                                   4532.8           lbs

  Ftot2                                   4085.6           lbs

  Ftot3                                   3593.7           lbs

  Ftot4                                   3146.6           lbs

  ∑Fr                                     10000.0          lbs
  --------------------------------------- ---------------- ---------------

![](media/image4.pct){width="4.479861111111111in"
height="2.723611111111111in"}

*Reaction of Vertical Forces*

Two load paths are available to react the vertical loads. The first (F9)
is via shear at the interface between the flag and the inner leg
assembly, and the second (F6) is via the shims/hub assembly/torque
collar/wet lay-up/ground/turn insulation. The former is much stiffer
than the latter, so it probably takes most of the load.

The maximum force on a flag occurs on the inner tier, and is the sum of
the forces generated on the flag and on the link to the outer leg, equal
to 7379 + 1855= 9234 lbs. Assuming a contact pressure of order 10000
lbs, a coefficient of friction of 0.9234 would be required to react this
force, which is unrealistic. Therefore if most of the load has to pass
through the joint it is clear that additional shear components (shoulder
bolts, keys, etc.) are necessary.

The torque collar will end up carrying some fraction of the total load
of 249324 lbs. Additional stress is imposed on the collar wet lay-up
from the torsional load due to J~TF~ x B~rOH~. The following table
estimates the shear stress on the wet lay-up system from the combined
vertical and torsional loads, assuming that the full fraction of the
vertical load appears on the collar.

**Worst Case Forces and Reactions on Collar**

  ---------------------------------------- ---------------- --------------
  Collar Height                            3.25             in

  Inner Leg Groundwall Outer Radius        3.96             in

  Circumference                            24.88            in

  Area                                     80.86            in\^2

  Vertical Force                           249324.7         lbs

  Torque                                   100000.0         N-m/m

                                           8255             N-m

                                           6088.3           ft-lbs

                                           73060.0          in-lbs

  Torsional Force                          22480.0          lbs

  Effective Force                          250336.1         lbs

  Average Shear Stress                     3095.9           psi
  ---------------------------------------- ---------------- --------------

cc: A Brooks M Bell J Chrzanowski L Dudek

P Heitzenroeder M Kalish M Ono M Peng W Reiersen J Schmidt A VonHalle M
Williams I Zatz