Summary of Twisted Racetrack / Clamp Analysis

1
Summary of Twisted Racetrack / Clamp Analysis

• 4-16-04
• K. D. Freudenberg

2
Twisted Racetrack FEA Mechanica Model
East
West
real clamp added to the model
Geometry restrictions unique to the twisted
racetrack coil prevent the use of 1/8 shim
plates at severe turn/twist areas. Pseudo
clamps left off at these locations
3
Restraints and loads

• Contact surfaces are used between the clamp
  winding and the tee.
• Thermal growth is imposed on the winding by
  utilizing the cte property and by applying a
  known strain over a given temperature change.
• Example strain -800µe , arbitrary temp
  difference 72 F. Therefore,
• Winging cte -800µe /72 F 1.11E-5 /F
• Tee cte 0

• Winding is broken into regions (between blue
  lines) on which the magnetic pressure loads are
  applied, pressures correspond to
  I42-kA/electrical turn.
• Max EM Running Loads
• Radial 1819 lb/in.
• Lateral 3946 lb/in.
• Pseudo clamps are restrained in their respective
  normal directions to simulate real clamp behavior.

The latest data indicates essentially no cure
shrinkage of the winding. Therefore, the -800µe
used in this analysis should be tailored down to
-400µe to account only for the cool-down
shrinkage between the tee and winding
(4-10-2004).
4
Clamp modeling
Wave spring in clamp pocket

• Modulus of washers is tailored to represent the
  spring constant of the belleville washers.
  Example k 26,000 lb/in, Awasher 0.81in2,
  Depthwasher 0.15 in2. Therefore E kdepth/A
  4814 psi
• The cte of the washer is used to impose a
  preload on the clamp and winding. Assume 0.1
  in/in strain Therefore cte 0.1 / -72 F
  -0.00138 /F and preload for hard springs is
  2600 lbs, and 1000 for soft springs
• All washers have the same spring constant but
  have different modulus values.
• The clamp is fixed to the
  tee by a stud at the top of
  the clamp and a representative
  bolt head on the lower
  end.

Fixed to tee
Contact Surfaces
Backside of washer is fixed to tee bolt
Contact Surfaces are used between the clamp and
the winding.
5
Clamp Design Iterations
Multiple case have been run to determine what the
correct design parameters should be for the
clamps and corresponding Belleville washers.
Cases 17 have one real clamp on board at west
location and the rest are pseudo clamps.
6
Displacement Comparison
7
How are Displacements from Tee Measured
K 26,000 lb/in Preload 650 lbs
K 10,000 lb/in Preload 125 lbs
Gap 0.0347
Gap 0.0285
K 10,000 lb/in Preload 250 lbs
K 26,000 lb/in Preload 975 lbs
Gap 0.022
Gap 0.0339
8
Clamp Stresses
K 26,000 lb/in Preload 650 lbs Peak Stress
81,000 psi
K 10,000 lb/in Preload 125 lbs Peak Stress
26,000 psi
K 10,000 lb/in Preload 250 lbs Peak Stress
46,000 psi
K 26,000 lb/in Preload 975 lbs Peak Stress
130,000 psi
9
Winding Modulus Comparison Deformation

• Points
• The modulus of the winding is a big player in
  determining the deflection of the coil.
• The deformation decreases with the lower modulus
  coil.

Case A
Case B
10
Winding Modulus Comparison Stress

• Points
• Stress in tee is higher for the less stiff
  winding.
• Winding stress decreases as winding modulus is
  lowered.
• Clamp Stress is relatively the same. Clamp is
  dominated by preloaded springs

Case A
Case B
11
Case 2 (Revisited 4-10-2004)

• Case 2 produced the best fit in terms of gap
  deflection, winding stress and clamp stress.
• Rerunning the case with the new cure shrinkage
  data produces the following results.

Case 2 K 5,000 lb/in Preload 125 lbs
Overall Deformation
Overall Stress
Obviously, the new data, if genuine, is
encouraging.
12
Considering the 4 Operating States (Case 2, No
Cure Shrinkage)

1. Immediately after cool down. -0.04 relative
   strain between winding and tee due to thermal
   expansion.
2. Beginning of Pulse. Magnetic loading applied
   with thermal expansion.
3. End of pulse. Magnetic loading applied without
   thermal expansion, heating of coil has resulted
   in a relative 0.04 strain difference between
   the winding and tee. (strain value is only
   coincidentally equal to the cool down strain
   difference).
4. Post Pulse. No magnetic loading, no thermal
   expansion (at rest state, coil will then cool
   back to state 1)

13
Is Mechanica Accurate, Can It Be Trusted For
Non-Linear Contact Analysis ?
A comparison study has been worked in Ansys for
modular coil 2.
Clamp is locked in Ansys model here
Mechanica
No Preload on clamp pads in Ansys version
14
Comparison Between Mechanica and Ansys (Von Mises
Stress)
Mechanica
The high stress is in the pin connecting the
clamp which the Ansys model does not have.
Is Mechanica Accurate? Yes, It agrees well with
Ansys
15
Summary

• Iterations show that Belleville washers should
  be designed with a stiffness of 5,000 - 10,000
  lb/in and a preload of 100 125 lbs. This
  corresponds to case 2 and case 6.
• Clamp Stresses depends mostly on preload.
• Soft windings stick to the tee better, but do
  raise stress in the tee.
• Using no clamps, results in larger displacements
  and gaps, but this effect is less for the stiff
  winding pack.
• Mechanica and Ansys give the same answers for
  non-linear contact analysis.

16
Future Work

• Modify Winding Stiffness based on results of
  ongoing tension and compression tests at PPPL.
• Provide a table for predicted strain values at
  experimental strain gage locations for the four
  loading states.
• Perform a detailed analysis of the actual clamp
  design (with all features)
  based on the max deflections
  measured in this analysis.

Actual clamp design
Strain Gauge Locations (ends and middle of
winding form) ?
Coil Leads
17
Extra Slides (description)

• Overall deformation and stress of several cases
  looked at but not necessarily in the table.
  (slides 18-19)
• Washer deflection as a function of preload.
  (slide 20)
• Washer schematic illustrating behavior of washer
  through analysis. (slide 21)
• Overall deflection if no clamps are on board.
  (slides 22-23)
• Clamps have been placed at various sections
  (straight curved, right next to each other.
  (slide 24)
• How do the real clamps compare to the pseudo
  clamps along a straight section. (slide 25)

18
Overall Coil Displacement
K 26,000 lb/in Preload 650 lbs
K 10,000 lb/in Preload 125 lbs
Notice the similarities between the coils in
areas away form the clamp.
K 10,000 lb/in Preload 250 lbs
K 10,000 lb/in Preload 975 lbs
Case 2
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Overall Coil Stress
K 26,000 lb/in Preload 650 lbs
K 10,000 lb/in Preload 125 lbs
Case 1
Case 4
K 10,000 lb/in Preload 250 lbs
K 10,000 lb/in Preload 975 lbs
Case 2
Case 5
20
Washer Displacement as a Function of Applied
Preload

• The displacement measured in washers A and B is
  a direct result of the preload applied, the coil
  loading has little impact on displacement for the
  chosen preloads.
• The displacement for the wave spring is very
  dependent on coil loading as lower preload forces
  result in larger deflections.

21
Washer Schematic
dp
ds
di
Subtract winding affect
Washer Initially
Add Preload
Dflat gt di dp ds

• For the lateral Washers, the winding affect is
  not greater than dp which is why the measured
  displacement (ds) is less than the added preload
  (dp). In fact, looking at the relatively small
  difference between the measured deflection and
  the preload deflection, one can assert that the
  preload is almost entirely responsible for the
  measured deflection and the winding produces a
  very small portion of the deflection.
• For the wave Springs, the measured displacement
  is greater than the added preload

22
No clamps Pressure and Temperature applied
Model is fixed at one leg. Separation on west
side of modular coils occurs on the inner coil
only. (Outer coil gap is essentially zero.)
Winding E 9.5E6 psi
23
No clamps Displacement Measured from clamp
coordinate system
Large Gap occurs here on the inner coil (approx
.025), largest gap occurs on opposite East side.
(not shown)
24
Clamp on Straight Section
Clamp on Curved Section
Notice how the clamp stress appears to be
independent of clamp location and is mostly a
function of spring preload.
25
Displacement Comparison
Clamp on Straight Section
No Clamp
Notice How the relative gap between the winding
and the tee is relatively the same in both
pictures. The color band difference on the scale
bar is only 0.0025