1. TQS Structure Design and Modeling
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TQS Structure Design and Modeling
Paolo Ferracin
LARP Technology Quadrupole Review
LBNL
November 29 – December 1, 2006

2. Outline TQS structure 3D finite element model Mechanical analysis
Magnet design and parameters
Assembly and pre-load
3D finite element model
General features
Assumptions and goals
Validation
Mechanical analysis
Coil azimuthal stress
Effect of axial loading
Coil and pole axial stress
Conclusions
11/29/2006
Paolo Ferracin

3. TQS magnet design Cross-section End region Shell stress 
Coil average stress
End region
Rod stress 
Total axial force on the coil
11/29/2006
Paolo Ferracin

4. TQS01 magnet parameters Layer 1 Layer 2 Temperature K 4.5 (1.9) Iss kA
12.1 (13.2)
Bpeak T
11.06 (11.96)
9.42 (10.16)
Gss
T/m
217 (234)
Fx (octant)
N/m
(+ 1576)
+ 71 (+ 53)
Fy (octant)
871 (- 1028)
800 (- 941)
Fr (octant)
+ 930 (+ 1085)
186 (- 247)
F (octant)
1185 (- 1404)
801 (- 948)
Lorentz stress ()
MPa
113 (- 135)
- 77 (- 91)
Fz (aperture) kN
+ 90 (+ 107)
+ 241 (+ 287)
11/29/2006
Paolo Ferracin

5. Shell-yoke sub-assembly
The yoke stacks are positioned inside the shell and locked with keys around a dummy coil
11/29/2006
Paolo Ferracin

6. Coil-pack sub-assembly
Iron pads and filler
G10 ground insulation between coils and fillers
Coil-pack assembled, squared and bolted
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Paolo Ferracin

7. Final assembly
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Paolo Ferracin

8. Axial loading (I) Components Four aluminum rods
48 mm diameter
Two stainless steel plates
75 mm thick
Bullets
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Paolo Ferracin

9. Axial loading (II)
By R. Hafalia
11/29/2006
Paolo Ferracin

10. Axial loading (III)
By R. Hafalia
11/29/2006
Paolo Ferracin

11. Axial loading (IV)
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Paolo Ferracin

12. Bladder operation Load key insertion Bladder insertion
Pre-assembly condition
Bladder insertion
Bladder pressurization
Key shimming
Bladder deflation
Bladder removal
11/29/2006
Paolo Ferracin

13. Pre-assembly condition
11/29/2006
Paolo Ferracin

14. Bladder pressurization
11/29/2006
Paolo Ferracin

15. Key insertion and bladder removal
11/29/2006
Paolo Ferracin

16. Cool-down
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Paolo Ferracin

17. Excitation
11/29/2006
Paolo Ferracin

18. Stress during assembly and pre-load
Aluminum rods
37 MPa at 293 K (230 kN)
128 MPa at 4.5 K (800 kN)
Small variation during ramp
Aluminum shell
30 MPa at 293 K
166 MPa at 4.5 K
Small variation during ramp
11/29/2006
Paolo Ferracin

19. Outline TQS structure 3D finite element model Mechanical analysis
Magnet design and parameters
Assembly and pre-load
3D finite element model
General features
Assumptions and goals
Validation
Mechanical analysis
Coil azimuthal stress
Effect of axial loading
Coil and pole axial stress
Conclusions
11/29/2006
Paolo Ferracin

20. 3D finite element model
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Paolo Ferracin

21. 3D finite element model
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Paolo Ferracin

22. 3D finite element model
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Paolo Ferracin

23. 3D finite element model
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Paolo Ferracin

24. 3D finite element model
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Paolo Ferracin

25. 3D finite element model General features
1/8th symmetric model
All volumes imported from CAD
Coil modeled as solid blocks
20-node solid element
8-node contact element
Sliding / Friction / Bonded
Computational steps
Axial loading
Bladder operation
Cool-down
Excitation
11/29/2006
Paolo Ferracin

26. 3D finite element model Lorentz forces
ANSYS
(x, y, z) coordinates of each coil element center
OPERA
Computation of J x B (N/mm3) at each (x, y, z) coordinate
Computation of J x B · Vel (N)
Final force applied to each coil node
11/29/2006
Paolo Ferracin

27. 3D finite element model Assumptions and goals
Initial iterations
All surfaces allowed to separate
Final iterations
Potted coil glued
Conductor blocks, poles, spacers
All other surfaces allowed to separate
Friction factors
0.5 yoke/shell and 0.2 pad/coil
Pre-load optimized to ensure pole turn under pressure at short sample
Straight section and end region
11/29/2006
Paolo Ferracin

28. 3D finite element model Validation (I)
Comparison: model results and TQS01b gauge measurements of shell azimuthal and axial strain
Shell strain well reproduced with a friction factor of 0.5 between shell and yoke
11/29/2006
Paolo Ferracin

29. 3D finite element model Validation (II)
Comparison: model results and TQS01b gauge meas. of rod axial strain
Friction factor of 0.2 between coil and pad
Computed
530 to 1620 strain
Measured
540 to 1480 strain
Rod strain at 4.5 K overestimated by 9%
11/29/2006
Paolo Ferracin

30. Axial stress in the rod (MPa)
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Paolo Ferracin

31. 3D finite element model Validation (III)
Comparison: model results and TQS01b gauge measurements of pole azimuthal and axial strain
Azimuthal pole strain at 4.5 K overestimated by 7%
Good agreement with axial pole strain
11/29/2006
Paolo Ferracin

32. Outline TQS structure 3D finite element model Mechanical analysis
Magnet design and parameters
Assembly and pre-load
3D finite element model
General features
Assumptions and goals
Validation
Mechanical analysis
Coil azimuthal stress
Effect of axial loading
Coil and pole axial stress
Conclusions
11/29/2006
Paolo Ferracin

33. Coil azimuthal stress Pole and mid-plane, inner layer
Average stress from 40 MPa at 293 K to 150 MPa at 4.5 K
Large stress gradient at the pole after cool-down
Peak of MPa (corner element, possible overestimation)
Significant margin at short sample current
11/29/2006
Paolo Ferracin

34. Coil azimuthal stress Pole and mid-plane, outer layer
Average stress from 40 MPa at 293 K to 155 MPa at 4.5 K
Small stress gradient
Significant margin at short sample current
11/29/2006
Paolo Ferracin

35. Effect of axial loading Coil axial displacement after cool-down
With aluminum rods
Separation allowed
Contact pressure between coil and end part
Coil more compacted
Without aluminum rods
Separation allowed
Gaps between coil and end parts
Coil less compacted
Displ. scaling: 50
Displ. scaling: 50
11/29/2006
Paolo Ferracin

36. Effect of axial loading Coil axial displacement at high field
With aluminum rods
Separation allowed
Small or no gaps between coil and end part
< 20 mm
With aluminum rods
Separation allowed
Larger gaps between coil and end parts
> 150 mm
Displ. scaling: 50
Displ. scaling: 50
11/29/2006
Paolo Ferracin

37. Effect of axial loading Contact pressure - tension
Coil glued
Inner layer
50 MPa contact pressure at short sample
Outer layer
3 MPa contact tension at short sample
No separation or epoxy cracking expected in the ends
Epoxy bonding strength in tension about MPa
Only 2 training quenches in the end during TQS01 and TQS01b tests
11/29/2006
Paolo Ferracin

38. Mechanical analysis Axial stress in the pole (I)
Coil glued
After assembly
Axial compression
After cool-down
Axial compression in the ends and tension in the center
Effect of aluminum rods in the end (penetration length)
Friction between pad (iron) and pole (bronze)
At 12 kA
Pole tension beyond epoxy bonding strength
Path from
center
to end
11/29/2006
Paolo Ferracin

39. Mechanical analysis Axial stress in the pole (III)
Separation allowed
Displ. scaling: 50
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Paolo Ferracin

40. Mechanical analysis Axial stress in the pole (III)
Separation allowed
Displ. scaling: 50
11/29/2006
Paolo Ferracin

41. Mechanical analysis Axial stress in the pole (III)
Separation allowed
Displ. scaling: 50
11/29/2006
Paolo Ferracin

42. Mechanical analysis Axial stress in the pole (III)
Separation allowed
Displ. scaling: 50
11/29/2006
Paolo Ferracin

43. Mechanical analysis Axial stress in the pole (III)
Separation allowed
Displ. scaling: 50
11/29/2006
Paolo Ferracin

44. Mechanical analysis Axial stress in the pole (III)
Separation allowed
Displ. scaling: 50
11/29/2006
Paolo Ferracin

45. Mechanical analysis Axial stress in the pole (III)
Separation allowed
Displ. scaling: 50
11/29/2006
Paolo Ferracin

46. Mechanical analysis Axial stress in the coil
Separation allowed at the pole cuts
After assembly
Axial compression
After cool-down
Axial compression in the ends and tension in the center
At 12 kA
Spike of axial tension where central gap is located
Path from
center
to end
11/29/2006
Paolo Ferracin

47. Conclusions Optimized friction factors
0.5 shell/yoke and 0.2 coil/pad
Good agreement between 3D model results and strain gauge measurements in shell, rods, and poles
No gaps or epoxy cracking expected in end region
Confirmed by TQS01 and TQS01b tests
Potential causes of magnet training/degradation
Peak azimuthal coil stress after cool-down approaching MPa (average of 150 MPa)
Axial tension in the pole beyond epoxy bonding strength
Peak of coil axial tension close to pole gaps
11/29/2006
Paolo Ferracin

48. Appendix
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Paolo Ferracin

49. Material properties Elastic modulus @ 293 K @ 4.3 K a · ΔT
GPa
Aluminum bronze
110
120
3.12  10-3
Stainless steel
193
210
2.84  10-3
Iron
213
224
1.97  10-3
Aluminum 70 79
4.19  10-3
2D*
Coil () 44
3.35  10-3
Coil (r) 52
3.09  10-3 3D 45
Coil (z)
* K.P. Chow and G.A. Millos, Trans. Appl. Superconduct., Vol. 9, No. 2, June 1999, pp
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Paolo Ferracin

50. Peak field in the conductor
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Paolo Ferracin

51. 3D mechanical analysis: comparisons with 2D analysis
Aluminum shell stress
Case study
With aluminum rods
Friction model
2D/3D: ± 1 MPa
Coil pre-stress (pole region)
Case study
With aluminum rods
Friction model
2D/3D: ± 3 MPa
11/29/2006
Paolo Ferracin

52. 2D mechanical analysis: coil azimuthal stress (friction)
After cool-down
Peak stress: 179 MPa
Mid-plane (average): MPa
After short sample
Peak stress: 167 MPa
Mid-plane (average): MPa
11/29/2006
Paolo Ferracin

53. Coil radial displ. at 4.5 K (mm)
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Paolo Ferracin