1. MKQXF
FEA Model
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2. Key Features Shell (15mm) Loading plate Collaring Shoe
Collaring Key
Ground Insulation
Trace
Filler wedge
Aluminum Bars
Tapered mid-plane
150 mm apperture
12° taper
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3. Shimming Positions Pole shim Pole adjustment shim Mid-plane shim
Collar-Yoke radial shim
Coil-Collar radial Shim
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4. Magnetic Analysis
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5. Magnetic Analysis @ 17.3 kA 11.82 T, 140 T/m Haris Kokkinos

6. @ kA T, 155 T/m
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7. Structural Analysis
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8. Material Properties St. Steel (5) - Collars St. Steel (10) - Shell
E(293K) = 195 Gpa E(4.2K) = 215 Gpa
Prxy(293K) = Prxy(4.2K) = 0.3
α= e-6
St. Steel (10) - Shell
E(293K) = 195 Gpa E(4.2K) = 215 Gpa
Prxy(293K) = Prxy(4.2K) = 0.3
α= e-06
Aluminum (55) - Bars
E(293K) = 70 Gpa E(4.2K) = 79 Gpa
Prxy(293K) = Prxy(4.2K) = 0.34
αx= 1.45e-5
St. Steel (52) - LoadingPlates
E(293K) = 193 Gpa E(4.2K) = 210 Gpa
Prxy(293K) = Prxy(4.2K) = 0.28
α= 9.83e-06
St. Steel (11) - Pins
E(293K) = 195 Gpa E(4.2K) = 215 Gpa
Prxy(293K) = Prxy(4.2K) = 0.3
α= e-06
Aluminum Bronze (53) - Wedges
E(293K) = 110 Gpa E(4.2K) = 120 Gpa
Prxy(293K) = Prxy(4.2K) = 0.3
αx= 1.08e-5
Titanium (57) - PoleWedge
E(293K) = 130 Gpa E(4.2K) = 130 Gpa
Prxy(293K) = Prxy(4.2K) = 0.3
α= 6.03e-06
St. Steel (52) – Collaring Shoe
E(293K) = 215 Gpa E(4.2K) = 195 Gpa
Prxy(293K) = Prxy(4.2K) = 0.3
α= e-06
St. Steel (6) - Keys
E(293K) = 190 Gpa E(4.2K) = 210 Gpa
Prxy(293K) = Prxy(4.2K) = 0.3
α= 9.01e-06
Magnetic Steel (7) - Yoke
E(293K) = 210 Gpa E(4.2K) = 225 Gpa
Prxy(293K) = Prxy(4.2K) = 0.3
α= e-06
Coil (51)
Ex(293K) = 52 Gpa Ex(4.2K) = 52 GPa
Ey(293K) = 44 Gpa Ey(4.2K) = 44 Gpa
Gxy(293K) = 21 Gpa Gxy(4.2K) = 21 Gpa
Prxy(293K) = Prxy(4.2K) = 0.3
αy= 1.16e-5
αx= 1.07e-5
G10 (56) - Insulation
E(293K) = 30 Gpa E(4.2K) = 30 Gpa
Prxy(293K) = Prxy(4.2K) = 0.3
αx= 2,44e-5
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9. Lorentz Forces Magnetic Mesh Structural Mesh Mapped Forces
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10. Parameters’ values used for the results presented below:
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11. Azimuthal Stress
Coil
Under 293 K
After 293 K
It’s very interesting that the collared is not really affected by friction. Maybe this is due to the small displacement (0.05mm) applied during collaring (compared to the 11T, 0.1mm). But the coil stress is also not really affected by friction in the 11T. So this is consistent.
After Shell 293 K
@ 4.2 K
@ 4.2 K, 140 T/m
@ 4.2 K, 155 T/m
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12. Azimuthal Stresses
Coil
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13. Radial Deformation
Coil
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14. Von-Mises Stress Collars
After Shell 293 K
@ 4.2 K, 155 T/m
@ 4.2 K
@ 4.2 K, 140 T/m
The areas with stress over 300 Mpa are indicated in grey colour and these are the areas around the keys that typically plastify during the assembly process.
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15. Deformation Collars Under Press, @ 293 K After Collaring, @ 293 K
After Shell 293 K
@ 4.2 K
@ 4.2 K, 140 T/m
@ 4.2 K, 155 T/m
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16. Von-Mises Stress Yoke After Shell Welding, @ 293 K @ 4.2 K
@ 4.2 K, 140 T/m
@ 4.2 K, 155 T/m
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17. Reaction Forces Collar-Yoke After Shell Welding, @ 293 K @ 4.2 K
@ 4.2 K, 140 T/m
@ 4.2 K, 155 T/m
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18. Contact Pressure Half Yokes Tapered After Shell Welding, @ 293 K
@ 4.2 K, 140 T/m
@ 4.2 K, 155 T/m
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19. Contact Pressure Gap Controllers After Shell Welding, @ 293 K @ 4.2 K
@ 4.2 K, 140 T/m
@ 4.2 K, 155 T/m
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20. Azimuthal Stress Shell Detailed View: Mean Azimuthal Stress 155 MPa
After Shell 293 K
@ 4.2 K
@ 4.2 K, 140 T/m
@ 4.2 K, 155 T/m
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21. Sensitivity Analysis
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22. Tolerances Yoke ± 3,8 μm Collar ± 6,3 μm Angle of loading plate ± 0,2°
Coil (outside diameter)
± 75 μm
The sensitivity analysis is conducted by utilizing the DOE method (Design of Experiments) which determines sampling points on a response surface
About 8 input parameters have to be checked.
About 100 variations of the model have to be run
Up to now, we have solved for 6 input parameters, ,corresponding to 45 variations
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23. Tolerances
Response Surface
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24. Tolerances
Sensitivity Chart
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25. Conclusions
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26. Conclusions
New mechanical design concept for a Nb3Sn quadrupole, suitable for industrial production
The FEA shows that the assembly is well controlled, with all parts staying generally within the accepted stress levels
Coil pre-stress is applied in a well-controlled manner and is easily tuneable with shims
The pole-loading concept allows to position the coil’s peak stress at the poles, and the min stress at the mid-plane
Assembly is possible with a dipole-type press, due to the tapered-shape mid-plane poles and the dipole-type collars
The Al-bars act like gap controllers at RT, while at cold the tapered - horizontally split iron yoke with a closed gap provides a rigid structure
The coil is symmetric at operating temperature
Robust parametric, FE multi-physics analysis
Next steps: 1) Sensitivity analysis
2) Alignment features at the collar – yoke interface
3) Report for phase II
Reference: M. Karppinen, “New Mechanical Concept for Nb3Sn Quadrupole”, CERN-ACC
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