Cable inventory, relative measurements and 1 st mechanical computations

1. Cable inventory, relative measurements and 1st mechanical computations STUDY OF THE QUADRUPOLE COLLAR STRUCTURE P. Fessia, F. Regis Magnets, Cryostats and Superconductors Group Accelerator Technology Department, CERN

2. Summary • Scaling collar thickness on existing magnets (MQXB, MQ) • Azimuthal stress in function of aperture and collar thickness (analytical approach) • Key dimensioning: • 1 key • 2 key • Key angular position optimization (FEM) • FEM computation on 120 and 130 mm aperture quads

3. Scaling collar thickness on existing magnets (MQXB, MQ) • Azimuthal stress in function of aperture and collar thickness (analytical approach) • Key dimensioning: • 1 key • 2 key • Key angular position optimization (FEM) • FEM computation on 120 and 130 mm aperture quads

4. Horizontal forces per octant Forces [N/mm] 1386N/mm

5. COLLAR Scaling based on MQXB • Scaling based on radial collar displacement • The collar width is obtained by solving:

6. COLLAR Scaling based on MQ

7. Collar scaling - Conclusions Horizontal magnetic forces increase with the aperture Scaling collar thickness on MQ radial displacement is more conservative For 130mm aperture the collar thickness is between 42 (MQXB) and 65 mm (MQ). For 120mm aperture the collar thickness is between 39 (MQXB) and 49 mm (MQ).

8. Scaling collar thickness on existing magnets (MQXB, MQ) • Azimuthal stress in function of aperture and collar thickness (analytical approach) • Key dimensioning: • 1 key • 2 key • Key angular position optimization (FEM) • FEM computation on 120 and 130 mm aperture quads

9. Azimuthal stress on mid plane • Mid-plane stress due to Lorentz forces for different apertures and coil thickness • Based on sector coil approach at SS current density (LHC MQ cable 02). Reference line: w=30mm

10. Azimuthal stress on mid plane • For small apertures, larger w and larger Gc correspond to a saturation of the stress values • For verylarge apertures, the stress decrease is due to a non effective cable add-on

11. Estimation of stress on pole • The stress on pole at each step of magnet life cycle has been analitycally estimated • After powering a specific residual stress must be envisaged • We use a safety margin of 25 MPa • The stress after powering has been computed averaging the stress distribution on mid plane 1. Average stress after powering ~ 25 Mpa 2. After Cool Down: 3. After Collaring:

12. stress on pole - powering

13. stress on pole – cool down 1.9K (s.f. 25MPa)

14. stress on pole – collaring 1.9K (s.f. 25MPa)

15. Azimuthal stress - Conclusions Analytical approach based on a pure 30 ⁰ sector coil shows that the increase of aperture between 112 mm and 135 mm increases the average azimuthal stress only of few MPa The required level of pre-stress at warm seems to be near to Apical creep limit (SS current and 25MPa safety margin) Azimuthal forces slightly increases with collar thickness (saturation effect to be checked)

16. Scaling collar thickness on existing magnets (MQXB, MQ) • Azimuthal stress in function of aperture and collar thickness (analytical approach) • Key dimensioning: • 1 key • 2 key • Key angular position optimization (FEM) • FEM computation on 120 and 130 mm aperture quad

17. Some Collar keys layouts MQM • MQM: 4 key layout (1 per quadrant) • MQ-MQXB-MQY: 8 key layout (2 per quadrant) MQ MQXB MQY

18. Horizontal forces

19. Key reaction force – 1 key layout • Rk,coll slightly increases with collar width after collaring • No significant variation between 115 and 135 mm apertures (~0.1%) during collaring • Rk,mag follows Fx trend • Rk,mag / Rk,coll> σyc/σyw • Key dimensioning can be done by assuming the smallest collar after powering (most conservative case)

20. Key dimensioning - compression • The VonMises stress is used to predict yielding of materials under any loading condition from results of simple uniaxial tensile tests. • A material is said to start yielding when its VonMises stress reaches a critical value known as the yield strenght Rp0.2

21. Key layout analysis α

22. 24 degrees 15 degrees Key layout analysis • Forces repartition on keys according to 1key or 2key layout per quadrant structure

23. 2 Keys at 10 degrees 2 Keys at 25 degrees

24. Key layout analysis • Coil radial displacement in function of the angular distance between keys • 130mm aperture and 35mm thick collar

25. Key analysis - Conclusions Horizontal forces decreases with collar thickness (saturation effect to be checked) The key dimension can be defined at the smaller collar thickness The used criteria is compression because pure shear is second order Factor 2 coefficient safety margin has been used to take into account possible tolerance effect and collar indentation Dimensioning done with phosphor bronze. Reduction of plasticization zone achievable only with different material 2 keys at 15 degrees provide a stiffer structure and lower force on each key. With key at 15 ⁰ we get a structure 15% more rigid then with keys at 5 ⁰

26. Scaling collar thickness on existing magnets (MQXB, MQ) • Azimuthal stress in function of aperture and collar thickness (analytical approach) • Key dimensioning: • 1 key • 2 key • Key angular position optimization (FEM) • FEM computation on 120 and 130 mm aperture quads

27. FE analysis – radial displacement • Dδr = δrmag - δrCD • The thicker the collar the lower is the bending effect on coil • 120 mm shows lower displacement due to a more rigid structure and lower e.m. forces

28. FE analysis – bending effect • The bending effect on coil can be looked as the difference in stress on upper coil edge =130mm I.L.

29. FE analysis – bending effect • The bending effect on coil can be looked as the difference in stress on upper coil edge =120mm I.L.

30. FE analysis – bending effect • The bending effect on coil can be looked as the difference in stress on upper coil edge =130mm O.L.

31. FE analysis – bending effect • The bending effect on coil can be looked as the difference in stress on upper coil edge =120mm O.L.

32. FE analysis – collar thickness

33. FE analysis – stress on collar 130mm 120mm • The VonMises stress has been verified at each step of magnet cycle. • σmax has been compared to Rp0.2/s.f., where safety factor is 1.5 • Collars made of YUS130 steel: Rp0.2 (293K)=445MPa, Rp0.2(4.2K)=1360MPa

34. Equivalent stress on collar – 20mm 130mm 120mm

35. Equivalent stress on collar – 35mm 130mm 120mm

36. Equivalent stress on collar – 45mm 130mm 120mm

37. FE analysis - Conclusions Displacements are lower for 120mm, due to a more rigid structure and lower magnetic forces Since a rectangular shim is used, the higher the inclination angle of I.L. pole, the higher the Dσφ. θI.L. is 36º (120mm) vs. 29.3º (130mm). On the O.L. this effect is much lower (same θ=21.5º) A first estimation of the collar thickness is proposed, based on MQXB scaling For 120mm, a collar thickness of 35mm can be proposed For 130mm, a collar thickness of 38mm can be proposed No relevant differences in stress distribution on collar