1. Cable inventory, relative measurements and 1 st 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. 1386N/mm Horizontal forces per octant Forces [N/mm]

5. COLLAR Scaling based on MQXB Aperture radius [mm]Collar thickness [mm] 5535 6039 6542 Scaling based on radial collar displacement The collar width is obtained by solving:

6. Aperture radius [mm]Collar thickness [m] 5545 6049 65 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 very large apertures, the stress decrease is due to a non effective cable add-on

11. 1. Average stress after powering ~ 25 Mpa 2. After Cool Down: 3. After Collaring: 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

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

18. Horizontal forces

19. Key reaction force – 1 key layout R k,coll slightly increases with collar width after collaring No significant variation between 115 and 135 mm apertures (~0.1%) during collaring R k,mag follows F x trend R k,mag / R k,coll > σ yc /σ yw 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 R p0.2

21. α Key layout analysis

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

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

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

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.  δr = δr mag - δr CD 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 FE analysis – radial displacement

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

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

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

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

32. FE analysis – collar thickness Aperture Collar thickness, δr = 60  m Collar thickness δr=60  m, key MQXB Estimated collar thickness MQXB scaling Proposed collar thickness (key15º) 120mm 33mm 35-37mm39mm 35mm 130mm 36mm 38-40mm42mm 38mm

33. FE analysis – stress on collar The VonMises stress has been verified at each step of magnet cycle. σ max has been compared to R p0.2 /s.f., where safety factor is 1.5 Collars made of YUS130 steel: R p0.2 (293K)=445MPa, R p0.2 (4.2K)=1360MPa 120mm 130mm

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

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

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

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  σ φ. 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