1. Engineering Design of Raon SC Cavities Myung Ook Hyun SCL Team Myung Ook Hyun SCL Team

2. Contents Mechanical Analysis of Cavities Quarter Wave Resonator (QWR) Single Spoke Resonator #2 (SSR2) Appendices QWR LHe Jacket Tuner Design Tuner Arm Design

3. Mechanical Analysis of Cavities

4. Quarter Wave Resonator – Basic Model Beam tunnel length : 340mm (bellows flange included) Add 4 tunnels @ top/bottom : coupler/pickup and HPR rod Change bottom shape : 30 pi fillet  500 pi + 15 pi fillet

5. QWR Cavity – Pressure Analysis Vacuum Pressure Analysis –Fixed support : flange area of every ports (6 areas) –Vacuum pressure : 10^5 Pa @ outer area except for port tubes –Mesh : free, quad, no refinement –Analysis type : structural –Material : copper alloy (OFHC) / for initial prototype

6. QWR Cavity – Pressure Analysis Vacuum Pressure Analysis –Left figure : deformation  58.38um (largest at bottom side) –Right figure : stress  21.94MPa (largest at bottom & around DD) –Deformation at bottom side is quite large, therefore we should change the shape of bottom side so that deformation can be decreased!

7. QWR Cavity – Pressure Analysis Vacuum Pressure Analysis –Changed bottom side : R500  R200 –Fixed support : flange area of every ports (6 areas) –Vacuum pressure : 10^5 Pa @ outer area except for port tubes –Mesh : free, quad, no refinement –Analysis type : Structural

8. QWR Cavity – Pressure Analysis Vacuum Pressure Analysis –Left figure : deformation  35.7um (before :58.38um) –Right figure : stress  19.67MPa (before : 21.94MPa) –Conclusion Stress due to vacuum is decreased properly. R200 shape change is acceptable for QWR cavity.

9. QWR Cavity – Niobium’s Properties Applying 4.2K niobium properties (attached file) Young’s Modulus : 111GPa Poisson’s ratio : 0.393 Tensile Yield Strength : 317.2MPa Tensile Ultimate Strength : 599.87MPa

10. QWR Cavity – Deformation Analysis Boundary conditions –Fixed support : every port flanges (red circles) –Pressure : 0.5MPa @ outer surface (port pipes are excluded.) Mesh size : 5mm (minimum edge length : 3mm) / default (quad)

11. QWR Cavity – Deformation Analysis Deformation –Maximum : 173.06um @ vertical side of beam tunnel Safety Factor : 2.995 –Weak points 1 st priority : topside of center core (red circle) 2 nd priority : around beam tunnel (yellow circle)

12. QWR Cavity – Deformation Analysis Equivalent stress –Weak points 1 st priority : topside of center core (right figure)  105.92MPa 2 nd priority : around beam tunnel (left figure)  94.15MPa Both weak points should be reinforced, even if values of two points have lower than tensile yield strength.

13. QWR Cavity – Deformation Analysis Modification #1 : add ring @ topside (right figure) Boundary conditions : same as initial analysis Mesh size : 5mm (minimum edge length : 3mm) / default (quad)

14. QWR Cavity – Deformation Analysis Deformation –Maximum : 186.05um @ vertical side of beam tunnel Safety Factor : increased to 3.871 (from 2.995) –Weak points 1 st priority : topside of center core (red circle)  reinforced! 2 nd priority : around beam tunnel (yellow circle)

15. QWR Cavity – Deformation Analysis Equivalent stress –Weak points 1 st priority : topside of center core (right figure)  decreased from 105.92 to 49.618MPa (53.2% ↓) 2 nd priority : around beam tunnel (left figure)  increased from 94.15 to 111.64MPa (18.6% ↑) Area around beam tunnel should be reinforced!

16. QWR Cavity – Stiffening Beam Tunnels Modification #2/#3 : add flange @ beam tunnel (left/right figures) Boundary conditions : same as initial analysis Mesh size : 5mm (minimum edge length : 3mm) / default (quad)

17. QWR Cavity – Stiffening Beam Tunnels Deformation –#2 Maximum : 188.25um @ vertical side of beam tunnel (increased) –#3 Maximum : 189.45um @ vertical side of beam tunnel (increased) –Both are not effective for decreasing deformation!

18. QWR Cavity – Stiffening Beam Tunnels Safety Factors –#2 : 2.9747 @ vertical side of beam tunnel (slightly decreased) –#3 : 2.8586 @ vertical side of beam tunnel (slightly decreased) –Both are ineffective for increasing safety factor!

19. QWR Cavity – Stiffening Beam Tunnels Equivalent stress –#2 (left) : increased from 94.15 to 106.63MPa (13.3% ↑) –#3 (right) : increased from 94.15 to 110.96MPa (17.9% ↑) –Both are ineffective for decreasing stress!

20. QWR Cavity – Deformation Analysis Modification #4 : add middle ring & #3-type flanges (right/left figures) Boundary conditions : same as initial analysis Mesh size : 5mm (minimum edge length : 3mm) / default (quad)

21. QWR Cavity – Deformation Analysis Deformation –Maximum : 181.27um @ vertical side of beam tunnel Safety Factor : increased to 3.871 (from 2.995) –Weak points 1 st priority : topside of center core (red circle)  reinforced! 2 nd priority : around beam tunnel (yellow circle)  reinforced!

22. QWR Cavity – Deformation Analysis Equivalent stress –Weak points 1 st priority : topside of center core (right figure)  decreased from 105.92 to 81.95MPa (22.6% ↓) 2 nd priority : around beam tunnel (left figure)  decreased from 94.15 to 81.95MPa (13% ↓) Area around beam tunnel should be reinforced!

23. QWR Cavity – Deformation Analysis Conclusions –Upper ring is effective to decrease topside stress and safety factor.  apply! –4&6-stiffner is ineffective to decrease stress.  design change! –Middle ring is effective to decrease stress and safety factor.  apply! –Also should find alternative design for decreasing max. deform.. TypeMax. deformation Equiv. stress (topside) Equiv. stress (beam tunnel) Safety factor Initial173.06um105.92MPa94.15MPa2.995 Upper ring186.05um49.61MPa111.64MPa3.871 4-stiffner188.25umTo Be Updated106.63MPa2.975 6-stiffner189.45umTo Be Updated110.96MPa2.859 6-stiffner & middle ring 181.27um81.95MPa 3.871

24. Modal Analysis – QWR Basic mode Bode plot of QWR cavity looks normal. (mode scattering at every range  structural complexity) Target analysis frequency range : >2kHz (which can make acoustic noise during operation) Main peak : 70Hz(1 st bending), 300Hz(2 nd bending), 710Hz(complex mode), 1200Hz(torsion & sway), 1890Hz(squeezing mode)

25. SSR2 - Pressure Analysis using ANSYS Modeling : borrowed from Dr. Jung Meshing : default (quad, free, auto mesh refinement) Fixed condition : beam tunnel (8 areas) Boundary condition : 0.5MPa Pressure @ outer areas except vacuum & coupler channel

26. SSR2 - Pressure Analysis using ANSYS Max. Deformation : 5.262mm around beam tunnel Max. Stress : 1.873GPa @ beam tunnel neck Should be reinforced around beam tunnel!

27. SSR2 - Pressure Analysis using ANSYS Modeling : borrowed from Dr. Jung –Modified : add flanges around beam tunnel Meshing : default (quad, free, auto mesh refinement) Fixed condition : beam tunnel (8 areas) Boundary condition : 0.5MPa Pressure @ outer areas except vacuum & coupler channel

28. SSR2 - Pressure Analysis using ANSYS Max. Deformation : 1.312mm between vacuum inlets and spokes Max. Stress : 292.92MPa @ spoke outlets Deformation & stress are distributed as intended.

29. SSR2 - Pressure Analysis using ANSYS Modeling : borrowed from Dr. Jung –Modified : changes donut shape to flat(red circle) for convenience of making press jig Meshing : default (quad, free, auto mesh refinement) Fixed condition : beam tunnel (8 areas) Boundary condition : 0.5MPa Pressure @ outer areas except vacuum & coupler channel

30. SSR2 - Pressure Analysis using ANSYS Max. Deformation : 8.498mm around beam tunnel Max. Stress : 2.951GPa @ beam tunnel neck Conclusion #1 : Flat shape can endure smaller pressure comparing with donut shape. Conclusion #2 : We still do not have exact condition about pressure endurance. Therefore, we cannot decide which design is proper or not.

31. SSR2 - Pressure Analysis using ANSYS Modeling : borrowed from Dr. Jung –Modified : add flanges around beam tunnel Meshing : default (quad, free, auto mesh refinement) Fixed condition : beam tunnel (8 areas) Boundary condition : 0.5MPa Pressure @ outer areas except vacuum & coupler channel

32. SSR2 - Pressure Analysis using ANSYS Max. Deformation : 2.064mm @ flat shape Max. Stress : 635.09MPa around flange welding area Conclusion #1 : donut shape comes from the reinforcement of two points, flange welding and side-wall deformation.

33. Appendices

34. Liquid Helium Jacket of QWR Cavity

35. QWR LHe Jacket – Deformation Analysis Multi-body Analysis –Cavity : copper alloy  will be update to niobium! –Liquid He jacket : stainless steel  pending! Contact condition : frictionless

36. QWR LHe Jacket – Deformation Analysis Mesh : default (quad-/10mm) Thermal condition –Cavity : -271 deg. (2K) at outer surface & inner core surface –Liquid He jacket : -271 deg. (2K) at inner surface

37. QWR LHe Jacket – Deformation Analysis Boundary conditions –Fixed : beam tunnel flange @ cavity –Frictionless : brazing btw beam tunnel & LHe jacket –Pressure : 100kPa @ cavity outer surface & jacket outer surface

38. QWR LHe Jacket – Deformation Analysis Deformation : 4.02mm @ QWR upper end –Apply deformation data for designing proper SUS jacket Stress : 1.42GPa @ beam tunnel flange edge –Weak at the beam tunnel flange, should be reinforced!

39. QWR LHe Jacket – Deformation Analysis Safety factor : lowest around beam tunnel (0.5~1) Contact occurs at beam tunnel & upper/lower ports Conclusions –Should define more precise boundary conditions!! –Should apply modified material properties (yield strength, strain, thermal expansion…)

40. Tuner Design

41. Tuner Arm – QWR (Initial Design) Circular-shape levers / pusher blocks Squeezed by levers (hinge, lever moving, effective force)

42. Tuner Arm - QWR Circular-shape levers / pusher blocks Squeezed by levers (hinge, lever moving, effective force)

43. Tuner Arm – QWR with LHe Jacket Pushing points Attachment btw cavity beam port & LHe jacket : blue circles Forces : tuner  jacket  beam port / frequency tuning is occurred!