1. Cavity support scheme options Thomas Jones 25/06/15 to 06/07/15 1

2. Cavity support The cavities will be rigidly supported by the input coupler. Additional supports are required that will be attached to a common adjustable alignment plate. The current design utilises rods, however, the following analysis proposes the use of ‘blade’ type flexures to increase stiffness in the required directions and therefore reduce low order vibrations. 2

3. Analysis models 1. Only coupler2. Ø4mm Ti Rods 3. Stainless Steel flexures (2mm thick)4. Additional flexure Thickness to give similar thermal conduction and therefore similar temperature profile and contraction as the input coupler 3

4. Analysis setup RFD cavity represents the ‘worst case’ as it is the most cantilevered support. The mass is approximate, but is valid for these comparative purposes. Standard earth gravity applied. Coupler, rods and flexures fixed at common support plate. Static total deformation, Max von-Mises Stress and first 4 modes were found. No mesh convergence check performed, but same meshing used for each analysis (see next). Material properties measured by FermiLab from 300K to 2K used. 4

5. Meshing 3mm 10mm 5

6. Analysis Result Analysis Max Deformation (mm) Max von- Mises stress (MPa) Mode 1 Frequency (Hz) Mode 2 Frequency (Hz) Mode 3 Frequency (Hz) Mode 4 Frequency (Hz) 13.91837.78.316.161.1 20.2465.28.525.338.370.9 30.02515.325.148.356.5122 40.01010.527.250.1566.9174 Performance is significantly improved using blade type flexures. The 3 flexure design is best, however, need to consider increased heat load. Analysis 3, i.e. with only 2 blades was then analysed for thermal deformation/stress. 6

7. Thermal analysis 295.15K 80K 2K 295.15K 80K 2K Flexures will ideally be thermalised the same as the coupler to minimise heat leak, however, optimisation to be completed. 7

8. Thermal results 8

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11. Thermal results 11

12. Result comment Stresses are well within acceptable limits. There are no detrimental stresses in the helium vessel and therefore there will be no additional deformation of the cavity due to the flexures. The elevated stressed are found in the interface between materials and are highly localised (see previous). The method of mounting can be optimised to reduce stress even further if required. This could be for example a Grade 2 Ti block, which the Stainless blade is then clamped into. The high stresses will be ofound anyway in the coupler were we have 316LN to Grade 2 Ti connections. It has been observed through experience with these joints that the stresses are below allowable for the material properties at 2K. i.e. CERN have brazed 316LN flanges to Nb and they do not fail. 12

13. Recommendations STFC recommend that first order frequencies in the system be above 25Hz to avoid unwanted high amplitude vibration. Blade flexures have been shown to increase stiffness, reduce deformation, reduce stress and raise the first order vibration mode above 25Hz. The current flexure geometry can be optimised to give minimised heat leak and/or increased stiffness. Flexure design currently used is a first order approximation. The use of the common adjustable support flange is compatible with the flexure system. The flexures require no penetration through the Outer Vacuum Chamber, simplifying the design and reducing the risk of leaks. They also take up no space externally on the module where space is at a premium. Flexures will require no adjustment after cooldown and can be thermalised using copper shunts to ensure the heat leak is minimal. 13

14. Inter-cavity supports A thermally neutral support system was developed for the UK4ROD. This relied on differences in thermal contraction of materials to maintain the same length after cooled down to 2K. It was shown to increase the stiffness and low frequency modes of the system. However, this was compared to a ‘coupler only’ type support. Also the UK4ROD had much more balanced forces, i.e. the coupler was in the centre of the cavity. This was by design, to improve the support system of the cavity. l @293K 14

15. Inter-cavity supports Invar integrated contraction from room temperature to 2K is L i x (0.037/100) 304 Stainless steel contraction from room temperature to 2K is L ss x (0.306/100) Therefore; 2L i x (0.037/100) = L ss x (0.306/100) AND 2L i – L ss = 1032mm (distance between fixed points) So, 2Li x (0.037/100) = (2Li – 1032) x (0.306/100) Solving the simultaneous equation gives L i = 587mm and Lss = 142mm l @293K 15

16. Analysis Models 1. 2 independent cavities on rods 2. Rods with inter-cavity in vertical 3. Blades with inter-cavity in vertical 4. Blades with inter-cavity in horizontal 16

17. Result summary Analysis Max Deformation (mm) Max von- Mises stress (MPa) Mode 1 Frequency (Hz) Mode 2 Frequency (Hz) Mode 3 Frequency (Hz) Mode 4 Frequency (Hz) 10.2465.28.525.338.370.9 20.4361.812.620.027.534.3 30.063*18.226.440.544.755.0 40.068*24.026.140.944.955.1 *deformation of the inter-cavity supports. 0.026mm Cavity deflection 17

18. Recommendations The use of the inter-cavity support in conjunction with the blade flexure supports offers no significant improvement. Some modes are actually lowered, due to the increased mass. Despite the inter-cavity supports adding rigidity the cold mass still ‘sways’ as one unit. The inter-cavity supports use invar which is a strongly magnetic material. Simulations have shown this not to be an issue, however, it seems in this instance that it is not worth the increased risk in using them for little to no gain. Using blades only also gives the ability to move the cavities freely independent of each other. If a ‘Plan B’ is required I suggest we investigate other options. 18

19. Support distance sweep Supports moved closer to input coupler in steps of 50mm from 700mm to 400mm. Note this is different to previous analysis as both flexures set at 700mm from coupler to begin with. They were previously slightly different distances. 19

20. Results Distance from coupler (mm) Max Deformation (mm) Max von- Mises stress (MPa) Mode 1 Frequency (Hz) Mode 2 Frequency (Hz) Mode 3 Frequency (Hz) Mode 4 Frequency (Hz) 7000.02514.525.848.457.7123.7 6500.02915.824.247.555.6120.2 6000.03417.222.546.253.5116.9 5500.04118.920.944.251.8113.9 5000.05020.719.341.950.4111.0 4500.06322.917.839.149.0107.0 4000.08125.416.336.147.699.3 20

21. Result comment Deformation and stress reduce the further the blades are from the coupler. Due to the increased stiffness of the system, the modes of vibration increase the further the blades are positioned from the coupler. It is recommended that the blades be as far into the corners of the vessel as practicable. 21

22. Blade width sweep Width ‘w’ varied from 20mm to 60mm. There is a limit of 0.2W per flexure heat load at 2 Kelvin. Width of thicker part was kept 5mm wider. Thickness remained constant at 2mm. 650mm ‘w’ ‘w’+5mm 22

23. Results Blade width (mm) Max Deformation (mm) Max von- Mises stress (MPa) Heat load to 80K (W) Heat Load to 2K (W) Mode 1 Frequency (Hz) Mode 2 Frequency (Hz) 200.04022.26.90.0715.844.3 300.02915.89.60.1124.247.5 400.02312.612.30.1433.248.7 500.01910.615.10.1841.149.3 600.0179.117.80.2148.250.0 Note that in the SPS area, and in fact most facilities around the world, there is a large amplitude of vibration around 50Hz, this is due to reciprocating pumps etc. Care should be taken in the design to avoid having a mode exactly on 50Hz. 23

24. Result comment As expected maximum deformation and stress is reduced by increasing blade width. The frequency of vibration modes increases with increasing blade width. However, increasing the blades does bring an increased risk of coupling to 50Hz vibration. A more detailed model should be analysed including HOM absorber geometry and masses to accurately predict the vibration frequencies. This should take place after integration of the blades as the exact space available is unknown. 24

25. Conclusion The RFD cavity has been used as this is the most cantilevered and therefore represents the worst case. Blade type flexures will perform significantly better than supporting rods. Maximum deformation is reduced by 10x. Stress reduced by 4x. The fundamental vibration mode with thin rods and coupler for this cavity may be as low as 8.5Hz, this would certainly be a risk. The blades increase the fundamental mode above 25Hz. With the blades there would be no need for any inter-cavity support therefore allowing independent movement of the cavities. Ways to optimise the blade structure have been analysed and can be used as tools in the integration of the structures into the overall cryomodule. In general the blades should be spaced as far as possible from the coupler. A more detailed analysis of the overall dress cavity, including HOM absorbers and tuner will be required to assess the final modes and to tune the blade width to avoid 50Hz coupling whilst optimising stiffness. 25