1. Assessing the mechanical resistance of PS bellows to a horizontal stroke D. Allard (AT/VAC), R. Brown, B. Salvant (AB/ABP), G. Villiger (TS/MME) ABP/LIS meeting - November 26, 2007

2. Agenda Motivations –Context –Orbit correction in the machine –Simulated horizontal displacement Experiments Simulations Conclusions and Perspectives Acknowledgements

3. Motivations : context  Need for horizontal translation of PS dipoles (max 1.7 mm) without disconnecting the bellows but AT/VAC warns that maximum bellow horizontal displacement allowed is 0.5 mm (no trace of justification). Manufacturers don’t mention any horizontal tolerance.  Need for the order of magnitude of possible bellow horizontal displacement Dipole Bellow Straight section SS89 SS93 Need for beam based orbit correction in the PS (AB/ABP)

4. Magnet Motivations : Orbit correction in the machine Straight Section n Magnet z x y Before beam orbit correction Straight Section n+1 Straight Section n+1 Straight Section n After beam orbit correction : rotation of the dipole by angle  < 10 -3 rad In a first approximation, this very small angle is neglected, and the vertical translation of the bellow on each side is studied. 

5. Straight Section Motivations : Simulated horizontal displacement Straight Section Magnet z x y Straight Section Magnet Imposed displacement Need to reproduce this imposed horizontal shear of the bellow : - experiments - simulations Before beam orbit correctionAfter beam orbit correction

6. Agenda Motivations Experiments –LHC Bellow test bench –Homemade test bench Simulations Conclusions and Perspectives Acknowledgements

7. Experiments 2 options: test bench for LHC bellow elongation in fatigue mode  available within AT/MCS Homemade test bench  real magnet and straight section  displacement performed by the geometers  design a setup to put this small assembly under vacuum

8. Experiments : 1st option  LHC bellow test bench Vacuum Bellow

9. Experiments : 1st option  LHC bellow test bench designed for a longitudinal stroke needs welding of the bellow But… easy to put under vacuum lateral stroke can be applied through a table => To be tested if more data is needed

10. Experiments : 2 nd option  Daniel’s bellow testbench Tube fixed to a movable table Clamps Vacuum Chamber PS Bellow Fixed upper part

11. Experiments : 2 nd option  Daniel’s bellow testbench 2 mm lateral stroke  convolution crests touch each other  not mechanically possible to go beyond no vacuum inside, so metal buckling due to vacuum not taken into account bellow not vacuum tested  no assurance that the bellow is still vacuum sound As a conclusion, 1.1 mm lateral stroke  substantial deformation and stress applied. It would be reasonable to stay at the max value of 1.1 mm allowed by AT/VAC

12. Agenda Motivations Experiments Simulations –Technique and general parameters –Main assumptions –Geometry –Mesh –Boundary conditions –Results for horizontal displacements (none, 0.5 mm, 1 mm) Conclusions and Perspectives Acknowledgements

13. Simulations : technique and general parameters Technique –ANSYS Finite Element Code –3D Catia drawing  2D surface mesh (elements with no thickness) System simulated: –« Standard » PS bellow (190mm x 70 mm, 8 spires) Material –Steel 304L (ideal) –Elastic behaviour law (Young’s modulus = 200 GPa) –CODAP fixes norms for safe operation of generic piece of equipment  maximum tolerated stress = 117 MPa

14. Simulations : main assumptions Ideal material properties –Different manufacturers, different grades (304L, 316L) –Real properties may differ from specs –Spatial Heterogeneity (properties and geometry) due to cold hydroforming process –Wear and sometimes damage due to installation and operation. –Welded interface with the vacuum chamber is a weak point and is not simulated. Behaviour law –Elastic behaviour law  no plastic « softening »  very conservative assumption –No idea of load history (process, operation)  no idea of state of yielding  no idea of available plastic deformation left * N. Haddar, FATIGUE THERMIQUE D’UN ACIER INOXYDABLE AUSTÉNITIQUE 304L […] PhD Thesis ENSMP, Paris, 2003 Deformation  Stress  Elastic plastic Yield Point Offset Yield Point 0.2 %Offset strain

15. Simulations : Geometry

16. Simulations : Mesh

17. Simulations : boundary conditions Vacuum inside –Load difference between outer and inner of the bellow = 0.1 Mpa Longitudinal elongation of the bellow –nominal elongation for stress analysis = 6 mm Horizontal imposed translation of one connecting surface of the bellow (the other one being fixed by one or two points) –Horizontal translations simulated : 0 mm, 0.5 mm, 1 mm P = 10 5 Pa  y = 6 mm  x = ? mm y z x

18. Simulations : boundary conditions no lateral stroke

19. Simulations : horizontal shear = 0 mm

21. Simulations : boundary conditions 0.5 mm lateral stroke

22. Simulations : horizontal shear = 0.5 mm

24. Simulations : boundary conditions 1 mm lateral stroke

25. Simulations : horizontal shear = 1 mm

26. PS: symmetry with respect to y can be broken, as only one fixed point in the translated surface was used, instead of 2 points for 0.5 mm  one additional degree of freedom  stress can be slightly released  Classical method in material simulation to prevent artificial rigidity at the boundaries

27. Simulations : conclusions From the simulations, 0.5 mm lateral stroke is already unacceptable if we apply the CODAP rules However the simulations are pessimistic: - stresses are overestimated due to the purely elastic law - bellows are supposed to operate in the plastic regime It is clear that small lateral strokes create large localized stresses within the bellows, especially in the roots

28. Agenda Motivations Experiments Simulations Conclusions and Perspectives Acknowledgements

29. Conclusions Even small lateral strokes (mm) create large deformations and localized stress within bellows A bellow failing under vacuum will lead to a long shutdown of the machine (example in the ISR). These strokes are necessary to orbit correction, but should be applied with care, and minimized where possible.

30. Perspectives More accurate simulations and experiments can be performed, but they would require a significant amount of work and personnel. TS/MME suggested some modifications of the vacuum chamber, to include double bellows system that could be designed to accept these lateral strokes It was also mentioned, if this has no other implications, that the whole straight section could be moved with the magnet to minimize the lateral stroke applied to the bellow.

31. Merci beaucoup pour leur aide à: Gianluigi Arduini (AB/ABP) Alessandro Bertarelli (TS/MME) Pierre Bourquin (TS/MME) Philippe Erieau (Centre de Technologie MICHELIN) Cédric Garion (AT/MCS) Simone Gilardoni (AB/ABP) Jan Hansen (AT/VAC) Edgar Mahner (AT/VAC) Thomas Sahner (TS/MME) Stefano Sgobba (TS/MME)