1. Cylinder FEA Status Report University of Oxford 11 Jan 2011 SLHC meeting in Edinburgh

2. Outline FEA work –Aim of the study –Understanding of the interaction between the stave and the cylinder via FEA using simplified plate Understand its static behaviour Understand its modal behaviour –Future work Re-visit current FE model using composite material properties for Cylinder and Stave Pull test of edge mounting mechanism –Jig set-up –Preliminary results

3. 3 Aim of this study We want to understand the performance of cylinder, the behaviour of Stave and locking mechanism, and the interaction between stave of cylinder. –To see if stave contributes to the stiffness of the support cylinder –To see how much does the stave deformation depend on the cylinder stiffness –Optimize stave mounting mechanics. –Optimize cylinder design.

4. 4 FEA model geometry Single cylinder FEA model was built (based on the strawman layout 07 v14 drawing). The cylinder model of OD 708 mm and 2.5m long is used throughout the study. There are 56 staves on the cylinder.

5. 5 FEA model input MaterialDensity (kg/m 3 ) E (MPa)Poisson's ratio Cylinder (OD708mm,1mm thick wall, 2.5m long)1300600000.3 Cylinder flange (W30mm, 2mm thick)1300600000.3 Stave (W120mm, L1.2m, 5mm thick)1389600000.3 Mounting brackets13003000000.3 Locking part1300600000.3 We have assumed a value of 60 GPa for the Stave - this was worked out by using the Core stiffness, the skin modulus established from the 3-point bend test of plank#1 and by assuming that the stave thickness remains at 5.5mm (including kapton tape). The same value used for cylinder More studies needed if this is justifiable. However by using a lower E value, we know our results are conservative. An artificially high E value was used for the mounting brackets. As this exercise concentrates only on the understanding of the behaviour of the stave and the cylinder, a very high value for the brackets eliminates any effect the brackets may have on their structural behaviour. However, future studies will include a more realistic E value for the brackets.

6. Case No. Stave Material E MPa Cylinder Out of plane max. deflection mm Max Cylinder. deflection mm without dimple effect 1 - a 60000 0.0147* 0.011 1 - b 30000 0.0167* 0.013 1 - c 10000 0.02* 0.0163 1 - d 5000 0.022* 0.0185 1 - e 1000 0.025* 0.0213 1 - f 100 0.027* 0.0233 Initial study on the contribution of stave stiffness to cylinder rigidity result summary: Results show that if the staves are “loosely” mounted on the cylinder, the cylinder could sag as much as 24 microns at mid-span Results also show a noticeable dependency of the cylinder rigidity on the stave rigidity! Its deflection increases nearly twice without the “contribution” from the staves Cylinder is modelled with solid carbon fibre plate of 1mm thick with effective E value of 60 GPa * Actual out-of-plane deflection on cylinder slightly spurious because of the local dimple effect on the cylinder surface. Actual results could vary by as much as 3 microns. Cylinder likely to deflect only 11 microns when dimple effect is removed Dimples on cylinder surface caused by rigid stave support (stave bends along supports)

7. Initial studies on the cylinder support conditions: Results indicate that as the interlinks becomes more rigid, the cylinder behaves more towards that of fully fixed boundary. Interlinks, however rigid, will not improve the cylinder deformation beyond that of a fully fixed boundary condition.

8. 8 no sliding of stave staves are allowed to slide No sliding of stave (stave bonded to locking points) Stave allowed to slide axially at locking points No staves, only stave weights added FE results: Deflection of the cylinder under various interface conditions Cylinder deflection more than halved when stave is bonded to the locks (no thermal movement); However, if stave is allowed to slide at locking points, change in cylinder deflection is insignificant compared with one that has no stave attached. δ max = 11μm δ max = 29μm

9. 9 FE results: Deflection of the stave under various interface conditions Deflection profile of the stave at the 12 o’clock position along its free edge. The sliding arrangement causes the Stave to deflect 3 times more than when it is ‘bonded’ to the locking points;

10. 10 FE results: Deformation vs cylinder thickness Cylinder deflection Stave free edge deflection

11. Comments received from the CERN meeting......... my understanding was you chose an equivalent thickness/modulus solid (shell?) that only matched the bending stiffness of your stave. If memory serves, what was presented was a study on coupling of the staves (or not) longitudinally to the shell. Your stave model uses some fictional thickness/modulus of stave material required only to meet the bending properties, but not necessarily the longitudinal stiffness. Effectively, by rigidly coupling the stave, you significantly increase the sectional inertia of the shell. The longitudinal stiffness of a stave is important here, but as your model was aimed at only matching bending, but not necessarily either cross-sectional area or longitudinal stiffness, the results presented were rather questionable...

12. Comments received from the CERN meeting What this means is that by choosing a stave thickness of 5mm (close to the actual stave thickness) we have to “fudge” the E value to ensure that it retains its bending properties (hence the E value of 60GPa). This might have over-estimated its longitudinal E value. Our view is that a stave with half (or twice) its longitudinal stiffness may have an effect on cylinder deflection if the stave is assumed to be fully bonded to the cylinder. However, we have largely ignored the fully bonded assumption as this gives us the least deflection for the cylinder and in any case is not real because the UK locking mechanism is designed to allow sliding of the staves to accommodate thermal movements. Under this condition, the longitudinal stiffness of the stave would have little on the bending behaviour of the cylinder. If we really must have a perfect match on both the longitudinal and bending properties we need to use a different stave thickness and E value. The following slide shows how the new values came out to be:

13. Stave equivalent E and t This shows that if we were to match both the bending and longitudinal stiffness of the stave, its thickness has to be increased to 8.75mm and an E value of 15.4 GPa.

14. 14 All staves are fixed at Z=0 position, but allowed to slide in Z direction at various frictional coefficient. Fictional coefficient μ max cylinder deflection mm 0 (frictionless)0.0255 0.20.0211 0.40.0179 0.60.0168 0.80.0166 10.0165 When stave locking parts are fully bonded to the mounting brackets, the max cylinder deflection is 0.0117mm. The results suggest that longitudinal reactive (frictional) force at the joints ceases to be effective when μ >0.5. The reason for this is explained in the next page. Based on the 1mm thick cylinder model: Frictional case study

15. 15 When μ = 0, the stave can slide freely along the joints, offering no resistance to the deflection of the cylinder; When μ increases above 0, there develops a frictional force acting along the longitudinal direction of the stave, resisting sliding at the joint. As long as the ratio of δx / δy remains small, sliding will continue to function, albeit reduces with increase in the δx / δy ratio. When the ratio of δx / δy becomes significant, the sliding joint becomes locked together and no further sliding is possible. We see this takes place when μ = 0.5. δx remains the same on further increase of μ. Deflection of the cylinder remains almost constant at 0.0165 mm when μ > 0.5; If however the joints are assumed bonded in the first place, δx would be kept at zero throughout. This reduce the cylinder deflection to a value of 0.0117mm, quite a bit lower than even when μ = 1. δxδx δyδy Initial dot position in un- deformed cylinder dot position in a deformed cylinder stave Deformed cylinder shape Cylinder slide along stave Asymptotic behaviour of the μ vs deflection:

16. 16 Remarks on the static load results When staves are bonded to the cylinder, the stiffness contribution to the cylinder is noticeable; When Stave is allowed to slide freely along the cylinder length (z=0 is fixed), the stiffness contribution to the cylinder is negligible. Deflection is comparable to the deflection of a cylinder with no stave attached to it; The asymptotic behaviour when the stave and cylinder joint at the frictional coefficient about 0.5. This implies that when deflection of the cylinder reaches a certain magnitude, the joints become locked.

17. 17 A frequency analysis was carried out on the full model (full length cylinder with 56 staves mounted). The aim is to understand: How the natural frequencies of the cylinder change with the changing thickness; How the mode shapes develop with the changing frequencies; The study will give us a better understanding of how to reinforce the cylinder, or how to pattern cut-outs in the cylinder if we were to reduce materials in the cylinder. Modal Analysis

18. 18 Sensitivity study: Modal Analysis at various interface conditions between stave and cylinder F=103.4 Hz when model is fully bonded, the first breathing mode frequency is 103 Hz F = 46.5 Hz when stave is allowed to frictionless slide in Z direction, the first breathing mode frequency is 46.5Hz Based on 1mm thick cylinder model:

19. 19 The first 5 modes for the 1mm thick full cylinder model (when stave is allowed to free sliding). F1 = 11.8 Hz F2 = 46.5 Hz F3 = 48.1 Hz F4 = 49.6 Hz F5 = 51.6 Hz

20. 20 Observations: 1.The 1 st frequency changes from 39 Hz with a 0.5 mm thick cylinder to 53 Hz with a 2mm thick cylinder. 2.When cylinder thickness increases by 4 fold, the frequency increases by less than ¼. 3.However, in the static analysis, an increase in cylinder thickness by 2 would reduce the deflection by nearly ½. 4.Does this mean that increase in cylinder thickness has less effect on its natural frequencies? Modal Analysis results:

21. Cylinder with stiffener rings Cylinder with no stiffener ringCylinder with 1 stiffener ringCylinder with 3 stiffener rings Frequency Hz182835 Deflection mm0.0247520.0247680.024808 Based on the 1mm thick cylinder model w/o staves but with the weight of staves included The stiffener rings added to the cylinder did not show the improvement on the deflection but it shows obvious improvement on its natural frequency F=18Hz (no stiffener ring)F=28Hz (1 stiffener ring) F= 35Hz (3 stiffener rings) * Stiffener ring: 1mm thick by 10mm wide

22. 22 Cylinder with cut-outs Started looking at the cylinder with cut-outs briefly, quite a few cut-outs configuration were looked at such as… Cylinder deflections on all these cut-out models are in no way as good as a solid cylinder model. However, the nature frequencies are somewhat different…. more to report later F=21Hz F= 12.7hz 43% material reduction 33% material reduction * Stave weight of 56kg is included in the analysis

23. 23 Thin Cylinder with “A-frame” ribs 42% of 1mm thick solid cylinder model material (i.e. a saving of ~ 60% material) 0.25mm thick cylinder with “A frame” ribs Ribs at 10mm wide and 1mm thick Max deflection: 0.085mm F = 28Hz Development potential !!!

24. 24 There is strong evidence that the stave contributes to the stiffness of the cylinder. The level of contribution depends on whether the stave is allowed to slide freely along its longitudinal direction or not; A test program is on going to establish the coefficient of friction at the locking parts. The test also examine if there exists any “free play” at the locking parts when it is in fully lock position The frequency analysis shows that the frequency increase is not proportional to the cylinder thickness increase. Again this indicates the effect of the stave contributing to the cylinder stiffness. Studies on different configurations of the cylinder, such as adding a stiffening rings to the cylinder, or making cut-outs etc. have been started. Some final comments…

25. 25 For simplicity reason, all our current FE models use an equivalent solid plate with a modified E value to simulate the effect of a composite sandwich plate. This provides a quick access to the understanding of the complex interface between the stave and the cylinder. We believe this is adequate but would prefer to re-run a few models using a more exact material properties on the sandwich panels to see if this makes any difference to our results. Future work will use composite material properties for both cylinder and stave. This is in hand as we have recently purchased the module that does this. Plan for Future work

26. Pull test set up The initial test was done when Locking mechanism was unlocked. The first test result is, about 10N to pull it out. More test will be carried out later….. To understand the realistic frictional coefficient of Locking Mechanism.

27. Back up slides

28. 28 Boundary conditions All the mounting brackets are bonded to the cylinder. All staves are fixed in the Z=0 position, but allowed to slide with and without friction in Z direction on other mount points along the length. Z=1.2m stave end is simply supported (sliding) on pins. Stave weight of 1kg is assumed. Cylinder is initially modelled with solid carbon fibre plate with an effective E value of 60 GPa (future study will consider sandwich plate properties).