1. Preliminary Calculation of the Tracking Detector Barrels and the Support Tube Szymon Sroka CLICdp Tracker Technology Meeting Szymon Krzysztof Sroka 30/07/2015

2. Szymon Krzysztof Sroka30/07/2015 Presentation Layout I.Tracking Detector Barrels  General Description  Analytical Solution  Comparison to FEA solution  Different Lay-ups 2 III.Beam Pipe & Support Tube  Beam pipe - Dimensions - Support - FEA Calculations  Support Tube - FEA Calculations IV.Conclusions & Outlook II.Conclusions

3. Szymon Krzysztof Sroka30/07/2015 Tracking Detector Barrels 3

4. Szymon Krzysztof Sroka30/07/2015 General Description Current tracker dimensions Gap for services of inner region (cables + air cooling ducts) and connection of support tube to the ECAL barrel Tracking Detector Barrels – Dimensions Number of Barrels Radii of Barrels [mm] Length of Barrels [mm] Thickness of Honeycomb Core [mm] Thickness of CF Skins [mm] Mass of each Barrel [kg] 1 230860100.62.85 3 8402060151.248.1 4 11452660251.290.1 5 14503260251.2140 Basic Requirements: -Lightweight structure -minimizing the radiation length -Maximum deflection in the range of 100 [µm] 4

5. Szymon Krzysztof Sroka30/07/2015 General Description Composite Construction Benefits of HONEYCOMB Sandwich Construction: Benefits of HONEYCOMB Sandwich Construction: Analogy Sandwich Panel to an I-Beam  The facing skins of a sandwich panel can be compared to the flanges of I-beam. They carry the bending stresses to which the beam is subjected. With one facing skin in compression and the other is in tension.  The Honeycomb Core corresponds to the web of I-beam. The core resists the shear loads, increase the stiffness of the structure by holding the facing skins apart 5

6. Szymon Krzysztof Sroka30/07/2015 General Description Cross section of the Barrels T2 T1 Inner Diameter T1 Outer Diameter Honeycomb Layer CFRS Layer 6 Deflection of Barrel Natural 1. vibration mode of Barrel Materials - choices (as an example) CF Skins - Toray M55J + Cycom 950-1 Honeycomb Core - XRH-10/OX-3/16-1.8

7. Szymon Krzysztof Sroka30/07/2015 General Description Different Honeycomb Features MaterialProperty Honeycomb Advantages Foam includes - polyvinyl chloride (PVC) Relatively low crush strength and stiffness Excellent crush strength and stiffness - polymethacrylimide Increasing stress with increasing strain Constant crush strength - polyurethaneFriable Structural integrity - polystyreneLimited strength Exceptionally high strengths available - phenolicFatigue High fatigue resistance - polyethersulfone (PES) Cannot be formed around curvatures OX-Core and Flex-Core cell configurations for curvatures Wood-based includes - plywoodVery heavy density Excellent strength-to-weight ratio - balsa Subject to moisture degradation Excellent moisture resistance - particleboardFlammable Self-extinguishing, low smoke versions available 7

8. Szymon Krzysztof Sroka30/07/2015 General Description Sandwich Structure – Failure Modes 1. Strength - Skin Compression failure 2. Stiffness – Excessive deflection 3. Buckling 4. Shear Crimping 5. Skin wrinkling 6. Intra cell buckling 7. Local compression 8

9. Szymon Krzysztof Sroka30/07/2015 General Description Boundary Conditions BC.s - Considered cases:  Simply Supported  Clamped  Clamped – Simply Supported  Cantilever 9 BC.s - Considered cases:  2-vertices plus Elastic Support  4-vertices Support (the most extreme case in the context of deflection)

10. Szymon Krzysztof Sroka30/07/2015  Two gravitational forces: - Own weight of the Barrels - External load = Mass of Modules + Mass of Cold plates+ Mass of Power Buses (Material budget for the modules, cooling system and cables was extrapolated for CLIC from ALICE’s upgrade project ) 10 External Load ComponentMaterialThickness [µm] Module FPC Metal LayerAluminium 50 FPC Insulating LayersPolyimide 100 Module PlateCarbon Fibre 120 Pixel ChipSilicon 300 GlueEccobond 54 100 Cold Plate Carbon fleece 40 Graphite foil 30 Cooling pipePolyimide 64 Cooling fluidWater - Carbon PlateCarbon Fibre 120 GlueEccobond 54 100 Power Bus Metal LayerAluminium 200 Insulating layersPolyimide 200 GlueEccobond 54 100 General Description Loads from ALICE

11. Szymon Krzysztof Sroka30/07/2015 Analytical Solution First step; easy and simple case Simplifications:  Composite Laminate material (Matrix plus Fibres) and Honeycomb Core are considered as a homogenous, isotropic material for the hand calculations  Carbon Fibre Skins are modelled as transversely Isotropic Material for FEA  Honeycomb Core is modelled as Orthotropic Material for FEA  The comparison between the hand calculations and FEA simulations was done without any Lay-up  BC.s - Simply supported Carbon Fibre Skins (top and bottom one)- selected material  Carbon Fibre Skins (top and bottom one)- selected material  Toray M55J + Cycom 950-1 11

12. Szymon Krzysztof Sroka30/07/2015 Orthotropic Material  An Orthotropic material has three planes of symmetry that coincide with the coordinate planes.  One plane of symmetry is perpendicular to the fibre direction, and to other two can be any pair of plane orthogonal to the fibre direction. -The x-axis is aligned with the fibre direction -The y-axis is in the plane of the layer and perpendicular to the fibres -The z-axis is perpendicular to the plane of the layer and thus perpendicular to the fibres.  Only nine constants are required to describe an orthotropic material. Transversely Isotropic Material  A transversely isotropic material has one axis of symmetry  Transversal isotropic materials are orthotropic materials characterized by isotropic material behaviour in one material symmetry plane  A unidirectional layer has transversal isotropic material behaviour with the fiber direction as symmetry axis -The z-axis is perpendicular to the plane of the layer and thus perpendicular to the fibres.  The number of constants to define is reduced to 5. 12 Analytical Solution

13. Szymon Krzysztof Sroka30/07/2015 Analytical Solution Deflections of the TD Barrels 1. Bending Deflection 2. Shear Deflection Calculation of the deflection due to bending:Calculation of the deflection due to shear: Assumption: B.C. - Simply supported Beam (Timoshenko Beam Theory) Bending depends on the skins properties; Shear depends on the core properties 13 x LQ Flexural Stiffness: Shear Stiffness:

14. Szymon Krzysztof Sroka30/07/2015 3. Total Deflection = Bending Deflection + Shear Deflection 14 Flexural Stiffness: Shear Stiffness: Analytical Solution Deflections of the TD Barrels

15. Szymon Krzysztof Sroka30/07/2015 Deflection of Barrels made of Sandwich Structure ( CF SKINS PLUS HONEYCOMB CORE) Number of CASE 1 Number Of Cylinders Radii Of Barrels [mm] Length Of Barrels [mm] THICKNESS OF CF SKINS [mm] THICKNESS OF HONEYCOMB CORE [mm] Mass Of each Barrels [kg] Mass of Equipment [kg] Deflection of Barrels - Handmade Calculations [µm] Deflection of Barrels - ANSYS [µm] Eigenvalue - Natural frequency of Cylinders [Hz] Difference between Handmade Calculations and Ansys Simulations [%] % Of Radiation Length of each Barrels - Mechanics [%] % Of Radiation Length of each Barrel - SEN+COOLING [%] % Of Radiation Length of each Barrel - TOTAL [%] % Of Radiation Length of Barrels - TOTAL SUM [%] 12308600.6102.8343.9165.39496.2065224.0413.076613230.53681.0121.549 9.387 252514600.61511.898915.15915.516220.574107.9724.583454850.5721.0011.573 384020601.21548.01833.39621.464731.04867.2130.866078331.038512.039 4114526601.22590.034959.11336.681155.58557.89734.008995231.10881.0042.113 5145032601.225139.736491.44955.018785.75940.17935.84498421.10881.0042.113 Comparison to FEA Solution Analytical Calculations vs FEA simplistic model 15

16. Szymon Krzysztof Sroka30/07/2015 Different Layup Tracking Detector Barrels Configuration number Lay -up 1 [0/-45/+45/+45/-45/0] 2 [90/-45/+45/+45/-45/90] 3 [90/-45/+10/+10/-45/90] 4 [0/-15/+15/+15/-15/0] ! 5 [90/-15/+15/+15/-15/90] 6 [0/-75/+75/+75/-75/0] 7 [0/-45/90/90/-45/0] 8 [90/-45/0/0/-45/90] 9 [90/30/-30/-30/30/90] 10 [0/60/-60/-60/60/0] 11 [45/-45/0/0/-45/45] 12 [0/90/0/0/90/0] 13 [90/0/90/90/0/90] 16 Each Lay-up consists of 6 sub-layers Thickness of 1 sub - layer: - 100 µm (Thickness of CFS -0.6 mm) - 200 µm (Thickness of CFS -1.2 mm)

17. 30/07/2015 17 Tracking Detector Barrels – Dimensions Number of Barrels Radii of Barrels [mm] Length of Barrels [mm] Thickness of Honeycomb Core [mm] Thickness of CF Skins [mm] Mass of each Barrel [kg] 1 230860100.62.85 3 8402060151.248.1 4 11452660251.290.1 5 14503260251.2140 Different Layup FEA simulations in ANSYS Thickness of CFS and Honeycomb Core Second Barrel is not treated here. It was replaced by the Support Tube 30/07/2015Szymon Krzysztof Sroka

18. 30/07/2015 Different Layup ANSYS Results 18

19. Szymon Krzysztof Sroka30/07/2015 19 Different Layup ANSYS Results

20. Szymon Krzysztof Sroka30/07/2015 20 100 [µm] – Limit Value Different Layup ANSYS Results

21. Szymon Krzysztof Sroka30/07/2015 21 100 [µm] – Limit Value Different Layup ANSYS Results

22. Conclusions: Szymon Krzysztof Sroka30/07/2015 22  Comparison between Analytical and FEA calculations on ≤ 40 %  Deformation critically depending on specific Lay-up and Boundary Conditions  All Tracker Detector Barrels seem to be feasible and can obtain small deformation

23. Szymon Krzysztof Sroka30/07/2015 Beam Pipe & Support Tube Beam Pipe & Support Tube 23

24. Szymon Krzysztof Sroka30/07/2015 Beam pipe - Dimensions SSt Be CFRP (based on modified CLIC_ILD design) Objectives: - Determining the z - location for the Supports in order to minimize stresses in the sensitive connection area between Beryllium & Stainless Steel 24 Cylindrical Part1: R1=30 [mm], L= 308 [mm], T1= 0.6 [mm] Conical Part2: R1=30 [mm], R2=240 [mm, L= 1820 [mm], T2= 4.8 [mm] Cylindrical Part3: R2=240 [mm], L= 381 [mm], T3= 4.8 [mm] Conical part2 Cylindrical part3 Cylindrical part1 Support_1 Support_2 z1 z2

25. Szymon Krzysztof Sroka30/07/2015 Beam Pipe - Support Iterative identification of the supports location Assumptions/ Simplifications:  Based on the symmetry was modelled one quarter of the Beam Pipe.  In the first approach the beam pipe is supported in two places on the edges (only displacements in x-axis and y axis are blocked).  During the determination of the support position, only solely weight of the Beam pipe is taken into account Support_1 –> z=1750 [mm] Support_2 –> z=350 [mm] Be SSt Cylindrical part1 Conical part2 Cylindrical Part1: R1=30 [mm], L= 308 [mm], T1= 0.6 [mm] Conical Part2: R1=30 [mm], R2=240 [mm, L= 1820 [mm], T2= 4.8 [mm] Cylindrical Part3: R2=240 [mm], L= 381 [mm], T3= 4.8 [mm] Cylindrical part3 25

26. Szymon Krzysztof Sroka30/07/2015 26 Beam Pipe - Support Iterative identification of the supports location

27. Szymon Krzysztof Sroka30/07/2015 27 Beam Pipe - Support Iterative identification of the supports location

28. Szymon Krzysztof Sroka30/07/2015 60 degrees S1_T S1_B S3_T S3_B 90 degrees S1_T S1_B 120 degrees S2_B S2_T 28 Beam Pipe - Support Design Proposal of the Beam Pipe Support

29. Max.Defomration = 2.4 [µm] Szymon Krzysztof Sroka30/07/2015 Beam Pipe - FEA Calculations Max.Defomration = 75 [µm] σ. max = 0.63 [MPa] Rod properties Sn ln [mm]kn [N/mm] Pre- Load [N] R.Force [N] S1_T 4281327.5 500440 S1_B 4281327.5 163122 S3_T 4281327.5 500440 S3_B 4281327.5 163122 S2_T 5371058 4042 S2_B 5381055 2019 The results under its own weight: 29

30. Szymon Krzysztof Sroka30/07/2015 Beam Pipe - FEA Calculations The results under its own weight and the pressure influence (UHV): σ. max = 44 [MPa] Max.Defomration = 42 [µm] Alert - Front flange of the Beam pipe only 1 mm thick ! Max.Defomration = 8210.9 [µm] ! 30

31. Szymon Krzysztof Sroka30/07/2015 Support Tube - FEA Calculations Assumptions for the analysis :  Support Tube is also modelled as a sandwich structure (Cylinder consists of three layers; honeycomb core including top and bottom carbon skin). We are considering two different Core thickness (15 and 30 mm) and two different thickness of Carbon Fibres Skins (0.6 and 1.2 mm).  Boundary conditions are the same for each of the Tracking Detector Barrels  Loads in the performed analysis take into account the weight of the Support Tube and all the forces coming from the beam pipe.  In the framework of FEA analysis have chosen only four lay- up Support Tube Configuration number Lay -up 1 [0/-45/+45/+45/-45/0] 6 [0/-75/+75/+75/-75/0] 11 [45/-45/0/0/-45/45] 1313 [90/0/90/90/0/90] 31

32. Szymon Krzysztof Sroka30/07/2015 Support Tube - FEA Calculations 32 Example: CFS thickness – 1.2 [mm] Honeycomb Core – 30 [mm] Max.Local.Deflection – 207 µm BC.s -Simply Supported Layup 6

33. Szymon Krzysztof Sroka30/07/2015 33 Support Tube - FEA Calculations

34. Szymon Krzysztof Sroka30/07/2015 34 Support Tube - FEA Calculations

35. Szymon Krzysztof Sroka30/07/2015 35 Support Tube - FEA Calculations

36. Szymon Krzysztof Sroka30/07/2015 36 Support Tube - FEA Calculations

37. Conclusions: Szymon Krzysztof Sroka30/07/2015 37  Front flange of Beam Pipe will need to be thicker as it, there is too much deformation under vacuum.  From the results the Support Tube is suitable but there is some local deformation due to gravitational load on the Beam Tube. Outlook:  Space Frame structure made of composite material maybe be valid for CLIC tracker - investigation needed  Continuation work on Support Tube validation plus more detailed Beam Pipe analysis