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UNIVERSITY OF CALIFORNIA

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Assessment of local compliance in joints and mounts of global support structures : Testing and Analysis of the STAR Inner Detector Support June 19, 2013 Neal Hartman on behalf of Joseph Silber, Eric Anderssen and the LBL Team 2

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Overview Brief description of the HFT upgrade at STAR, and the new inner global support structure, the IDS (“Inner Detector Support”) Early deflection analysis results (overly optimistic) Testing of the IDS for model verification (a scheduled milestone) Re-analysis (detailed discussion) Lessons learned Time permitting - Brief discussion of HFT’s pixel insertion system, and implications for complexity / mass 3

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STAR HFT HFT is a new inner tracking system for STAR, with 4 layers of silicon and 6 gem disks Timeline: Nov 2011 main support structures + FGT were installed July-Dec 2012 PXL support and PXL for engineering run Summer 2013 full PXL + IST + SSD Key component is PXL: 2 innermost silicon layers Truly rapid insertion/removal Very low mass TPC is great; PXL will much improve pointing At LBL we’re building / have built: All the support structure (IDS) All of PXL IST local supports 4

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STAR HFT Inner Detector Support (IDS) 5 4.6 m 0.8 m Structure Mass = 35kg Applied Load = 200kg

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WSC/ESC MandrelWSC/ESC Layup Cone Layup Flange Layup Insertion Rail BondingAssembled Structure at LBNLJust before insertion at BNL Cone Machining Flange Bonding 6

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Initial FEA model 7 Careful accounting of masses Modulus properties based on multiple tensile tests for the composite materials Layered anisotropic composite properties fully specified, ply-by-ply Quasi-kinematic BCs at designed locations Face-face contacts at joints Apparently good nominal performance: 607 μm max vert defl @ full load)

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And yet… Pre-test predictionsMeasured deflections 8 1.88 mm @ 250kg central load 5.23 mm @ 250kg central load Predicted deflection only 36% of actual measured value in the “model verification” test (Note: the 250kg central load applied during test is equivalent to > 2x the distributed 194kg installed load.)

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Load Test Setup (Model Verification) 9 Kinematic turnbuckle supports (same as used in final install) Test does not use actual, distributed, installed loads. Test has a significantly higher load, centrally located.

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Many “DOF” measured during test Dial test indicators were placed at 18 locations about the structure during test – avoiding prejudice as to which would be redundant, which important Thus capturing a rich description of how the real object deforms This data was invaluable in diagnosing the model, particularly because the angled flat feature of the ESC and WSC causes sideways coupling with the vertical deformation the mounting points are quasi-kinematic, due to constraints on assembly procedure multiple bolted joints, where bolt preload is necessarily non-optimal, due to material constraints 10 angled flat

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Diagnosis of the model Identified as many possible sources of compliance and independently studied each; then integrated all into the global model Must identify sources bottom-up and close loops with independent tests, not twiddle with parameters at the top A perfect model would have an additional amount of compliance over the original equal to measured/orig.model – 1 = 5.258/1.881 – 1 = 1.79 Immediately identified one simple BC error, accounting for 23% of the total error (0.41 out of the 1.79) The rest of the compliance sources are more subtle and interesting 11

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Integration of the independent compliance sources 12

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3.1.1 Double boundary condition in Z In the design, the axial (Z) direction is constrained at one point only In the model, an extra erroneous constraint had been applied on the opposite side of the structure Removal of extra constraint accounts for 0.41 of 1.79 (again, this is an arbitrary unit indicating normalized missing compliance) 13

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3.1.2 Overconstraint boundary condition in Y A more subtle and interesting BC error Design requirement that any one vertical support turnbuckle be removable at any time Intentional state of overconstraint, for assembly purposes In reality, when 4 vertical supports are present: only 2 (at diagonal corners) carry the load (because torsional stiffness of structure is so high) 3 rd support stabilizes structure with essentially no load 4 th is free to deflect to any vertical position (within constraints of thread pitch clearance, etc) Examination of deflection data for turnbuckle supports (wisely recorded during load test) showed that NW and SE supports carried the weight load, with NE the stabilizer Removal of SW vertical support from model 0.12 of the 1.79 compliance error 14

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3.1.3 Finite stiffness of vertical constraints in test fixture In original model, vertical supports treated as perfect point constraints in the Y direction Calculating the stiffness of these turnbuckles a priori would be complex, due to thread-on- thread and spherical bearing interfaces From turnbuckle deflection data, however, could extract real, accurate stiffness of 3e6 N/m per support -- 0.406mm @ 250kg, directly contributing 0.07 of 1.79 to global compliance With good stiffness values, simple to replace vertical constraints with spring elements in the model (and model then confirmed that only the diagonals actually carried load) 15

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3.2 Bolted Joint 16 Key CFRP bolted joints Strain plot indicates how joint/flange locations are crucial to global deflection Revised model joint geometry, bolts and thick sections all solid modeled, parameterized stiffness of contact faces (more discussion to come) CONE OSC Original model joint geometry, face-face contacts at joints, some thick sections modeled as shells OSC CONE (not shown) Note: Simply replacing face-face contacts with point contacts at hole locations would increase compliance 9% (separate study). Still insufficient to capture compliance accurately. Nearly equivalently, can model as 6 DOF springs

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Picture shows original FE model stackup of CN60 plies in the cone Original model treats entire cone as shell body in this way But as approach edges, we have a thick section deforming in modes where typical thin wall, in-plane assumptions do not apply The middle section, even though 4mm thick, is ok to model as shell At edges, where discrete joint loads effective, the shell assumption breaks down 17 3.2, Bolted joint grip integral with cone FLEXURE FLEXURE + TORSION + THRU- THICKNESS NORMAL LOADS

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3.2.1 Bolted Joint Nonlinear Contact Model Bolted joints thru CFRP grips: key point of compliance in the overall structure. To quantify this compliance, local model of the joint analyzed with high mesh refinement and nonlinear contact definitions. “Nonlinear” evaluate over a series of substeps to capture the changing contact stiffness as the grip rotates and compresses. Computationally very expensive, and adverse on convergence. Global model still needs to be linear, so make a linear approximation of the joint based on the nonlinear local model (next slide). The effect of changing from a standard, high normal stiffness bonded contact to this nonlinear model is 39% increase in compliance (0.39 of 1.79). 18

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3.2.1 Linear approximation of nonlinear joint model Via contact stiffness parameter, method essentially includes a spring in the flange – the separate nonlinear model sets the stiffness for the larger linear model Abscissa at right shows varying the normal stiffness factor of a linear joint model. Ordinate is correlation to the nonlinear model Resulting contact stiffness parameter: 0.002, with a sensitivity of 12% for every Δ of 0.001 This parameter is the linear “knob” one can bring into the global model, to approximate the nonlinear effects. 19 Disadvantages of this approach: Decouples joint design from global model Obscures joint behavior in global model Advantages of this approach linear and convergent far more accurate than a bonded contact

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3.2.2 Wedged joint gap Partial wedge-shaped gap observed at the OSC bolted joint during assembly of the IDS Caused by a springback effect after facing the contact surfaces under clamped conditions in the mill. Gap up to approximately 0.2mm in some locations. To quantify effect on global joint stiffness, a nonlinear contact joint model run with a partial wedged gap. Plot on right shows joint closure (nonlinear model) under bolt preload 20

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3.2.2 Wedged joint gap Top plot: measured bolt torques (confirming preload repeatability) for titanium M4 threaded fasteners in IDS Bottom plot: nonlinear local model’s predictions of gap’s effect on global stiffness Depends on stiffness of adjacent bonded member For the situation at hand, it’s 7-10% i.e., 0.07 of the 1.79 compliance error 21

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3.2.3 Grip material anisotropy Grip of the bolted joints modeled as solid body, due to low aspect ratio Approximated as isotropic in original model, since layup is quasi-isotropic In reality, anisotropic (transverse isotropy), with much reduced moduli thru the thickness in normal (E Z ) and shear (G YZ, G XZ ) Laminate shear moduli bracketed on the high and low end by a unidirectional ply’s out-of-plane shear moduli: 2.1 GPa = G 23 ≤ G YZ = G XZ ≤ 6.3 GPa So value of 4 GPa chosen as reasonable Conversion to transverse isotropy 22% increase in global compliance (0.22 of 1.79) 22

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3.3.1 CPT of woven laminate Generally for thin laminates, CPT isn’t important for mechanical FEA – just needs to agree with the moduli inputs IDS however, has thick CN60 weave laminates at key locations (cone, bolt flanges) And in these thick sections, flexure is dominant deflection mode Original model had CPT = 264 μm, calculated a priori before test objects existed Subsequent measurements showed CPT to be 250 μm. This 5.3% lesser thickness indicates flexural stiffness reduction of 1 - (94.7%)³ = 15% (0.15 of 1.79) 23 Thickness measurements of as-built parts

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3.3.2 Woven in-plane stiffness reduction factor FEA model treats each CN60 woven ply as stacked pair of half-thickness uni plies at right angles In original model, out-of-plane undulation of the weave not accounted for. In reality, it’s significant. Typical engineering rules of thumb call for reduction factor of 5% to 15% 3pt and 4pt tests made of CN60 test beam to assess Also 6061 reference beam on same setup, to confirm test validity 24

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Tests gave woven stiffness reduction factor = 13% (0.13 of 1.79) Note in table below that an FEA of the beam using original model definitions versus corrected properties is 30% stiffer. This agrees well with simply combining the 15% CPT reduction with the 13% factor due to weave 25 Woven in-plane stiffness reduction factor

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3.4.1, 3.4.2 Minor effects Changed bonded contact joints throughout model from “pure penalty” contact formulation to slightly more computationally expensive Lagrangian method increases global deflection 3% (0.03 of 1.79) Original model didn’t include 2x ø100mm access holes in each cone increases global deflection 1% (0.01 of 1.79) 26

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Integration of the independent compliance sources 27

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Results after incorporating all changes into the model 28 MEASURED CENTRAL DEFL ORIGINAL MODEL FINAL MODEL Also note that the other deflection terms (besides central) agree much better in the final model. (Exception “ESC –X”: after much study this is believed to have been an anomalous bottoming-out of indicator probe tip during test – not included in weighted average figure of merit)

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Summary / lessons learned… There is a big difference between nominal initial studies and eventual as-built performance: Original FEA with installed loads: 0.607 mm central deflection Corrected model (with benefit of physical test): 2.501 mm Careful deflection test of final global support essential; plentiful distribution of indicators very useful Redundant measurements not only error check They also identify rigid body modes vs deformations As early as possible, key BC support points in model should be modeled as spring elements with physically-tested stiffnesses Take nothing for granted in modeling of bolted joints with CFRP grip – the low transverse stiffness of CFRP + low allowable preloads can defy our usual engineering intuition Subtle CPT effects become important to quantify for thicker cross-sections in bending In a larger sense, the D-matrix becomes important In-plane stiffness reduction factors for weave can be significant, even with excellent compaction / process control 29 Takeaway point: Most of the simple geometries, tubes and plates and so forth, are almost rigid bodies in our application. The materials are that good. But it is the difficult-to-model components – interfaces, bolted joints, low aspect ratio flanges – which cause a large amount of the deflection.

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Clam-shelled Insertion Mechanism 30

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HFT pixel insertion mechanism Rapid (< 1 working day) replacement of innermost 2 pixel layers Clamshelling of 2 halves in around pipe as approach IP – hinged, tracked design Cantilevered from kinematic mounts (engaged at end of insertion) Air cooling makes service routing much easier Somewhat similar radii (26mm, 82mm) as Cartigny Trade-off is complexity and significant mass at Z ≥ 575 mm on east side Rough scaling guess as to mass if one were to implement something like this at ATLAS size: 870 g of carbon fiber @ Z ~ 800 mm 3640 g of aluminum @ Z ~ 1100 mm Might be able to swap some CF for alum ~2250 g CF, ~1450 g alum 31

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STAR: PXL Insertion Test-bed Hinge mechanism Dovetail plate supports pixel staves 32

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STAR PXL Kinematic Mounts Design constraints 50μm positioning repeatability for all parts (6x detector halves) Insertion is remote (detector tracks in ~3m along circuitous route before engaging mount); no tool access Confined space, low mass, nothing magnetic High enough retention force to keep detector stably located, but low enough to insert/remove detector without significant impact One could design a mechanism with rotating components, i.e., cams and locks; chose the other route, to make it a flexures-with-friction problem. This allows: Simple FBD analysis (as long as you test μ first!) Accurate spring stiffnesses machined-in to parts by design Upper kinematic mount (XY or XYZ)Lower kinematic mount (X) PXL Support Half engaged in master tool Test Stand 33

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STAR PXL Kinematic Mounts Force-Disp Results on Test Stand μ = 0.2 Insertion Retraction END STOP “click-in” “break-out” Calculated max (μ = 0.2) Calculated min (μ = 0.2) TOP EAST KIN MOUNT, TEST 2011-08-29 34

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Rough guess as to how HFTs pixel insertion mechanism’s mass would scale to something of ATLAS size 35

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Backup 36

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IDS Loads and BCs, corrected arrangement 37

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Method of summing the compliances in the integration of separate effects 38

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Distributed loading of IDS (installed loads), and oversizing of central test loads 39 Load test was performed with 250kg central load In fact, if solve the force diagram above, the correct test load for 150% proof should have been 180kg central load, plus 110kg end load on east side only (to get the moments correct)

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Andrew Biehl. The objective of this project is to develop a method for determining the nut factor of a bolted joint using the finite element method.

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