Interpretation of MC Interface Analysis Results

Interpretation of MC InterfaceAnalysis Results Wayne Reiersen April 11, 2007

Joint strength design criteria • A design handbook for bolted joints was developed to provide a unified approach for the project • Design criteria for joint strength include the following… • The separation of a preloaded joint must not occur due to an external load • The minimum bolt preload shall be used to calculate the friction force • The allowable coefficient of friction (a) must always be determined in a conservative manner. Testing under representative conditions should be performed in order to determine the allowable coefficient of friction. • Friction coefficient extremes must be considered as anticipated upset conditions in the design. For allowable coefficients of friction above 0.45, use amin=2/3 a and amax=4/3 a. • In shear-loaded joints, with members that slide, the joint members transmit shear loads to the bolt and the minimum preload must be sufficient to hold the joint members in contact and without additional sliding during the stress cycle.

Gettelfinger’s friction test resultsAlumina coated samples • Results indicate a favorable dependence for COF v. contact pressure • A “design curve” can be characterized by an equation of the form COF = 0.4 + 0.02P where P is the contact pressure in ksi • The average contact pressure through which the bolt preload is transmitted at the shim/flange interface is approximately 10 ksi (based on Fan’s FEA analysis and Viola’s Fuji film test) resulting in an effective COF of 0.6 • Additional tests are being performed to investigate the sensitivity to flange surface finish and alumina coating (with and without binder)

ab2tl ab2tru aatl bc2tru bc2tl aatr cc2t ab2trl ab2int aaint cc2int bc2int bc2trl bc2bru ab2inb aainb cc2inb bc2inb ab2br aabr cc2b bc2brl aabl bc2bl ab2bl -60 deg 0 deg bctl abtl bctru cct abtr bcint bctrl ccint abint bcinb bctrl ccinb abinb abbru ccb bcbl abbrl bcbrl abbl +60 deg Brooks/Fan linear analysisRegion identification

Brooks/Fan linear analysis

Brooks/Fan linear analysis 74 kips/bolt preload

Brooks/Fan linear analysis

Brooks/Fan linear analysis 74 kips/bolt preload

Brooks/Fan linear analysisConclusions • In order to prevent slip on the inboard C-C interface, an average coefficient of friction (COF) of 0.4 is required. • In order to prevent slip on the other inboard interfaces (B-C, A-B, and A-A), the required COF is 0.3 with the added bolts preloaded to 74 kips per bolt. Without the added preload, the required COF was 0.74. • On the outboard region, the normal load per bolt is small relative to the bolt preload of 74 kips, ranging from -15 to +15 kips – flange separation should not be an issue • In order to prevent slip on the outboard interfaces, the required COF is a maximum of 0.15 and typically, 0.1.

Fan single bolted joint analysisShear load only • Shear load of 15 kips • Lateral deflection small w/o slip – 1.3 mils • Lateral deflection large w/slip – 10.7 mils Bonded Frictionless

Fan single bolted joint analysisShear load only Large lateral deflections result in large bolt bending and contact stresses (34 ksi) in frictionless case. Stresses are a maximum near where bolt bears on the end of the bushing. Small lateral deflections in bonded case result in low bolt stresses (1 ksi) Bonded Frictionless Sz Seqv Sz Seqv

Fan single bolted joint analysisShear load only Contact pressure on bushing peaks near shim interface and is two orders of magnitude higher in the frictionless case (34 ksi) than in the bonded case (0.4 ksi) Bonded Frictionless

Fan single bolted analysisShear load only Bonded Frictionless high local stress at edge is the combination of the bearing stress and shear stress primarily in the y direction

Bonded Frictionless Fan single bolted joint analysisCombined 60 kip preload, 15 kip shear In bonded case, dominant deformation is bolt shortening due to preload (6 mils) In frictionless case, lateral deflection is dominant (12 mils)

Fan single bolted joint analysisCombined 60 kip preload, 15 kip shear Frictionless Bonded Peak stresses in frictionless case are 27% higher Average tensile stress due to 60kip preload is 40ksi Peak stresses occur at the faces of nuts due to the assumption that stud and nut are bonded Sz Seqv Sz Seqv

Fan single bolted joint analysisCombined 60 kip preload, 15 kip shear Bonded Frictionless No contact pressure on bushing due to Poison’s effect of the preload on bolt and small shear displacement

Fan single bolted joint analysisCombined 60 kip preload, 15 kip shear Bonded Frictionless high local stress located at the washer bearing surface primarily due to preload

Fan single bolted joint analysisG11 v. SS bushings 15 kip shear load applied Replacing the G11 bushing with a SS bushing cuts lateral displacement in half Frictionless with SS bushing Frictionless with G11 bushing

Fan single bolted joint analysis G11 v. SS bushings Frictionless w/G11 bushing Frictionless w/SS bushing Bolt stresses due to shear loads are significantly reduced with SS bushings

Fan single bolted joint analysis G11 v. SS bushings Contact pressures with SS bushings are substantially higher Frictionless w/ G11 bushing Frictionless w/ SS bushing

Fan single bolted joint analysis G11 v. SS bushings Loads at flange interface are also higher w/SS bushing Frictionless w/SS bushing Frictionless w/G11 bushing

Fan single bolted joint analysis Imperfect fit-up • For baseline case, perfect fit-up between the stud and bushing and between the bushing and flange was assumed • In order to assemble the bolted joint, there needs to be finite assembly gaps to insert the bushing into the hole and to insert the stud into the bushing • Poisson effect also opens a gap between the stud and bushing when the stud is preloaded • The limiting case of no contact between the stud and bushing was modeled assuming a 15 kip shear load • The no contact case is compared to the tight-fitting G11 bushing case (with frictionless shims)

Fan single bolted joint analysis Imperfect fit-up The joint is markedly less stiff with imperfect fit-up, deflecting 61 mils (4 mils/kip) versus 10.7 mils (0.7 mils/kip) with perfect fit-up

Fan single bolted joint analysis Imperfect fit-up Bolt stresses increase by an order of magnitude, from 34 ksi to 364 ksi Location of peak stresses moves from bearing contact area to nut/stud interface Seqv Sz Sz Seqv

Fan single bolted joint analysisConclusions • A friction joint in which shear loads are transferred through the shim via friction is a better joint than one in which shear loads are transferred via bolt bending and contact pressure on the bushing • If friction is adequate to prevent slip, the incremental stresses and deflections due to a 15 kip shear load are small relative to the stresses and deflections due to the 60 kip bolt preload • If friction is inadequate to prevent slip and the shear load are transferred to the bolt, deflections due to a 15 kip shear load will be dominant. Bolt stresses will be substantially higher than from a 60 kip preload alone. • With imperfect fit-up between the stud and bushing, markedly higher bolt stresses result until contact is made with bushing • It would be prudent to set the preload as high as possible to maximize the shear capability of the friction path. This leaves essentially little or no headroom for bolt stresses should slippage occur. De-rating the preload to allow more shear to be put into the bolts is contraindicated. • Design philosophy should change from providing “belt and suspenders” to providing a stronger “belt” • The “suspenders” are inherently weaker than the “belt” • The neighboring “belt” may well pick up excess shear loads before the “suspenders” do any work. A lateral displacement of only 1 mil loads the friction joint to 15 kips. A lateral displacement of 6 mils is required to load the bolt (through hole assuming a perfect fit and a SS bushing). Tapped holes will be somewhat stiffer. Assembly gaps will make the load path through the bolts much softer.

Fan single bolted joint analysisSteps toward providing a stronger belt • Increase the preload • Add bolts where possible, even on the inbd/outbd feet if appropriate • Use low CTE washers and shims • Measure the preload with high accuracy • Re-tension the bolts after allowing them to relax • Increase the COF • Optimize and control preparation of the alumina coating and flanges to ensure a high COF • Provide small contact areas that result in high but manageable contact pressures (because of the apparent favorable trend of COF v. contact pressure) • Provide good fit-up • Ensure the preload is not lost • Monitor preload during operation. Re-tension bolts where needed. • Positively secure nuts so they do not back off. • Avoid overstressing bolts • Bushings serve no apparent purpose (except perhaps to register adjacent coils to each other) if we have no slippage. Where we have through bolts, additional preload could be provided by eliminating the bushings and going to a larger (1.5”) bolt size, especially on the C-C interface.

Myatt analysis on 1/2/07Frictionless single bolted joint 15 kip lateral load results in 12 mil lateral deflection with zero friction. Consistent with Fan’s later calculations.

Myatt analysis on 1/2/07 Frictionless single bolted joint Tapped holes are stiffer than through holes. 15 kip shear load results in 7 mils lateral deflection v. 12 mils.

Myatt analysis on 1/2/07 Frictionless single bolted joint Bearing stresses on the bushings are also consistent with Fan’s later calculations. Provides confidence in Fan/Myatt models of single bolted joint. 25 kip lateral load Max bearing stress is 67ksi 2.68 ksi/kip 15 kip lateral load Max bearing stress is 35ksi 2.35 ksi/kip

Myatt analysis on 1/2/07Frictionless model of A-B joint • Interface modeled as sliding (frictionless) but always in contact because of numerical difficulties with gaps opening

Myatt analysis on 1/2/07Frictionless model of A-B joint • Concluded that ORNL results (aka Brooks/Fan no slip calculations) underestimates the shear force distribution compared to this quasi-nonlinear approach • Not clear that the comparison is meaningful • Max shear per bolt is calculated to be 19 kips on Bolt 17, but may be lower if “missing bolt” added to model. Max would then be 16 kips on Bolt 26.

Myatt analysis on 1/2/07Frictionless model of A-B joint • Observed that max shear per bolt seems to peak on end and isolated bolts • Concluded that applying a reference preload of 73 k-lbf and using friction to carry the shear force will require a minimum friction coefficient, μ, of 16k/73k or 0.22

Myatt analysis on 3/22/07Model of A-A joint with friction • Added 5 bolts on inboard side. Middle bolt was found to carry no shear so effectively only 4 bolts were added. • Bolt preload of 81 kips with a COF of 0.3 were used

Myatt analysis on 3/22/07Model of A-A joint with friction • Max shear loads were on the added inboard bolts with a range of 12-15 kips/bolt

Myatt analysis on 3/22/07Model of A-A joint with friction • Concluded that contact slippage would occur and that friction would not suffice to prevent slippage on each cycle • Cyclic loading of the bolt in bending was flagged as a concern

Myatt analysis on 3/22/07Conclusions • We should eliminate the bolt on the midplane and add two more off the midplane on the A-A flange • We should add as many bolts as possible on the A-B flange. The number was upped to six. • We already added as many bolts as possible (4) on the B-C flange. • Assuming a COF of 0.6 (representative of a 10ksi contact pressure under the shims), the 2/3 criterion would result in a minimum COF of 0.4. Lowering the preload to 74kips and increasing the minimum COF to 0.4 would increase the shear capability per bolt by 5 kips. This reduces the max shear carried by the bolts in the outboard region to near zero. The shear carried by the four inboard bolts would be reduced to 7-10 kips/bolt. • Adding the two additional inboard bolts would increase the shear reacted by friction by 30 kips per bolt. This will likely reduce the max shear carried by the six inboard bolts to zero.

Summary of bolted joint analysis • All of the analysis is driving us in the same direction – do whatever we can to ensure that slippage does not occur • Shear loads transmitted by friction results in low incremental stresses. The opposite is true for shear loads transmitted by bolt bending and bushing contact. • Assembly gaps between the bolt and bushing have no effect when shear loads are transmitted by friction. They have a very detrimental effect when shear loads are transmitted by bolt bending and bushing contact. • Slippage in the inner leg increases shear loads on the end bolted joints, reducing our structural margins • Adding bolts on the inner leg reduces the COF required to prevent slippage to 0.4 which is significantly below what is being achieved in the tests.

Managing shear loads in the unbolted regions • We do not have a workable design for managing the shear in the unbolted regions • This is recognized as a major cost and schedule risk in addition to being a major technical risk • The history is as follows… • Friction relying on conventional SS shims found to be inadequate • Studs welded to flanges with potted shear plate had assembly and performance issues • Shear pucks mounted in plates welded to the flanges proposed. Weld stresses and assembly fit-up are lingering concerns. Analysis and weld trials underway. • High friction (alumina coated) shims suggested as an alternative

Freudenberg analysis of shear puckBasic model • Puck Size = 1” • Holder shim = 1.5” diameter • Weld = 3/16” perimeter. • Weld connects shim to flange only (no contact under shim to flange face except at welds, small 5 mil gap under shim) • Sliding contact between two shims (mu = 0) • Initially bonded contact between shim and puck. • All materials have Stainless steel properties at LN2. Fixed on face Front view with 1/8” weld and 1” puck, 1.5” long shim

Freudenberg analysis of shear puckShear loads Current models use 4.2 kips/in Consistent with running shear load from Brooks’ calculations (in the absence of bolts)

Freudenberg analysis of shear puckDeflections Max deflections in flanges are 1.7 mils Comparable to stiffness of bolted joints in no-slip condition

Freudenberg analysis of shear puckStresses Weld size of 3/16” Peak stresses of 42 ksi in weld Allowable stresses are TBD

Freudenberg analysis of shear puckAlternate model of weld region • Changing the weld profile from curved to triangular reduces the peak stresses from 42 ksi to 33 ksi • Changing the plate from square to circular did not reduce peak stresses

Shear puck optionWeld distortion trials • A substantial 3/16” perimeter appears needed to transmit the shear loads from the plate to the flange • The concern is that applying the weld will bow the plate and open/distort the hole due to weld shrinkage • Dudek has initiated a weld trial to be performed • Circular plate • Reliefs cut on top/bottom of the plates to minimize distortion of the circular hole • First results should be available this week

Shear puck option Requirements and performance • Provide structural continuity in the toroidal direction so radial centering forces can be reacted by hoop compression • Requires good fit-up, either by machining to fit or using thin shim material • There is a risk that bowing of the plates after welding could degrade toroidal fit-up • React shear loads to prevent relative motion and keep the bolted joints from being overloaded • The stiffness of the shear puck design is comparable to the stiffness of the bolted joint in the no-slip condition so in principle, shear loads could be shared • There is a risk that the weld stresses will be too high. Allowables are TBD. • Provide for manageable assembly • This concept requires simultaneous blind fit-up of dozens of pucks on the three C-C interfaces into tight fitting holes – major technical risk • Assembly tolerances between the puck and the mating hole are needed because of potential distortion from welding plus the need to simultaneously fit dozens of pucks. If a puck does not fit, it will be virtually impossible to determine which one is the problem. • Dudek has estimated that annular gap of perhaps 30 mils will be required between the shear puck and the hole that receives it. • Our ability to measure and position is likely to be in the 20 mil range at best • If the assembly tolerances are indeed large relative to the deflections under load (1.7mils), then the shear pucks will not pick up initial shear loads and will not share the load evenly. Individual shear pucks plus the bolted joints will likely be overloaded. THIS LOOKS LIKE A SHOWSTOPPER.

Friction puck optionDescription • An alternative to having a positive shear connection (a la the shear puck option) in the unbolted region is to rely on friction • One concept would be to provide constant thickness shims like we are providing in the bolted region attached to one flange via a stud welded to the flange • The primary purpose of the stud is to retain the friction shim • The shim would be alumina coated on both sides, providing high COF surfaces and electrical isolation

The friction puck optionDescription • Compressive loads on the C-C interface are about 6.1 kips/in. Shear loads are about 2.5 kips/in. • With 1.75 in OD pucks on 2.75” centers featuring a 1” ID hole for attaching a retaining nut to the stud, the compressive stress due to EM loads should be in the neighborhood of 10 ksi with shear loads of 4 ksi • Compressive stresses are the same as for the shims under the bolts • The expected COF is 0.6 and the required COF is 0.4, providing a factor of safety of 50% • We may want a retaining plate around the friction pucks to ensure they never fall out • A special arrangement might be required for the narrow band near the midplane on the C-C interface

Requirements and performanceFriction puck option • Provide structural continuity in the toroidal direction so radial centering forces can be reacted by hoop compression • Requires good fit-up. Using alumina coated shims, we should have almost a continuum of thicknesses to choose from. • React shear loads to prevent relative motion and keep the bolted joints from being overloaded • The stiffness of the friction puck design should be directly comparable to the stiffness of the bolted joint in the no-slip condition so in principle, shear loads could be shared • Shear loads and compressive loads come from the same coil currents. Net radial centering forces HAVE TO be reacted by hoop compression – there is no other load path. In a friction joint, hoop compression provides shear capability. You cannot have add shear loads w/o added shear capability – analogous to wedged TF coils. • Provide for manageable assembly • In this option, the coils will be pre-fit, the gaps will be measured, and shims of the appropriate thickness installed • Assembly risks are minimal

Interpretation of MC Interface Analysis Results