Development of a low material endplate for LP1 and ILD Dan Peterson, Cornell 2010-11-11 At previous meetings, 2010-04-08 models of LP1 endplate and FEA calculation of deflection 2010-04-22 getting ready to make small beam prototypes to measure ability of FEA to model mechanical properties 2010-06-03 start of an ILD endplate (space-frame) model convergence problems with FEA calculations 2010-07-01 convergence problems with FEA calculations for a simplified ILD endplate (space frame) model 2010-10-28 construction of small beam prototypes, modeling updates, addressing FEA calculations for the ILD endplate model introduced the Equivalent-Plate-Spaceframe Today support of ILD endplate – add inner field cage “Equivalent-Plate-Spaceframe” model of LP1 endplate measurements of deflections of the small beam prototypes

Promotional picture – 8 layers, Equivalent-Plate-Spaceframe

(inside view) As a reminder (from 2010-10-28) , The “equivalent-plate” model of the ILD endplate is fully populated with spaceframe-separator-plates: above-rows and and in-rows (in the same row, between modules). This model has a full thickness of 100mm, radius 1.8m, and a mass of 136kg. the thickness is then 1.34g/cm2, 6%X0.

FEA calculations of deflection and stress (ok, stress is not shown) 20101028-Complete Model “space-frame-separator-plates” ring outside layer 8 ring inside layer 1 all intermediate rings all radial lines within rows Endplate Support: outer field cage deflection=0.056 mm/100N or 1.23 mm New Endplate Support: outer and inner field cages deflection=0.00991 mm/100N or 0.22 mm (not simply a factor of 4 because the support is at non-zero radius)

Modeling updates (from 2010-10-28) All space frame models (small beam, LP1, ILD) use a common calculation form for the parameters describing the mounting block that provides the flat for the center screw, the ability to turn on/off the wings for the side screws, and reduces errors. For the LP1 endplate, radial orientation struts have added in “row 4” and “row 0”.

(from 2010-10-28) A further simplified model is required for the FEA of the ILD spaceframe endplate. I observed earlier that simple vertical struts can be analyzed. In the “equivalent-plate” model, pairs of struts are replaced with a plate. Optimizing the parameters for equal material in the plate as in the struts, equal deflection of the beam in the two models, The plate width is 35% of the span of a pair of struts, the plate thickness (into the page) is 50% of the strut thickness. “equivalent plate” “realistic struts”

Completed “equivalent-plate” model of the LP1 endplate Revised specifications for equivalent plates (equal material, equal deflection) width multiplier thickness multiplier small beam 0.378 (was 0.35) 0.40 (was 0.50) LP1 0.390 0.43

Simple beam prototypes (updated from 2010-10-28) So, the prototypes and the different levels of modeling and construction fit into the design of the ILD endplate. Models of “strut” Space frame Models of “equivalent plate” Space frame Construction Simple beam prototypes Calibrate “equivalent plate” to “strut Calibrate the model to reality July 2011 LP1 endplate Apply LP1 experience to ILD design. Use the “equivalent plate” for FEA ILD endplate

Progress on the Small Beam Prototypes (from 2010-10-28) “Strut” space frame Al-carbon hybrid Parts have been delivered by the vendor. “LP1” is ready to measure. The “Strut” space frame was easier to assemble than expected. “LP1” The aluminum-carbon fiber hybrid requires assembly. I am using these fiber chips, experimenting with the mixture. I also have Kevlar fiber in bulk form.

An issue with the FEA calculations is that they are based on solid models; the real devices include several joints: where the threaded rods meet both the struts and mounting blocks, and where the mounting blocks connect to the plates. The parts were constructed to calibrate the FEA of the models.

Measurements of the Strut Spaceframe The physical device was loaded with 8.5 lbs (38.6 N) concentrated is a 15cm wide region at the center. The unloaded profile shows wiggles ~ 150 microns (0.006 inch) peak-to-peak. This is expected without the iterative machining and stress relief. For the current LP1, the material remaining was 750 microns, 250 microns. Or, the wiggle may be due to poorly balanced struts. TBD (2) The difference of loaded w.r.t. unloaded is my result. (3) Single measurements were recorded to significance 0.0001 inch (2.5 micron) and have σ≈0.00005 inch (1.25 micron).

Measurements of the LP1 Mullion design The physical device was loaded with 8.5 lbs (38.6 N) concentrated is a 15cm wide region at the center. The unloaded profile shows wiggles ~ 50 microns (0.002 inch) peak-to-peak. This tends to support the speculation that this is from not employing the iterative machining and stress relief; less wiggle is expected with the LP1 mullion. (2) The difference of loaded w.r.t. unloaded is my result. (3) Maximum deflection is 0.339 mm vs. 0.042 mm for spaceframe. Ratio is 8. From 2010-04-22, expected 6. Some parameter have changed and this is isolated loading.

Analysis of measurements of the LP1 Mullion design Here, the FEA calculation is artificially increase by a factor of 1.16 . The measurements are calibrated to a 100N load, over a 15cm region in the center. Note that the deflection for the LP1 Mullion beam is MORE than the FEA calculation, by 16% but the shape is accurately reproduced.

Analysis of measurements of the Strut Spaceframe This is without any artificial calibration of the data or FEA. One might say, based on the result from the LP1 Mullion, that the spaceframe measurement is 16% low w.r.t. the FEA. The shape is accurately reproduced. There may be several sources of error in the measurement. The model struts have diameter: 6mm solid, 28.3mm2 area, the physical device has struts with 7mm OD, 4.8mm ID, 20.2mm2 area. (The physical device has much of the ID filled with threaded rod; there is some uncertainty in the effective cross sectional area.) However, changing the area of the strut in the model to 20.2 mm2 area results in an increase of the maximum deflection from .1111 mm to .1181mm, 6%. Similarly, uncertainty in how to treat the exposed threaded rod leads to an uncertainty of ~1%.

Conclusions The FEA calculations of the “strut spaceframe” is consistent with the measurements of the physical device, to ~16%. The largest uncertainty is due to the discrepancy observed for the LP1 mullion. The calibration of the “equivalent-plate spaceframe” to the “strut spaceframe”, for the case of the LP1 endplate, is similar to the small beam. Can/should we make the “equivalent-plate spaceframe” for LP1 and ILD? I am considering making LP1 endplates in both “strut” and “equivalent-plate” designs. The inner plate (supports the modules) and outer plate can be identical. We should still think about stiffness requirements for the ILD endplate and how much more space (in Z) can be allowed. I still must make the advanced LP1 endplate by July. The drawing are not still ready. I am still going to complete the aluminum/carbon hybrid small-beams.