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A Stress Analysis of the TS Magnet Prototype – No Layer-to-Layer Insulation

This study analyzes the stress and forces on the TS Magnet Prototype, specifically focusing on the absence of layer-to-layer insulation. The analysis considers the conductor cross-section, insulation, coil properties, and constituent materials. The results show the effects of various parameters like axial pressure, reversing currents, and axial shimming. Conclusions are drawn regarding the effectiveness of radial interference and axial shimming in increasing stress due to cool down, as well as the limitations of bolting in the case of reversed currents.

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A Stress Analysis of the TS Magnet Prototype – No Layer-to-Layer Insulation

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  1. A Stress Analysis of the TS Magnet Prototype – No Layer-to-Layer Insulation Bob Wands September 23, 2013

  2. Conductor Cross Section and Insulation Turn-to-Turn insulation = 0.25 mm fiberglass No layer-to-layer insulation is used

  3. Derivation of Coil Material Properties Coil properties were derived from an FEA of a short length of a single conductor. 0.25 mm fiberglass (turn-to-turn) 0.25 mm fiberglass (turn-to-turn) superconductor Hi-purity aluminum

  4. Properties of Constituent Materials Superconductor (at all temperatures) High-purity aluminum Fiberglass (at all temperatures)

  5. Coil Properties Used in the Analysis In the coil cylindrical coordinate system shown below (x=radial, y=azimuthal, z=axial): Elastic Properties Thermal Contraction (dl/l between 300 K and 4 K)

  6. The Finite Element Model Solid Model FE Mesh • Model is constrained at a remote point scoped to the upper flange surface. Constraint allows radial thermal contractions to occur stress-free • Coil interface with bobbins and wedges is frictionless everywhere • Bolts are 2024-T4 Al, 0.75 in dia, and preloaded to 12000 lbs (0.9 Fy)

  7. Magnetic Forces on Prototype – Comparison with Forces for Operation in Full TSu Magnet (to scale) Note: In global assembly the bobbin for coils 14 and 15 also see large forces coming from adjacent bobbins 440 kN 121 kN 115kN Forces for Operation in Full TSu Magnet (coils 14 and 15) 440 kN Forces on Prototype (reversing current in one coil gives the same forces with signs reversed)

  8. Coil Stresses (no shimming) for Nominal CTC and +/-2% CTC

  9. Coil Stresses for Various Radial and Axial Shims

  10. Axial Pressure (MPa) between End Flange and Wedge – no shimming assembly cool down energize

  11. Axial Pressure (MPa) between Bobbin and Coil – no shimming assembly cool down energize Note: The axial magnetic force is 440 kN. The area of contact is 0.184 m2. Average stress is 2.4 MPa

  12. Reversing Currents Due to the frictionless assumption of the ground plane interfaces to the bobbin and wedges, all axial force is reacted by the end flange. This results in displacements of about 0.9 mm. The results indicate that the coil will lift completely off the bobbin, leaving a gap possibly as large as 0.5 mm The bolt preload is 12000 lbs. Bolt load increases by about 780 lbs/bolt due to cool down, and a maximum of 552 lbs when the currents are reversed. Total load on a single bolt is then 13332 lbs, for a maximum bolt stress of 39900 psi, which is slightly less than the yield stress of the 2024-T4 bolting material

  13. Reversing Currents – cont’d Can we estimate the frictional force between the outer radius of the coil and the bobbin? Pressure on OR of coil when energized for the case of no shimming and reversed currents From the figure above, assume a pressure of 1.5 MPa over a total area of 0.556 m2. The total radial force is then 834 kN. To counter a 440 kN shear force would require a coefficient of friction of 0.5. This may be within reachfor the materials and conditions.

  14. Running at 120% of Design Current • Forces are proportional to the square of the current • All calculated stresses from the present models can be multiplied by 1.44 • There should be no special problems for the case of same-direction currents • Reversed current run should not be taken to 120% due to limitations of bolting.

  15. Conclusions • The radial interference is highly effective in increasing the compressive hoop stress due to cool down. Gain is about 8 MPa per 100 microns • Axial shimming is much less effective in increasing the compressive axial stress due to cool down. Gain is about 0.8 MPa per 100 microns • An error in the CTC for the coil material of +/- 2% causes a variation of preload of about +/- 3 MPa in hoop stress • Axial results for even the worst case of no shimming are not alarming – average stresses are small and compressive. • Reversing the currents and assuming that the coils are contained in a frictionless envelope loads the flange bolts very heavily. Also, under the frictionless condition the coil would likely unload from the bobbin entirely. • For normal operation a 100 micron radial interference at room temperature seems prudent. • Axial preloading is of such limited effectiveness that either 100 microns of shimming, or no shimming, could be used.

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