US LHC Accelerator Research Program bnl fnal lbnl

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US LHC Accelerator Research Program bnl - fnal- lbnl - slac Supporting FEA for

US LHC Accelerator Research Program bnl - fnal- lbnl - slac Supporting FEA for TQC I. Novitski LARP Technology Quadrupole Review Nov 29 – Dec 1

TQC Design and Model Skin Bronze outer pole piece Inner bronze pole piece with

TQC Design and Model Skin Bronze outer pole piece Inner bronze pole piece with stress relief slot Yoke Gap Collar. Yoke Preload Shim Yoke Collaring Key Control Spacer Coil midplane shim LARP TQ Review Nov 29 – Dec 1, 2006 Collar Coil Midplane Shim Yoke Collar Coil Control spacer Near Splice Body area LJ area Supporting FEA for TQC Splice area 2

Model Material Properties, Boundary Conditions and Loads 1. Assembly at room temperature 300 K

Model Material Properties, Boundary Conditions and Loads 1. Assembly at room temperature 300 K Stress in the coil pole block controled by material placed in the groove Prestress in the coil during collaring generated at midplane by coil-to-coil interference, Mp shim DRcoil TQC 01 TQC 02 During skin welding the yoke-to-collar interference at the coil parting plane compresses coil radially Rsh The yoke outer mid-plane gap (contact elements) is always open after skin welding (Sk). 2. Cool down from 300 K to 1. 9 K 3. LF at 1. 9 K , B=233 T/m Fx=1. 44 MN/m Fy=-2. 19 MN/m Material properties Small reaction forces at pole of the first layer should remain Coil peak stress should be less than 165 -170 MPa at all loads (based on TQS model result, 2 D model singularities). Stress in all structural elements should be below yield point. LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC 3

TQC Baseline Design with G 10 in the pole groove, Mp=0. 15 mm, Rsh=0.

TQC Baseline Design with G 10 in the pole groove, Mp=0. 15 mm, Rsh=0. 075 mm, St=0 -0, Sk=0. 3 mm -100 MPa 162 MPa 300 K 67 mm -95 MPa -58 MPa -64 mm 44 mm 144 MPa 1. 9 K -109 mm -42 MPa -260 mm -178 mm -9 MPa 146 MPa Bmax 233 T/m +9 MPa -129 mm -8 MPa -228 mm -191 mm DRcoil 160 -190 MPa 270 -320 MPa 280 -340 MPa Coil saz: 300 K: 162 MPa, 1. 9 K: 144 MPa, B 233 Tm: 146 MPa LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC 4

TQC-01 Real Body Model with epoxy in the groove, Mp=0. 075 mm, Rsh=0. 05

TQC-01 Real Body Model with epoxy in the groove, Mp=0. 075 mm, Rsh=0. 05 mm, St=0. 05 -0, Sk=0, 3 mm -42 MPa -36 MPa -37 MPa 21 mm 66 MPa -37 mm 300 K 38 mm -24 MPa 55 MPa -238 mm 1. 9 K -13 MPa -161 mm -194 mm -7 MPa 57 MPa I=8 k. A +9 MPa Training start DRcoil +70 MPa -162 mm +11 MPa +26 MPa +3 MPa +12 MPa +2 MPa saz 107 MPa I=14 k. A 233 T/m 85 MPa -196 mm +26 MPa -193 mm I=12 k. A +11 MPa +12 MPa 12 k. A slow training Coil saz: 300 K: 66 MPa, 1. 9 K: 55 MPa, B 233 T/m: 107 MPa LARP TQ Review Nov 29 – Dec 1, 2006 66 MPa I=9 k. A slow training Separation starts at 9 k. A, quenches, consistent with observed training behavior Supporting FEA for TQC 5

TQC-01 Real LJ Model with epoxy, Mp=0. 075 mm, Rsh=0. 075 mm, St=0. 05

TQC-01 Real LJ Model with epoxy, Mp=0. 075 mm, Rsh=0. 075 mm, St=0. 05 mm-0, Sk=0. 3 mm -47 MPa 83 MPa I=14 k. A 233 T/m Coil saz LARP TQ Review Nov 29 – Dec 1, 2006 -171 mm 67 MPa -251 mm 35 mm 1. 9 K -200 mm DRcoil 111 MPa -31 MPa -53 mm 300 K +36 MPa -53 MPa 16 mm -38 MPa +20 MPa -194 mm +15 MPa -217 mm -25 MPa -15 MPa 78 MPa I=8 k. A -17 MPa -10 MPa +3 MPa 93 MPa Training start -10 MPa 84 MPa +15 MPa -216 mm I=12 k. A +3 MPa 12 k. A slow training I=9 k. A -5 MPa 9 k. A slow training No separation up to 12 k. A, no quenches, consistent with observed training behavior Supporting FEA for TQC 6

Model for TQC-01 Splice Area with Stainless Steel Yoke -5 mm -57 mm 300

Model for TQC-01 Splice Area with Stainless Steel Yoke -5 mm -57 mm 300 K -247 mm Extreme parameters Mp=0. 075 mm Rsh=0. 075 mm St=0. 05 mm Sk=0. 4 mm 21 mm -331 mm 1. 9 K -155 mm Coil saz: 300 K-142 MPa 1. 9 K -153 MPa Not a problem area LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC 7

TQC-01 Model near Splice Area with Stainless Steel Yoke Mp=0. 075 mm Rsh=0. 125

TQC-01 Model near Splice Area with Stainless Steel Yoke Mp=0. 075 mm Rsh=0. 125 mm St=0. 05 mm Sk=0. 3 mm 300 K 1. 9 K Coil seqv: 300 K-163 MPa 1. 9 K -175 MPa Coil seqv may reach >200 MPa at 1. 9 K if count on parameters variation due to collared coil OD elliptical shape (measured after disassembly). Cable stress sensitivity Coil m-p shim 10 -12 MPa/25 mic Collar-yoke radial shim Skin shrinkage after welding LARP TQ Review Nov 29 – Dec 1, 2006 20 -25 MPa/25 mic Normalized Ic vs. transverse pressure for all samples tested at 12 T. 3 -4 MPa/25 mic Supporting FEA for TQC 8

Summary for TQC-01 Coil prestress was generally lower than expected due to difference from

Summary for TQC-01 Coil prestress was generally lower than expected due to difference from design parameters: –Epoxy in the pole groove (~30 MPa, possible yielding of pole) –Bigger size of two control spacers (attempt to correct calculated yoke asymmetry during assembly) –Smaller coil midplane shim Coil seqv near splice area may reach >200 MPa at 1. 9 K if parameter variations due to collared coil OD elliptical shape are considered (measured after disassembly). TQC Baseline TQC-01 as built (Body) 300 K 1. 9 K 14 k. A 300 K 1. 9 K 12(14)k. A Pressure at Inner pole, MPa -100 -95 +/-9 -47 -53 +15(+36) Pressure at Outer pole, MPa -58 -42 -8 -31 +3(+20) Max azim. stress, MPa 162 144 146 83 67 93(111) Coil d. R at pole up, mm 67 -109 -129 16 -171 (-194) Coil d. R at midplane, mm -64 -260 -228 -53 -251 (-217) Coil d. R at pole near yoke split, mm 44 -178 -191 35 -200 (-216) LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC 9

TQC-02 Model Features 1. 2. 3. 4. 5. LARP TQ Review Nov 29 –

TQC-02 Model Features 1. 2. 3. 4. 5. LARP TQ Review Nov 29 – Dec 1, 2006 G 10 in the pole groove Possible glued pole inserts Full round collars Wider collar radial support Full length iron yoke Supporting FEA for TQC 10

TQC-02 Model (LJ) with G 10, Mp=0. 15 mm, Rsh=0. 075 mm. F, St=0

TQC-02 Model (LJ) with G 10, Mp=0. 15 mm, Rsh=0. 075 mm. F, St=0 -0, Sk=0. 3 mm -100 MPa -95 MPa -75 MPa 42 mm 169 MPa 300 K -64 mm 29 mm DRcoil 170 -210 MPa 168 MPa 1. 9 K -60 MPa -124 mm -266 mm -249 mm 280 -330 MPa -20 MPa -145 mm 173 MPa -236 mm Bmax 233 T/m-1 MPa -39 MPa -233 mm 290 -350 MPa Coil saz: 300 K: 169 MPa, 1. 9 K: 168 MPa, B 233 Tm: 173 MPa LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC 11

TQC-02 Model (Body) with G 10, Mp=0. 15 mm, Rsh=0. 075 mm. F, St=0

TQC-02 Model (Body) with G 10, Mp=0. 15 mm, Rsh=0. 075 mm. F, St=0 -0, Sk=0. 3 mm -100 MPa -95 MPa -75 MPa 58 mm 170 MPa 300 K -67 mm 33 mm DRcoil 170 -210 MPa 164 MPa 1. 9 K -60 MPa -109 mm -266 mm -20 MPa -134 mm 167 MPa Bmax 233 T/m -209 mm 280 -330 MPa -236 mm +/-2 MPa -39 MPa -222 mm 290 -345 MPa Coil saz: 300 K: 170 MPa, 1. 9 K: 164 MPa, B 233 Tm: 167 MPa LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC 12

Model for TQC-02 Near Splice Area with Iron Yoke 21 mm -74 mm Mp=0.

Model for TQC-02 Near Splice Area with Iron Yoke 21 mm -74 mm Mp=0. 075 mm Rsh=0. 075 mm St=0 Sk=0. 3 mm -269 mm -256 mm -8 mm DRcoil -150 mm Coil seqv: 300 K-125 MPa 1. 9 K -116 MPa Stresses reduced to safe level LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC 13

Model for TQC-02 Splice Area with Iron Yoke 24 mm -55 mm -136 mm

Model for TQC-02 Splice Area with Iron Yoke 24 mm -55 mm -136 mm Mp=0. 075 mm Rsh=0. 075 mm St=0 Sk=0. 3 mm 17 mm -256 mm -224 mm DRcoil Coil saz: 300 K-132 MPa 1. 9 K -133 MPa Stresses at safe level LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC 14

TQC-02 Summary TQC Baseline TQC-02 (LJ) 300 K 1. 9 K 14 k. A

TQC-02 Summary TQC Baseline TQC-02 (LJ) 300 K 1. 9 K 14 k. A Pressure at Inner pole, MPa -100 -95 +/-9 -100 -95 -20/-1 Pressure at Outer pole, MPa -58 -42 -8 -75 -60 -20/-39 Max azim. stress, MPa 162 144 146 169 168 173 Coil d. R at pole up, mm 67 -109 -129 42 -124 -145 Coil d. R at midplane, mm -64 -260 -228 -64 -266 -236 Coil d. R at pole near yoke split, mm 44 -178 -191 29 -249 -233 Increase contact area of yoke upon collars : –Reduced coil bending –Increase coil prestress for second layer –Increased skin stress by ~15 MPa Full length iron yoke: –Coil seqv near splice area is 125 MPa/300 K and saz at splice area is 133 MPa/1. 9 K LARP TQ Review Nov 29 – Dec 1, 2006 Supporting FEA for TQC 15