Agenda

EuCARD-HFM ESAC reviewof the high field

dipole design

FRESCA2conceptual design

Attilio Milanese 20 January 2011

https://eucard.web.cern.ch/EuCARD/index.html

20 Jan. 2011, A. Milanese 2

Agenda2D design• magnetic• mechanical

3D design• magnetic• mechanical

Extras(parametric analyses, what-if, details, …)



Magnetic cross section

1140 mm100 mm



Magnetic cross section156 turns (per pole)

36 + 36 + 42 + 42Bcenter = 13.0 T

I13 T = 10.5 kA

Bpeak = 13.2 T

82.7 % load line @ 4.2 K76.3 % load line @ 1.9 K[ 15.7 T s. s. 4.2 K 17.0 T s. s. 1.9 K ]

DBy/Bcenter < 0.2 % (2/3 bore, Bcenter > 10 T)

E = 3.58 MJ/m

L = 46.8 mH/m



Effect of the ironunit no

ironiron

≈ 7.6 t

Bcenter [T] 13.0 13.0

I13 T [kA] 12.8 10.5

Bpeak [T] 13.9 13.2

load line 4.2 K [%] 89.8 82.7

Bss at 4.2 K [T] 14.5 15.7

Bstray 570 mm [mT] 465 270

Bstray 1000 mm [mT] 150 82

Bstray 2000 mm [mT] 38 20

The distance for Bstray is taken from the center.

plus the effect on field quality



What happens without prestress?1

X

Y

Z

13 T at warm with no prestress

DISPLACEMENT

STEP=1SUB =3TIME=1DMX =.001504

Lorentz forces at 13 T:Fx,qua = 7.70 MN/mFy,qua = −3.81 MN/mapplied at warm with no prestress

coil not gluedto the poles

displ. scale x 15

horiz. displ. ≈ 1.5 mm



Structure, 2D

iron

Ti alloy

potted coil

Al bronze

G10

steel

The coil pack.



70 mm

Structure, 2D

iron

Al alloy

The yoke and the shrinking

cylinder.

409 mm

1000 mm



Structure, 2D

iron

Ti alloy

potted coil

Al bronze

G10

steel

Al alloy

bladders

Structure partially prestressed at warm.



Structure, 2D

iron

Ti alloy

potted coil

Al bronze

G10

steel

Al alloy

The full prestress is achieved at cold.



0

20

40

60

80

100

120

140

layer 1 layer 2 layer 3 layer 4

p ave

[MPa

]

warm

cold

13 T

Prestress in the cross section• horizontal keys with 700 mm interference• vertical keys with 300 mm interference• Al alloy shell: I.D. = 1000, O.D. = 1140 mm• the bottom layers remain prestressed under excitation

average stress between coil and pole

layer 1

layer 2

layer 3

layer 4



Stresses on the coil

max s [MPa] warm cold 13 Tcoil, sx 55 142 138coil, sy 38 47 75

warm cold 13 T

The potted coil stays below 150 MPa, the

“comfort zone” for Nb3Sn.

sx

1

X

Y

Z

no tube, 13 T, ix = 0.700 mm, iy = 0.300 mm

-.150E+09-.133E+09

-.117E+09-.100E+09

-.833E+08-.667E+08

-.500E+08-.333E+08

-.167E+080

NODAL SOLUTION

STEP=3SUB =1TIME=3SX (AVG)RSYS=0DMX =.686E-03SMN =-.138E+09SMX =.342E+07

1

X

Y

Z

no tube, warm, ix = 0.700 mm, iy = 0.300 mm

-.150E+09-.133E+09

-.117E+09-.100E+09

-.833E+08-.667E+08

-.500E+08-.333E+08

-.167E+080

NODAL SOLUTION

STEP=1SUB =1TIME=1SX (AVG)RSYS=0DMX =.156E-03SMN =-.556E+08SMX =-.192E+08

1

X

Y

Z

no tube, cold, ix = 0.700 mm, iy = 0.300 mm

-.150E+09-.133E+09

-.117E+09-.100E+09

-.833E+08-.667E+08

-.500E+08-.333E+08

-.167E+080

NODAL SOLUTION


1

X

Y

Z


-.150E+09-.133E+09

-.117E+09-.100E+09

-.833E+08-.667E+08

-.500E+08-.333E+08

-.167E+080

NODAL SOLUTION




Coil geometry, 3D

straight

hard-way bendRmin = 700 mm

inclined straight17 deg

easy way bend

(no spacers)

Total axial length of coil: 1500 mm about 730 mm of straight section



Field on coil without iron, 3D

Without the iron there is fieldconcentration on the ends (+ 0.7 T).

14.6 T13.9 T



Iron geometry, 3D

yoke (laminations)

top pole(solid piece)

vertical pad(laminations)

365 mm 135



Field on the coil with iron, 3D

Bcenter = 13.0 T

I13 T = 10.2 kA

Bpeak = 13.4 TThe peak field is in the straight section.



Magnetic field in the bore, 3D

0

+2%

+1%

−1%

− 2%

field on 100 mm diameter circle, z = 0



Plot of |B| on the axis

no iron

reference layout

no extra block in

vertical pad12.5

12.6

12.7

12.8

12.9

13.0

13.1

0 50 100 150 200 250 300 350 400

|B|

[T]

z [mm]

365 extra365no iron1%2%straight

The field on the axis is within 2% of the central field, almost for the all length of the straight section.



Structure, 3D



Structure, 3D



3D stress effectsTo be more investigated, in a full 3D FEM:• different thermal contractions• Poisson effect• axial preload• local effects on the coil near the ends

1

XY

Z

cold

DISPLACEMENT

STEP=2SUB =1TIME=2DMX =.003832

model with dummy coil



Estimated weights[kg] x [kg]

impregnated bottom coil 95 2 190

impregnated top coil 112 2 224

yoke 3569 2 7138

shell 985 1 985

top plate / vertical pad 307 2 614

horizontal rail and pad 225 2 449other (end plate, wedge, end shoe, rod, keys) 424

total 10024

Cailler of Switzerland, Sublim retails at 30 CHF/kg (for WS’ law)

1

2

3

4

5

6

7



Thank you.



Extras



Extras: magnetic design 2D• only two layers closer to the midplane• only two layers farther away from the midplane• nonlinear sextupole• no iron in top pole• sensitivity analysis on multipoles• more / less turns?• a different cable / strand (modified HD2)• breakdown of Lorentz forces in 2D



Extras: mechanical design 2D

• pressure in the bladders• table of stresses in the structure• stresses in various components (pole pieces, horizontal pad, vertical plate / pad, yoke, shell)• dimensioning the yoke and the shell • stresses on the coil, different friction among them• alternative coil pack structure, with inner tube• material properties for 2D analyses



Only layers 1 & 2

I = 10.5 kA

Bcenter = 8.0 T[8.0/13.0 = 61.5 %]

Bpeak = 9.4 T


b3 = 512.1b5 = 20.0

• same current as for the full dipole, 13 T case• same iron configuration



Only layers 3 & 4

I = 10.5 kA

Bcenter = 6.8 T[6.8/13.0 = 52.3 %]

Bpeak = 8.3 T


b3 = −625.5b5 = −64.4

• same current as for the full dipole, 13 T case• same iron configuration



Nonlinear sextupole

• due to the highly saturated iron close to the bore (in particular, in the pole area)• the decapole b5 sees only ≈1 unit variation from 5 to 15 T

-100

-75

-50

-25

0

25

50

75

100

125

150

175

200

5 6 7 8 9 10 11 12 13 14 15

b 3[/

]

Bcenter [T]

all ironno top poleno iron



• no iron in top pole (only vertical pad and yoke)• that piece can make a difference on the margin / short sample

No iron in top pole

I = 10.8 kA

Bcenter = 13.0 T

Bpeak = 13.8 T


b3 = 110.3b5 = −19.1



Sensitivity analysis on multipoles• current is kept the same (I = 10.5 kA) • same iron configuration

case B1[T]

b3[/]

b5[/]

b7[T]

b9[T]

load line [%]

nominal 13.00 57.3 −20.1 0.7 −0.0 82.7

Dx = −1 mm all coil 13.06 53.1 −20.4 0.6 −0.1 83.7

Dx = +1 mm all coil 12.94 61.4 −19.8 0.7 0.1 82.4

Dy = −1 mm all coil 13.09 76.0 −17.5 1.6 0.2 83.6

Dy = +1 mm all coil 12.91 38.7 −22.8 −0.2 −0.2 82.1

insulation 100 mm 13.25 69.2 −22.1 0.3 −0.0 84.4



More / less turns?

case Bcenter[T]

I13 T[kA]

load line 4.2K [%]

Bss, 4.2 K[T]

b3[/]

b5[/]

140 turns 13.0 11.5 84.2 15.4 45.8 −22.0

148 turns 13.0 11.0 83.3 15.6 51.9 −21.0

156 turns (nom.) 13.0 10.5 82.7 15.7 57.3 −20.1

164 turns 13.0 10.1 82.1 15.8 62.0 −19.3

172 turns 13.0 9.8 81.6 15.9 66.0 −18.6

• current changed to reach 13 T in the bore• same midplane thickness • same iron configuration• the turns are added / subtract on the far sides



Different cable / strand?• HD2 naked cable dimensions used: 22.0 × 1.4 mm• but insulation kept at 200 mm• 51 strands 0.8 mm in diameter, but Cu/nonCu kept at 1.25 • same iron configuration (center blocks on top pole)• 188 turns instead of 156 (similar potted coil size)

• according to and with the above

assumptions, only the filling factor k has an effect• the filling factor changes slightly, for this HD2 (modified) case being about 2% lower than for the FRESCA2 cable• simulation confirms the guess: Bcenter = 13.0 T at I13 T = 8.7 kA 83.6 % load line @ 4.2 K, 15.5 T s. s. 4.2 K (instead of 15.7 T)• inductance increase significantly, L = 68.5 mH/m (+46%)

strong impact on k



Lorentz forces in 2D

13 T 1

3

2

4

Block Fx [MN/m]

Fy [MN/m]

Fx/w [MPa]

1 1.73 -0.00 792 1.65 -0.47 763 2.24 -1.15 1034 2.08 -2.18 95

total 7.70 -3.80 n. a.



Pressure in the bladders, 2D

opening of the yoke+

opening of the horiz. pad[mm]

friction coefficient betweeniron yoke and Al alloy shell

0.1 0.2 0.5 1.0

only top bladders(yoke / yoke) 246 + 0 230 + 0 190 + 0 143 + 0

only bottom bladders(yoke / horizontal pad) 199 + 40 188 + 40 159 + 39 129 + 38

all horizontal bladders 446 + 40 420 + 39 347 + 36 271 + 33

• for full prestress at 13 T, an horiz. interference of ≈ 700 mm is needed• add 100-200 mm for the clearance• interferences open for horizontal keys, pbladders = 10 MPa = 100 bar• wbladd = 75 mm (all the same)



Stresses in the structure, 2Dmaterial [MPa] warm cold 13 T

bottom pole Ti alloy seqv 270* 670* 600*

top pole ironseqv 240 560* 614*s1 15 25 50

horizontal pad steel seqv 120* 250* 315*

yoke ironseqv 280* 320* 345*s1 135 100 100

shell Al alloy seqv 75 200 205

* = corner value; seqv = Von Mises stress, s1 = 1st principal stress[ values computed in plane stress ]

They are all within the yield values of the various materials.

[At 15 T, about 33% more (pre)stress is needed.]



1

X

Y

Z


0

.556E+08

.111E+09

.167E+09

.222E+09

.278E+09

.333E+09

.389E+09

.444E+09

.500E+09

NODAL SOLUTION

STEP=2SUB =1TIME=2SEQV (AVG)DMX =.287E-03SMN =.268E+08SMX =.669E+09

1

X

Y

Z


0

.556E+08

.111E+09

.167E+09

.222E+09

.278E+09

.333E+09

.389E+09

.444E+09

.500E+09

NODAL SOLUTION


Stresses on top and bottom poles

cold cold, 13 T

seq

1

X

Y

Z


0

.556E+08

.111E+09

.167E+09

.222E+09

.278E+09

.333E+09

.389E+09

.444E+09

.500E+09

NODAL SOLUTION




1


0

.333E+08

.667E+08

.100E+09

.133E+09

.167E+09

.200E+09

.233E+09

.267E+09

.300E+09

NODAL SOLUTION

STEP=3SUB =1TIME=3SEQV (AVG)DMX =.934E-03SMN =326.63SMX =.314E+09

1


0

.333E+08

.667E+08

.100E+09

.133E+09

.167E+09

.200E+09

.233E+09

.267E+09

.300E+09

NODAL SOLUTION


Stresses on horizontal pad / rails

cold

seqcold13 T

1


0

.333E+08

.667E+08

.100E+09

.133E+09

.167E+09

.200E+09

.233E+09

.267E+09

.300E+09

NODAL SOLUTION




1


0

.333E+08

.667E+08

.100E+09

.133E+09

.167E+09

.200E+09

.233E+09

.267E+09

.300E+09

NODAL SOLUTION

STEP=2SUB =1TIME=2SEQV (AVG)DMX =.614E-03SMN =884774SMX =.307E+09

Stresses on vertical pad / platecold

seq

cold, 13 T

1


0

.333E+08

.667E+08

.100E+09

.133E+09

.167E+09

.200E+09

.233E+09

.267E+09

.300E+09

NODAL SOLUTION


1


0.333E+08

.667E+08.100E+09

.133E+09.167E+09

.200E+09.233E+09

.267E+09.300E+09

NODAL SOLUTION




Stresses on yoke, part 1cold

seq

cold, 13 T1


0.389E+08

.778E+08.117E+09

.156E+09.194E+09

.233E+09.272E+09

.311E+09.350E+09

NODAL SOLUTION

STEP=3SUB =1TIME=3SEQV (AVG)DMX =.001064SMN =.617E+07SMX =.346E+09

1


0.389E+08

.778E+08.117E+09

.156E+09.194E+09

.233E+09.272E+09

.311E+09.350E+09

NODAL SOLUTION


1


0.389E+08

.778E+08.117E+09

.156E+09.194E+09

.233E+09.272E+09

.311E+09.350E+09

NODAL SOLUTION




Stresses on yoke, part 2cold

s1

cold, 13 T1


0.111E+08

.222E+08.333E+08

.444E+08.556E+08

.667E+08.778E+08

.889E+08.100E+09

NODAL SOLUTION

STEP=3SUB =1TIME=3S1 (AVG)DMX =.001064SMX =.989E+08

1


0.111E+08

.222E+08.333E+08

.444E+08.556E+08

.667E+08.778E+08

.889E+08.100E+09

NODAL SOLUTION


1


0.111E+08

.222E+08.333E+08

.444E+08.556E+08

.667E+08.778E+08

.889E+08.100E+09

NODAL SOLUTION




Stresses on shellcold

seqv

cold, 13 T1


.100E+09.111E+09

.122E+09.133E+09

.144E+09.156E+09

.167E+09.178E+09

.189E+09.200E+09

NODAL SOLUTION


1


.100E+09.111E+09

.122E+09.133E+09

.144E+09.156E+09

.167E+09.178E+09

.189E+09.200E+09

NODAL SOLUTION


1


.100E+09.111E+09

.122E+09.133E+09

.144E+09.156E+09

.167E+09.178E+09

.189E+09.200E+09

NODAL SOLUTION




Dimensioning the yoke and the shell• avg. pressure 3rd layer coil / pole, for ix = 700 mm and iy = 300 mm • the (AA) shell thickness dictates the prestress increase at cold• steel doesn’t buy enough at cold aDT = 2.84 10∙ −3 vs. 4.02 10∙ −3

• stresses tend to go down when there is more material, and “real estate” is important

-60

-40

-20

0

20

40

60

80

100

120

30 mm Al 50 mm Al 70 mm Al 30 mm steel

p ave

,3[M

Pa]

ryoke400 mm

warm

cold

13 T

-60

-40

-20

0

20

40

60

80

100

120


p ave

,3[M

Pa]

ryoke450 mm

warm

cold

13 T

-60

-40

-20

0

20

40

60

80

100

120


p ave

,3[M

Pa]

ryoke500 mm

warm

cold

13 T

chosen



Stresses on the coil

warm cold 13 Tsx

1

X

Y

Z


-.150E+09-.133E+09

-.117E+09-.100E+09

-.833E+08-.667E+08

-.500E+08-.333E+08

-.167E+080

NODAL SOLUTION


1

X

Y

Z


-.150E+09-.133E+09

-.117E+09-.100E+09

-.833E+08-.667E+08

-.500E+08-.333E+08

-.167E+080

NODAL SOLUTION


1

X

Y

Z


-.150E+09-.133E+09

-.117E+09-.100E+09

-.833E+08-.667E+08

-.500E+08-.333E+08

-.167E+080

NODAL SOLUTION


1

X

Y

Z


-.150E+09-.133E+09

-.117E+09-.100E+09

-.833E+08-.667E+08

-.500E+08-.333E+08

-.167E+080

NODAL SOLUTION


top / bottom sliding

(friction 0.2)

top / bottom glued

1

X

Y

Z


-.150E+09-.133E+09

-.117E+09-.100E+09

-.833E+08-.667E+08

-.500E+08-.333E+08

-.167E+080

NODAL SOLUTION

STEP=3SUB =1TIME=3SX (AVG)RSYS=0DMX =.686E-03SMN =-.138E+09SMX =.342E+07

1

X

Y

Z


-.150E+09-.133E+09

-.117E+09-.100E+09

-.833E+08-.667E+08

-.500E+08-.333E+08

-.167E+080

NODAL SOLUTION


1

X

Y

Z


-.150E+09-.133E+09

-.117E+09-.100E+09

-.833E+08-.667E+08

-.500E+08-.333E+08

-.167E+080

NODAL SOLUTION


It’s the same, as the contact is “sticking”.



Alternative coil pack structure, 2D

iron

Ti alloy

potted coil

Al bronze

G10

steel

An inner steel support tube is

present.



Material properties for 2D analysis ! potted Nb3Sn coil [1]mptemp,1,4.3,293mpdata,ex,1,1,42000e6,30000e6mpdata,prxy,1,1,0.3,0.3mp,alpx,1,1.16E-5 !3.36e-3

! stainless steel [2]mptemp,1,4.3,293mpdata,ex,2,1,210000e6,193000e6mpdata,prxy,2,1,0.28,0.28mp,alpx,2,9.83E-6 !2.84e-3

! aluminum bronze [3]mptemp,1,4.3,293mpdata,ex,3,1,120000e6,110000e6mpdata,prxy,3,1,0.3,0.3mp,alpx,3,1.08E-5 !3.12e-3

! iron [4]mptemp,1,4.3,293mpdata,ex,4,1,224000e6,213000e6mpdata,prxy,4,1,0.28,0.28mp,alpx,4,6.82E-6 !1.97e-3

! aluminum [5]mptemp,1,4.3,293mpdata,ex,5,1,79000e6,70000e6mpdata,prxy,5,1,0.34,0.34mp,alpx,5,1.45E-5 !4.2e-3

! G10 [6]mptemp,1,4.3,293mpdata,ex,6,1,30000e6,30000e6mpdata,prxy,6,1,0.3,0.3mp,alpx,6,2.44E-5 !7.06e-3

! Nitronic 40 [7]mptemp,1,4.3,293mpdata,ex,7,1,225000e6,210000e6mpdata,prxy,7,1,0.28,0.28mp,alpx,7,0.90E-5 !2.6e-3

! titanium [8]mptemp,1,4.3,293mpdata,ex,8,1,120000e6,110000e6mpdata,prxy,8,1,0.3,0.3mp,alpx,8,6.25E-6 !1.8e-3



Lorentz forces in 3D


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