cable inventory, relative measurements and 1 st mechanical computations study of the quadrupole...

Cable inventory, relative measurements and 1st mechanical computationsSTUDY OF THE QUADRUPOLE COLLAR

STRUCTURE

P. Fessia, F. RegisMagnets, Cryostats and Superconductors Group

Accelerator Technology Department, CERN

Summary

Scaling collar thickness on existing magnets (MQXB, MQ)Azimuthal stress in function of aperture and collar thickness (analytical approach)Key dimensioning:

1 key2 keyKey angular position optimization (FEM)

FEM computation on 120 and 130 mm aperture quads

Scaling collar thickness on existing magnets (MQXB, MQ)Azimuthal stress in function of aperture and collar thickness (analytical approach)Key dimensioning:

1 key2 keyKey angular position optimization (FEM)

FEM computation on 120 and 130 mm aperture quads

40 60 80 100

0

500

1000

1500

2000

2500

A p e rtu re ra d iu s m m

For

ces

NmN b T i, k 0 .2 5

w 4 5 .3 m m

w 3 0 .2 m m

w 1 5 .1 m m

1386N/mm

Horizontal forces per octant

For

ces

[N/m

m]

40 60 80 100

20

40

60

80

100

A p e rtu re ra d iu s m m

Col

lar

thic

knes

smm

N b T i, k 0 .2 5

w 4 5 .3 m m

w 3 0 .2 m m

w 1 5 .1 m m

COLLAR Scaling based on MQXB

Aperture radius [mm]

Collar thickness [mm]

55 35

60 39

65 42

Scaling based on radial collar displacementThe collar width is obtained by solving:

40 60 80 100

20

40

60

80

100

A p e rtu re ra d iu s m m

Col

lar

thic

knes

smm

N b T i, k 0 .2 5

w 4 5 .3 m m

w 3 0 .2 m m

w 1 5 .1 m m

Aperture radius [mm]

Collar thickness [m]

55 45

60 49

65 65

COLLAR Scaling based on MQ

Collar scaling - Conclusions

Horizontal magnetic forces increase with the apertureScaling collar thickness on MQ radial displacement is more conservativeFor 130mm aperture the collar thickness is between 42 (MQXB) and 65 mm (MQ). For 120mm aperture the collar thickness is between 39 (MQXB) and 49 mm (MQ).

Scaling collar thickness on existing magnets (MQXB, MQ)Azimuthal stress in function of aperture and collar thickness (analytical approach)Key dimensioning:

1 key2 keyKey angular position optimization (FEM)

FEM computation on 120 and 130 mm aperture quads

Azimuthal stress on mid plane

Mid-plane stress due to Lorentz forces for different apertures and coil thickness Based on sector coil approach at SS current density (LHC MQ cable 02).

Reference line: w=30mm

Azimuthal stress on mid plane

For small apertures, larger w and larger Gc correspond to a saturation of the stress valuesFor very large apertures, the stress decrease is due to a non effective cable add-on

1. Average stress after powering ~ 25 Mpa

.. fsmagCD 2. After Cool Down:

cwcc

cwmag E

E

Efs ..03. After Collaring:

Estimation of stress on pole

The stress on pole at each step of magnet life cycle has been analitycally estimatedAfter powering a specific residual stress must be envisagedWe use a safety margin of 25 MPa The stress after powering has been computed averaging the stress distribution on mid plane

2 0 3 0 4 0 5 0 6 0

5 5

6 0

6 5

7 0

7 5

C o lla r w id th w c o ll m m

MPa

P O W E R IN G P R E S S U R E O N M ID P LA N E

ri 6 7 .5 m mri 6 5 m mri 6 2 .5 m mri 6 0 m mri 5 7 .5 m mri 4 5 m mri 3 5 m m

stress on pole - powering

2 0 3 0 4 0 5 0 6 0

9 4

9 6

9 8

1 0 0

1 0 2

C o lla r w id th w c o ll m m

MPa

P R E S S U R E O N P O LE A F T E R C O O L D O W N

ri 6 7 .5 m mri 6 5 m mri 6 2 .5 m mri 6 0 m mri 5 7 .5 m m

stress on pole – cool down 1.9K (s.f. 25MPa)

2 0 3 0 4 0 5 0 6 0

8 0

8 5

9 0

9 5

1 0 0

C o lla r w id th w c o ll m m

MPa

P R E S S U R E O N P O LE A F T E R C O LLA R IN G

ri 6 7 .5 m mri 6 5 m mri 6 2 .5 m mri 6 0 m mri 5 7 .5 m mri 4 5 m mri 3 5 m m

stress on pole – collaring 1.9K (s.f. 25MPa)

Azimuthal stress - Conclusions

Analytical approach based on a pure 30 ⁰ sector coil shows that the increase of aperture between 112 mm and 135 mm increases the average azimuthal stress only of few MPaThe required level of pre-stress at warm seems to be near to Apical creep limit (SS current and 25MPa safety margin)Azimuthal forces slightly increases with collar thickness (saturation effect to be checked)

Scaling collar thickness on existing magnets (MQXB, MQ)Azimuthal stress in function of aperture and collar thickness (analytical approach)Key dimensioning:

1 key2 keyKey angular position optimization (FEM)

FEM computation on 120 and 130 mm aperture quad

MQXB

MQM

Some Collar keys layouts

MQYMQ

MQM: 4 key layout (1 per quadrant)MQ-MQXB-MQY: 8 key layout (2 per quadrant)

2 0 3 0 4 0 5 0 6 0

1 2 0 0

1 3 0 0

1 4 0 0

1 5 0 0

1 6 0 0

1 7 0 0

1 8 0 0

C o lla r w id th w c o ll m m

rorCos

d Nmm

ri 6 7 .5 m mri 6 5 m mri 6 2 .5 m mri 6 0 m mri 5 7 .5 m m

Horizontal forces

xri Fdwr cos

Key reaction force – 1 key layout

Rk,coll slightly increases with collar width after collaringNo significant variation between 115 and 135 mm apertures (~0.1%) during collaringRk,mag follows Fx trend

Rk,mag / Rk,coll > σyc/σyw

Key dimensioning can be done by assuming the smallest collar after powering (most conservative case)

2 0 3 0 4 0 5 0 6 0

6

7

8

9

1 0

1 1

C o lla r w id th w c o ll m m

Key

wid

thmm

K e y d im e ns io n b a s e d o n V o nM is e s c rite rio n

ri 6 7 .5 m mri 6 5 m mri 6 2 .5 m mri 6 0 m mri 5 7 .5 m mri 4 5 m mri 3 5 m m

Key dimensioning - compression

The VonMises stress is used to predict yielding of materials under any loading condition from results of simple uniaxial tensile tests. A material is said to start yielding when its VonMises stress reaches a critical value known as the yield strenght Rp0.2

5.0223

213

2122

2 e

α

Key layout analysis

0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

K e y a ngle ra d

Rk

MA

GNmm

K e y re a c tio n c o m p a ris o n

S ingle k e y

D o u b le k e y

24 degrees15 degrees

Forces repartition on keys according to 1key or 2key layout per quadrant structure

Key layout analysis

2 0 3 0 4 0 5 0 6 03 .5

4 .0

4 .5

5 .0

5 .5

6 .0

6 .5

7 .0

C o lla r w id th w c o ll m m

Key

wid

thmm

K e y d im e ns io n b a s e d o n V o nM is e s c rite rio n

ri 6 7 .5 m mri 6 5 m mri 6 2 .5 m mri 6 0 m mri 5 7 .5 m mri 4 5 m mri 3 5 m m

2 0 3 0 4 0 5 0 6 06

7

8

9

1 0

1 1

1 2

C o lla r w id th w c o ll m m

Key

wid

thmm

K e y d im e ns io n b a s e d o n V o nM is e s c rite rio n

ri 6 7 .5 m mri 6 5 m mri 6 2 .5 m mri 6 0 m mri 5 7 .5 m mri 4 5 m mri 3 5 m m

2 Keys at 10 degrees

2 Keys at 25 degrees

Coil radial displacement in function of the angular distance between keys130mm aperture and 35mm thick collar

Key layout analysis

0

10

20

30

40

50

60

70

80

0.0 5.0 10.0 15.0 20.0 25.0 30.0

key angle (deg)

δr (

µm

)

δr_pt10

δr_pt11

Key analysis - Conclusions

Horizontal forces decreases with collar thickness (saturation effect to be checked)The key dimension can be defined at the smaller collar thicknessThe used criteria is compression because pure shear is second orderFactor 2 coefficient safety margin has been used to take into account possible tolerance effect and collar indentationDimensioning done with phosphor bronze. Reduction of plasticization zone achievable only with different material 2 keys at 15 degrees provide a stiffer structure and lower force on each key. With key at 15 ⁰ we get a structure 15% more rigid then with keys at 5 ⁰

Scaling collar thickness on existing magnets (MQXB, MQ)Azimuthal stress in function of aperture and collar thickness (analytical approach)Key dimensioning:

1 key2 keyKey angular position optimization (FEM)

FEM computation on 120 and 130 mm aperture quads

δr = δrmag - δrCD

The thicker the collar the lower is the bending effect on coil120 mm shows lower displacement due to a more rigid structure and lower e.m. forces

FE analysis – radial displacement

0

20

40

60

80

100

120

140

15 20 25 30 35 40 45 50

collar w (mm)

δr

(m m)

120_δr_pt10

120_δr_pt11

130_δr_pt10

130_δr_pt11

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

15 20 25 30 35 40 45 50

collar w (mm)

σy

(MP

a)

T=293K

T=1.8K

T=1.8K+powering

Inner Layer: σ8-σ7

The bending effect on coil can be looked as the difference in stress on upper coil edge

FE analysis – bending effect

=130mm I.L.

-40.0

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

15 20 25 30 35 40 45 50

collar w (mm)

σy

(MP

a)

T=293K

T=1.8K

T=1.8K+powering

Inner Layer: σ8-σ7

FE analysis – bending effect

=120mm I.L.

The bending effect on coil can be looked as the difference in stress on upper coil edge

-80.0

-60.0

-40.0

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

15 20 25 30 35 40 45 50

collar w (mm)

σy

(MP

a)

T=293K

T=1.8K

T=1.8K+powering

Outer Layer: σ12-σ11

FE analysis – bending effect

=130mm O.L.

The bending effect on coil can be looked as the difference in stress on upper coil edge

-80.0

-60.0

-40.0

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

120.0

15 20 25 30 35 40 45 50

collar w (mm)

σy

(MP

a)

T=293K

T=1.8K

T=1.8K+powering

Outer Layer: σ12-σ11

FE analysis – bending effect

=120mm O.L.

The bending effect on coil can be looked as the difference in stress on upper coil edge

FE analysis – collar thickness

ApertureCollar thickness, δr = 60mm

Collar thickness δr=60mm,key MQXB

Estimated collar thickness MQXB scaling

Proposed collar thickness (key15º)

120mm 33mm 35-37mm 39mm 35mm

130mm 36mm 38-40mm 42mm 38mm

FE analysis – stress on collar

The VonMises stress has been verified at each step of magnet cycle.σmax has been compared to Rp0.2/s.f., where safety factor is 1.5

Collars made of YUS130 steel: Rp0.2 (293K)=445MPa, Rp0.2(4.2K)=1360MPa

120mm 130mm

Equivalent stress on collar – 20mm

120mm 130mm

Equivalent stress on collar – 35mm

120mm 130mm

Equivalent stress on collar – 45mm

120mm 130mm

FE analysis - Conclusions

Displacements are lower for 120mm, due to a more rigid structure and lower magnetic forcesSince a rectangular shim is used, the higher the inclination angle of I.L. pole, the higher the σφ.

θI.L. is 36º (120mm) vs. 29.3º (130mm). On the O.L. this effect is much lower (same θ=21.5º)A first estimation of the collar thickness is proposed, based on MQXB scalingFor 120mm, a collar thickness of 35mm can be proposedFor 130mm, a collar thickness of 38mm can be proposedNo relevant differences in stress distribution on collar