Mechanical Design & Analysis Igor Novitski. Outlines Electromagnetic Forces in the Magnet Goals of Finite Element Analysis Mechanical Concept Description

Mechanical Design & Analysis

Igor Novitski


Outlines

• Electromagnetic Forces in the Magnet• Goals of Finite Element Analysis• Mechanical Concept Description• FEA Models • Material Properties• Magnet Components at Different Loads• End Plate Stress and Deformation• Summary13 May 2011, FNAL-CERN CM1 Igor Novitski 2


Electromagnetic Forcesin the Magnet

To reduce the probability of spontaneous quenches due to turn motion and stabilize the magnet field harmonics, it is necessary to ensure the mechanical stability of turns.

Turn mechanical stability is achieved by applying the prestress to the coil during magnet assembly and supporting the compressed coil during operation with a rigid support structure.

The required prestress value is determined by magnet design, nominal operating field and mechanical properties of structural materials.

Horizontal EM-force Fx/side at Inom=11.85kA, kN 9170 Vertical EM-force Fy/side at Inom=11.85kA, kN 4846 Longitudinal EM-force Fz/end at Inom=11.85kA, kN 455

13 May 2011, FNAL-CERN CM1 Igor Novitski 3


Goals of Finite Element Analysis

• ANSYS finite element (FE) 2D parametric models been created to analyze the mechanical characteristics of the dipole design at several magnet stages:o magnet assembly (collaring, yoking and skinning), o cool-down to operation temperature, and o excitation to the nominal current of 11.85 kA.

• The mechanical structure was optimized to keep coil under compression up to the maximum design field of 12 T and to maintain the coil stress below 160 MPa at all times, which is considered a safe level for brittle Nb3Sn coils.

• Stresses in all structural materials should be less than yield stress limit.



Mechanical Concepts


B C A

The 30-mm horizontal collar width is virtually the maximum possible in the available space between the two coils in the double-aperture configuration with two independent collared coils.

The 20-mm width is the minimal collar width determined by stress limits in the collar and key materials.


Titanium Poles withstress-relive slot

Phosphor Bronze KeyCS-Bump

controls Inner Yoke Gap

AL Clamp controlsOuter Yoke Gap

Uniform MP Shims

Stainless Steel Skin

Aluminum Clamp

Iron Yoke

Nb3SnCoil

Stainless SteelCollars

Coil mechanical support is provided by stainless collars, vertically split iron yoke, aluminium clamp and welded stainless steel skin.

Strong collars and iron yoke create the “rigidity belt” around Nb3Sn coil for conductor protection.

Coil midplane shims generate initial coil azimuthal prestress at collaring stage.

Skin and clamp tensions deform the iron, reduce the vertical collars spring-back and finalized coil compression.

Collar-yoke-clamp-skin interferences support horizontal LF action.

Magnet Mechanical Concept


Shims forinterference


Magnet Body FE Model• The 2D ANSYS parametric model of the dipole

includes the coil, the two layers of collars (front and lock-leg ), the key, the iron yoke, the clamp and the skin.

• The model has a quarter-symmetry.• The coil inner and outer layers, and interlayer

insulation are glued together.• The Ti coil poles freely separates from the coil. • The coil is surrounded by two layers of stainless

steel collars • Front and leg collars have symmetric boundaries

along X-axis (CP and CE equations simulate line motion).

• The phosphor bronze key locks collar laminations fixing the coil azimuthal prestress.

• Clamped iron yoke supports the collars, and the welded stainless steel skin restrains the iron yoke from outside.

The design components are represented with 4-node plane quadrilateral elements (PLANE 42). Material interfaces are modelled with contact elements (CONTACT 169-172).



End Plate FE Model• 3D ANSYS model for the end plate consists

of a 50-mm thick end plate welded to a 12.7-mm thick skin, with the skin length extended back to the 2D lead end cross section.

• One quarter symmetry is used in the model.

• The end plate consists of two mechanically connected concentric rings with a central round hole for the magnet beam pipe and four holes for the instrumented bullets in the innermost ring, and four round cooling holes in the ring attached to the skin.

• The Lorenz force in one quadrant was applied in the location of the bullet hole.

The design components are represented with 8-node elements (SOLID 95) with contact elements (CONTACT 170-174).



0

20

40

60

80

100

120

140

160

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

Strain

Str

ess,

MP

a

4.2 K300 K300K: Monotonic Loading

0

10

20

30

40

50

60

70

80

90

100

0 0.001 0.002 0.003 0.004 0.005 0.006

Strain

Str

ess,

MP

a

Parameter unit 2D Model Straight section 293 K 4.3 K Ey – Azimuthal direction GPa 44 44 Ex – Radial direction GPa 44 55 x E-3 2.6 y E-3 3.5

Coil data from HFM dipole programs Load-Unload-Reload TestsCyclic Loading Tests

44GPa

Structural element

Material

Thermal contraction (300-2 K),

Elasticity modulus, GPa

Yield stress, MPa

mm/m warm cold warm cold Clamp 7075-T6 4.1 70 85 460 650 Pole blocks Ti-6Al-4V 1.7 115 125 650 >900 Collar 316LN 2.7-2.9 190 210 520 850 Key Phosphor Bronze 3.3 110 123 380 >500 Yoke Soft Iron 2.05 205 225 180-305 >600 Skin 304L 2.9 190 210 240 600

Material Properties



Coil Stress DistributionAfter Collaring After Skin Welding After Cooling Down, 300-2K

After 11T, 2K After 12T, 2K


Avg.=28MPa

41

8959

49 85 99

113 129 135124

23

2

91

86

53 26 66

35

12

Max Seqv.=77MPa

118 148

144 146


Coil Stress Coil average stress, MPa Inner pole Outer pole Inner midplane Outer midplane Collaring 28 41 53 26 Assembly 89 59 49 85 Cooldown 91 86 66 99 Inom=11.85 kA 12 35 113 129 Bmax=12 T 2 23 124 135

The expected prestress variation with respect to the nominal coil prestress at the 50 m azimuthal coil size variation is within 10 MPa in the inner layer and within 23 MPa in the outer layer.

Analysis shows that at the maximum design field of 12 T the minimal coil prestress in pole regions is 2-23 MPa.

The maximum coil prestress at room temperature does not exceed 160 MPa, which is acceptable for the Nb3Sn cable and coil insulation.



Poles StressAfter Collaring After Skin Welding After Cooling Down, 300-2K

After 11T, 2KAfter 12T, 2K


Max Seqv.=133MPa

510 588

128 136


Collar Stress

After Collaring

After Skin Welding

Lock and Leg CollarsFront Collar


Max Seqv.=527MPa 490

413

339


Collar Stress

After Cooling Down, 300-2K

After 11T, 2K



Max Seqv.=562MPa

469

476 397


Collar Stress

After 12T, 2K



Max Seqv.=494MPa

401


Key StressAfter Collaring After Skin Welding After Cooling Down, 300-2K



Max Seqv.=362MPa 133 124

185 202


Iron Yoke StressAfter Skin Welding After Cooling Down, 300-2K



Max Seqv.=351MPa

455

362 387


Clamp StressAfter Skin Welding After Cooling Down, 300-2K



Max Seqv.=261MPa

287

282 281


Skin Stress

After Skin Welding After Cooling Down, 300-2K



Max Seqv.=365MPa

489

498 499

Avg.=170MPa 266

269 270


Structure Maximum Stress

Maximum stress, MPa

Inner/outer poles Collar Key Yoke Al clamp Skin/avg/max

Collaring 133/90 527 362 n/a n/a n/a

Assembly 510/180 412 132 351 261 170/365

Cooldown 588/263 562 124 455 287 266/489

Inom=11.85 kA 100/128 476 184 362 282 269/498

Bmax=12 T 50/136 494 202 387 281 270/500

The maximum stress in the collars and compression in the iron yoke achieves the material yield stress in small regions near key grooves and iron yoke corner (model singularities, mesh size).

To minimize the stress concentrations, the key grooves and iron corners have been rounded.

All stress values are below yield stress of corresponding materials.13 May 2011, FNAL-CERN CM1 Igor Novitski 20

Mechanical Design & Analysis 13 May 2011, FNAL-CERN CM1 Igor Novitski 21

Skin Welding


Cooling Down and LF action


Coil IR deflections Magnet cross-section is deformed due to the coil prestress, cool-down and Lorentz

forces action. Bore deflections from the warm unstressed round geometry (magnetic design) calculated for the above mentioned effects at room and helium temperatures in the dipole straight section are summarized below:


Bore radial deflection, m Pole Midplane 45 degree Collaring 58 -11 58 Assembly 87 -122 13 Cooldown -21 -240 -96 Inom=11.85 kA -51 -163 -74 Bmax=12 T -57 -149 -70

As it follows from the above data, at the nominal operating current of 11.85 kA the radial cross-section deflection from the magnetic design in the magnet midplane is ~165 m.


End PlateDeformation and Stress

• The 50-mm end plate deflection and coil end motion under the nominal LF is about 75 m.

• The maximum stress in the end plate is 160 MPa. • Taking into account that usually only 20% of the Lorentz force is

transferred to magnet end plates, the coil end motion is even smaller.



End Plate Load


Summary• ANSYS analysis of the mechanical structure of the demonstrator dipole

model shows:o chosen mechanical design provides the coil prestress required for the

operating current range with sufficient margin; o design reliably restricts turn radial, azimuthal and longitudinal motion under

the Lorentz forces up to 12T;o the maximal mechanical stresses in the major elements of coil support

structure are below the limits for the materials used.• The mechanical design, structural materials and components, coil collaring

and cold mass assembly procedures will be experimentally studied and further optimized using instrumented mechanical models. The results of experimental studies of mechanical models and measurements during demonstrator dipole test will be compared with the described ANSYS analysis.


Documents

Mechanical Design & Analysis Igor Novitski. Outlines Electromagnetic Forces in the Magnet Goals of Finite Element Analysis Mechanical Concept Description