1. Mechanical Design & Analysis Igor Novitski

2. 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 Summary 13 May 2011, FNAL-CERN CM1Mechanical Design & AnalysisIgor Novitski 2

3. Electromagnetic Forces in 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. 13 May 2011, FNAL-CERN CM1Igor Novitski 3Mechanical Design & Analysis

4. 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 Nb 3 Sn coils. Stresses in all structural materials should be less than yield stress limit. 13 May 2011, FNAL-CERN CM1 Igor Novitski 4Mechanical Design & Analysis

5. Mechanical Concepts 13 May 2011, FNAL-CERN CM1Mechanical Design & AnalysisIgor Novitski 5 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.

6. Titanium Poles with stress-relive slot Phosphor Bronze Key CS-Bump controls Inner Yoke Gap AL Clamp controls Outer Yoke Gap Uniform MP Shims Stainless Steel Skin Aluminum Clamp Iron Yoke Nb 3 Sn Coil Stainless Steel Collars 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 Nb 3 Sn 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 13 May 2011, FNAL-CERN CM1 Igor Novitski 6Mechanical Design & Analysis Shims for interference

7. 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). 13 May 2011, FNAL-CERN CM1 Igor Novitski 7Mechanical Design & Analysis

8. 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). 13 May 2011, FNAL-CERN CM1 Igor Novitski 8Mechanical Design & Analysis

9. Coil data from HFM dipole programs Load-Unload-Reload TestsCyclic Loading Tests  GPa Material Properties 13 May 2011, FNAL-CERN CM1Igor Novitski 9Mechanical Design & Analysis

10. Coil Stress Distribution After CollaringAfter Skin WeldingAfter Cooling Down, 300-2K After 11T, 2K After 12T, 2K 13 May 2011, FNAL-CERN CM1 Igor Novitski 10Mechanical Design & Analysis Avg.=28MPa 41 89 59 498599 113129135124 23 2 91 86 532666 35 12 Max Seqv. =77MPa 118148 144146

11. Coil Stress 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 Nb 3 Sn cable and coil insulation. 13 May 2011, FNAL-CERN CM1 Igor Novitski 11Mechanical Design & Analysis

12. Poles Stress After CollaringAfter Skin WeldingAfter Cooling Down, 300-2K After 11T, 2K After 12T, 2K 13 May 2011, FNAL-CERN CM1 Igor Novitski 12Mechanical Design & Analysis Max Seqv. =133MPa 510588 128136

13. Collar Stress After Collaring After Skin Welding Lock and Leg CollarsFront Collar 13 May 2011, FNAL-CERN CM1 Igor Novitski 13Mechanical Design & Analysis Max Seqv. =527MPa 490 413 339

14. Collar Stress After Cooling Down, 300-2K After 11T, 2K Lock and Leg CollarsFront Collar 13 May 2011, FNAL-CERN CM1 Igor Novitski 14Mechanical Design & Analysis Max Seqv. =562MPa 469 476397

15. Collar Stress After 12T, 2K Lock and Leg CollarsFront Collar 13 May 2011, FNAL-CERN CM1 Igor Novitski 15Mechanical Design & Analysis Max Seqv. =494MPa 401

16. Key Stress After CollaringAfter Skin WeldingAfter Cooling Down, 300-2K After 11T, 2K After 12T, 2K 13 May 2011, FNAL-CERN CM1 Igor Novitski 16Mechanical Design & Analysis Max Seqv. =362MPa 133124 185202

17. Iron Yoke Stress After Skin WeldingAfter Cooling Down, 300-2K After 11T, 2KAfter 12T, 2K 13 May 2011, FNAL-CERN CM1 Igor Novitski 17Mechanical Design & Analysis Max Seqv. =351MPa 455 362387

18. Clamp Stress After Skin WeldingAfter Cooling Down, 300-2K After 11T, 2KAfter 12T, 2K 13 May 2011, FNAL-CERN CM1 Igor Novitski 18Mechanical Design & Analysis Max Seqv. =261MPa 287 282281

19. Skin Stress After Skin WeldingAfter Cooling Down, 300-2K After 11T, 2KAfter 12T, 2K 13 May 2011, FNAL-CERN CM1 Igor Novitski 19Mechanical Design & Analysis Max Seqv. =365MPa 489 498499 Avg.=170MPa266 269270

20. Structure Maximum Stress Maximum stress, MPa Inner/outer polesCollarKeyYokeAl clampSkin/avg/max Collaring133/90527362n/a Assembly510/180412132351261170/365 Cooldown588/263562124455287266/489 I nom =11.85 kA100/128476184362282269/498 B max =12 T50/136494202387281270/500 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 20Mechanical Design & Analysis

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

22. 13 May 2011, FNAL-CERN CM1 Igor Novitski 22Mechanical Design & Analysis Cooling Down and LF action

23. 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: 13 May 2011, FNAL-CERN CM1Mechanical Design & Analysis Igor Novitski 23 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.

24. End Plate Deformation 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. 13 May 2011, FNAL-CERN CM1 Igor Novitski 24Mechanical Design & Analysis

25. 13 May 2011, FNAL-CERN CM1 Igor Novitski 25Mechanical Design & Analysis End Plate Load

26. 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. 13 May 2011, FNAL-CERN CM1 Igor Novitski 26Mechanical Design & Analysis