Hybrid Structure with Cooling John Cozzolino LARP Collaboration Meeting Port Jefferson, NY November 4-6, 2009

Outline Basic Design Features 2-D Magnetic Analysis – Compute Lorentz forces in coil at 200 T/m flux gradient 2-D Mechanical Analyses – Determine maximum coil azimuthal pre-stress sustained by collar – Study stresses and deflections during assembly and operation Determine necessary bladder pressure and yoke shim sizes Check critical gaps, clearances and stops, as well as coil and shell stresses Note spring-back loss of coil stress after yoke shim installation Note cool-down effects on coil stress and shell stress Check coil pre-stress loss at pole due to Lorentz forces during full power Determine coil mid-plane horizontal deflection from 0 -> 200 T/m Conclusions Recommendations and Remaining Tasks 11/04/2009 John Cozzolino2

Basic Design Features 7000-Series Aluminum Collar (450 MPa yield strength) – Alternating RH and LH laminations joined into pairs with press-fitted pins (spot welding not an option with this grade of aluminum). – Single tapered collaring key per quadrant – Mid-plane stop to prevent over-compressing coil during yoke assembly – Titanium pole inserts Laminated inner and outer iron yoke – Large slots for bladders – Alignment key in-line with coil pole – Large helium bypass hole 25mm thick Aluminum shell 10mm thick stainless steel shell (not modeled here) 11/04/2009 John Cozzolino3

2-D Magnetic Analysis 11/04/2009 John Cozzolino4 Large Bypass Hole Yoke Alignment Key Bladder Slot Outer Yoke Aluminum Shell Area PlotCoil Nodal Force Vector Plot

2-D Magnetic Analysis – (cont’d) 11/04/2009 John Cozzolino Tesla Magnetic Flux Contour Plot

2-D Mechanical Analysis (Collared Coil) 11/04/2009 John Cozzolino Tesla Azimuthal Coil Stress during Collaring Maximum Azimuthal Coil Stress at Inner Coil Pole = 50 MPa Note: Actual coil stress per unit length is ½ of this due to interlocking collar design

2-D Mechanical Analysis (Collared Coil) – cont’d 11/04/2009 John Cozzolino7 Maximum collar Key Lug Stresses (Von Mises) during Collaring

2-D Mechanical Analysis (full C.S.) 11/04/2009 John Cozzolino8 ANSYS Element Plot for Mechanical FEM 2-D 8 or 6-node structural solid elements as well as contact elements at interfaces Friction coeff. = 0.2 Five load steps: 1 – Collared (baseline) 2 - Full Bladder Pressure 3 - Yoke shims installed – bladders off 4 - Cool-down to 4.3K 5 - Power to 200 T/m peak flux gradient

2-D Mechanical Analysis (full C.S.)- cont’d 11/04/2009 John Cozzolino9 Material Properties

2-D Mechanical Analysis (full C.S.)- cont’d 11/04/2009 John Cozzolino10 Step 1: Collared Coil in Iron – Warm Without Yoke shims Coil stress = 22 MPa

2-D Mechanical Analysis (full C.S.)- cont’d 11/04/2009 John Cozzolino11 Step 2 – Full Bladder Pressure applied (47 MPa)

2-D Mechanical Analysis (full C.S.)- cont’d 11/04/2009 John Cozzolino12 Step 3 – Insert Shims, Remove Bladder Pressure Pole shim:.48 mm Middle shim:.84 mm Mid-plane shim: 1.08 mm

2-D Mechanical Analysis (full C.S.)- cont’d 11/04/2009 John Cozzolino13 Step 4 – Cool-Down to 4.3K Lateral Coil Defl MPa

2-D Mechanical Analysis (full C.S.)- cont’d 11/04/2009 John Cozzolino14 Step 5 – Apply Current to reach 200 T/m peak flux gradient Lateral coil defl. (tension)

2-D Mechanical Analysis (full C.S.)- cont’d 11/04/2009 John Cozzolino15 Summary of Shell and Coil Stresses During Assembly and Operation (tension)

Conclusions FE analysis results indicate that this design has merit – At no point during assembly and operation do coil azimuthal stresses exceed 200 MPa. – At no point during assembly and operation does the bearing stress at the collar mid-plane stop reach yield (with relief set at.1mm). – Collar strength is adequate (based on lug stresses). – Non-uniform yoke shimming yields the best results (assuming an insertion clearance of.13mm). – The innermost portion of the inner coil pole goes into tension (27 MPa) at full power. – Coil lateral deflection is 100 microns outward at the mid-plane Due to strain, not clearance take-up Bladder Pressure is manageable (47 MPa {6800 psi}. 11/04/2009 John Cozzolino16

Recommendations and Remaining Tasks This design requires further optimization – Perform a complete analysis of the collars including the press-fit structural shear pins – Look at possible ways to reduce lateral movement of the coil at the mid- plane – Further investigate using a stainless steel inner shell in place of aluminum. Eliminates the need for a separate inner shell So far, this has not been successful – Attempt to reduce coil tension against the pole Increase collaring pre-stress – Consider replacing tapered collaring key with a stainless steel clamp (i.e., “keeper”) » Eliminates the 50% loss of pre-stress due to interlocking lugs » Eliminates the need for shear pins 11/04/2009 John Cozzolino17