# Presentation: 947463

## Long racetrack supporting structuredesign and analysis

- Paolo Ferracin
- Review of the 1st LARP Long Racetrack (LRS01)
- LBNL
- April 24, 2006

## Outline

- Introduction
- General concept
- From SM to LR
- LR design features
- Assembly and pre-loading
- 2D and 3D magnetic analysis
- Peak field in the coil
- Magnet parameters
- Field in the ends
- 2D and 3D mechanical analysis
- Shell and coil stress
- Fabrication tolerance
- Yoke/shell and coil/island displacements
- Test plan
- Conclusions

- Paolo Ferracin

- 04/24/2006

## Introduction

- LR supporting structure
- Task goals
- Provide supporting structure for test of 4 m long racetrack coils
- Develop a shell-based supporting structure for long magnets
- Steps
- Design, procure the structure
- Define a procedure for assembly and disassembly
- Test structure at LBNL with dummy coils
- Check uniform load with
- Strain gauges mounted on the shell
- Pressure sensitive films
- Ship structure to BNL
- Design based on the support structure for the SM program

- Paolo Ferracin

- 04/24/2006

## Outline

- Introduction
-  General concept
- From SM to LR
- LR design features
- Assembly and pre-loading
- 2D and 3D magnetic analysis
- Peak field in the coil
- Magnet parameters
- Field in the ends
- 2D and 3D mechanical analysis
- Shell and coil stress
- Fabrication tolerance
- Yoke/shell and coil/island displacements
- Test plan
- Conclusions

- Paolo Ferracin

- 04/24/2006

- SM coil layout

- 2 coil modules
- 2 layers per module
- 21 turns per layer
- Iron island (pole)
- Horseshoe – end shoe
- “Common coil” configuration

- Paolo Ferracin

- 04/24/2006

## SM cross-section

- Aluminum shell
- Thickness: 12.7 mm
- Outer diameter: 240 mm
- Iron yokes
- Iron pads
- Stainless steel skins
- 2 bladders and 4 loading keys for assembly and pre-load

- Paolo Ferracin

- 04/24/2006

## From SM to LR

- Paolo Ferracin

- 04/24/2006

## LR cross-section

- Aluminum shell
- Larger diameter: 305 mm
- Thicker iron yokes
- Bigger yoke gaps
- Simplified iron pads
- Thicker stainless steel skins
- 2 bladders and 4 loading keys for assembly and pre-load
- 2 pull shims for bladder removal

- Paolo Ferracin

- 04/24/2006

## LR 3D design

- Aluminum shell
- Single piece
- Length:  3.6 m
- Iron yokes
- 50 mm thick laminations
- Iron pads
- Half length (1.8 m)
- Stainless steel skins
- Full length (3.6 m)
- Bladders
- Half length (1.8 m)
- Keys and shims
- Half length (1.8 m)

- Paolo Ferracin

- 04/24/2006

## AssemblyCoil-pad sub-assembly 

- Coils and skins are placed between two iron pads
- Pads are lightly bolted together

- Paolo Ferracin

- 04/24/2006

## AssemblyYoke-shell sub-assembly 

- The yoke halves are inserted in the shell
- The shell is lightly            pre-tensioned (gap keys)

**Gap keys**

**Load keys**

- Paolo Ferracin

- 04/24/2006

## Pre-load

- Coil-pad sub-assembly insertion
- Bladders insertion
- Bladders pressurization
- Gap key removal
- Load key shimming
- Bladders deflation and removal (with pull shim)

**Bladder location**

**Pull shim**

- Paolo Ferracin

- 04/24/2006

## Outline

- Introduction
- General concept
- From SM to LR
- LR design features
- Assembly and pre-loading
-  2D and 3D magnetic analysis
- Peak field in the coil
- Magnet parameters
- Field in the ends
- 2D and 3D mechanical analysis
- Shell and coil stress
- Fabrication tolerance
- Yoke/shell and coil/island displacements
- Test plan
- Conclusions

- Paolo Ferracin

- 04/24/2006

## 2D magnetic analysisFlux lines and peak field

- “Common-coil” (quadrupole) flux line profile
- Peak field located in the inner surface of the coil, approximately between turn 11 and turn 13.

- Paolo Ferracin

- 04/24/2006

## 2D magnetic analysisMagnet parameters

- Jc (4.2 K, 12 T) = 2800 A/mm2
- Cu/SC = 0.9
- Bpeak (4.2 K) = 12.2 T
- Iss (4.2 K) = 10.8 kA
- Stored energy (4.2 K) = 86 kJ/m
- Inductance (4.2 K) = 1.5 mH/m

- Paolo Ferracin

- 04/24/2006

## 3D magnetic analysisMagnetic model

- Iron parts
- Island, pad, key, yoke
- Straight section of 300 mm (twice as SM)

- Paolo Ferracin

- 04/24/2006

## 3D magnetic analysisField in the ends

- The field decreases from 12.2 T at the center to 11.6 T at the end of the straight section
- In the end region, the field further decreases to 11.0 T

- Paolo Ferracin

- 04/24/2006

## Outline

- Introduction
- General concept
- From SM to LR
- LR design features
- Assembly and pre-loading
- 2D and 3D magnetic analysis
- Peak field in the coil
- Magnet parameters
- Field in the ends
-  2D and 3D mechanical analysis
- Shell and coil stress
- Fabrication tolerance
- Yoke/shell and coil/island displacements
- Test plan
- Conclusions

- Paolo Ferracin

- 04/24/2006

## 2D mechanical analysisLorentz forces

- At short sample current
- Fx (quadrant) = + 1903 kN/m
- x = 62 MPa
- Fy (quadrant) =  - 9 kN/m
- y < 1 MPa

- Paolo Ferracin

- 04/24/2006

## 2D mechanical analysisShell pre-load

- After assembly
- 45 MPa
- After cool-down
- 175 MPa
- Force to the coil pack
- 2.2 kN (Fx = 1.9 kN)

- Paolo Ferracin

- 04/24/2006

## 2D mechanical analysisCoil pre-load

- After cooldown
- Force to the coil pack provided by
- Bladder operation (293 K)
- Aluminum shell (4.2 K)
- Thermal contraction
- Coil = 3.3 e-3
- SS rails = 2.8 e-3
- Iron pole = 2.0 e-3
- Most of the force to the rails and pole
- “Low pre-stress & rigid boundary” condition

- Paolo Ferracin

- 04/24/2006

## 2D mechanical analysisCoil horizontal stress

- After cool-down
- About 30 MPa coil pre-stress

- At full field
- 75 MPa of coil max. stress

- Paolo Ferracin

- 04/24/2006

## 2D mechanical analysisTolerance analysis

- Tolerance of the components
- Shell ID
- -0.000” / +0.0025”
- Yoke OD
- -0.003” / +0.000”
- Yoke key slot
- - 0.002”/ +0.002”
- Pad thickness
- -0.003” / +0.003
- Total range
- -0.008” / +0.008

- Paolo Ferracin

- 04/24/2006

## 2D mechanical analysisIron yoke tension

- Paolo Ferracin

- 04/24/2006

## 3D mechanical analysisMechanical model

- 3D geometry
- Full length
- Interaction between shell and yoke in the axial direction
- Straight section of 300 mm
- Effect of axial Lorentz forces on the contact area coil-island

- Paolo Ferracin

- 04/24/2006

## 3D mechanical analysisContraction of aluminum shell

- 4 m long shell
- Shell azimuthal stress at 4.3 K
-  = 150 MPa
- Frictionless model
- Shell *z* contraction = 9.5 mm
- (shell  lshell) + ( / Eshell    lshell)
- Yoke *z* contraction = 3.9 mm
- (yoke  lyoke)
- Relative z shell-yoke = 5.6 mm
- Friction model ( = 0.2)
- Shell *z* contraction = 5.7 mm
- Yoke *z* contraction = 4.2 mm
- Relative z shell-yoke = 1.5 mm

**Friction = 0.2**

**Friction = 0.0**

- Paolo Ferracin

- 04/24/2006

- 3D mechanical analysisLorentz forces

- At short sample current
- Fz (quadrant) = 20 kN
- z (straight sec.) = 40 MPa
- Comparison
- TQ
- Fz (quadrant) = 44 kN
- SQ
- Fz (quadrant) = 43 kN

- Paolo Ferracin

- 04/24/2006

## 3D mechanical analysisCoil-island contact region

- After cool-down
- Coil in axial tension because of different thermal contraction
- Coil = 2.7 e-3
- Iron pole = 2.0 e-3

- Paolo Ferracin

- 04/24/2006

## 3D mechanical analysisCoil-island contact region

- Frictionless model
- After cool-down
- Coil: z = + 20 MPa
- Island: z = - 50 MPa
- Fz contact = ~ 20 kN
- Still contact at high field

- Paolo Ferracin

- 04/24/2006

## 3D mechanical analysisCoil-island contact region

- Friction model
- After cool-down
- Fz contact = ~ 10 kN
- Friction is limiting axial motion
- Still contact at high field

- Paolo Ferracin

- 04/24/2006

## Outline

- Introduction
- General concept
- From SM to LR
- LR design features
- Assembly and pre-loading
- 2D and 3D magnetic analysis
- Peak field in the coil
- Magnet parameters
- Field in the ends
- 2D and 3D mechanical analysis
- Shell and coil stress
- Fabrication tolerance
- Yoke/shell and coil/island displacements
-  Test plan
- Conclusions

- Paolo Ferracin

- 04/24/2006

## Test plan

- Insertion of pressure sensitive films
- Dummy coils – skins
- Load keys – yoke/pads
- Strain gauges
- Mid-plane (both sides)
- 5 axial locations
*Y *and *Z *directions
- Temperature compensators
- Total: 40 gauges
- Pressurize bladders and insert keys in several steps
- Monitor stress level and uniformity
- Inspect pressure sens. films

- Paolo Ferracin

- 04/24/2006

## Outline

- Introduction
- General concept
- From SM to LR
- LR design features
- Assembly and pre-loading
- 2D and 3D magnetic analysis
- Peak field in the coil
- Magnet parameters
- Field in the ends
- 2D and 3D mechanical analysis
- Shell and coil stress
- Fabrication tolerance
- Yoke/shell and coil/island displacements
- Test plan
-  Conclusions

- Paolo Ferracin

- 04/24/2006

## Conclusions

- Design and analysis of the LR supporting structure
- Design
- Modifications implemented with respect to SM structure to facilitate assembly and increase rigidity
- Magnetic analysis
- Computation of peak field, load line, and field in the ends
- Mechanical analysis
- Low stress in the coil after cool-down and at high field
- Effect of fabrication tolerances within acceptable stress range
- Acceptable sliding between shell and yoke
- Coil in good contact with the island during excitation

- Paolo Ferracin

- 04/24/2006