in 14 T Nb 3 Sn Solenoid of 08 m IR and 10 m OR amp Half Length Bob Weggel 10710 Hoop stress σ Bjr B j coil r if each turn supported its own Lorentz force Range 235 MPa ie compression to 926 MPa ID: 574008
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Slide1
Stresses and Deformationsin 14 T Nb3Sn Solenoid of 0.8 m I.R. and 1.0 m O.R. & Half Length
Bob Weggel
10/7/10Slide2
Hoop stress,
σ
Bjr
= B jcoil r,if each turn supported its own Lorentz forceRange −235 MPa (i.e., compression) to +926 MPaAlso, contour lines Bz =14 T & 15 T
Cross section of upper half of Nb
3
Sn magnet with 0.8 m I.R. and 1 m O.R. & half length
Current density
j
coil
= 74.93 A/m
2
; central field B(r=0, z=0) = 14 T Slide3
1st principal stress, σφ, with isotropic winding packRange = 250 to 476
Mpa
,
51% the peak σBjr stress Slide4
2nd principal stress, σrMaximum magnitude ≡
σ
max
= 28 MPa, compressionSlide5
3rd principal stress, σz σ
max
= 198 MPa, compression
. Slide6
Von Mises ductile-material yield criterion,σvM ≡ sqrt{½ [(σ
φ
−σ
r)2 + (σφ−σz)2 + (σr−σz2)]}Range = 250-598 MPa, 65% of the peak σBjr stressSlide7
Deformation, exaggerated tenfold, with isotropic winding pack of100 GPa Young’s modulus Range:
2.63-3.42 mm