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12.0 Bellows Design

There are four areas where bellows are employed to allow thermal differential contraction, and to add thermal conduction length. All of these will be specified in terms of required operating pressure, and lateral and axial displacements. The stress analyses presented in this section are intended to be an “existence proof” for the bellows space allocation. The CVIP consulted with the bellows manufacturer for appropriate convolution details, and the manufacturer provided qualifications of the bellows designs in accordance with the EJMA standards.

Table of Bellows Specifications Revision 2: Item # Location Operating

Pressure Axial Displacement

Lateral Displacement

Axial temp Gradient

Material

BNL-002 #27

End of Bore Jacket

Vacuum 3mm 1 mm (Radial) 30K-292K

316 SST

BNL-002 #24

Cover end of Vacuum Jacket

Vacuum 3mm 1 mm(Radial) 30K-292K

316 SST

BNL-002 #30

Leads (Normal Operation)

15 atm 0.7 mm .25mm 30K-292K

316 SST

BNL-002 #30

Leads (extreme Thermal Differential)

15 atm 3mm 1mm 30K-292K

316 SST

BNL-002 #40

Gravity Support Pads

Vacuum ~2mm 2.2mm Only 292K

304 or 316 SST

BNL-002 #21

He/LN Outlet 15 atm ~2mm 2mm ~0 K 316 SST

All bellows have a critical pressure at which they become unstable. Instability can occur in either of two modes, column instability (or squirm), or inplane deformation of the convolution side wall.

Squirm is the phenomena whereby the centerline of a straight bellows develops a sideways or lateral bow.

The critical pressure at which this instability occurs is a direct function of the diameter and spring rate, and an inverse function of the length. If the bellows is bent, or angulated, the centerline can begin to move away from the center of curvature. In each case, the effective length of the bellows increases, lowering the material available to withstand the pressure, thereby increasing the hoop stresses. As the length increases, the tendency to squirm increases and the stresses become higher and higher until catastrophic failure occurs. A simple way to visualize this phenomena is to remember that the bellows is a

Cryostat Simulation Showing Axial Displacements near Bellows

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cylinder of given volume. Internal pressure tries to increase a vessel's volume. Since a bellows is flexible in the axial direction, it can increase its volume by increasing the length of its centerline. With the ends fixed, it does so by simulating the appearance of a buckling column. In the BNL Pulsed Magnet, bellows “squirm” is stabilized with tension rods for the lead and LHe/LN2 bellows.

Bellows materials are specified as 316 for sub- LN2 temperature service, and 304 for RT service. Room temperature yields of highly cold worked materials should be in the range of 500 MPa for 316 and 1000 MPa for 304. All the bellows must see their pressure service at room temperature. The gravity support bellows worst loading is due to a lateral displacement due to cryostat contraction.

.Gravity support bellows, Stress due to cooldown. 008” thick stock. 4.0 inches in inner diameter, 6mm convolution pitch with 2.5mm flats, 2.2mm lateral displacement due to cryostat cooldown.

Bellows Displacement during Vacuum Test.

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Repaired Bellows?

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Joint and LN2/He Bellows. These bellows must accept the axial differential thermal motions between the 30 K cryostat and the magnet. Nominally this is the difference between cryostat, and the coil at 100K. Both Copper and Stainless Steel have coefficients near 10e-6, and the magnet/cryostat assembly is about 1 m. long. The intention is to have the plenum inlet side of the magnet and plenum to be held to the same displacement via spacer blocks, and the joint end of the magnet is spaced off the cover with a Belleville spring stack. The differential displacements thus appear in the joint bellows. Nominal differential motion is 1m*10e-6*70K=.0007m or 0.7mm. A worst case differential axial motion might occur if the cryostat was at 30 K and the magnet accidentally was heated beyond it’s normal high temperature, to RT. The system interlocks should shut down the magnet current well before this. This would yield a differential axial motion of 2.62 mm. There is a radial differential motion. The outer joint at a radius of .35m would see a little over 1/3 the axial motion or about 1mm. Early in the design a large axial compression was needed to expose joint connections but the gland nut- penetration design does not require this.

Bellows used for the Joint penetration. The overall length of this model is .127m or 5 inches. The convolution pitch is 12mm with 5mm flats. The inner diameter is 6.25 cm or about 2.5 inches. The stock thickness is .016”

Stress in the joint bellows for one cm axial displacement.

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Joint Bellows Thermal Stresses The bellows are used to absorb differential motions, and also to provide long thermal paths to minimize heat leaks – See section 14.0. The joint bellows model was analyzed with a 30K to RT (292K) axial gradient. With this linear axial thermal gradient, appropriate for conduction from the 30K cryostat cover to the LN2 or RT end of the joint break-out, the stresses are minimal.

Von Mises Stress of the bellows convolutions with the axial temperature gradient applied. The peak stress in this analysis is 8.4 MPa

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An attempt was made to “invent” a temperature distribution that wasn’t quite so uniform. This is shown at right. The axial (vertical in these plots) displacement is not uniform. . The peak stress for this non-ideal temperature gradient is 15.2 MPa, up from the previous 8.4 MPa, but it is clear that thermal stresses are not critical for the temperature gradients we expect at the joint penetrations.

Axial thermal displacement in meters.

The peak Von Mises stress is 15.2 MPa

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Vacuum Jacket Outer Flange Axial Displacements.

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