1. executive summary€¦ · jlab torus magnet 1 phase i final report, rev 02 technology &...

JLab Torus Magnet 1 Phase I Final Report, Rev 02

Technology & Engineering Division

To: Distribution

From: Craig Miller, MIT-PSFC

Date: April 3, 2012

Re: Jefferson Lab Torus Magnet Cold Mass Structural Analysis, Final Report, Rev 02

1. EXECUTIVE SUMMARY

A third design for the Jefferson Lab torus magnet cold mass is analyzed structurally. This third design

closely resembles the design analyzed in Reports #1 and #21,2 as it includes two thin fiberglass layers: (1)

between the outer perimeter of the winding pack and the coil case, and (2) between the inner perimeter

of the cooling tubes and the coil case. It differs from previous designs as it adjusts the orientation of the

struts supporting the cold mass such that they remain in tension for both cool down and charging of the

coil. Updating the design of the support struts is absolutely necessary and reasonable changes are

presented. The post-processing of the data includes the resulting forces in all support struts as well as

the failure criteria applied to both layers of fiberglass, the aluminum coil case and the conductor. The

regions of highest stress in both the coil case and the winding pack are the focus of separate

substructure analyses, which are used to evaluate the stresses on the weld points between the coil case

and its cover and the stresses within the winding pack, respectively. Other than proper redesign of the

support struts, no significant structural issues are found. Several recommendations are outlined in the

Summary, Section 9.

2. GEOMETRY

2.1. GLOBAL MODEL

The geometry considered for the “global model” is a 3D depiction of 1/12th (30°) of the cold mass of the

torus magnet shown in Figures 1(A-C). Boundary conditions constraining motion normal to the planes of

symmetry are used on all areas lying on the planes of symmetry to account for the structure that is

being neglected. This global geometry assumes the coil case is symmetric and continuous – no

attachment of a coil case cover. The coil case substructure analysis addresses this limitation by including

welds, the coil case and its lid as separate parts. Figure 1C shows a cross section through the

353mmx21.5mm cut-out in the Aluminum coil case and how it is filled in the model. G10 fiberglass

material is included as shown in Figure 1C with the purple color and fills the regions between the

winding pack and the case and then the cooling tubes and the case. The fiberglass is assumed to be

transversely isotropic and its material properties are reported in Table 3.

The torus magnet system implements several support struts that suspend the cold mass from the

cryostat and each has a tensile pre-load. The global model considers eight of these support struts: 4 in-

plane, 2 out-of-plane, and 2 axial. Figure 2 shows the global structural model with spring connections

used to simulate the support struts. Because the global model considers only 1/12th of the total

structure, all 4 in-plane support struts and the 2 axial support struts are modeled with ½ the stiffness

and ½ of the pre-load of the full geometry.



Changes have been made to the location of the axial strut connections to the hub and to the orientation

of both in-plane and out-of-plane support struts. The changes are made from the design provided by

Jefferson Lab in order to keep all support struts in tension during cool-down and charging of the coil.

The updated location of axial struts connection points to the hub are shown in Figure 2B. The

orientations of the out-of-plane and in-plane support struts are adjusted such that they are

approximately 95° to the displacement vector at the connection location, as shown in Figures 2B & 2C.

The displacement vector, shown in red in Figure 2, is taken from data presented in Figure 14. These

design changes correct the problems encountered in the previous design whose structural analyses

indicated several of the support struts carry a compressive load.

In addition to proper orientation of the support struts, this set of analyses considers the thermal

contraction of the support struts during cool down. This shrinkage is embedded in the properties of the

springs specified in the analyses and are summarized in Table 1. The properties specified in the analysis

are stiffness and pre-load of each strut. Strut stiffness is defined as: k=(ES2/epoxy*A)/L, where

ES2/epoxy=55GPa, L is strut length, and A is cross-sectional area, taken from dimensions in Figures 3 and

24. The pre-load is specified in the design analyses provided by JLab. The shrinkage is predicted using a

1-D FEA model where one end of the support strut is 4K and the other is 296K. This linear temperature

profile is input to a structural model which uses a 1mm/m (from 296K to 4K) thermal contraction to

predict the strut contraction, dth in Table 1, for various strut lengths. The strut thermal contraction is

incorporated into the effective preload, Peff, that is specified for the spring property for the reduced

model. These spring links connect two points in the model: one is the location the strut is connected to

the cryostat and is assumed to be rigid, the second is the location the strut connects to the coil case and

is deformable. The assumption that the cryostat is rigid may create additional stresses in the coil case.

Note that in the simulations, these struts can carry tensile and compressive loads (in reality they are

tension only struts).

Table 1. Summary of support strut properties.

Strut Property

Strut Location

OOP IP Axial

Top Bottom Front Back

Area, A (m2) 1.52E-04 1.50E-04 1.50E-04 1.50E-04 1.50E-04

Length, L (m) 0.439 0.405 0.412 0.5354 0.9134

Stiffness, k=E*A/L (N/m) 1.91E+07 2.04E+07 2.00E+07 1.54E+07 9.03E+06

Pre-Load, P (N) 13,000 10,000 10,000 10,000 10,000

Extension due to Preload, dpre=k/P (m) 6.81E-04 4.91E-04 4.99E-04 6.49E-04 1.11E-03

Thermal Shrink from FEA, dth (m) 2.18E-04 2.01E-04 2.01E-04 2.65E-04 4.50E-04

Effective Pre-extension,deff=dpre+dth (m)

8.99E-04 6.92E-04 7.01E-04 9.14E-04 1.56E-03

Effective Preload, Peff=k*deff (N) 17,162 14,103 14,034 14,086 14,067

(1/2)*Peff (N) N/A 7,052 7,017 7,043 7,034

k/2 (N/m) N/A 1.02E+07 1.00E+07 7.70E+06 4.52E+06



Figure 1. (A) Torus magnet cold mass with planes of symmetry separated by 30°. (B) Isometric view of

global model. Coil is shown with copper color. (C) Cross section of global model -- location shown in

Figure 1B.

Figure 1A

Figure 1B Figure 1C

30°

Planes of

Symmetry

Central Axis

Of Hub

Smeared winding pack

(copper color)

21.5mm x 116*2.86mm

G10 (purple color)

21.5mm x 2.68mm

Smeared cooling Tubes

(beige color)

21.5mm x 16.22mm

353mm=2.68mm + 116*2.86mm + 16.22mm + 2.34mm

Dimensions from Figure 7

G10 (purple color)

21.5mm x 2.34mm



Figure 2. Global model including updated design of springs used to simulate support strut pre-tension

loads and stiffness. (A) Zooms to out-of-plane strut location showing change in orientation. (B) Zooms

to axial struts that are identified in Drawing #Torus-4028 – locations that the front and back axial struts

are connected to hub are switched from the design provided by JLab. (B&C) Zooms to in-plane support

struts and shows displacement vector in red. The new orientation of the in-plane support struts are 95°

to the displacement vector obtained from FEA results discussed in Section 5 of this report.

Struts fixed at

end connected

to cryostat

From 82°

to 95°

From 87.3°

To 95°

From 84°

to 95°

Figure 2

Figure 2A

Figure 2B Figure 2C

Back Axial

Strut Hub

Connection

Front Axial

Strut Hub

Connection

Displacement

vector



Figure 3. Drawings used to attain dimensions for support struts.

2.2. WELDED COIL CASE SUBSTRUCTURE

A substructure analysis is performed to evaluate the stresses on the weld points joining the coil case

cover to the coil case. The location on the coil case where peak stresses are found from the global

model results is selected for the substructure geometry. This location is shown in Figure 4. The purpose

of Figure 4 is to indicate the dimensions of the weld used in the model attaching the lid to the coil case.

There are 2 weld beads – one along the inside perimeter and one on the outside – that have the same

cross-section. In the substructure analysis the weld bead is bonded to the coil case lid and to the coil

case, whereas the contact between the coil case and the lid is simulated using frictional contact. These

locations are shown in Figure 4 and this allows for separation between the lid and the coil case. There is

no heat affected zone included in the substructure model and the weld uses the same material

properties as Aluminum 6061-T6 coil case. This is essentially a large fillet weld that has a 4mm depth of

penetration into the coil case with a chamfer for weld prep on the lid. An alternate weld geometry is

also modeled that assumes only a 1mm depth of penetration into the coil case and a smaller chamfer

(2mm X 2mm) for weld prep on the lid. These dimensions are labeled ‘ALT’ in Figure 4 and are used to

investigate any effects of weld size on weld stress.

In plane support

strut

Out-of-plane

support strut link



Figure 4. Geometry of coil case for substructure analysis used to evaluate stresses in welds. The

dimensions of the chamfer used as a weld prep on the lid and the depth of weld penetration into the

coil case are marked with two dimensions as these are the parameters used to investigate effects of

weld size. Units are m.



2.3. WINDING PACK SUBSTRUCTURE

A second substructure analysis is performed on winding pack to evaluate the integrity of the turn wrap

as well as the stresses in the copper channel in the conductor. Figure 5 indicates the location from

within the global model the winding pack substructure is taken – this corresponds to the location of

highest von Mises stresses in the smeared winding pack from the global model. The detailed winding

pack used for the substructure analysis includes fiberglass turn wrap, copper channel, smeared

solder/SC wire and 0.5mm thick copper sheet as shown in Figure 6. The material properties for these

parts are described in Section 3.

Figure 5. Winding pack substructure geometry and its location on the global model.

40°

10°

View for

Figure 6



Figure 6. Detailed geometry used for substructure analysis of winding pack. Units are mm.

3. MATERIAL PROPERTIES

All the 3D models use two types of material properties: isotropic or orthotropic. The epoxy and

Aluminum materials are isotropic and their temperature dependent material properties are listed in

Table 2. The cooling tube and the winding pack have too many details to describe fully in these 3D

simulations. Both the winding pack and the cooling tubes are reduced to orthotropic material

properties that use values averaged, or smeared, through their respective volumes. In the 3D system

model, many coordinate systems are assigned to the winding pack and cooling tubes to continuously

align the orientation of their material properties with the winding direction.

In order to determine the orthotropic material properties of the cooling tubes and winding pack, two

methods are implemented. First, in the direction of the winding (labeled in Table 3 as the hoop

direction), material properties were calculated from standard rule-of-mixtures formulas. These

formulas determine smeared values based upon constituent values and weighs them based upon % of

cross-sectional area each constituent represents. Second, the in-plane material properties were

determined using detailed 2D FEA models.



The detailed geometry of the 2D plane stress FEA model used to determine the in-plane orthotropic

material properties of the cooling tubes is shown in Figure 8(A-B). All dimensions are obtained from

drawings shown in Figure 7. The specific material properties used in these 2D models are outlined in

Tables 2 and 3. The G10 fiberglass material is assumed to be transversely isotropic, so it is isotropic in-

plane and has different material properties through its thickness. Its orientation for the models is

indicated in Figures 8 & 9 by its thickness.

To get the radial modulus of the cooling tubes, the left side is fixed so that radial displacements are zero

and a uniform radial displacement is applied to the right side. An elastic foundation boundary condition

is applied to the top and bottom edges to prevent the thin walls of the cooling tubes from bulging in the

axial direction. (Note the elastic foundation stiffness value is estimated from the modulus of copper,

and its value does not impact the resulting reaction force.) The reaction force to the applied radial

displacements is reported by the model. For example, at room temperature, for a 0.1mm radial

displacement, a 1.22e7N reaction force is reported. The effective radial modulus is calculated to be:

where a unit depth is assumed such that A=.04274m*1m. The calculation of the room temperature axial

modulus is shown in Figure 8B. This same procedure is repeated at various applied displacements to

check the linearity of the response. It is also repeated at different key temperatures and the

temperature dependent orthotropic moduli of the cooling tubes are summarized in Table 3.

A similar approach is taken to estimate the smeared material properties of the winding pack with one

key difference: the model for the cooling tubes considers the entire cross section of the tubes, G10 and

copper sheet. This is not feasible for the winding pack because there are 232 turns with 36

superconducting wires in each turn. Therefore, the smeared properties of the winding pack are

estimated from a portion of the entire structure. The detailed geometry used is shown in Figure 9 and

implements 12 conductors. This model also uses the elastic foundation boundary condition on sides

opposite of the applied displacements. The algorithm used to determine the axial and radial moduli of

the winding pack are the same as for the cooling tubes. For example, at room temperature, for a 0.1mm

axial displacement, a 2.78e6N reaction force is reported. The effective axial modulus of the winding

pack is calculated to be:

As with the cooling tubes, this procedure is repeated for several displacements to check the linearity of

the response and at key temperatures to reveal its temperature dependence.



The axial and radial coefficients of thermal expansion for the cooling tubes and winding pack uses the

same geometry used to determine their stiffness. However, the elastic foundation boundary condition

is removed and minimum displacement boundary conditions are applied to the corners to maintain

alignment and not apply reaction forces. Uniform temperature steps are applied to the model and the

resulting average expansions/contraction are calculated in the radial and axial directions. These average

expansions at the applied temperature steps are used to determine the average thermal expansion and

the results are summarized in Table 3.

The failure criteria used to compare to the resulting stress distributions in the coil case and within the

winding pack considers the yield and tensile strength & safety factors specified by ASME pressure vessel

code. The material for the copper conductor specified is: “OFHC fully annealed RRR>100.” NIST

Monograph reports a yield strength of fully annealed OFHC as 123MPa at 4K, whereas 10% cold worked

OFHC at 4K yields at 247MPa. Furthermore, the NIST Monograph indicates a 100RRR is possible with

10% cold worked copper, whereas fully annealed implies 0% cold work. Cold work does not have nearly

the effect on copper tensile strength as fully annealed copper at 4K strength is 410 MPa and 10% cold

worked is 430MPa. The primary membrane stress intensity failure criteria, Sm, of the supported

winding pack is the lower of UTS/3 and (2/3) yield, so for the coil: Sm=82MPa (fully annealed) or

Sm=143MPa(10% cold worked)3,4. For OFHC copper with 3% cold work: UTS/3=(2/3) yield=138MPa. This

will be a seen as the recommended minimum amount of cold work to be used for the copper in the

conductor. The copper most likely will experience some cold work during the spooling and winding

operations, but it is difficult to determine the amount of cold work generated during such operations.

Plots of the von Mises stresses in the winding pack are presented and used to compare to Sm.

The same failure criteria are applied to the supporting structure of Aluminum 6061-T6. It is decided that

Sm is the lower of UTS/3 and (2/3) yield. The UTS=496MPa and yield=362MPa at 4K for Aluminum 6061-

T6, so its Sm=165MPa5. The UTS=398MPa and yield=243MPa at 4K for welded Aluminum 6061-T6, so its

Sm=133MPa6. It will be the von Mises stress distributions on the case that will be compared to these

failure criteria. Contour plots of the von Mises stresses on the coil case are shown with the following

colors: yellow exceeding 133MPa, orange exceeding 165MPa, and red exceeding (2/3)*362=241MPa.

The failure criteria used to evaluate the winding pack are the stresses leading to delamination of the

fiberglass insulation. It is critical to minimize tension and shear stresses in the winding pack that causes

delamination leading to coil quench. The failure criteria historically used compares: (1) the shear force

to a combination of the bond strength and compressive forces, and (2) any tensile forces normal to the

surface. This is applied to the layers of fiberglass installed in the global model and to the small amount

of turn insulation in the winding pack substructure geometry.



Table 2. Summary of isotropic Material Properties.

Material

Property

Elastic Modulus (Gpa) Nu

Secant Thermal Expansion=

1e-6/K)

4K 22 C 120 C 4K-22C 4K-120C

Aluminum 6061-T-6 80.9 71.8 71.8 0.33 14.38 17.4

OFHC 138 126 126 0.31 11.4 13.0

Solder (50/50 Pb/Sn) 43 18.5 18.5 0.35 17.8 19.3

SC Wire 90 80 80 0.33 11.3 13.0

Smeared SC/Solder 66 49 49 .33 12.1 14.4

Epoxy w/ Alumina filler, CTD-521-S40

11.3 3.1 0.15 0.4 4K-22C 22C-46C*

17.2 22.5

*:While the epoxy has a 3x increase in thermal expansion above the 46C Tg, it also has a 20x decrease in elastic

modulus. Epoxy thermal expansion input to the model stops at 46C, otherwise the model will apply huge thermal

expansions from the 120C cure to 4K with a large 4K modulus. There is no pure epoxy in any of the models.

Table 3. Summary of orthotropic Material Properties.

Material Direction (see Fig

3)

Property

Elastic Modulus (Gpa) Nu

Secant Thermal Expansion=

1e-6/K)

4K 22 C 120 C 4K-22C 4K-120C

Coil

Hoop 100 87.6 85

0.33

11.5 12.5

Radial 71.3 51.4 50 13.1 14.3

Axial 87.0 69.1 65 12.7 14.1

Cooling Tube

Hoop 76.0 69.1 75

0.33

11.1 12.1

Radial 51.3 45.4 45 12.4 13.7

Axial 31.4 27.1 26.8 11.7 13

Fiberglass (G10)

Thru-Thickness

22 14 14 *

24.4 24.5

In-Plane 27 22 22 8.32 8.35

*: varies with direction and temperature from 0.36 to 0.147



Figure 7. Dimensions for 2D models described in Figures 4 & 5 taken from these drawings.



Figure 8. Geometry of 2D plane stress FEA model used to determine (A) radial and (B) axial modulus of

cooling tubes. Similar model is used to determine thermal expansion coefficient of cooling tubes.

Radial

Axi

al

Copper Tubes:

19.05mm X

15.88mm with

12.7mm hole

2x0.17mm G10 Radial thickness

Hoop direction is out-

of-plane and is also the

winding direction

0.5mm Copper

Sheet

2x1.31mm+6x0.17mm G10

(Slight adjustment made to

create 42.4mm thickness) Axial thickness

Figure 8A

Figure 8B

Reaction force=1.03e6N

Applied displacement = 0.1mm

Eaxial=(1.13e6/.01622)/(.1/42.74)

Eaxial=27.1e9GPa

16.22mm

42.74mm



Figure 9. Geometry of 2D plane stress FEA model used to determine (A) radial and (B) axial modulus of

winding pack. Similar model is used to determine thermal expansion coefficient of cooling tubes.

Axial

Ra

dia

l

Copper Channel:

20mm X 2.5mm w/

12mm X 1.37mm groove

0.18mm G10 Radial thickness

SC wire: 0.5mm

36x per conductor

0.5mm Copper

Sheet

0.5mm Copper

Sheet

Hoop direction is out-

of-plane and is also the

winding direction

.18mm + 2x

0.17mm G10 Axial thickness

2x0.18mm G10 Radial thickness

.18mm + 2x.17mm + .18mm G10

42.74mm

17.16mm Solder: 12mm X

1.37mm with 36x

0.5mm voids for

SC wires

Reaction force=1.28e7N

Applied displacement = 0.1mm

Eradial=(1.28e7/.04274)/(.1/17.16)

Eradial=51.4e9GPa

.18mm + 2x

0.17mm G10 Axial thickness



4. MAGNETO-STATIC ANALYSIS

The first model that is performed is the magneto-static model of the reduced geometry torus magnet.

This model includes the coils and an air enclosure that extends 2m around the coil in all directions

except the two planes of symmetry. It neglects all other parts that are included in the structural

analysis. A 62.64A/mm2 current density is applied to the coil, flux parallel is applied to the outer

surfaces and flux normal is applied to the two planes of symmetry. Figure 10 shows the BC’s applied and

Figure 11 shows a contour plot of the flux density magnitude on the surface of the coils. The peak flux

density is 3.64T and it is located on the front inside corner. The stored energy of the modeled portion of

the reduced coil is 1.15MJ, so because this is half of one of the six coils, the total stored energy of the

torus magnet calculated by ANSYS to be 13.8MJ. Ultimately, the purpose of this model is to prepare the

Lorentz forces on the coils to be input to the structural analysis.

To provide more confidence in the results, a structural analysis is performed including only the Lorentz

forces coupled into the structure from this magneto-static analysis. Figures 12 & 13 only show results

on the coil, but the results were generated using the entire 3D global model structure previously

described. Figure 12 is a vector plot of the coil displacements and includes the point the axial

displacements are fixed on the hub. Figure 13 is a contour plot of the vertical stresses on the coil

surface. The 13.5MPa compression on the very bottom of the coil which reduces to 2MPa tensile stress

on the inner edge of the bottom portion of the coil is expected. Note the magnitudes of these stresses

as they are small compared to the thermal loads.

Figure 10. BC used for magneto-static FEA used to generate Lorentz forces on coil.



Figure 11. Contour plot of magnetic flux density on coil surface.

Figure 12. Vector plot of coil displacements resulting from Lorentz loads on coils. Magnitude is small

(0.5mm max).

Location on hub for

thermal contraction

center



Figure 13. Normal stresses in direction indicated on coil with only Lorentz loads applied to coil within

reduced system model. Compressive stresses are negative and tensile stresses are positive.

5. GLOBAL DISPLACEMENTS & SUPPORT STRUT LOADS

To simulate the manufacturing of the torus magnet, the model reports stress distributions through the

entire structure at three key steps. These steps are outlined in Table 4. The system is injected with

epoxy and heated to 120 C to cure the epoxy and this is the stress free condition. Step #1 cools the

bonded system to room temperature and applies the pre-loads on the support struts. Step #2 applies a

uniform temperature of 4K and with the stress free temperature at 120 C. Step #3 charges the coil by

adding the Lorentz forces on the coil determined from the magneto-static analysis. Note that the

preload, Peff, defined in Table 1 is used for Steps #2, #3 because it considers the thermal contraction of

the support struts.

Normal stresses in

the y-direction of

highlighted

coordinate system



Table 4. Load included for each step of the structural analysis. (See Table 1 for definition of P and Peff.)

Step # Temperature Coil-to-Case

Contact Strut Pre-Tension

Lorentz Forces

N/A 120 C Stress- Free Condition for Steps #1-3

1 22 C Bonded Yes, P No

2 4 K Bonded Yes, Peff No

3 4 K Bonded Yes, Peff Yes

Gravity is not considered in this analysis. The global geometry has a mass of 760kg and its affect would

be most significant in the struts of the torus magnet that lie closest to the horizontal plane. These

effects require a minimum 180° model and will be analyzed in Phase II of this study.

The first set of results presented is the deformation vector plots for Steps #2 and #3 are shown in Figure

14(A-B). The point furthest from the hub contracts almost an inch (25.2mm in Step #2) as the cold mass

is cooled to 4K. Note the thermal contraction center-point is located between the points the axial

support struts are connected to the hub.

Table 5 summarizes the forces in each of the support struts at each of the load steps in the analysis.

Figure 11A labels each of the 8 support struts in order to locate the loads reported in Table 5. A

negative load indicates compression and a positive load indicates tension. Notice all the struts are in

tension and that, with the exception of strut #3, the loads are evenly distributed among the struts.

Changes in the loads between Steps #2 and #3 correspond to the displacements due to the charged coil,

shown in Figure 12. For example, the load in strut #6 is unchanged with charging of the coil, as there is

little displacement at this location in Figure 12. The load in strut #3 initially appears too high – such load

would create a (40,544N*2)/1.5e-4m2=541MPa stress. Fortunately, this stress is well below S2 glass

tensile strength of 1800MPa.

Table 5. Loads in support struts at each load step.

Step

Strut Load (N)

Out-of-Plane In Plane Axial

1 2 3 4 5 6 7 8

1 13,000 13,000 5,000 5,000 5,000 5,000 5,000 5,000

2 26,908 25,867 36,445 17,020 15,572 18,035 17,967 16,381

3 26,782 25,814 40,544 14,036 18,193 18,121 17,390 16,348



Figure 14. Deformation vector plots for the coil support structure for (A) Step #2 and (B) Step #3.

(A) Labels the struts for Table 5

Axial support

connections to hub

Thermal contraction

centerpoint

1

2

1

3 4

5 6

8 7

Figure 14A

Figure 14B



6. STRESSES ON THE COIL CASE

6.1. GLOBAL MODEL

The first set of stress distributions presented is contour plots of the von Mises stresses on the surface of

the coil case and big & small rings. The colors of the legend indicate locations exceeding the failure

criteria previously discuss. The yellow/orange/red colors of the contour legend exceed the welded

Sm=133MPa, the orange/red color exceeds Aluminum 6061-T6 Sm=165MPa, and the red exceeds

(2/3)* yield=241MPa. Figure 15A shows the stresses for the pre-tension loads applied to the assembly at

room temperature and have low stresses.

Figures 15B & 15C show the stresses at Step #2 are large and are obviously due to the large differential

expansions among the parts of the assembly. There are two locations where stresses are concerning: (1)

the sidewall of the coil case near the inside corners of the coil, and (2) the outside wall of the coil case

where the coil transitions from curved to straight. These are not only locations of high stresses, but also

locations where the case cover is to be attached to the coil case. The substructure analysis is presented

in Section 6.2 that focuses on the stresses in the welded joint between the lid and the coil case.

Figures 12D & 12E show the stresses at 4K with a charged coil, or Step #3. The stress levels and the

amount of material in yellow and red, and their locations are similar to those from Step #2. Note that

the stresses reported in Fig 15B vs Fig 15D and Fig 15C vs Fig 15E are not for the same nodes. For

example, the 260MPa stress in Fig. 12B cannot be directly compared to the 293MPa stress because

these values are not for the exact same node. Furthermore, notice that some stresses increase and

some stresses decrease when comparing Figs 15B & 15D. Therefore, it can be safely concluded that the

cool-down is the cause of the high stresses at these concerning locations of the coil case.

There are also stress concentrations of the corners of the cut-outs through the center of the coil case.

While these stresses are high, simply increasing the radius of the fillet on the corners should reduce this

to an acceptable level.

Step# Contours of von Mises stress on case Comments

1: Struts

+ 22 C

Von Mises stress

contour.

Very low stresses

Fig. 15A



2: Struts

+ 4K

Fig. 15B is a perspective

from the inside of the

coil case.

High stresses in outside-wall of coil case at three of the four corners.

Stresses exceed

welded Sm, but not

unwelded.

Stress close to allowable in

coil case sidewall close to location of highest field.

2: Struts

+ 4K

Fig. 15C is a perspective

from the outside of the

coil case.

Stresses exceeding Sm

penetrate through the thickenss of the coil case

sidewall. These are

located just inside of each corner of coil.

Fig. 15B

Fig. 15C



3: Struts

+ 4K +

EM

Same view as

Fig. 15B

Stresses remain similar upon charging of the coil at concerning locations identified

from Step #2

Location of substructure

analysis

3: Struts

+ 4K +

EM

Same view as Fig. 15 C

Peak stresses are similar in magnitude

from Step #2 to Step #3.

Fig. 15D

Fig. 15E



6.2. SUBSTRUCTURE OF WELDED COIL CASE

The geometry used for the substructure analysis of the coil case was presented in Figure 4. This

geometry corresponds with the locations of highest stress in the coil case presented in Figure 15. This

substructure geometry continues to assume that the coil case is symmetric because only half of the coil

case is considered. This implies that there are welds on both sides of the coil case. An important

conclusion from the global model is that the cool down is the primary source of the stresses. There is

significant difficulty to include the Lorentz forces in the substructure model. Therefore, the substructure

model of the welded coil case use the boundary conditions for Step #2 presented in Table 4.

Displacements from Step #2 of the global model are imported as a boundary condition on all areas

created when cutting through the global model to create the substructure geometry. Thermal

contraction from 393K to 4K is applied to all bodies in the substructure. The stresses from these

displacements are distributed around the welded substructure by the analysis. Recall that the welds are

bonded to the coil case and lid, there is a 1mm clearance between the lid and the coil case, and there is

sliding contact between the lid and coil case. There is no heat affected zone included in this analysis and

the welds, lid and coil case all are modeled with Aluminum 6061-T6 material properties. The G10

fiberglass, smeared cooling tube and smeared winding pack all have the same dimensions and material

properties as used for the global model.

Figure 16 shows a contour surface plot of the von Mises stresses on the welded coil case substructure

model. The stresses in the most concerning location of the coil case sidewall along the inside corner of

the coil are 171MPa remain greater than allowable, but less than the 206MPa and 201 MPa predicted in

Figures 15 B & D, respectively. Notice also the high stresses in the outside wall of the coil case are now

140MPa – less than the Sm=165MPa and less than the 168MPa and 172MPa stresses reported in Figs 12

B & D, respectively. Figure 16 indicates locations cross-sections are taken to present stress distributions

through the thickness of the structure, including the welds. It is critical that these cross-sections are

away from locations the displacement boundary conditions are applied as stresses at these locations are

not reliable. Figure 16 also circles the location along each cross-section that the contour plots of the

stress distributions are focused on.



Figure 16. Geometry used for the substructure of the welded coil case. Dashed lines indicate locations

of cross-sections used to evaluate the stresses through the thickness of the structure.

There are two structural weak points in the design of a lid welded to the coil case and they are discussed

in order of how problematic they are. Cross section #1 in Figure 16 slices through the first weak point.

The von Mises stresses and the radial stresses along cross section #1 are shown in Figures 17A&B,

respectively. Note that the fiber glass and the cooling tubes are hidden in Figure 17 to shown the

stresses in the inside wall of the coil case. Also, the deformations are magnified 5x, so that the small

separation between the lid and the coil case is negligibly small. There are three observations to be

made from these plots:

The stresses in the weld and coil case sidewall are radial and in tension,

The maximum von Mises stress in the inside weld is 107MPa – almost 20% below the

Sm=133MPa,

The peak stresses in the sidewall of the coil case that were concerning from the global model do

not go through the thickness of the sidewall,

Displacements

applied on areas

created when

cutting into global

model

X-Section #1

X-Section #2



The peak stress on the surface of the coil case sidewall is 171MPa (3.6% above Sm=165MPa).

This stress is tensile and radial and is due to the bending of the lid from the differential thermal

expansion between the winding pack and the coil case in the z-direction (through-thickness

direction). This differential thermal expansion is approximately 20 m.

The stress along the inside weld is almost 20% below Sm and the stress in the sidewall is slightly above

the Sm=165MPa, but comfortably below (2/3)* yield=241MPa. Furthermore, the 171MPa stress is a

result from a model using smeared winding pack and smeared cooling tube materials, whereas in reality

there will exist thin layers of softer fiberglass that should absorb 20 m of differential expansion without

transmitting stresses to aluminum.

Cross section #2 in Figure 16 slices through the second weak point identified in the global model. The

maximum von Mises stress in the weld along the outside perimeter is 134MPa, slightly greater than

Sm=133MPa. The location of the weak point (168MPa von Mises stress in Figure 15C) is only predicted

to be 140MPa in the substructure model, as shown in Figure 18A. This is 15.1% below Sm=165MPa.

For the weld design presented, the welded coil case design will be structurally sufficient to hold the

charged coil at 4K. Note that there should be some weld prep incorporated into the design of the coil

case and its lid, as the design provided is to be bolted together. In the current design only a fillet can be

performed. The weld prep proposed includes a 4mmx8mm chamfer on the lid and a 4mm depth of

penetration into the coil case. These are large values require a lot of filler material and, because it is

aluminum, a lot of energy that may lead to over-heating of the winding pack. These large values may

also account for the low stresses in the welds.

A substructure analysis on an alternate weld design using a 2mmx2mm chamfer as a weld prep on the

lid and a 1mm depth of penetration into the coil case is performed and results are presented in Figure

19. The von Mises stress on the corners of the inside weld (Figure 19A) are 149MPa and 160MPa. The

von Mises stresses on the corners of the outside weld (Figure 19B) are 106MPa and 150MPa. In reality,

these locations will not be sharp as in the analysis geometry. The bulk of the inside and outside welds

are 97MPa and 132MPa, respectively, and are both below Sm=133MPa. While these stresses are

borderline, this weldment design will be the minimum recommend as anything smaller will concentrate

the stresses beyond Sm. Therefore, it is recommended that the weldment design maintains a minimum

2mm x 2mm weld prep on the lid and 1mm depth of penetration into the col case. In order to increase

the volume of the contact region through which the differential thermal expansions are transmitted, it is

recommended that the weld fills the region of the weld prep in the lid and leaves a fillet between the

coil case and lid.

It is also highly recommended that there be some experiment to measure the temperature rise in the

coil case during the weld operation to prevent overheating of a fabricated winding pack (hence, proper

heat sinking design for the welding operation). Proper design of the welding operation will also address

the variation in the clearance between the lid and the coil case (nominally 1mm as seen in Figure 4).

The problem could occur if this clearance approaches zero and a gap is created between the lid lip and



the coil case as shown in Figure 19B. This gap could be lead to bending of the lid during the welding

operation.

Figure 17. (A) Von Mises stresses and (B) radial stresses along cross section #1 in Figure 16. Note that

the inner G10 layer and hidden in these contour plots.

Fig. 17A. Peak 107MPa von Mises stress

in weld.

Fig. 17B. Stresses are radial and in tension.



Figure 18. (a) Von Mises stress and (B) hoop stress contours along cross section #2 in Figure 18. Note

the outer G10 layer is hidden.

Fig. 18A. Peak 134MPa von Mises stress

in weld.



Figure 19. Von Mises stresses for alternate weld design along (A) inside and (B) outside.

Fig. 19A. Peak 149MPa and 160MPa von

Mises stress in weld corners and 97MPa at

center of inside weld.

Fig. 19B. Peak 150MPa and 106MPa von

Mises stress in weld corners and 132MPa

at center of outside weld.

If this 1mm nominal gap goes

to zero, gap could be created

here.



7. PRIMARY RESPONSE OF THE WINDING PACK

7.1. GLOBAL MODEL

The maximum allowable stress, Sm, of copper for different amounts of cold work was presented in

Section 3. The debate arises whether the stresses in the copper of the winding pack should be classified

as primary membrane stresses or as secondary stresses. The production solenoid for MECO analyzed an

externally supported series of coils that assumed the stresses in the coils were primary membrane

stresses, so the failure criteria used was Sm. However, for this torus magnet, because the winding pack

experiences primarily thermally driven stresses and because it is contained by the coil case, then the

stresses in the copper could be classified as secondary stresses. The failure criteria for secondary

stresses is 3*Sm, a significant difference as the 3x multiplier removes all safety factors from the failure

criteria. It is recommended that a conservative approach be taken and use the failure criteria as Sm.

Figure 20(A-C) presents the contour plots of the von Mises stresses on the coil at the end of Steps #1, #2

and #3. The global model uses the smeared properties for the winding pack, so a conservative

assumption is that the copper in the winding pack bears all the loads in the winding pack. This

assumption calls for a multiplier to be applied to the copper failure criteria that is equal to the ratio of:

(Coil Volume)/(Copper Volume within the coil)=1.73. Therefore, the coil Sm=82/1.73=47MPA

(3*Sm=141MPa) for fully annealed copper and Sm=143/1.73=83MPa (3*Sm=249MPa) for 10% cold

worked copper at 4K. The von Mises stress contour presented have colors corresponding to these

values: Sm=47MPa (light blue) for fully annealed copper and Sm =82MPa (green) for 10% cold worked

copper.

The maximum stresses occur in the winding pack at cool down and are located at the top as seen in

Figure 20B. This value is 105MPa in the straight and 110MPa in the corner – both are greater than the

Sm=82MPa for 10% cold worked copper, but less than 3*Sm=141MPa for fully annealed copper. The

stresses are slightly lower once the coil is charged as shown in Figure 20C. It is important to point out

that for 10% cold worked copper yield=251MPa (123MPa for annealed). The conservative assumption

that copper bears all loads reduces the yield to 145MPa wrought (71MPa annealed). Therefore, it is

unlikely the copper actually yields at a von Mises stress of 110MPa, but it does exceed the allowable Sm

that includes the safety factors for yield and ultimate strengths. The substructure analysis is performed

on the region highlighted in Figure 20B for Step #2 to further evaluate the copper in the winding pack.

Figures 20(D-G) are surface contour plots of the normal stresses parallel to the winding direction to help

describe the high average stresses in Figures 20(B-C). These are not stresses to compare to failure

criteria, but help give a sense of the direction and whether the stresses are compressive or tensile.

Figures 20(D-G) indicate the high stresses in the coil are compressive and along the direction of the

winding.

It is difficult to make a definitive conclusion regarding these stress values because: (1) the assumption

that the copper bears all loads, and (2) the unknown amount of cold work in the copper channel. A

more detailed analysis is performed to improve the evaluation of the conductor.



Step# Contours of von Mises stress on coil Comments

1: Struts

+ 22 C

Von Mises stresses

Very low stresses

Fig. 20A



Step #2:

Struts +

4K

Von Mises Stresses

High stresses in the top of the winding

pack.

Peak stresses highlighted on ID and is location of

windingpack substructure

analysis.

Step #3:

Struts +

4K +

EM

Von Mises Stresses

Stresses lower than

Step #2 (stresses

highlighted in Figs 20 B&C may are not at the same locations).

Fig. 20B

Fig. 20C



Step #2:

Struts +

4K

Normal

stersses, y (using coord

system hidden

behind stress label, y-dir is

parallel to winding

direction)

Hence, the large von

Mises stresses in Figure 20D

are compressive

and in the direction of the winding.

Step #3:

Struts +

4K +

EM

Normal

stersses, y (same as

Figure 20D)

The large von Mises stresses

continue to be in the

direction of the winding.

Fig. 20D

Fig. 20E



Step #2:

Struts +

4K

Normal

stersses, y (using

coordinate system

highlighted

As in Figure 20D & E, high

von Mises stresses are compressive

and in the direction of the winding.

Step #3:

Struts +

4K +

EM

Normal

stersses, y

(same coord system as Fig

20F)

Stresses continue to

be compressive

and in direction of

winding

Fig. 20G

Fig. 20F



7.2. SUBSTRUCTURE OF WINDING PACK

The geometry used for the substructure analysis of the winding pack was introduced in Figures 5 and 6.

This geometry is located at the highest stress as predicted by the global model as shown in Figure 20B.

Displacements from the global model are applied to the external surfaces of the substructure and all

bodies of the substructure are subjected to a 393K to 4K temperature change, where the stress free

temperature is 393K (as in the global model). These displacements are distributed through the detailed

substructure model to create stresses that can be compared to the failure criteria previously discussed.

If the conductor stresses are assumed to be primary membrane stresses, then there is some concern if

the copper is fully annealed. Figure 21 shows the von Mises stresses on the exterior of the copper

conductor with Sm=143MPa of 10% cold worked copper in red, Sm=138MPa of 3 % cold worked copper

in orange, and Sm=82MPa of fully annealed copper in yellow. It should be noted that stresses close to

the applied displacement boundary conditions are typically not reliable numbers, so values from the

cross section of the substructure in Figure 21B are used to compare to failure criteria. For this reason,

the peak 155MPa stress value is suspect because it occurs 0.18mm from the location of applied

displacements. Other than this peak location, all the von Mises stresses in the copper conductor are

below Sm for 10% cold worked copper and most are below Sm for 3% cold worked copper. However,

they all exceed Sm=82MPa for fully annealed copper and are close to yield=123MPa of fully annealed

copper.

If the conductor stresses are assumed to be secondary, then the stresses reported in Figure 21(A&B) are

of little concern. With 3*Sm=246MPa for fully annealed copper, no stresses in the conductor approach

this level.

The conservative approach taken here to evaluate this design recommends a minimum 3% cold work be

specified for the copper channel. The spooling operation may be enough to generate this amount of

cold work in the copper. A tensile test on a sample section of the conductor is highly recommended, or

at the minimum a hardness measurement of the copper should be taken, before the winding process

begins to provide a higher level of confidence as to the yield strength of the conductor.

It should also be noted that the normal strain in the smeared solder/SC wire is also compressive and has

a 0.1% magnitude.



Figure 21. Von Mises contour plots on surface of copper within substructure of winding pack. (A) Entire

section of copper, (B) cross section shown in (A).

Cross section used for Fig. 21B



8. DELAMINATION OF THE FIBERGLASS

The G10 fiberglass ground insulation is assumed to fail either due to (1) normal tensile stress, or (2)

shear stresses exceeding an allowable level. Up to 10% by volume of the fiberglass is allowed to fail

either of the criteria for a structurally acceptable design. These failure criteria are applied to the global

model to evaluate the ground insulation along the inside and outside perimeters of the winding pack

(purple material in Figure 1). The failure criteria are also applied to the substructure analysis of the

winding pack discussed in Section 7.2 to evaluate the small amount of turn insulation in the substructure

geometry.

In the global model, 99% of the 2 layers of ground insulation fiberglass pass the failure criteria after cool

down (Step #2). Of the 2 layers, 97% pass the failure criteria after charging of the coil (step #3). All

failure is due to tensile normal stresses and most occur on the bottom layers, as shown in Figure 22.

Figure 22 plots the stress in the ground insulation in the y-direction (normal to the straight lengths

highlighted). Tensile stresses are in yellow/orange/red and they are shown to grow slightly upon

charging of the coil.

In the substructure analysis of the winding pack, 94.9% of the turn wrap passes both failure criteria.

This is especially encouraging because this is 95% passing within the region with the highest stresses in

the winding pack. As in the global model, most of the failure is due to normal tensile stresses, as 95.2%

normal stress criteria and 99.5% pass shear criteria. Figure 23 shows the through-thickness [normal]

stress contours on the substructure g10 layers. It can be seen that the only tensile stresses that exist

close to the applied displacements in the layers between pancakes and surrounding the 0.5mm thick

copper sheets.

While it is good that most of the insulation in the substructure model passes the failure criteria, it is

important to use the substructure results to comment on the integrity of the turn insulation in the entire

winding pack. To do this, the winding pack is divided into two regions: (1) curved and (2) straight

regions. The substructure is taken from a curved portion with the highest von Mises stress. This inside

corner should have the highest shear and the normal stresses are all mostly in compression. The

straight regions are essentially in a generalized plane strain stress state, with limited shear stresses and

most of the normal stress existing along the direction of the winding. These arguments lead to the

conclusion that the turn insulation is safely within the fiberglass failure criteria. Therefore, there are no

issues in the current design for the integrity of the ground or turn insulation.



Figure 22. Stresses along the y-direction of the fiberglass ground insulation (normal to the straight

lengths shown) for (A) Step #2 and (B) Step #3.

Fig 22A. Stresses normal to fiberglass

regions between arrows

Fig 22B. Regions of tensile stress

leading to fiberglass failure

(yellow/orange/red) grow slightly

upon coil charging



Figure 23. Fiberglass layers shown in winding pack substructure – all other materials are hidden. (A)

Only fiberglass layers shown whose thickness is in the radial direction, shown. Contour of radial stresses

shown. All radial stresses are compressive, hence no normal fiberglass failures. (B) Only fiberglass

layers shown whose thickness is in the z-direction, highlighted. Stresses in z-direction plotted with

tensile stresses shown in yellow/orange/red. Note most tensile stresses are close to edges of

substructure geometry (locations of applied displacement boundary conditions).

Fig. 23A. Radial direction

shown in red is normal to

thickness of all turn

insulation shown.

Fig. 23B. Contour plot of

stresses normal to the z-

direction.



9. SUMMARY

The most important conclusion from the structural analysis of the torus magnet is the support struts

must be reoriented such that they bear tensile loads during both cool-down and coil charge. A design

has been presented here that provides the desired tensile loads in the struts that support the cold mass

off the cryostat. It is strongly suggested that the current design be changed to something similar to that

presented here.

The welded aluminum coil case does not produce stresses that surpass the failure criteria. This includes

the bulk of the coil case, the 3.6mm thick sidewalls and the welds. There are three recommendations to

made for the design of the coil case:

1. Weld preps and weldment design should be specified using minimum dimensions outlined in

Section 6.2,

2. The radii of the eight fillets on the cut-outs for the in-plane struts in the center of the coil case

should be increased,

3. Proper heat sinking of the weld operation must be developed to prevent overheating of the

winding pack.

The stresses in the copper channel carrying the superconducting wires carry compressive stresses in the

direction of the winding. These stresses exceed Sm and are similar to yield for fully annealed OFHC

copper, but are comfortably below the 3*Sm failure criteria for secondary stresses. It is recommended

that there be a minimum 3% cold work in the conductor to keep these stresses comfortably below the

yield point. This amount of cold work may result from the spooling and winding operations. A tensile

test or a hardness measurement on a sample of the conductor should be performed to provide an

indication of amount of cold work before the winding process begins.

The fiberglass insulation comfortably passes its failure criteria. The global model indicates a 97% passing

rate for the ground insulation located along the inside and outside perimeters of the winding pack. The

winding pack substructure model predicts 95% of the turn insulation passes in the location of highest

stress in the winding pack.

10. REFERENCES 1. “JLab Torus Magnet Cold Mass Structural Analysis – Report #1”, Miller, C.E., 2/15/12. 2. “JLab Torus Magnet Cold Mass Structural Analysis – Report #2 - DRAFT”, Miller, C.E., 3/6/12. 3. Chattopadhyay, Somnath, Pressure Vessels: Design and Practice, CRC Press, 2005. 4. NIST Monograph 177, “Properties of Copper and Copper Alloys at Cryogenic Temperatures,” Simon,

N.J, et. al., Feb. 1992.



11. APPENDIX

Figure 24A. Cross sectional view of hub including front and back axial supports. The lengths of the axial

supports used in the model are shown.

Back Axial Support Length:

913.4

Front Axial

Support Length:

535.4



Figure 24B. In plane (IP) supports showing lengths of the top and bottom supports. The lengths of the supports used in the model are shorter because they are attached to the inside face of the cut-out, not

the hole in the coil case.

IP-Top Support Length = .429m

In model L=.405m

IP-Bottom Support Length = .436m

In model L=.412m

Support attached to model here

Support attached to coil case in

actual design here



Figure 24C. The length of the OOP support used in the model.

OOP Support Length in model

= .439m

1. executive summary€¦ · jlab torus magnet 1 phase i final report, rev 02 technology &...

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