Joint Institute for Nuclear Research

Further optimization of the solenoid design

A.Efremov, E.Koshurnikov, Yu.Lobanov, A.Makarov, A.Vodopianov

GSI, Darmstadt, 05.03.2008

2

Coil and yoke dimensions

Barrel part1490 mm < r < 2300 mm60 mm + 11×30 mm + 60 mm steel; 12 gaps of 30 mm

Upstream doorUpper radius: -1970 mm < z < -1585 mmLower radius: -1970 mm < z < -1734 mm

Downstream door2465 mm < z < 2865 mm5×60 mm steel; 4 gaps of 25 mm

Cryostat-1190 mm < z < 1900 mm

Gaps between the coil and cryostat ends: 170 mm (upstream) and 155 mm (downstream)

In ZEUS: both gaps are 150 mm

3

Solenoid cross-section

Side view

4

Solenoid cross-section

Top view

5

Coil parameters

Coil axial dimensions -1020 mm < z < 1745 mm

Cable cross-section (without insulation)

3.4 mm × 24.6 mm

Design current density 54 A/mm2

Subcoil turns in each of 2 layers 225, 116, 211

Operation current 5.1 kA

Axial magnetic force (coil rated position)

+99 kN

Field inhomogeneity (coil rated position)

ΔB/B < 1.8%

Radial component integral (coil rated position)

|Iup| < 1.72 mm

6

Magnetic flux density distribution

The flux density in the upstream door is B < 1.7 T and the flux density near it in the downstream direction is B < 1 T.

7

Magnetic flux density distribution

8

Field homogeneity

%100),(

0

0

B

BzrB B0 = 2T

|δ| < 1.78%

9

Radial component integral

0

400

0 ),(/),(),(Z

Zrup dzzRBzRBZRI

|Iup| < 1.72 mm

10

Dependence of parameterson the coil position

dzBz

BrΔZ [mm] Fz [kN] ΔB/B [%] [mm]

0 +99 -1.78 ÷ 1.61 -1.72 ÷ 1.39

-10 +51 -1.96 ÷ 1.66 -1.52 ÷ 2.00

+10 +148 -1.60 ÷ 1.55 -1.98 ÷ 0.75

Coil configuration is defined using our computer code

11

Barrel part of the solenoid

12

Impact of the cable passages across the barrel part of

solenoid

800 x 60 mm2 at the octagon corners

both at the upstream and downstream barrel ends

Axisymmetric model: use of effective magnetic permeability

fill factor: 446.0total

steel

S

Sc

Stotal and Ssteel – cross-sections of barrel beam and its steel part

in the plane crossing the gaps perpendicular to Z

The calculations are not sensitive to the place of the gap on this plane

13

Impact of the cable passages across the barrel part of

solenoid

14

Impact of the cable passages across the barrel part of

solenoid

dzBz

BrGaps square Fz [kN] ΔB/B [%] [mm]

No gaps +99 -1.78 ÷ 1.61 -1.721 ÷ 1.390

Gaps +10% +99 -1.70 ÷ 1.71 -1.716 ÷ 1.412

Gaps +100 -1.69 ÷ 1.72 -1.718 ÷ 1.418

Gaps -10% +101 -1.68 ÷ 1.73 -1.720 ÷ 1.423

The passages have small influence on the homogeneity and field integral in central region

15

Solenoid front view

16

Solenoid cross-section

17

Stress-strain analysisdownstream door, inner (first) plate

Fixation scheme Axial displacement [m]

ΔZ < 0.05 mm

18

0

1

Stress-strain analysisdownstream door (second plate)

Axial displacement [m]

19

Stress-strain analysisdownstream door (second plate)

Number of welded spacers

Maximal bending deflection [mm]

No spacers 8.1

1 spacer 1.1

3 spacers <0.2

Fixation scheme

20

Stress-strain analysisdownstream door (second plate)

Equivalent stress

(Von Mises)

σ < 25 MPa

Allowable value:

[σ] = 140 MPa

3 welded spacers

21

Stress-strain analysisupstream door

The door consists of 8

steel plates of 30 mm

thickness consolidated in

a package

Equivalent stress

(Von Mises)

σ < 3 MPa

22

1

0

Stress-strain analysisupstream door

Maximal axial displacement

ΔZ < 0.5 mm

23

Beam deformationin the cross-section

Yoke barrel gravity load G = 2000 kN

Maximal value of the deformation: uy = 1.5 mm, ux = ± 1 mm

gravity load and Px  = 0.25 G, Py  = 0.18 G (seismic load)

Maximal value of the deformation: uy = 1.6 mm, ux = 2 mm

Maximal stress σmax = 35 MPa Maximal stress σmax = 50 MPa

With outer frames

24

Solenoid coil

Al cylinder

subcoil 1 subcoil 2 subcoil 3

subcoil solid Al Al with slits

(for shear stress reduction)

25 mm

25

Solenoid coil

Shear stress at the subcoil end face < 5 MPa

1

0

subcoil

solid Al

26

Solenoid general view

27

Solenoid general view

28

Solenoid general view

29

Solenoid details

30

Solenoid details

31

Solenoid details

32

33

Yoke beam construction(old dimensions)

34

Mechanical analysis

Design criteria for the solenoid structural parts produced from metal alloys are chosen in accordance with “Codes of design to calculate the strength of equipment and pipe-lines of nuclear power plants” PNAE-G-002-86 and “Codes of strength calculations for high pressure vessels” (GOST 1429-89).

Design criteria for the yoke and support frames include building norms and codes for steel constructions (Russian) and Eurocodes 3 .

Allowable membrane stress in a solenoid structural part in the normal operation regime has to be chosen as follows:

u

um nn

;min2.0

2.0

where safety coefficients (safety margins) for the coil are

;5.12.0 n 3un

and for the yoke are ;5.12.0 n 6.2un

Allowable bending stress in a structural part in the normal operation regime has to be chosen as follows:

mben 3.1

35

Beam deformationin the cross-section

Yoke barrel gravity load G = 2000 kN

Maximal value of the deformation: uy = 4.3 mm, ux = ± 2.5 mm

gravity load and Px  = 0.25 G, Py  = 0.18 G (seismic load)

Maximal value of the deformation: uy = 5.8 mm, ux = 9.6 mm

Maximal stress σmax = 115 MPa Maximal stress σmax = 140 MPa

Without outer frames