WENDELSTEIN 7-X Max-Planck-Institut für Plasmaphysik André Dübner Dok.-Kennz.: Y-xxxx.x KKS.-Nr.: 1-AAD00 Design-Review on Planar-Support-Elements, 25th.

WENDELSTEIN 7-XMax-Planck-Institut für Plasmaphysik

André Dübner

Dok.-Kennz.:

Y-xxxx.x KKS.-Nr.:

1-AAD00 Design-Review on Planar-Support-Elements, 25th of April 2004

Planar support element calculation at the Non-planar-

coil side – Analytical calculation

A.Dübner

Design Review on Planar SupportGreifswald, 27.04.05


André Dübner

Dok.-Kennz.:

Y-xxxx.x KKS.-Nr.:


Aims and Boundary conditions

• Aim: Determination of size and numbers of required boltas for the Planar-supports in the support blocks

• Restrictions: – Limited space on each support block– Limited space around the blocks– Use of the 4 standard thread holes

(4xM24) in each block


André Dübner

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Y-xxxx.x KKS.-Nr.:


Analysis type

• The analysis was done by using the simplified spring model for the bolts

• The PSE’s were considered as rigid beams, transferring the forces into the bolt cross-section and creating moments in it

• This allows a fast analytical determination of the required bolt size and number


André Dübner

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Y-xxxx.x KKS.-Nr.:


Local coordinate systems for the design forces


André Dübner

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Table of the design-gaps between the pads and the Planar-coil

contact plates

Stütze

x -x y -y z -z

A 1 2 mm 2 mm32,5

mm

32,5 mm

5 mm -

A 2 - 2 mm15

mm

15 mm

21 mm

-

A 3 - 2 mm - - - -

A 4 - 2 mm15

mm

15 mm

5 mm -

B 1 2 mm 2 mm 2 mm 2 mm 5 mm -

B 2 - 2 mm - - - -

B 3 - 2 mm - - - -

B 4 - 2 mm15

mm

15 mm

5 mm -

xx

zz x

z


André Dübner

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Y-xxxx.x KKS.-Nr.:


Example for bolt calculation on PSE-A2

x

z

y

xx

zz

yy

Local coordinate system in the flange cross

section

x’x’

y’y’z’z’

Local coordinate system for the design forces

Fb

Fs

Fb…resulting force on the bolt

Fs…resulting shear force on the bolt


André Dübner

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Y-xxxx.x KKS.-Nr.:



r1 48.552mmr1 8mm( )2 45 mm

cos 180

2

r2 32mm

20

Fz 3.852 kNFz F'z sin 180

F'x sin 180

Fy F'y

Fx 25.202kNFx F'x cos 180

F'z cos 180

f 30mm

b 145mm

e 82.4mm

a 70mm

d 90mm

h 97mm

70 20Dimensions:

n 3number of bolts:

F'z 5kNF'y 5kNF'x 25kNDesign-loads on PSE A1:

MPa 106PakN 1 10

3NDefinition of kN and MPa:

Dimensions and Forces:

Forces from the force equilibrium:

case a:) Pivot point at the end of the plate

Fsx

Fx

n Fsx 8.401kN

Fsy

Fy

n Fsy 1.667kN

Fsz

Fz

n Fsz 1.284 kN

Fsx…forces on bolt in x-direction

Fsy…forces on bolt in y-direction

Fsz…forces on bolt in z-direction


André Dübner

Dok.-Kennz.:

Y-xxxx.x KKS.-Nr.:



Forces from the momentum equilibrium:

Fy h FsMx d 0

FsMx

Fy h

d FsMx 5.389kN

Fx h Fz b FsMy1 a FsMy1f

2

a 0

FsMy1

Fx h Fz b

af

2

a

FsMy1 22.763kN

FsMy2f

aFsMy1 FsMy2 9.756kN

Fy e 2 r1 FsMz1r2

2

r1FsMz1 0

FsMz1

Fy e

2 r1r2

2

r1

FsMz1 3.486kN

FsMz2 FsMz1

r2

r1 FsMz2 2.297kN

Force vector components:

FMx FsMx 0 FsMx

FMy FsMy1 FsMy2 FsMy1

FMz FsMz1 FsMz2 FsMz1

Longitudinal bolt forces:

FB Fsz FMy FMx

FB 26.868 8.472 16.09( ) kN


André Dübner

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Y-xxxx.x KKS.-Nr.:



xx

yyThreaded

holes

Shear forces:

3

2 atan

2 8 mmd

02

atan2 8 mm

d

180

259.919 0 100.081( )

sf 2

sf 6.107 1.571 3.318( )

Fs Fsx cos sfT

FMz

T

2

Fsy sin sfT

FMz

T

2

FsT 11.88 9.289 5.08( ) kN

Maximum values:

max FB 26.868kN

max Fs 11.88kN

FFsysyrr

FFss

FFsxsx FFMzMz


André Dübner

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Y-xxxx.x KKS.-Nr.:


T=4 °KT=293 °K


• Simplified spring model for plate and bolt

• Linear relation between bolt forces and elongation of the bolts

• Change of remaining pre-load occurs by bolt load, temp difference and change of material properties through temperature change

Fp

F

Fpr

Fb Fbt

Fbs

fs fp

Fpr

Fb Fbt

Fbs

Fpr

Fb Fbt

Fbs

fs fp

Fpr

Fb Fbt

Fbs

Cs,4K

Cp,4K

Cs,293K

Cp,293K

Fpr>µ·Fs


André Dübner

Dok.-Kennz.:

Y-xxxx.x KKS.-Nr.:



Design

criterion:

1

4,

s

s

Kprs F

F


André Dübner

Dok.-Kennz.:

Y-xxxx.x KKS.-Nr.:


Old and new design forces

Planar-Suppor

t-Elemen

t

Fx[kN]

Fy[kN]

Fz[kN]

A1 100 40 210

A2 100 40 40

A3 100 40 40

A4 150 40 223

B1 600 150 -460

B2 100 40 40

B3 150 40 40

B4 100 40 780

Planar-Support

-Elemen

t

Fx[kN]

Fy[kN]

Fz[kN]

A1 Pad a 120 20 25

A1 Pad b 35 10 10

A2 25 5 5

A3 170 30 25

A4 160 35 10

B1 Pad a 530 95 95

B1 Pad b 170 25 35

B2 160 20 30

B3 220 35 40

B4 160 20 30

Additional forces for the 2nd pad

Additional forces for the 2nd pad


André Dübner

Dok.-Kennz.:

Y-xxxx.x KKS.-Nr.:


Relative change of the design values realting to the old design

values

Fx Fy Fz

[%] [%] [%]

A1 20 -50 -88

- - -

A2 -75 -88 -88

A3 70 -25 -38

A4 7 -13 -96

B1 -12 -37 117

- - -

B2 60 -50 -25

B3 47 -13 0

B4 60 -50 -96


André Dübner

Dok.-Kennz.:

Y-xxxx.x KKS.-Nr.:


Hole configurations

Config. 1 Config. 2

Config. 0 Config. 3


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Results for old and new design forces

Planar-

Support

number of bolts

size of

bolts

bolt check

safety

factor

against

sliding scheck

based-

hole configuration

A1 8 M24 ● 1 1,18

A2 3 M30 ● 3 1,24

A3 4 M24 ● 0 1,43

A4 8 M24 ● 2 1,4

B1 4 M30 ● 0 1,27

B2 4 M24 ● 0 1,02

B3 4 M24 ● 0 1,21

B4 8 M30 ● 2 1,4

PSEFx Fy Fz Ft Fs s

[kN] [kN] [kN] [kN] [kN] [ - ]

A1 120 20 2560,7

68,03 8,05

A2 20 40 524,9

310,9

310,9

1

A3 170 30 25103,

744,3 1,00

A4 160 35 1056,1

827,6 2,14

B1 520 95 95 N.A. N.A. N.A.

B2 160 20 3090,6

82

45,3 1,12

B3 220 35 4093,9

956 0,89

B4 160 20 3055,0

821,9 5,47


André Dübner

Dok.-Kennz.:

Y-xxxx.x KKS.-Nr.:


PLS – B1

• For PLS-B1 FEM simulation were carried out due to the high loads from the old design values

• Safety could be reached by introducing crossed ribs to take the shear forces

• The resulting tension forces on the bolts were used as input for the bolt size dimensioning


André Dübner

Dok.-Kennz.:

Y-xxxx.x KKS.-Nr.:


Summary of the results

• Outcome:– With the new design forces, most

PSE’s become less critical (Mostly B4)– Only the elements A3 and B3 become

now more critical than before (with same hole configuration and thread diameter)

– Problems can be solved by using of M30 instead of M24 bolts

– Recalculation of PLS-B1 FE-model is necessary to determine the bolt loads


André Dübner

Dok.-Kennz.:

Y-xxxx.x KKS.-Nr.:


Final drilled holes in the support blocks on NPC-side


André Dübner

Dok.-Kennz.:

Y-xxxx.x KKS.-Nr.:


WENDELSTEIN 7-X Max-Planck-Institut für Plasmaphysik André Dübner Dok.-Kennz.: Y-xxxx.x KKS.-Nr.: 1-AAD00 Design-Review on Planar-Support-Elements, 25th.

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