Mechanical Design & Analysis

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Nov 29, 2013 (3 years and 9 months ago)

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Mechanical Design & Analysis

Igor Novitski

Outlines


Electromagnetic Forces in the Magnet


Goals of Finite Element Analysis


Mechanical Concept Description


FEA Models


Material Properties


Magnet Components at Different Loads


End Plate Stress and Deformation


Summary

13 May 2011, FNAL
-
CERN CM1

Mechanical Design & Analysis

Igor Novitski
2

Electromagnetic Forces

in the Magnet



To

reduce

the

probability

of

spontaneous

quenches

due

to

turn

motion

and

stabilize

the

magnet

field

harmonics,

it

is

necessary

to

ensure

the

mechanical

stability

of

turns
.



Turn

mechanical

stability

is

achieved

by

applying

the

prestress

to

the

coil

during

magnet

assembly

and

supporting

the

compressed

coil

during

operation

with

a

rigid

support

structure
.



The

required

prestress

value

is

determined

by

magnet

design,

nominal

operating

field

and

mechanical

properties

of

structural

materials
.

Horizontal

EM
-
force F
x
/side at
I
nom
=11.85kA,

kN

9170

Vertical



EM
-
force
F
y
/side at

I
nom
=11.85kA,

kN

4846

Longitudinal EM
-
force F
z
/end at I
nom
=11.85kA,

kN

455


13 May 2011, FNAL
-
CERN CM1

Igor Novitski
3

Mechanical Design & Analysis

Goals of

Finite Element Analysis


ANSYS finite element (FE)
2D parametric models
been created to
analyze

the mechanical characteristics of the
dipole design at several

magnet
stages:

o
magnet assembly
(collaring, yoking and skinning),

o
cool
-
down

to operation temperature, and

o
excitation to

the nominal current of
11.85 kA
.



The
mechanical structure was optimized to
keep coil under compression
up to the maximum design field of
12 T
and to maintain the
coil stress
below 160
MPa

at all times, which is considered a
safe

level
for brittle
Nb
3
Sn

coils.



Stresses in all
structural materials

should be less than
yield stress limit
.

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
4

Mechanical Design & Analysis

Mechanical Concepts

13 May 2011, FNAL
-
CERN CM1

Mechanical Design & Analysis

Igor Novitski
5


B

C


A

The 30
-
mm horizontal collar width is
virtually the maximum possible in the
available space between the two coils in the
double
-
aperture configuration with two
independent collared coils.

The 20
-
mm width is the minimal collar
width determined by stress limits in
the collar and key materials.

Titanium Poles with

stress
-
relive slot

Phosphor

Bronze Key

CS
-
Bump

controls

Inner

Yoke Gap

AL Clamp

controls

Outer

Yoke Gap

Uniform

MP Shims

Stainless Steel Skin

Aluminum Clamp

Iron Yoke

Nb
3
Sn

Coil

Stainless Steel

Collars

Coil

mechanical

support

is

provided

by

stainless

collars,

vertically

split

iron

yoke,

aluminium

clamp

and

welded

stainless

steel

skin
.



Strong

collars

and

iron

yoke

create

the

“rigidity

belt”

around

Nb
3
Sn

coil

for

conductor

protection
.


Coil

midplane

shims

generate

initial

coil

azimuthal

prestress

at

collaring

stage
.



Skin

and

clamp

tensions

deform

the

iron,

reduce

the

vertical

collars

spring
-
back

and

finalized

coil

compression
.


Collar
-
yoke
-
clamp
-
skin

interferences

support

horizontal

LF

action
.


Magnet

Mechanical Concept

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
6

Mechanical Design & Analysis


Shims for

interference

Magnet Body FE Model


The

2
D

ANSYS

parametric

model

of

the

dipole

includes

the

coil
,

the

two

layers

of

collars

(front

and

lock
-
leg

),

the

key
,

the

iron

yoke
,

the

clamp

and

the

skin
.



The

model

has

a

quarter
-
symmetry
.


The

coil

inner

and

outer

layers
,

and

interlayer

insulation

are

glued

together
.


The

Ti

coil

poles

freely

separates

from

the

coil
.



The

coil

is

surrounded

by

two

layers

of

stainless

steel

collars



Front

and

leg

collars

have

symmetric

boundaries

along

X
-
axis

(CP

and

CE

equations

simulate

line

motion)
.


The

phosphor

bronze

key

locks

collar

laminations

fixing

the

coil

azimuthal

prestress
.



Clamped

iron

yoke

supports

the

collars,

and

the

welded

stainless

steel

skin

restrains

the

iron

yoke

from

outside
.

The design components are represented
with 4
-
node plane quadrilateral elements
(PLANE 42). Material interfaces are modelled
with contact elements (CONTACT 169
-
172).

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
7

Mechanical Design & Analysis

End Plate FE Model


3
D

ANSYS

model

for

the

end

plate

consists

of

a

50
-
mm

thick

end

plate

welded

to

a

12
.
7
-
mm

thick

skin
,

with

the

skin

length

extended

back

to

the

2
D

lead

end

cross

section
.



One

quarter symmetry

is used in the model.


The

end

plate

consists

of

two

mechanically

connected

concentric

rings

with

a

central

round

hole

for

the

magnet

beam

pipe

and

four

holes

for

the

instrumented

bullets

in

the

innermost

ring,

and

four

round

cooling

holes

in

the

ring

attached

to

the

skin
.



The

Lorenz

force

in

one

quadrant

was

applied

in

the

location

of

the

bullet

hole
.


The design components are represented with

8
-
node elements (SOLID 95) with contact
elements (CONTACT 170
-
174).

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
8

Mechanical Design & Analysis

0
20
40
60
80
100
120
140
160
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
Strain
Stress, MPa
4.2 K
300 K
300K: Monotonic Loading
0
10
20
30
40
50
60
70
80
90
100
0
0.001
0.002
0.003
0.004
0.005
0.006
Strain
Stress, MPa
Parameter

unit

2D Model

Straight section


293 K

4.3 K

Ey



Azimuthal direction

GPa

44

44

Ex



Radial direction

GPa

44

55


x

E
-
3

2.6


y

E
-
3

3.5


Coil
data from HFM dipole
programs

Load
-
Unload
-
Reload Tests

Cyclic Loading Tests

44
GPa

Structural

element

Material

Thermal
contraction

(300
-
2 K),

Elasticity modulus,

GPa

Yield stress,

M
Pa

mm/m

warm

cold

warm

cold

Clamp

7075
-
T6

4.1

70

85

46
0

650

Pole blocks

Ti
-
6Al
-
4V

1.7

115

125

65
0

>9
00

Collar

316LN

2.7
-
2.9

190

210

520

850

Key

Phosphor
Bronze

3.3

110

123

38
0

>500

Yoke

Soft I
ron

2.05

205

225

180
-
3
0
5

>6
00

Skin

304L

2.9

190

210

24
0

6
00


Material Properties

13 May 2011, FNAL
-
CERN CM1

Igor Novitski
9

Mechanical Design & Analysis

Coil Stress Distribution

After Collaring

After Skin Welding

After Cooling Down, 300
-
2K

After 11T, 2K

After 12T, 2K

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
10

Mechanical Design & Analysis

Avg.=28MPa

41

89

59

49

85

99

113

129

135

124

23

2

91

86

53

26

66

35

12

Max
Seqv
.

=77MPa

118

148

144

146

Coil Stress


C
oil
average

stress, MPa


Inner pole

Outer pole

Inner midplane

Outer midplane

Collaring

28

41

53

26

Assembly

89

59

49

85

Cooldown

91

86

66

99

I
nom
=11.85 kA

12

35

113

129

B
max
=12 T

2

23

124

135


The

expected

prestress

variation

with

respect

to

the

nominal

coil

prestress

at

the


50


m

azimuthal

coil

size

variation

is

within


10

MPa

in

the

inner

layer

and

within


23

MPa

in

the

outer

layer
.


Analysis

shows

that

at

the

maximum

design

field

of

12

T

the

minimal

coil

prestress

in

pole

regions

is

2
-
23

MPa
.


The

maximum

coil

prestress

at

room

temperature

does

not

exceed

160

MPa
,

which

is

acceptable

for

the

Nb
3
Sn

cable

and

coil

insulation
.

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
11

Mechanical Design & Analysis

Poles Stress

After Collaring

After Skin Welding

After Cooling Down, 300
-
2K

After 11T, 2K

After 12T, 2K

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
12

Mechanical Design & Analysis

Max
Seqv
.

=133MPa

510

588

128

136

Collar Stress

After Collaring

After Skin Welding

Lock and Leg Collars

Front Collar

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
13

Mechanical Design & Analysis

Max
Seqv
.

=527MPa

490

413

339

Collar Stress

After

Cooling Down,

300
-
2K

After 11T, 2K

Lock and Leg Collars

Front Collar

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
14

Mechanical Design & Analysis

Max
Seqv
.

=562MPa

469

476

397

Collar Stress

After 12T, 2K

Lock and Leg Collars

Front Collar

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
15

Mechanical Design & Analysis

Max
Seqv
.

=494MPa

401

Key Stress

After Collaring

After Skin Welding

After Cooling Down, 300
-
2K

After 11T, 2K

After 12T, 2K

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
16

Mechanical Design & Analysis

Max
Seqv
.

=362MPa

133

124

185

202

Iron Yoke Stress

After Skin Welding

After Cooling Down, 300
-
2K

After 11T, 2K

After 12T, 2K

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
17

Mechanical Design & Analysis

Max
Seqv
.

=351MPa

455

362

387

Clamp Stress

After Skin Welding

After Cooling Down, 300
-
2K

After 11T, 2K

After 12T, 2K

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
18

Mechanical Design & Analysis

Max
Seqv
.

=261MPa

287

282

281

Skin Stress

After Skin Welding

After Cooling Down, 300
-
2K

After 11T, 2K

After 12T, 2K

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
19

Mechanical Design & Analysis

Max
Seqv
.

=365MPa

489

498

499

Avg.=170MPa

266

269

270

Structure Maximum

Stress

Maximum stress,
MPa

Inner/outer poles

Collar

Key

Yoke

Al clamp

Skin/
avg
/max

Collaring

133/90

527

362

n/a

n/a

n/a

Assembly

510/180

412

132

351

261

170/365

Cooldown

588/263

562

124

455

287

266/489

I
nom
=11.85 kA

100/128

476

184

362

282

269/498

B
max
=12 T

50/136

494

202

387

281

270/500

The
maximum stress in the collars and compression in the iron yoke
achieves the
material yield stress in
small regions near key grooves and iron yoke corner
(model
singularities, mesh size).

To minimize the stress concentrations, the key grooves and iron
corners have been
rounded
.

All stress values
are
below yield stress

of corresponding

materials.


13 May 2011, FNAL
-
CERN CM1


Igor Novitski
20

Mechanical Design & Analysis

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
21

Mechanical Design & Analysis

Skin Welding

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
22

Mechanical Design & Analysis

Cooling Down and LF action

Coil IR deflections


Magnet

cross
-
section

is

deformed

due

to

the

coil

prestress
,

cool
-
down

and

Lorentz

forces

action
.

Bore

deflections

from

the

warm

unstressed

round

geometry

(magnetic

design)

calculated

for

the

above

mentioned

effects

at

room

and

helium

temperatures

in

the

dipole

straight

section

are

summarized

below
:

13 May 2011, FNAL
-
CERN CM1

Mechanical Design & Analysis


Igor Novitski
23


B
ore radial deflection,

m


Pole

Midplane

45 degree

Collaring

58

-
11

58

Assembly

87

-
122

13

Cooldown

-
21

-
240

-
96

I
nom
=11.85 kA

-
51

-
163

-
74

B
max
=12 T

-
57

-
149

-
70


As it follows from the above data, at the nominal operating current of 11.85
kA the radial cross
-
section deflection from the magnetic design in the magnet
midplane

is ~165

m.

End Plate

Deformation and Stress


The

50
-
mm

end

plate

deflection

and

coil

end

motion

under

the

nominal

LF

is

about

75


m
.


The

maximum

stress

in

the

end

plate

is

160

MPa
.



Taking

into

account

that

usually

only

20
%

of

the

Lorentz

force

is

transferred

to

magnet

end

plates,

the

coil

end

motion

is

even

smaller
.

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
24

Mechanical Design & Analysis

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
25

Mechanical Design & Analysis

End Plate Load

Summary


ANSYS
analysis

of the mechanical structure of the demonstrator dipole
model
shows:

o
chosen
mechanical design provides

the coil
prestress

required for the
operating current range
with sufficient margin
;

o
design reliably
restricts turn

radial, azimuthal and longitudinal
motion

under
the Lorentz forces
up to 12T
;

o
the maximal mechanical
stresses

in the
major elements

of coil support
structure are
below the limits for the materials

used.


The

mechanical design
, structural materials and components, coil collaring
and cold mass
assembly procedures will be experimentally studied
and
further optimized
using instrumented mechanical models
. The
results

of
experimental studies
of mechanical models
and measurements during
demonstrator dipole test
will be compared with
the described ANSYS
analysis
.

13 May 2011, FNAL
-
CERN CM1


Igor Novitski
26

Mechanical Design & Analysis