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ANNUAL REPORT 2011 ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical Behavior of Continuous Casting Funnel Molds Lance C. Hibbeler (Ph.D. Student) (Ph.D. Student) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 1 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 1 Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign Objectives Explore the thermal and mechanical response of the mold plates to the heat load experienced during regular casting, using a steady-state elastic nonlinear finite- element model Validate with plant measurements Recommend adjustment to taper to Recommend adjustment to taper to account for mold thermal distortion University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 2

ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

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Page 1: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

ANNUAL REPORT 2011ANNUAL REPORT 2011UIUC, August 18, 2011

Thermomechanical Behavior of Continuous Casting Funnel Molds

Lance C. Hibbeler (Ph.D. Student)(Ph.D. Student)

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 1University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 1

Department of Mechanical Science and EngineeringUniversity of Illinois at Urbana-Champaign

Objectivesj

• Explore the thermal and mechanical response of the mold plates to the heat load experienced during regular casting, using a steady-state elastic nonlinear finite-element model

• Validate with plant measurements

Recommend adjustment to taper to• Recommend adjustment to taper to account for mold thermal distortion

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 2

Page 2: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

Funnel Mold GeometryOuterFlat

InnerCurve

OuterCurve

InnerFlat

InnerCurve

OuterCurve

OuterFlat

90136.8 top106 bottom

23.4 top8 bottom

260

750

1200 (Variable)

All dimensions

in mm( )

• Cu-Cr-Zr alloy– 350 W/(m·K) thermal conductivity

8900 k / ³ d it– 8900 kg/m³ mass density– 385 J/(kg·K) specific heat capacity– 117 GPa Young’s modulus, 0.181 Poisson’s ratio

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 3

g• No coating layers

Water Box Geometry

• 316 stainless– 200 GPa Young’s

1105

930

1365

580200 GPa Young s modulus

– 0.3 Poisson’s ratio

50

400

50 50

20

3030

2060

Clamping Force

230

2512

512

512

521020

0

850

All dimensions in mm

695

685

895

2512

512

512

512

150

1100

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 4

145

212.5 212.5 212.5 212.5 255 260

1275

20155

3072

Page 3: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

Water Channel Geometry

B lt

e

Bolt HoleCopper Backing Plate

Bolt Hole

Sym

m72

The

rmoc

oupl

e H

ole

Water Tube 510

metry

H t F

T

21.3 23

.7 15

35

Wat

er

Cha

nnel

90

Hot Face

10.5 20

3

Copper Mold

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 5

Hot Face

Narrow face Wide face

Mathematical Thermal-Stress Model

2 0k T∇ =Isotropic Fourier heat conduction

0∇ ⋅ =σMechanical equilibrium without body forces

: el=σ C ε

( ) ( ) ( )( )2 1 1 1 2ijk ik j i jk ij k

E EC

νδ δ δ δ δ δν ν ν

= + ++ + −

Hooke’s law

Isotropic linear elasticity ( ) ( )( )2 1 1 1 2ν ν ν+ +el th= −ε ε ε

( )th T Tαε I

Strain decomposition

Th l t i t

( )( )12

T= ∇ + ∇ε u u

( )0T Tα= −ε IThermal strain tensor

Linearized total strain tensor

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 6

Employ the finite element method to solve the boundary-value problem

Page 4: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

Finite Element Mesh

Part Nodes Elements

Thermal DOF = 1,089,166

Mechanical DOF = 4,830,081Wide Face Mold Plate 855,235 4,223,072

Wide Face Water Box 185,534 190,457

Narrow Face Mold Plate 233,931 495,566

Narrow Face Water Box 83,269 239,604

Bolts and Tie Rods 110 55

Total 1,358,081 5,148,754ota ,358,08 5, 8, 5

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 7

Thermal Boundary Conditions

• Specified heat flux on mold hot faces• Convection BC on water channels

spk T− ∇ ⋅ = ⋅n q n

( )k T h T T∞− ∇ ⋅ = −n

• All other faces thermally insulated• Values calculated from CON1D calibrated to plant measurements

[Santillana et al., ISIJ Int. 2008]

0k T− ∇ ⋅ =n

[ ]

0

100

200

mm

)

Meniscus Meniscus

0

100

200

Dist

Meniscus

300

400

500

600

ow

To

p o

f M

old

(m

WFNF

300

400

500

600

ance B

elow

To

p o

f

Qmeas = 2.8 MW/m²Q = 2 7 MW/m²700

800

900

1000

Dis

tan

ce B

el

WFNF

700

800

900

1000

f Mo

ld (m

m)

WFNF

Qcalc = 2.7 MW/m²

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 8

1100

0 1 2 3 4 5 6 7 8 9

Heat Flux (MW/m²)

WFNF

33 37 41 45 49 53 57

Convection Coefficient (kW/m²·K)

32 34 36 38 40 42 44 46

Water Temperature (ºC)

1100

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Mechanical Boundary Conditions

• Ferrostatic pressure on hot faces• Symmetry on appropriate planes

p g zρ=

0• Symmetry on appropriate planes– Wide face mold and waterbox centerline– Narrow face mold and waterbox centerline

0⋅ =u n

– Tie rod centerlines

• Mechanical contact on mating faces– “Hard” contact algorithm within ABAQUS– Copper-copper coefficient of static friction μ = 1.0 [-]

Copper-steel coefficient of static friction μ = 0 5 [-]– Copper-steel coefficient of static friction μ = 0.5 [-]

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 9

Mold Bolts and Tie RodsBolt Length

(mm)Cross-Sectional

Area (mm²)Applied Torque

(N·m)Pre-Load

(kN)Pre-Stress

(MPa)Stiffness (MN/m)

NF (Short) 150 181 100 30 168 240NF (Short) 150 181 100 30 168 240

WF Short 87 187 100 30 162 424

WF Long 449 143 100 30 212 63

Upper Tie Rod 1335 1215 -- 40 33 34.8

• Bolts modeled as truss elements and prestressed according to

Lower Tie Rod 1335 1215 -- 70 58 33.4

p gplant practice– See [Thomas et al., Iron and

Steelmaker 1998]• “Distributing coupling

Narrow Face Waterbox

Truss Element

Distributing coupling constraints” tie bolt ends to surfaces on mold pieces

• Simulated tie rods account for actual tie rods and spring packs

Narrow Face Mold

Reference Points

Distributing Coupling

Constraints

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 10

actual tie rods and spring packsConstraints

Page 6: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

Simulation ResultsHeat transfer: 12 minutes on 8-core 2.66 GHz Intel Xeon

Stress analysis: 44.6 days on 8-core 2.66 GHz Intel Xeon

50× scaled distortion

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 11

Thermocouple Validation

175

212.5 mm212.5 mm212.5 mm

OuterFlat

Outer Curve

InnerCurve

InnerFlat

215 mm

125 mm

1

239210

W W W

A A A

227258

220209

48--

185173

177154

161163

46--

5 mm

134 m

W

199191

160160

Tcalculated (ºC)

Tmeasured (ºC)

125 mm

125 mm

A A A

A A A166150

160148

145154

46--

155150

151130

138144

46--

m134 m

m134W

W160

147155

125 mm

125 mm

A A A

A A A148154

144140

131145

47--

154152

150154

138150

48

4 mm

134 mm

1

W

W

137148

141149

m125 m

m125 m

A A A

A A A152154150--

152151

151144

143151

48--

19719919664

134 mm

134 mm

XYW

W

147145

150132 NF WF

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 12

mm

W W W

197194

199185

196186

64--

m

ZZW132 NF WF

Page 7: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

Measured Thermocouple Adjustment

• To account for heat removal along thermocouples:

( )2

gap TCTC TC TC amb

gap

d hDkT T T T

k D′ = + −

T’TC Adjusted TC temperature

TTC Actual TC temperature

Tamb Ambient temperature, 25 ºC or local water temperatureamb b e e pe a u e, 5 C o oca a e e pe a u e

dgap Gap between copper and TC, 0.01 mm

kgap Thermal conductivity of gap, 1.25 W/(m·K)

kTC Thermal conductivity of thermocouple, 212 W/(m·K)

D Diameter of thermocouple wire, 4 mm

h Convection coefficient, 5 kW/(m²·K) for water or 0.1 kW/(m²·K) for air

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 13

, ( ) ( )(previous slides mark with ‘W’ and ‘A’ which are adjusted for which)

Wide Face Temperature ProfilesSlight 2D heat transfer in funnel region (less than 2 ºC), but change in cooling around bolts has more significant effect

350

400

(°C

) .

Inner Flat Inner Curve Outer Curve Outer Flat

z = 152 mm

Significant

200

250

300

Tem

per

atu

re

z = 1050 mm

z = 850 mmz = 416 mm

z = 251 mm

Significant change in cooling

near mold exit

100

150

200

Fac

e H

ot

Fac

e z = 850 mm

z = 650 mm

z = 100 mm olt C

olum

n

0

50

100

Wid

e F

Bol

t Col

umn

Bol

t Col

umn B

o

Mol

d Le

vel

Sen

sor

Bol

t Col

umn

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 14

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700

Distance from Centerline (mm)

Page 8: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

Cooling Near Mold Exit

Hot face stays relatively cool with straight water tubes

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 15

Hot face heats up as channels curve away

Narrow Face Distortion

Temperature (ºC)50× scaled distortion

0

100

200

0 50 100 150 200 250 300 350 400

mm

)

Meniscus

Bolt

Bolt

d sto t o

300

400

500

600

To

p o

f M

old

(m

Narrow FaceCenterline

Bolt

Bolt

600

700

800

900stan

ce B

elo

w

TemperatureDisplacement

Bolt

Bolt

Bolt

1000

1100

Di

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Displacement (mm)

SEN WaterboxBolt

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 16

Page 9: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

Narrow Face Distortion

21 13481 m

m

-0.34

Short34

-4

Bolt Stress in MPa

mm

134 mm

1

Short-0.23

-0.10Bolt z-Displacement

in mm

14

10

34 mm

134 mm

0.00

0 1010

-4

134 mm

134 m

0.10

0.21

-23

36

Y

Z

mm

134 mm

0.29

0.39

Y

Z

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 17

Z Z

Out-of-plane displacement, bolt stresses In-plane displacement, bolt displacement

Narrow Face Distortion

• Narrow face distorts into roughly-parabolic arcTypical behavior– Typical behavior

– Elongates by 2 mm

• Low bolt operating stresses• Low bolt operating stresses– No risk of bolt tensile failure

• Small bolt displacement at mold/waterbox interface• Small bolt displacement at mold/waterbox interface– 16 mm bolts in 22 mm holes

– No risk of mold overconstraint or bolt shearing failureo s o o d o e co st a t o bo t s ea g a u e

• Waterbox hooks provide extra rigidity to assembly– Causes wobble in distortion profile

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 18

p

– Bolts near hooks do not overcome prestress

Page 10: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

Wide Face Distortion

50× scaled

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 19

distortion

Wide Face Distortion:

Out-of-Plane BehaviorOut of Plane Behavior

277116 817Long

212.5 mm212.5 mm212.5 mm

50 mm

1

Short

120 863 137Bolt Stress

10720219

102

24231

60

175 mm

125 mm

Fla

t

urve

urve

Fla

t

120

98

863

158

137

18

in MPa102

24

60

79

125 mm

125 mm

Out

er F

Out

er C

Inne

r C

u

Inne

r F

137

137

181

157

57

52

13

23

78

68

m125 m

m125 m

299 549 225

X

87

13619418565

54

35

mm

125 mm

125

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 20

Z 1281581584113

mm

Page 11: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

Wide Face Distortion:

Out-of-Plane BehaviorOut of Plane Behavior-0.5

-0.4

Inner Flat Inner Curve Outer Curve Outer Flat

-0.3

-0.2

men

t (m

m)

.

z = 251 mm z = 152 mm

SEN

-0.1

0

e D

isp

lace

m z = 1050 mm

z = 850 mm

n

0.1

0.2

0.3ace

Ho

t F

ac

z = 650 mm

z = 416 mmz = 100 mm

mn

mn

Bol

t Col

umn

eln

0.4

0.5

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700

Wid

e F

Bol

t Col

um

Bol

t Col

um

Mol

d Le

veS

enso

r

Bol

t Col

umn

Waterbox

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 21

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700

Distance from Centerline (mm)

Wide Face Distortion:

Out-of-Plane Behavior at CenterlineOut of Plane Behavior at Centerline

0

0 50 100 150 200 250 300 350 400 450

Temperature (ºC)

100

200

300

(mm

)

Meniscus

Bolt

Bolt

300

400

500

To

p o

f M

old

Wide FaceBolt

Bolt

Bolt

600

700

800

nce

Bel

ow

T Centerline

Temperature DisplacementBolt

Bolt

Bolt

900

1000

1100

Dis

tan

SEN Waterbox Bolt

Bolt

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 22

1100

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

Displacement (mm)

Page 12: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

Wide Face Distortion:

Out-of-Plane Behavior at OC Middle

0

0 50 100 150 200 250 300 350 400 450

Temperature (ºC)

100

200

300

(mm

)

Meniscus

300

400

500

To

p o

f M

old

Wide Face600

700

800

nce

Bel

ow

T Outer Curve M iddle

Temperature Displacement

900

1000

1100

Dis

tan

SEN Waterbox

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 23

1100

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

Displacement (mm)

Wide Face Distortion:

In-Plane Behavior, Towards NFIn Plane Behavior, Towards NFLong 0.000.320.73 0.580.77

0.77 0.44 0.00

Short 0.000.400.72

0.43

0.440.70

0.66Bolt x-Displacement in mm

0.80

0.81

0.52

0.55

0.00

0 00

0.38

0.35

0.66

0.69100× scaled distortion in0.81

0.85

0.55

0.59

0.00

0.00

0.35

0.35

0.69

0.76

distortion in x-direction

0.90 0.65 0.00

X

0.38

0.000.410.761.01

0.89

1.08

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 24

Z 0.000.470.941.271.34

Page 13: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

Wide Face Distortion:

In-Plane Behavior, Towards Mold Exit,

-0.61-0.54-0.35 -0.39-0.21

Long

Short

-0.19 -0.37 -0.32

-0.53 -0.55-0.33

-0.35

-0.48-0.19

-0.18

Bolt z-Displacement in mm

-0.06

0.00

-0.02

0.10

0.00

0.18

-0.02

0.17

-0.16

-0.14

100× scaled distortion in

di ti

0.09

0.19

0.26

0 47

0.18

0.38

0.17

0.37

-0.11

-0.08

z-direction

0.47 0.61

X

0.60

0.840.790.690.28

0.28

-0.06

-0.04

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 25

Z0.760.710.58

Wide Face Distortion

• Distorts into a ‘W’ vertically and horizontally– Largely because of different stiffnesses of bolts

• Distortion follows bolting pattern more than the thermal response

• Cold edges constrain against distortiong g

• Most severe distortion– Just below meniscus and just above mold exit– Just below meniscus and just above mold exit

– In between bolt columns

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 26

Page 14: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

Wide Face Distortion

• Short bolts in middle regionsProvide most of the resistance to distortion– Provide most of the resistance to distortion

– Larger bolt stresses

– Smaller displacements of hot faceSmaller displacements of hot face

• Long bolts at top and bottom– Compliant bolts, not reinforced with stiffener platesCompliant bolts, not reinforced with stiffener plates

– Lower bolt stresses

– Larger displacements of hot face

• Small bolt displacement at mold/waterbox interface– 16 mm bolts in 24 mm holes

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 27

– No risk of mold overconstraint or bolt shearing failure

Mold Interface0

100Meniscus

WF100 mm

200

300

400

of

Mo

ld (

mm

)

Narrow Face Wide Face

NF

500

600

700

e B

elo

w T

op

o

135 mm800

900

1000

Dis

tan

ce

BoltsBoltsNF

WF

1100

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Normal Displacement (mm)

• Good contact in regions of highest temperatures

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 28

Good contact in regions of highest temperatures• Small gap along most of the length of the interface• Large gap at meniscus, can fill with slag or steel and lead to “finning” defects

Page 15: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

Effect of Distortion on Taper• Calculate perimeter of

mold as function of di t d th ld

0

100distance down the mold

• Contributions from– Funnel geometry

Wide face expansion

100

200

300s (m

m) Total

Interfacial– Wide face expansion

– Narrow face distortion

– Prevented sliding of WF relative to rigid NF

400

500

ow

Men

iscu

s

Narrow Face Distortion

Interfacial Sliding

• Sliding should be considered during startup and in molds

600

700

800Dis

tan

ce B

elo

Wide Face Distortion

startup and in molds with rigidly positioned NFs

800

900

1000

D

Nominal Funnel

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 29

-1.50 -1.25 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00

Perimeter Change (mm)

Validation

• Slopes of NF measured at top and bottom of mold with inclinometers at the Tata IJmuiden DSPwith inclinometers at the Tata IJmuiden DSP

• During startup, the effect of WF expansion on NF shape must be accounted forshape must be accounted for

• During steady casting after a width change, the WF behavior no longer affects the shape of the NFbehavior no longer affects the shape of the NF

• Two cases to consider in calculating NF shape:1) “sliding” – assume rigid NF that allows WF to slide past1) sliding assume rigid NF that allows WF to slide past,

so “interfacial sliding contribution” to NF shape is ignored

2) “sticking” – NF contacts and moves together with WF

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 30

(due to backlash or other play-mechanisms) so the “interfacial sliding contribution” is included in NF shape

Page 16: ANNUAL REPORT 2011ANNUAL REPORT 2011 - …ccc.illinois.edu/s/2011_Presentations/10_HIBBELER-Lance... · ANNUAL REPORT 2011ANNUAL REPORT 2011 UIUC, August 18, 2011 Thermomechanical

Taper Measurements

36 45

Startup (filtered) Steady casting

32

34

36

Top 30

35

40

45

North top

26

28

30

Tap

er (

min

)

15

20

25

Nominal

Taper changesWidth change

Width changes

Tap

er (

min

)

20

22

24Bottom

5

0

5

10 North bottom

South bottom

Width changes

0 5 10 15 20 25 30 35 40 45 5020

Time (s)0 50 100 150 200 250

-5

Time (min)

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 31

After width change

Validation

MeasuredCalculated,

lidi NFCalculated, ti ki NF

Startup

MeasuredCalculated,

lidi NF

Steady casting, after width change

Measuredsliding NF sticking NF

Top 35.8’ 39.6’ 33.7’

Bottom 20.5’ 14.6’ 19.6’

Measuredsliding NF

Top 34’ 33.2’

Bottom 6’ 6.1’

0

100

200

(mm

)

Measured 35.8'0

100

200

(mm

)

Measured 34'

Bottom 20.5 14.6 19.6 Bottom 6 6.1

300

400

500

600

ow

To

p o

f M

old

Slidi NF

300

400

500

600

low

To

p o

f M

old

700

800

900

1000

1100

Dis

tan

ce B

el Sliding NF

Sticking NF

Measured 20.5'

700

800

900

1000

1100

Dis

tan

ce B

el

Sliding NF

Measured 6'

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 32

1100

0 1 2 3 4 5 6 7 8 9 10

Relative Position of Hot Face (mm)

1100

0 1 2 3 4 5 6 7

Relative Position of Hot Face (mm)

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Ideal Taper?• Compare shell shrinkage

from 2D thermal-stress d l* f lidif i

0

100 Shell Shrinkage

model* of solidifying shell with Total Distortion and a 1%/m linear taper

• Shell-mold friction very

200

300

cus

(mm

)

. w ithout Friction

Shell mold friction very important at early times

• When all effects are considered, applied

400

500

600elo

w M

enis

c

Hot Mold

taper does good job of matching shell shrinkage

600

700

800Dis

tan

ce B

e

• *See Hibbeler Masters Thesis for detail of the shell model

900

1000

-9.0-8.0-7.0-6.0-5.0-4.0-3.0-2.0-1.00.0

Shell Shrinkage w ith Friction

Cold Mold

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 33

shell modelPerimeter Change (mm)

Deviation from Ideal Taper• Shell shrinks too

much = gap opens ( ti b )

0

100Cold Mold(negative numbers)

• Mold pushes too much = mold wear (positive numbers)

200

300

us

(mm

)

. Mold

(positive numbers)

• Both distortion and friction lessen the amount of required

400

500

elo

w M

enis

c Hot Mold

Hot Mold

Cold Mold

NF taper 600

700

800Dis

tan

ce B

e Mold

800

900

1000

D

GapPenetration

without Frictionwith Friction

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 34

-3.5-3.0-2.5-2.0-1.5-1.0-0.50.00.51.0

Shell Penetration into Mold (mm)

GapPenetration

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Mold Wear Validation

• Wear contributions:– “Steady” wear

0.0

100 0Mismatch from creep in mold?Steady wear

– Ferrostatic pressure

– Distortion effects

100.0

200.0

300.0

us

(mm

)

creep in mold?

• Fitting constants:

400.0

500.0

ow

Men

iscu

( )0 pW c c g z d zρ= + +

• Fitting constants: 600.0

700.0

800 0Dis

tan

ce B

el

0 0.97mmc =800.0

900.0

1000.0

0 0 5 1 1 5 2 2 5 3

DMeasuredPredicted6 mm5 10

Papc−= ⋅

Mismatch from spray corrosion?

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 35

0 0.5 1 1.5 2 2.5 3

Mold Wear (mm)

Mold Distortion Conclusions

• Constructed large 3D thermal-stress model of a funnel mold and its water boxfunnel mold and its water box

• Narrow face shows typical distortion behavior• Wide face distortion complicated due to widelyWide face distortion complicated due to widely

varying constraint from different bolts• No operational problems with bolts due to distortion• Possible fin defect problems• Localized distortion causes regions of excessive

( lid t d b t ) b l iwear (validated by measurements) below meniscus and near mold exit– Can lead to shell buckling and cracks

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 36

– Can lead to shell buckling and cracks

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Mold Distortion Conclusions

• Mold distortion has a significant effect on taper

Th th l di t ti f h f th ld i• The thermal distortion of each of the mold pieces, the effect of the changing funnel geometry, and the interfacial sliding of the wide and narrow facesthe interfacial sliding of the wide and narrow faces all contribute to the effective taper seen by the solidifying shell, each in a nonlinear fashion with y g ,distance down the mold

• The thermal expansion of the wide face works against the applied taper and the effect of the funnel, so calculations based only on room-t t di i i ffi i t

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 37

temperature dimensions are insufficient

Transient Behavior – Model Study

• Transient heat transfer analysis with ABAQUS

St t f if 30 ºC• Start from uniform 30 ºC

• Allow time stepping until steady stateD fi d i ΔT 0 001 ºC– Defined as maximum ΔT < 0.001 ºC

– Accuracy-controlled time step for max ΔT < 0.2 ºC

• Steady state (by this definition) reached in 70 s37 2 hours wall clock on 8×2 66 GHz computer– 37.2 hours wall clock on 8×2.66 GHz computer

(excessive paging despite 8 GB RAM, might have memory bug)

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 38

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Thermocouple Temperatures

200

140

160

180

)

1

2

100

120

140

era

ture

(ºC

)

TC 1

TC 2

2

3

4

40

60

80

Te

mp

e TC 2

TC 3

TC 4

TC 5

TC 6

4

5

0

20

40

0 10 20 30 40 50 60 70

TC 6

TC 76

7

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 39

0 10 20 30 40 50 60 70

Time (s)

First-Order Response

• Many thermal systems exhibit first-order behavior

( ) ( ) T Tτ Time Constant( ) ( )

( ) ( ) exp0 τ

− ∞ = − − ∞

T t T t

T T( )0T

( )∞T

Initial Temperature

Steady-state Temperature

τ Time Constant

y = -0.2208x

R2 = 0.9978-1

0

1

y = -0.2342x

R2 = 0.999-3

-2

TC 1

TC 2

TC 3

( ) ( )( ) ( )ln0

− ∞ − ∞

T t T

T T

1τ−

1

-5

-4TC 4

TC 5

TC 6

TC 74.5sτ =

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 40

-6

0 2 4 6 8 10

Time (s)

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First-Order Response

• Time constant characterizes transient behavior200

1160

180

200

86.5%

95.0%98.2%

99.3%

2

3100

120

140

ratu

re (

ºC)

TC 1

63.2%

4

560

80

Te

mp

er TC 2

TC 3

TC 4

TC 5

6

70

20

40 TC 6

TC 7

τ τ τ τ τ

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 41

70 10 20 30 40 50 60 70

Time (s)

Scaling Analysis

• The characteristic time for diffusion is

h L i h t i ti l th d

2

α=cL

t

where L is a characteristic length and α = k/ρ·cp is the thermal diffusivity

• Using properties on slide 3 and L = 22.5 mm (average distance from hot face to channels), tc = 5 s is the characteristic time

• “Back of envelope” agrees with FE model

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 42

p g

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Startup Transient

• Measured transient periods of about 15 seconds agree with prediction of time constantagree with prediction of time constant

• Measured top and bottom NF taper also show 15 second transient periods

34

36

second transient periods

70

75

28

30

32

per

(min

)

Top

50

55

60

65

TC

(o C)

22

24

26

Tap

Bottom

30

35

40

45

T

1234

5

6

7

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 43

0 5 10 15 20 25 30 35 40 45 5020

Time (s)

0 5 10 15 20 25 30 35 40 45 5025

Time (s)

Transient Behavior - Conclusions

• Time constant of NF mold calculated to be about 5 sTransient periods take about 15 s– Transient periods take about 15 s

– Measurements suggest this is approximately correct

• Measured slopes of mold exhibit same transients• Measured slopes of mold exhibit same transients– Thermal behavior dictates mechanical behavior

• Higher frequency behavior likely stick-slip action at• Higher frequency behavior likely stick-slip action at WF/NF interface

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 44

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Acknowledgements

• Tata Steel IJmuiden – Willem van der Knoop, Eddie Nixon, Andy Smith, Ronald Schimmel, and Gert , y , ,Abbel

Continuous Casting Consortium Members• Continuous Casting Consortium Members(ABB, Arcelor-Mittal, Baosteel, Tata Steel, Magnesita Refractories, Nucor Steel, Nippon Steel, P t h P SSAB ANSYS Fl t)Postech, Posco, SSAB, ANSYS-Fluent)

• National Center for Supercomputing Applications• National Center for Supercomputing Applications (NCSA) at UIUC – “Cobalt” and “Abe” clusters

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 45

• Dassault Simulia, Inc. (ABAQUS parent company)