12 hibbeler mold taper measurements -...

CCC Annual ReportUIUC, August 14, 2013

Lance C. HibbelerPh.D. Student and Lecturer

Department of Mechanical Science & Engineering

University of Illinois at Urbana-Champaign

Modeling and On-Line Measurements

of Narrow Face Mold Taper

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

Introduction

• Narrow face mold taper has been measured online

with inclinometers at Tata Steel IJmuiden

– Funnel-mold thin slab caster

• Modeling of thermomechanical behavior of mold

has been able to match steady-state

measurements of taper

• This work focuses on the behavior of the narrow

face mold during startup


Funnel Mold Geometry

90136.8 top106 bottom

OuterFlat

InnerCurve

OuterCurve

InnerFlat

InnerCurve

OuterCurve

OuterFlat

260

750

1200 (Variable)

23.4 top8 bottom

All dimensions

in mm

• Cu-Cr-Zr alloy– 350 W/(m·K) thermal conductivity– 8900 kg/m³ mass density– 385 J/(kg·K) specific heat capacity– 117 GPa Young’s modulus, 0.181 Poisson’s ratio

• No coating layers


Water Channel Geometry

72

90

Hot Face

Therm

ocouple

Hole

Water

Tube

Bolt Hole

21.3

23.7

10.5 20

510

15

35

Hot Face

Wate

r

Channel

Copper Backing Plate

Copper Mold

Bolt

Hole

Sym

metry

Narrow face Wide face


Waterbox Geometry

• 316 stainless

– 200 GPa Young’s modulus

– 0.3 Poisson’s ratio

All dimensions

in mm

50 50

695

145

685

895

230

212.5 212.5 212.5 212.5 255 260

125

125

125

125

125

125

125

125

75

210

20

20

20

155

50

3030

3072

1100

850

2060

1105

930

1365

50

400

80

Clamping Force


Finite-Element Mesh

Part Nodes Elements

Wide 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 5,148,754

Thermal DOF = 1,089,166

Mechanical DOF = 4,830,081


Thermal Boundary Conditions

• Specified heat flux on mold hot faces

• Convection BC on water channels

• All other faces thermally insulated

• Values calculated from CON1D calibrated to plant measurements [Santillana et al., ISIJ Int. 2008]

0

100

200

300

400

500

600

700

800

900

1000

1100

0 1 2 3 4 5 6 7 8 9

Heat Flux (MW/m²)

Dis

tan

ce B

elo

w T

op

of

Mo

ld (

mm

)

WFNF

Meniscus

33 37 41 45 49 53 57

Convection Coefficient (kW/m²·K)

WFNF

Meniscus

32 34 36 38 40 42 44 46

Water Temperature (ºC)

0

100

200

300

400

500

600

700

800

900

1000

1100

Dis

tan

ce B

elo

w T

op

of M

old

(mm

)

WFNF

Meniscus

spk T− ∇ ⋅ = ⋅n q n

( )k T h T T∞

− ∇ ⋅ = −n

0k T− ∇ ⋅ =n

Qmeas = 2.8 MW/m²Qcalc = 2.7 MW/m²


Mechanical Boundary Conditions

• Ferrostatic pressure on hot faces

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

– Narrow face mold and waterbox centerline

– 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 [-]


Mold Bolts and Tie Rods

• Bolts modeled as truss elements and prestressed according to plant practice– See [Thomas et al., Iron and

Steelmaker 1998]

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

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

Narrow Face

Waterbox

Narrow

Face Mold

Truss

Element

Reference

Points

Distributing

Coupling

Constraints

Bolt Length (mm)

Cross-Sectional Area (mm²)

Applied Torque (N·m)

Pre-Load (kN)

Pre-Stress (MPa)

Stiffness (MN/m)

NF (Short) 150 181 100 30 168 240

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

Lower Tie Rod 1335 1215 -- 70 58 33.4


Steady-State Simulation Results

• Heat transfer: 12 minutes on 8-core 2.66 GHz Intel Xeon

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

• Marched through pseudo-time to get a solution

50× scaled distortion


Thermocouple ValidationCorrected for Wire Convection

17

5 m

m125 m

m125 m

m125 m

m125 m

m125 m

m125 m

m125 m

m

239210

212.5 mm212.5 mm212.5 mm

Outer

Flat

Outer

Curve

Inner

Curve

Inner

Flat

W W W

W W W

A A A

A A A

A A A

A A A

A A A

A A A

227258

220209

48--

185173

177154

161163

46--

166150

160148

145154

46--

155150

151130

138144

46--

148154

144140

131145

47--

154152

150154

138150

48--

152151

151144

143151

48--

197194

199185

196186

64--

21

5 m

m1

34

mm

13

4 m

m1

34

mm

13

4 m

m1

34

mm

13

4 m

m

X

Z

Y

ZW

W

W

W

W

W

W

199191

160160

147155

137148

141149

147145

150132

Tcalculated (ºC)

Tmeasured (ºC)

NF WF


Cooling Near Mold Exit

Hot face heats up as channels curve away

Hot face stays relatively cool with straight water tubes


Wide Face Temperatures

0

50

100

150

200

250

300

350

400

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

Distance from Centerline (mm)

Wid

e F

ace H

ot

Face T

em

pera

ture

(°C

) .

Inner Flat Inner Curve Outer Curve Outer Flat

z = 1050 mm

z = 850 mm

z = 650 mm

z = 416 mm

z = 251 mm

z = 152 mm

z = 100 mm

Bolt

Colu

mn

Bolt

Colu

mn B

olt

Colu

mn

Mold

Level

Sensor

Bolt

Colu

mn

Slight 2D heat transfer in funnel region (less than 2 ºC), but change in cooling around bolts is more significant

Large change in cooling near mold

exit


Wide Face Mold Distortion

50× scaled distortion



Out-of-Plane Behavior

Ou

ter

Fla

t

Ou

ter

Cu

rve

Inn

er

Cu

rve

Inn

er

Fla

t

Short

120

98

137

137

299

863

158

181

157

549

137

18

57

52

225

X

Z

Bolt Stress

in MPa

10720219

102

24

13

23

87

13619418565

12815815841

242

277116 81

31

60

79

78

68

54

35

13

7Long

212.5 mm212.5 mm212.5 mm

50 m

m175 m

m125 m

m125 m

m125 m

m125 m

m125 m

m125 m

m125 m

m



Out-of-Plane Behavior

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

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

Distance from Centerline (mm)

Wid

e F

ace H

ot

Face D

isp

lacem

en

t (m

m)

.

Inner Flat Inner Curve Outer Curve Outer Flat

z = 1050 mm

z = 850 mm

z = 650 mm

z = 416 mm

z = 251 mm z = 152 mm

z = 100 mm

Bolt

Colu

mn

Bolt

Colu

mn

Bolt

Colu

mn

Mold

Level

Sensor

Bolt

Colu

mn

SEN

Waterbox



Behavior at Centerline

0

100

200

300

400

500

600

700

800

900

1000

1100

0 50 100 150 200 250 300 350 400 450

Temperature (ºC)

Dis

tan

ce B

elo

w T

op

of

Mo

ld (

mm

)

-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

Centerline

SEN Waterbox

Temperature Displacement

Meniscus

Bolt

Bolt

Bolt

Bolt

Bolt

Bolt

Bolt

Bolt

Bolt



In-Plane Behavior – Towards NF

0.77

0.80

0.81

0.85

0.90

0.44

0.52

0.55

0.59

0.65

0.00

0.00

0.00

0.00

0.00

Short

X

Z

Long

0.000.400.72

0.43

0.38

0.35

0.35

0.38

0.000.410.761.01

0.000.470.941.27

0.44

0.000.320.73 0.58

0.70

0.66

0.66

0.69

0.76

0.89

1.08

1.34

0.77

100× scaled distortion in x-direction



• Distorts into a ‘W’ vertically and horizontally

– Largely because of different stiffnesses of bolts

• Distortion follows bolting pattern more than the thermal response

– Short bolts provide most resistance to distortion

• Cold edges constrain against distortion

• Most severe distortion

– Just below meniscus and just above mold exit

– In between bolt columns


Narrow Face Mold Distortion

0

100

200

300

400

500

600

700

800

900

1000

1100

0 50 100 150 200 250 300 350 400

Temperature (ºC)

Dis

tan

ce B

elo

w T

op

of

Mo

ld (

mm

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Displacement (mm)

Narrow Face

Centerline

SEN Waterbox

TemperatureDisplacement

Meniscus

Bolt

Bolt

Bolt

Bolt

Bolt

Bolt

Bolt

Bolt


NF Taper Measurements

0

100

200

300

400

500

600

700

800

900

1000

1100

0 1 2 3 4 5 6 7 8 9 10

Relative Position of Hot Face (mm)

Dis

tan

ce B

elo

w T

op

of

Mo

ld (

mm

)

Sliding NF

Sticking NF

Measured 20.5'

Measured 35.8'0

100

200

300

400

500

600

700

800

900

1000

1100

0 1 2 3 4 5 6 7

Relative Position of Hot Face (mm)

Dis

tan

ce B

elo

w T

op

of

Mo

ld (

mm

)

Sliding NF

Measured 6'

Measured 34'

MeasuredCalculated, sliding NF

Calculated, sticking NF

Top 35.8’ 39.6’ 33.7’

Bottom 20.5’ 14.6’ 19.6’

Measurements during startup

MeasuredCalculated, sliding NF

Top 34’ 33.2’

Bottom 6’ 6.1’

Measurements during steady casting


Narrow Face Mold Distortion

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

– Elongates by 2 mm

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

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

– No risk of mold overconstraint or bolt shearing failure

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

– Bolts near hooks do not overcome prestress


Effect of Distortion on NF Taper

• Calculate perimeter of mold as function of distance down the mold

• Contributions from

– Funnel geometry

– Wide face expansion

– Narrow face distortion

– Prevented sliding of

WF relative to rigid NF

• Sliding should be considered during startup and in molds with rigidly positioned NFs

0

100

200

300

400

500

600

700

800

900

1000

-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)

Dis

tan

ce B

elo

w M

en

iscu

s (

mm

) Total

Nominal

Funnel

Narrow Face

Distortion

Wide Face

Distortion

Interfacial

Sliding


ConclusionsMold/Waterbox Behavior

• WF distortion complicated because of bolts

• NF distortion typical

• Good design principle: oversize bolt holes in the waterbox to allow transverse movement

• Distortion has a significant effect on taper

– Not linear with distance down the mold

– Room-temperature calculations are insufficient

• More details found in

– Hibbeler et al., Met. Trans. B, 43 (2012) p. 1156.


1

2

3

4

5

6

7

Startup Transient

0 5 10 15 20 25 30 35 40 45 5020

22

24

26

28

30

32

34

36

Time (s)

Taper

(min

)

Top

Bottom

0 5 10 15 20 25 30 35 40 45 5025

30

35

40

45

50

55

60

65

70

75

Time (s)

TC

(oC

)

1234

5

6

7

• Inclinometer and thermocouple data from a startup provides great validation for exploring mold behavior during a startup

• TC temperature show first-order behavior– Time constant about 5 seconds


Startup Heat Flux Profile

• Assume that the heat flux profile has a certain shape, , applied over a region from z = ztop to z = zbot.

• Stretch this profile by changing ztop according to filling a rectangular prism and zbot

according to dummy bar movement

• Estimate filling rate: Q = 0.0048 m3/s

• Filling time gives

� � ��

1 � �

�� /�

��

�� ! ��

��

�� ! ��


Startup Heat Flux Profile

A rough first approximation to the startup heat flux


Startup Thermal Behavior

5 s 10 s 15 s 20 s 30 s 40 s 50 s


Thermocouple History

• Obviously, heat load BC needs improvement

• Two-stage filling of mold– “Waterfall” until mold level covers nozzle ports

– “Pipe flow” after ports are submerged

0 5 10 15 20 25 30 35 40 45 5025

30

35

40

45

50

55

60

65

70

75

Time (s)

TC

(oC

)

1234

5

6

7


ConclusionsMold Startup Behavior

• Preliminary study of mold startup provides

reasonable results

– Mechanical simulations to come: try to match taper

measurements

• Heat flux boundary condition needs improvement

– Use plant data (stopper rod position, nozzle geometry,

dummy bar/casting speed history, etc.)

• Inclinometers are a good tool to use for measuring

taper during casting


Acknowledgments

• Continuous Casting Consortium Members(ABB, ArcelorMittal, Baosteel, MagnesitaRefractories, Nippon Steel and Sumitomo Metal Corp., Nucor Steel, Postech/ Posco, Severstal, SSAB, Tata Steel, ANSYS/ Fluent)

• National Center for Supercomputing Applications (NCSA) at UIUC

• Ronald Schimmel, Gert Abbel, Henk Visser, Dirk van der Plas, and others at Tata Steel IJmuiden

12 hibbeler mold taper measurements -...

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