Post on 07-Sep-2018
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
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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
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
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
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
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actual tie rods and spring packsConstraints
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
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
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0 50 100 150 200 250 300 350 400 450 500 550 600 650 700
Distance from Centerline (mm)
Cooling Near Mold Exit
Hot face stays relatively cool with straight water tubes
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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
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
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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
Wide Face Distortion
50× scaled
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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
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
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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:
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
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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
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
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
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
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(due to backlash or other play-mechanisms) so the “interfacial sliding contribution” is included in NF shape
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)
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
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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
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
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
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)
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
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
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)