cold shut formation in castings - mcgill...
TRANSCRIPT
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COLD SHUT FORMATION IN CASTINGS G ,1
r ...... ' ....
by
Luiz Augusto Siqueira Bittencou-rt
A Thesis, Submitted to the Faculty of Graduate Studies and Research
in Partial Fulfillment; of the Requirements for the Degree of Master of Engineering.
Oepartment of Mining and Metallurgica1 Engineering McGill University Montreal ~ Canada
~ September 1979
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ri To my parents
Augusto and Lady,
to my wife Eliane,
and to my sons .~
Claudio and Eduardo. )
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ABSTRAIT
An experimental investigation into cold shut formation in ,
castings has been carried' out. Results indicate that cold shuts are
formed when liquid metal. overflowing solid metaI, does not compietely "
remelt the soUd. As the occurrence of the defect depends upon the
thermal energy of the liquid, effective super~at (superheat at which
the liquid meets the solid metal) is the most important variable
affecting the co Id shut formation. TIlis superheat is controlled by
both the pouring rate and the 'superheat at pouring. \
'A mathematical model was developed. to predict the remeiting
phenomena (invoived in the formation of the defect) of ~n idealised
system. Critical conditions for::. cold shut formation ha~J been caIcu-
Iated in terms of melt superheat, temperature of solid metal and distance'
from the point of pouring.
The collision of two liquid metaI,streams also causes' the
formation of cold shuts due ta splashes which 'quickly sOlidify on the
mold wall. ' ,
The alloy composition was found to affect the appearance of
~he defect due to the mode of solidification.: While pure Pb and the , ,
Pb- Sn eutectic produced very marked defects, a Pb-I9% Sn alloy wi tp a
wide freezing range formed cold shuts which were neither as visible
nor as continuous as those formed in congruent meiting alloys.
Results have shawn that the head of metai has a strong
influence on the occurrence of misruns.
It waS foulld that water is an adequate fluid for simulating "
the collision of two strearns of liquid metai inside a channel.
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RESUME -'--
r ~, ) Une recherche expérimentale sur la formation de "reprise"
1 \1" ,~_
" '1:01'5 d'itine' coulée a été faï te. ç,' ," •
Cl' ~~
Les resultats indiquent que cette "reprise"
/ ."" '. e'~t formée,' lo~sque le métal liquide qui reCOllvre le métal soHd~ ne , 1
fait pas com1ètement fondre le méta} solide. La f~rrJ~tion de cette \ ..
imperfection dép'~nds de l'énergie thermique du liquid, mais la tempéra-"
"
ture du liquide (température qui est supérieure au point de 'fusion)
lorsque le métal liquide entre en contact ave'c le métal solide, est
la facteur le plus important, quant à cette format:lon e ce "reprise ll•
Cette tempé~ature'est contrôlée à la fois par le coulee et
par la temperature de la coulée.
Un modele iÎlathématique a 'été développe afin de prevoir ce
phénomene de refonte (impliqué dans la formation de cet imperfection).
dans un systeme ideal.
Les conditions critiques pour la formation de cette "reprise"
ont été calculées en fon~ion de la température de fusion. de la
température du métal solide et de la distance à partir du point de coul(!e.
La collisiun de deux courrants de métal liquide causes aussi "
la formation de IIreprise" dû !iux éclaboussures qui se solidifient' tres
rapidement sur les parois du moule.
La composition de l'alliage joue aussi tUl rôle dans la forma
tion d'imPerfections, dO au mode de solidification. Par exemple, le ~
Pb pure et le Pb-Sn eutectique produisent des imperfections tres marquées.
Par contre un alliage dé Pb-19% Sn. av~c un large echelle de congelation.
produit des "reprise" qui ne si sont ni visibles. ni continus, tel.s ceux "
formes' par des a,Uiages qui ont un même point de fusion.
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Les resul tats montrent que' la pression de chute (tête de
chute) a 'une forte influence sur la formation d'imperfections.
iii.
Il 'a été trouve que l'eau est un fluide adéquat pour
simuler la collision de deux courrants de metal liquide à l'intérieur
d'un canal.
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ACKNOWLEDGEMENTS
The author wishes to. express his profound gratitude to those
, who hav'e, in various ways, contributed to this work. He 1s particularly
indebted to:
Dr. J.E. Gruzlesk1 and' Dr. R.I.L. Guthrie, directors of this ,
study, for their constant interest, understanding and encouragement
during the course of this work.
Messrs. S. Argyropoulos, F. Mucciardi, M. Tanaka, R. Harris
and R. Barnhurst, graduate students of this department, for giving
invaluable assistancé in several phases of this study.
·Mr. M. Knoepfel, for his help in ,constructin~ the appa~atus,
Mr. J. Quaroni, for correcting the English languag~ of this thesis and
Mrs. H. Rousseau for typing this manuscript.
The National Science and Engineering Research Council of
'Canada. the Canadian International Development Agency, Sec~etaria de
Tecnologia Industrial and Companhia Siderurgica Nacional for their
financial·support.
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TABLE OF CONTENTS
ABSTRACT RESUME ACKNOWLEDGEMENTS TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLES
CHAPTER 1. INTRODUCTION
1.1 A General View on Casting Defects 1.2 Cold Shuts: A Literature Revie\'l
1.2.1 Cold Shuts in Sand Castings 1. 2. 2 Fluidity: An Important Factor 1.2.3 Cold Shuts in Electron lleam Welds 1. 2. 4 Cold Shuts in Die Casting
1.3 Aims of the Present Work
QIAPTER 2. MODEL EXPERIMENTS WITII WATER AND ,MERCURY
2.1 Similarity Criteria 2. 2 Appara tus 2.3 Experimental Procedures 2.4 Results
CHAPTER 3. EXPERIMENTS WITH LEAD AND LEAD-TIN ALLOYS
3.1 Molding Procedures 3.2 Mel ting Procedures 3.3 Pouring Procedures 3. 4 Experiments
3.4.1 3.4.2 3.4.3 3.4.4 3.4.5
3.4.6 3.4.7
::;.5 Results
3.5.1 3.5.2 3.5.3
Simple Experiments without Lad1e Simple Experiments using Ladle Experiments using Obstacles Experiments without Cope Experiments with a Chili Bottom in Ha1f Mold Experiments using Solid Inserts Exper iment s'' using a Stepped Mo1d
Simple EXperiments without Ladle Simple Experiments using Ladle Experiments using Obstacles
v.
i, ii iv v
vii xii
1
1 9
11 13 21 23
25
26
26 28 28 39
44
44 50 50 50
SI SI 52 54
S4 SS 60
63
63 63 74
y y 'i7 qz 7";-
r 16 1
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3.5.4 Experiments without Cope 3.5.5 Experiments with a ChilI Bottom in
Half Mold 3. 5 .6 Experimen ts us ~ng So lid Inserts 3.5.7 Experiments using a Stepped Mol~
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CHAPTER 4. HEAT TRANSFER MODEL
4.1 Definition of the Problem 4.2 General ,Equations 4.3 Initial and Boundary Conditions 4.4 As sumptions 4.5 Explicit Finite-Difference Technique 4.6 Stability 4.7 Computer Mode1' 4. B Experiments for Temperature M~asurement 4.9 Resu1ts \
4.9.1 Comparison between Expe_~rentâl and Theoretica1 Resul ts
4.9.2, Predictions of the Model 4.9.3 Effect of SoUd Temperature and
Superheat on Co1d Shut Fo~tion 4.9.4 Effect of Position in the Mold on
Cold Shut Fomati-ôJr \
CHAPTER 5. DISCUSSION
5.1 Mechanism of Cold, Shut Formation 5.2 Erfeet of Superheat and Alloy Composition on
Cold Shut Formation 5.3 Effect of Superheat and Head of Metal on
Misrun 5.'4 Effect of Position in the Mo1d on Co1d Sh'ut
Formation 5.5 Eff èet of Pouring Rate on CoId ~hut Formation
QIAPTER 6. CONCLUSIONS AND SUGGESTIONS FOR FURrrHER WORK
6.1 Conclusions 6.2 Suggestions for Further Work
APPENDIX A
REFERENCES
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vi.
Page
74
75 \ 7S \ 81 \
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B8 89 92 95 96
106 106 107 111
116 lIB
127
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143 146
147
147 148
,149
161
Figure
1.1
1.2
1.3
s 1.4
1.5
, 1.6
1.7
~I 1.8
1.9
l.lOa
1. lOb
1.11
1.12
1.13
1.14
1.15
1:16
1.17
1.18
LIST OF FIGURES
Typical gas evolution cavity on a cope surface.
Typica1 shrinkage defect occurring in a thick section which could not be fed.
Typical surface defeet defined as inclusions.
Expansion scab caused by slO\~ pouring which permitted ,excessive heating of the cope surface before meta1 contact.
A hot tear in a steel· casting.
Typical parting line runout occurred as a result of the core holding the cope out.
A typical mo1d shift is shown where a cope and drag did ,not match.
Typica1 wash or cut in the gate area.
Typical erosion scab on the core surface.
Lion' s head - the who1e casting.
Detail or co Id shut.
Mold .develop~d to study the rnechanism of bp fonnation.
Influence of tapping temper~ture on cold shut formation.
Relationship between fluidity and alloy compos i tion, in lead-tin system.
Relationship between fluidity and superheat for the Pb-6S.25% Sn al1~y.
Schematic diagram 01: flow and solidification of a pure metal in a fluidity channel (no superheat).
Schematic ,diagram of flow and solidification of a .pure mataI in a fluidity channel (with superheat).
Schematic diagram of flow and solidification of a dilute alloy in a fluidl.ty channel (no superheat).
Schematic diagram of flow and solidification of an alloy which readily nucleates fine grains (no superheat) •
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3
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7
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10
10
12
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Figure
1.19
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2.1
2.2
2.3
2.4
2.5 '
2.6
2.7
2.8
2.9
2.10
, 3.1
3.2
3.3
3.4a
3.4b
3.5
3.6
3.7
3.8
3.9
Influence of cold shut on fatigue of 5083 aluminum alloy.
Plastic mold for water and mercury.
I?lastic mold wi thout cover showing the runner.
Dimensions of the plastic mo1d and direction of flou ins ide the channel.
Tank used for reproducible pouring rates.
Friction factor as a function of Rèyno1ds number.
SCRcmatic representation of h10 strearns of liquid meeting inside a channel.
Flow visualization for a channel 1.27 cm high (water).
Flow visualization for a channel 1. 2I' cm high (mercuIY.) •
, Flow visualization for a channel 0.635 cm high (water).
Flow visualization for a ·channel 0.635 cm high (mercury) .
Dimensions of the sand mold and directions of flow inside the channel.
Section AB o'f the sand mold.
Flask.
Graphite ladle.
Graphite plug.
Sand mo1d for experiments using soliq inserts.
l ,
Two sohd samples as placed on the channel.
Pb- Sn phas e diagram.
The stepped mo1d. \ ,
Typical cold shuts formed in experiments without ladle (superheat = 50oe).
viii.
24
29
30
31
32
33
34
35
36
37
38
4S
46
'48
49
49
57
58
61
62
64
Figure
3.10
3.,11
3.12
3.13
73 3.14
3.15
3.16
3.17
3.18
3.19
3.20
3.21
3.22
3.23
3.24
3.25
3.26
ix.
Typical cold shuts formed' in experiments using Iadle (superheat = SOOe). 66
Typical cold shuts formed in experiments using Iadle (superheat = 70°C). 66
Typical cold shuts formed in experiments using low pouring rate (superheat = IOO°C). 67
Flow visualization for a channel 1.27 cm high (lead). 68-69
Typical de.fect at the bottom of the samples when sprue diameter exceeded 1.0 cm. 73
Typical cold shuts formed in experiments wi thout cope (superheat = 70°C).
Typical cold shuts formed on the bottom surface of the sample (superheat = 15°C).
Typical structure obtained from experiments using inse;rts (not remelted).
,Typical structure obtained from experiments using inserts (almast totally remelted).
Typical cold shut formed in alloy of eutectic composition.
Structural difference in both sides of cold shut for eutectic (not etched).
Typical cold'shut formed in Pb-19% Sn alloy.
Structural difference ,in both sides of cold shut for Pb-19% Sn alloy (not etched).
Bottom surface of sample from stepped mold (Pb -superheat : 25°C).
Bottom surface of sample from stepped mold (Pb -superheat = 75°C).
Cold shuts formed at, the side of samples from s4epped mold (Pb - superheat = 25°C).
Cold shuts formed at the side of samples from stepped mold. (Pb - superheat = ISOOC).
76
76
83
83
84
84
85
85
87
87
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Figure
4.1
4.2
{O C, 4.3
,0 4.4
(1 "L 4.5 J ,
1/3> 4.6
1 l '-{ 4.7
11\ 4.8
1 ( 7 4.9
\
4.10
4.11
4.12
4.13
(7 ") 4.14
1 2 Cf 4.15
4.16
4.17
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Schema tic cross section of the mold.
Network of nodal points.
Positions of thermocouples inside the samp1es.
Positions of thermocouples in the bath.
Re1ationship betl'leen bath temperature in front of position 1 and time (Pb).
1
Relationship between bath temperature in front of position 3 'and time (Pb).
Re1ationship between bath temperature in front of position 1 and time (Pb.19% Sn).
Relationship between bath temperature in front of position 3 and time (Pb-l9% Sn).
Comparison of experimental and predicted temperature at nodal point 10 (Pb - position 1).
Comparison of experimental and predicted temperature at nodal ~int 10 (Pb-19% Sn - position 1).
1
Comparison of e~perimental and predicted temperature , at nodal' point 10 (Pb - position 2).
Comparison of experi~1 and predicted temperature at nodal point 10 (Pb-~9~ Sn - position .2).
Comparison of experimental and predicted temperature at nodal point 10 (Pb - position 3).
Comparison of experimental and predicted temperature at nodal point 10 (Pb-19% Sn - position 3)".
Predicted temperatures at nodal point 10 at different' positions in the mold (Pb-superheat ~ 60~C).
Predicted temperatures ,t nodal point 10 at different positions in théi mold (Pb-19% Sn - superheat = 60°C).
Predicted temperatures at nodal point 10 at different positions in the mold ..... {.E!>-superheat = 20°C).
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x.
Page
90
97
109
110
112
113
114
115
117
119
120
121
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124
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126
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Figure
4.18
4.19
4.20
4.21
4.22
4.23
4.24
4.25
5.1
5.2
'-Il... 5.3
5.4'
5.5
5.6
Relationship between critical superheat to form co1d shuts and temperature of solid sample (Pb -position 1). ,1 l,
Relat~onship between crit.ical superheat to form co1d shuts and temperature of solid sample {Pb -'position 2).
Re,lationship between critical superheat to form cold shuts and temperature of solid samp1e (Pb -position 3).
Relationship between critical superheat to form co1d shuts and temperature of solid 7~mple (Pb-19% Sn-- position 1). \
\ Relationship between critical superheat to form co1d shuts and temperature of solid sample (Pb-19% Sn - position 2).
Relationship between critical superheat to forro co1d shuts and temperature of s61id sample (Pb-19% Sn - position 3).
Re1ationship between critica1 superheat to foim cold shuts and position in the mold (Pb). '
Re1ationship between critical superheat to form co1d shuts and position in the mo1d (Pb-19% Sn).
Schematic diagram of co1d shut formation.
Relationship between·,~ffective superheat. alloy composition and occurrence of cold shuts.
Schema tic diagram for the remelting of an unalloyed metal.
Schematic diagram for the remelting of a large freezing range al1oy.
Relationship between the head of metaI, the superheat and the occurrence of misruns.
Re1ationship between position in the mold and the superheat at which the ~iquid reaches the position.
xi.
129
130
131
132
133
134
135
136
138
140
142
142
144
145
7
1,- l
!Î
71
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Table
, 1.1
1.2
2.1
2.2
2.3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
\.11
3.12
4.1
4.2'
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LIST OF TABLES
Causes of Cas~~~efects
Principal c(uses of Cold Shut in Die Casting
Dime~~~s Groups Pertaining to Fluid Flow
Exper al Variables for the Flow of Water and Mercury in a Runner 1.27 cm High
Experimental Variables <for the Flow of l'later and Mercury in a Runner 0.635 cm High
Physical Properties of Quartz Glass
Experimental Varia,ble·s for Experiments without Lad1e
Exper!.:glental Variables for Experiments usiIJ.g Ladle "
Experimental Variables ror Experiments using Obstacles
Experimental Variables for Experiments without Cape
Experimental Variables for Experiments with a ChiH Bottom in Half Mold
Experimental Variables for Experiments using Solid Inserts
Experimental Variab1es,using a Stepped Mold
Experimental Variables for the Flow of Water, Mercury and Lead in a Runner 1.27 cm High
Schematïc Diagram of the Remelting Phenomenon
Schematic Diagram of the Remelting for Clean Samples
Schema tic Diagram of the Remelting for Oxidized Samples
Thermophysical Properties Used
Experimental Values of ,Temperature Measurements
xii.
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60
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~ 80
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CHAPTER 1. INTRODUCTION
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1.
1.1 A General View on Casting D~fects
The art of metal casting is one of the aldest and most
durable exampIes of the production of metaI objects and will probably
continue to be ~he best w~y to produce comp1icated shapes. The casting
process, involving the flow of molten metal and the flow of heat, is
the central part of the foundry industry. Basically, for a S~UDd metal
casting, the liquid me~al should both fill the mold cavity as quicklY.
as possible and soUilly, by losing heat, from the remotest regions in-
\'lard tOl'lard the source of molten metal. Only if the metal and heat
flow sequence is properly coordinated, "can the final product be expected
to be free from defects. Otherwise, there will be a high probability
of the occurrence of imperfections.
Many times, the appearance of a simple défect, weIl known to
the foundryrian, becomes a complex problem because the causes of casting
defects are ~idespread throughout the foundry process. Table 1.1,
showing the influence of Il processes in the foundry on 10 ,common ,
defects, illustrates where these defects can occur. I~ can be seen
that metal composition, melting and patterns are, generally, less fre-
quent, but not less important, causes of defect formation in castings.
At this point, a general explanation on those defects shown
on Table 1.1 is useful.
Gas Defects (Blowholes, Pinholes" Blisters and' Body Scars)
are cavities (Fig. 1.1) causèd by localized gas pressure that exceeds 1
the metal pressure.
Shrinkage Cavities are ragged cavities lined wi~h dendrites1
(Fig. 1.2). This defect can be easily confused, with some of the gas
defects. A helpful simple difference is that gas d~fects are smooth
f
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2.
TABLE 1.1
Causes of Casting Defects
bl)
= = .,.-4
b4 cu 0 .j.J
= (J .,-j al .,-j Vl .,-j +.> I-t b4 H cu .j.J .,-j> Vl cu b4 cu '1:1 U U Vl ;:3 8-.,-j Vl = .,-j al 0 0 ~ .,.j al +.> I-t ~ cu
~ tJ) u Q., = ~ Vl <Ill' cil 0 CIl 0
.~ tl!T bIl H bIl b4 b() U .... Vl
So Vl = Q. = = = .... I-t H
~J ..10: Vl .,.-4 .,-j .,-j .,-j ri cu cu 0 • .-1 Vl cu '" cu '" ~ I-t al u .o~ Vl ~ al ~ .... H .... .... ;j +.> Vl El (J
Defects cu Ils ri Ils 0 0 0 cu 0 cu ..-1 ;j al~
CI Q., ~ t.:l ::E: u ::E: ::=: Q., ::=: ;:;: z~
1 Gas Defects x x x x x x x x x x 10 . 2 Shrinks x x x x x x x 8
3 Inclusions x ,,-_.)t x x x Ji: x x 8
4 Expansion Defects x x x x x x x 7
5 Hot Tears x x x x x x x x x x x 11
- 0
6 Misruns & Co1d Shuts. x x x x x x x x x x x Il
7 Runouts & Bleeders x x x x x x " x x 8
v
ST' x x x x x x 6
9 ,ts. &
~ Washes x x :lt X x x x 8
10 Erosion Scabs x x x x x x x 8
Number of Defects . Caused by Each Factor 9 6 9 9 9 9 9 5 10 4 6
Sources: References 1 and 2.
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FIGURE 1.1 Typical gas evolution cavity on a cope surface. 1
~IGURE' i.2
'.
Typica1 shrinkage defect occurring in a thick section which could not be fed. 1
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4.
and shrinkage cavities are dendritic, but the diagnosis must be as
careful as P?ssible. This defect is caused by lack of sufficient feed
metal.
Inc'lusions (non-metallic) are particles of foréign IIl8;terial
embedded in, the metal l (Fig. L 3) and may be due to the presence of
slag or oxide particles in the molten metaI.
Expansion Defects (Expansion Scabs, Buckle, Rat-tai1,
Blackening Scab and Pull Down) are indentations in the surface or
rough layers of metal on the surface of the casting1 (Fig. '1.4). These .'
'defects arise from faults in mold construction or from poor-quality
~and.
Hot Tears are cracks (Fig. 1. 5) developed during solidifica-
tion and are caused by a restriction from contracting in certain areas
, which become under tension.
Misruns and Cold Shuts will be analyzed in Section 1.2.
Runout~.and Bleeders'are incomplete castings l (Fig. 1.6) and
are due to, for instance, a weak mold or premature removal of clamp.
Shift is a mismatch of the ,castLQg at the parting linel
(Pig. 1.7) and is probably caused by pat~ern equipment, flask equipment ,
or molding practice.
Cuts and Washes are rough spots and areas of excess metal l
(Fig. 1.8) caused by erosion of the mold.
Erosion Scab is an expansion defect in whieh the loosened
sand has been eroded awày by.~he motion of metal l (Fig. 1.9).
On the appearance of any type of defeet, a very careful
analysis must be made in order to avoid incorrect diagnosis which can
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FIGURE 1.3 Typical surface defect defined as inclusions. l
. FIGURE 1.4 Expansion scab caused by.slow pouring which permitted
excessive heating of the cope surface before metal Contact. 1
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FIGURE 1.S A hot tear in a steel casting. 4
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FIGURE 1.6 Typical parting iine runoui occurred as a result of the core holding the cape out.
6.
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FIGURE 1. 7 A typical mold shift is shmm where a cope ana-drag did not match. l
FIGURE 1. 8
1 r--
1 Typical wash or cut in the gate, area.
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FIGURE 1. 9 Typical erosion s~ab on the core surface. 1
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be expensive. Many times the cures for the actual defeet are the , )
opposite of those for the defect' the analyst has in mind.
Ec~nomically, the occurrence of any imperfection i5 always
detrimèntal ta the fOUndry industry. This is particularly true if the
defect is not detected before delivery of the casting to the customer.
If the defect is discovered in the foundry, some extra process will
become necessary, for instance grinding, in arder to avoid scrapping
the entire casting. In either case, there is a waste of both manpower
and energy.
A common defect which increases the cost of' any casting ls !>
cold shut. Various aspects of the formation of this defeet will now
be reviewed. 1
1. 2 Cold Shuts: A Literature Review ~
Although the appearance of any casting defeet is beeoming
economica.lly more and more important, due ta qua lit y and energy con-
sideration, the mechanism of formation of many imperfections remains
unknown because few attempts have been made ta treat these common
defects in a scientific manner. Cold shuts, for instance, are a quite
common surface defect being, in many cases, the number one source of
unsalable castings. Despite this, the exact conditions governing their
formation have not yet been identified.
A cold shut can be described as a definite discontinuity on
the cast~ng surface with.the appearance of,a crack,with roundéd edges
(Fig. 1.10). A 1iterature rev'Îew has shown that' it 'ha,s generally been
assumed to be caused by the meeting of two streams of metaI. 1,3-7
, '
\
FIGURE 1.10 a) Lion's Head - the who le casting. Material: commercial pure lead Magnification: , O.3x
. '\ FIGURE l.ID b) Det~il of cold shut. 0
Material: commercial ·pure lead Magnification: O.5x
, - ~ 1:- ~ =- ::;.: ....... :::;,. -""'~r" _" h ~- ,: , __ ~:~,.t_:;.., ~.i:'i~:;;:~.~~,jffgfA~~ ... :.:.......&.:c-~=-.;:;c,;:~ ___ ~ ,~~~t" __ <"'.A><,,"'."' .. m.=""'""-. ___ ~ __ _
10.
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11.
Al though few researchers have worked on this defect ~ sorne
interesting conclusions can be drawn from their work which is dea~t
with in the remainder of this chapter.
1. 2. 1 Cold Shuts in Sand Cas tings
Gorbachev and Zhukov8, studying the formation of soft struc-
tures in the white ir~nJ poured wedge samples in sand molds with a
steel plate as a chilI in the small end. These samp1es were poured in (,
an intermittent stream of variable pause and compared with wedges poured
without intermission. They found that the soft structure in the chilled
layer had a much lower hardness than the fully chilled structure and
they concluded that the local 1055 of hardness in the white iron layer
is due t,o the eddy formation in the chill areas. In this case, the cold
shut for~ation depends on whether the eddy is completely or partially
solidified. In the first case, a cold shut is formed. In the second
case, cold shut is avoided.
9 Kvasha .!:!. al. have developed a special mold. (~ig. 1 ~ 11) to
study the lap formation on the surface of iron castings'. They have , {
found that the carbon; formed by pyrolisis of the hydroc.arbons contained
.on the metal/mold interface. is adsorbed on the surface of the meta!.
If, sl,lbsequent ly, the accumulations of carbon are not absorbed by the
metal, laps are formed on the surface of' the castings. Thus, the
material in the laps and visible on the surfaces is amorphous carbon.
They have aIso found that:
- ,For a giv(m sand, the number of laps formed is propoftional
h . ')
to t e degree of compactJ.on.
/
. '
12.
\
1-FIGURE 1.11 Mo1d developed to study' the mechanism of lap formation. 9
70
20 0
1
1 1 1 1 1
-..
90
14
1
1 1 1 1 1
20 1 1 1
1 1 -.-1'-1 -1 1 1 00 1 n -1 1 1 >
1 1 1
~ 1 1 1
200
UN IT = Not given ln reference 9.
Likely to be cm.
(
13.
- AlI other parameters being constant, between 3.5 % and 7.0%,
water content has a low effect on 1ap formation.
- The meta! composition is not important but the poul'ing
temperature exerts a strong influence on the defect formation.
- There is not any significant change in structure of the metaI
at the points wher~ most of the laps are found.
Lillieqvist lO • working on the influence of temperature on the
surface appearance of steel castings has found that the cold shut for-
mation is inverse!y proportional to the tappi~g temperature of a basic
open hearth furnace (Fig. 1.12).
1.2.2 Fluidity: An Important Factor
A superficial analysis of Table 1.1 shows that the cold shut
is on'e of the few casting defects l'ihose causes can be found in almost
every pr'Ocess in the foundry, the cleaning operation being the only
exception. Although'metal composition is not a very common cause of
most of the defects, it is of utmost importance to the cold shut forma
tion aqd it is generally blamed, together with pouring practice, for
the major percentages of cold shuts. This is 'because the 'composition "rte
exerts ~ strong influence on the fluidity whi~ is accepted ta be among
4 11 the most usual causes of cold shuts.' Here, it should be pointed
out that the term "fluidity", in the foundry sense, means the ability
of the metai to fili the mold cavity and it is the value of ~n empirical
measure of the distance the molten met.aI can reach in a standard meld
(spiral channeI3 or vacuum fluidi ty test 12) befere being stopped by
solidification.
FIGURE 1.12 Influence of tapping temperature on cold shut formation,lO
. '
14 .
, , .
,~ "
"
4r-------------------------------__________ ~
Z :::l'
'" III oach point reprosonts
~ 3 monlhly ovoroge
1-:::1 X III
Q .... 0 U 1
lOI 2 p
> ;: U o lOI ... lOI 0
0-
Z lOI
\~\ ~ .......... U
'" , , lOI a.
o
2925 2950 2975 3000 TEMPERATURE lOf)
(
, j
.- ....... ,....,....~~~~4. ............... ----------"---....--.... ... _~~=<"', h';:r. -~,Ir'l';:r.:_';; ~~1.~- -:: .,.,.~' ... * ___ , ", ~ -
15.
The rela'tionship betlleen metal composition and fluidity has
been studied by sorne workers and it is explained on the basis of the
12 mode of solidification. Ragone ~ al. ,working on Ph-Sn alloys and
using the vacuum fluidity test (which has better accuracy thân the
spiral test because it avoids the human factor in pouring -and because
the pressure head' 1S instantaneousIy applied) show that fluidity is ~~ 1 _ J
inversely proportional to the freezing range (liquidus temperature -
solidus temperature) and proportionaI to the §uperheat. This is shown
in Figures 1.13 and 1. 14 and i t is du~ to the solidification behavior
''Ihieh is wei~ explained by Niesse et al. 13
Pure metai \..rith no superheat, entering the mold èavity, begins
solidification immediately wi th a smoot~ liquid-solid interface (~ig.
1.ISa). Metal continuing to flow continues solidification alon'g the
mold wall (Fig. 1.1Sb) but- flow is eventuaHy choked-off at the entrance
(Fig. 1. ISe). The only effect of superheat on this mechanism is that·
the point where flow stoppage oecurs is moved downstream w~th increasing
superheat as can be seen in Fig. 1.16 ..
Adding a small amount of alloying element, sufficient to
bring about dendritic growth during solidification, causes the liquid-
solid interface to become corPlgated. S~li~ification and f10w stoppage 1
are similar ta that for pure metais (Fig. 1.17) but for di1ute alloys
the friction is much greater than in the case of pure metals because
of the dendrites. If the alloy contains a high percentage qf alloying
elenient. dendrites can grow deep into the stream 50 that the friction -
becomes so high that choking-off occurs when only a small amount of
solidification has taken place. /' 1
! ' i
,;,-
l' ,
o
FIGURE 1.13 Relationship between fluidity a~d alloy composition in Pb-Sn system. 12
\
16.
\
J
-~~ ..
(
-." 41
.r; v c:
>-t--0
:::::l .-J
U-
u 0
W 0.:: :::::l
'1' ' t-< 0.:: w 0-
~ W t-
10
0
200
10°0 Pb
20 40
O-liquidus â -/iquidus + 25 Oc v -liquidus + 50 Oc
60 80 .
WEIGHT PERCENT Sn
. '
100
fJ
FIGURE 1.14
(
Relationship between fluidity and superheat for Pb-65.25% Sn alloy.12
'.
17.
o
. '!.: ~ ~ : ~~',
,'~ "1 :
VI cu
...c v c: ->-
t-,-a ::::> -' &1-
30
25
' 1
20
15 180
1 1 1 1 1 1 • liquidus
\
200 220 240 260 280 TEMPERATURE (OC)
1
i
FIGURE 1.15 Sche,mâtic diagram of flow and solidification of a pure lnetal in a fluièfity channel (no superheat) .. 13
p ,j
\
18.
r
\
j
(
!
Il -- -- - -- - ~
( b) j, ,
(1
)'
FIGURE 1.16 Schematic diagram of f10w ~~ solidification of a pure metaI in a fluidity channel (with superheat).13
19.
î 1
~ i
( l
(b)
'f~ (c)
1 t
'-1 ,-,
i i I-I
k-
1 r-1 t 1 1
J-, . f : . 1
1..
20.
FIGURE 1.17 Schema tic diagram of f10w and solidification of a . dilute alloy in a fluidity, channel (no superheat) .13
" \
\
· (b)
\ \
\
~ ( c), ,
(1
21.
Another type of solidification can occur in alloys with a
high percentage of solute and in which nucleation is'not a problem. . . These alloys-solidify with equiaxed dendrites. When the solid is,
growing, fine grains form at the front of the stream. Figure 1.18
shows that fiow can ~e choked off at this front part of the metai ,1
'" stream wh en friction b~comes sufficiently high. Thus, it can be
conciuded that pure metals and eutectics which freeze with smooth
liquid-solid interfaces have a high fluidity. On the other hand,
alloys with a freezing ran~e solidify dendriticaIly, and these den-, .
drites prevent passage of further liquid. thereby causing a low fluidity.
Flemings et ~., working on Mg alloys14 and on Al alloyslS,
and using thè vacuum fluidjty test as weIl, have obtained the same
resul ts as_ "those for _the _Pb-Sn system.
(
1.2.3 Cold Shuts in Electron Bearn We1ds
, The cold shut is not confined to sand castings alone, and it ,
can be found in electron beam welds as weIl as in die castings. Its
causes are thought to be much the same in ail of these processes. '
Wo~d and Mara16 , studying the elimination of cold shuts in
deep, single-pass e1ectron beam welds in ur~ium. have developed a
technique for avoiding such a defect. This technique consists of using
shims of,a proper a110ying metal. During the weld process, the shim is
melted and mixed into the weld metal,' enhancing, the effective superheat
by lowering the melting point on cooling.
Arata !::!. !!: 17, working (nAi and iron-based alloys, and
studying the characteristics of weld defects, have concluded that:
t~\
1
1
~I
10
i 1
l'
1 t
,-
j
1
~ -
,-..
t:
t , -
f
FIGURE 1.18 Schematic diagram of flow'and solidification of an alloy which readily nùc1eates fine g'rains (no superheat) .13
i /
,\
22.
. ::~ .. ~ ..... IlL: .' .. w •
( b)
( c )
"
(
23.
- The aluminum alloys had a higher number of cold shuts than
the iron based alloys.
Many of the cold shuts in aluminum alloy w~lds took place d
.at ~he adjacent zone of maximum penetration weld. This did
not occur with the iron-based alloys.
- Cold' shuts tend to lower the fatigue strength, but it is not
possible to state an exact relation between the number of
cold shuts and their influence on fatigue (Fig. 1.19).
1. 2.4 Cold Shuts in Die Cas ting
Surface defects also requï.re attention in die casting. In
this process, where molten metal is forced under'pressure into metal
18 rnolds (dies), the principal causes of co Id shut (Table 1.2) ar~ the
sarne as in sand casting (T~ble 1.1). Die casting has two types 'of sur"; ,
face defects18: l:ow die temperature defeet and high die temperature
defect. Cold shut is ~n example of the first kind of defect. High
die temperature defects include blisters, èraters or pits, shadows or
images, shrinkage areas and the defects resulting from die soldering • ...
In order to aVQid cold shut formation, the die temperature
can be raised. The defect elimination becomes complex when ~his over-~
heating causes the appearanee of sorne of the high temperature~defect
before the cold shut is totally eliminated. This complexity would be
avoided if heat transfer. principally in thi~ sections, could be
retarded. 19 This can be successfully achie~ed by applying proper
coating ma~erials, such as nickel-p~osph~rus al1oyt~, which d~c~ease the therma~ conductivity of the die, extend the solidification time
, ,
1 significantly» and therefore prevent' the formation of cold shuts.
(~ ~
J
1 ! f-,
r f , 1
j \
f
, . ,
, 1 ;
• t
FIGURE 1. 19 Influence of co1d shut on fatigue of 5083 a1uminum alloy.F
"cai$;;M
24.
1 (
(
---v ..... CD :;) __ ..J:.
CD 0/1
'"0-0
- 0 :) U o
..r:. ..J:. .......... o~ o~
~-- .... - c:: c o 0- 0-
... 0 0 ~ .-'.-;-'
E -0 -0 CD II)
Q) -0 ""0 0/1--
~~3 1 1 1 o <l ~
CI N
o -(~WW/6)1 ) 30nJ.1 ldWV SS3~J.S
l • o
"o
-00 ~ -u
>u u.. o a:: w
'cQ
~ ::> Z
p
'-
\
C,I
25.
TABLE 1.2
Principal Causes of Cald Shut in Die Casting
1. Law inj ect ion pressure.
2. Cald dies.
3. Law metal- temperature.
4. Oxide in the molten metal.
5. Improper die design.
1.3 Aims of the Present Work
As was pointed ou~. few attempts have been made to und er-
stand the mechanism of cold shut farm&l!ion in castings. The works •
founcf in the literature are concerned with trying to avoid the defect
formation without an extensive research as to its principal .causes.
The present work involves an attempt ta determine the exact ,
conditions governing cold shu,t formation by the use of model systems
combined with a study of the solidification of'Pb and Pb-Sn al10ys
cast in a sand mold of simple geometry.
This work intends to anS\wer the following questions:
1.
2.
l'
What exactly.is cold shut?
Uncler which/conditions does i;,form?
i) '. "
Î
1
, l •
CHAPTER 2. MODEL EXPERIMENTS Wlrn WATER AND MERCURY
( •
26.
With the most connnon,and accepted definition of a· cold shut
in mind.. that being na surface defect formed by the meeting of two .
streams of metal", experiments were designed to pr.oduce this surface
disco»tinuity by promoting the collision of two liquid streams~ As
the liqui4 behaviour·promoting this particular phenomenon was not known;
sorne simple experiments using water and mercury were scheduled before
working on Pb and Pb-Sn a1loys.
2.1 Simi1arity Criteria
For one system to be similar to another, conditions known as
simi1arity criteria need to be satisfied. These criteria"being ratios
of magnitudes, are expressed as dimensionless numbers and are of utmost
importance in the design of models or pilot plants. ' Generally., in
order to simulate aH aspect's of a process, it is necessary to achieve
the four major states of similarity2l: . geometric, mechanic~l (s-t;aÜe,
kinematic and dynamic), thermal and chernieal. In modelling a flow
system, two of these criteria would have to be satisfied, these being:
dynamic similarity (which aut~matically imposes kinematic similar~ty21) , ,
and geometric similarity (for whieh the dimensionless initial and
boundary conditions are the same22).
for geometric similarity, the physical dimensions of the model
were chosen to be the same as the casting unit used, as will be seen
later.
For dynamic similarity, the relevant dimensional groupings ,
pertaining ta the flow of fiuid through a channel following release
from a raised reserVoir are given in Table 2.1. The nomenclature used
in this table i5 presented below:
,
u
g
L
p
D
TABLE 2.1
Dimension1ess Groups Pertaining ta Fluid Flow
Quantities Group Formula Equation
, Represented
2 in6dal forces Froude u 2.1
gL po~ntial forces
Reynolds pUD' 2.2 inertial force's li vis cous torces
2 . inertial forces Weber ~ 2.3 ct surface t,ension forces
Fanning lIPfD shear stress Friction 2.4 Factor, f pu2l velocity head
fluid velocity at channel entrance
- acceleration due to gravit y
characteristic length dimension of system
- fluid density
- fltiid viscosity
surfaèe tens ion
- friction head
- length of pipe
- hydraulic diameter of conduit
27.
28.
To obtain dynamic similari ty, one, two, three or ail four
" dimensionless numbers must be close for the fluids involved. Keeping
these numbers almost constant, provides the desired similatity between
~._2 _ Apparatus -------------- --- -A transparent plastic U101d of simple geometry (s~e Figs. 2.1
and 2. 2) ~a_~ ~o.n~_~~cted _t~ ~!lo~_fo~ !isual ,observation of _flow
phenomena involving IWO convergent_ streams. The mold dimensions and
flow channels are shown in Figure 2.3. Three plastic plates 0.635 cm -- -- - ;--------::- ----------- - - -- -
thick were also shaped in such a_ way that the height of the' runner or , .
channels could be reduced by placing plates ove~ the base of the channel. - - --- -----------_':.1- __ _ 1
Thus, experiments could ~e carried out with four different heights of - -
ronner:- 0.635 CID) '1-.27 cm, 1.905 cm and 2.54 cm.
of the same material as the mold and was stoppered by a tapered circular'
section plug (llll}de of soft rubber), to ensure l'eproducible pouring
c~nditions and rates ,as far as possible.
As can be sèen in Figure 2.1, the mold had a cover in which'
there ,were seven rectangular holes. Silk treated with a water repellent
agent was glued onto the cover over these hales so that, by preveIiting
the flow of ~ater and by. permitting the flow of air, the cloth would
simulate the permeability of sand molds.
2.3 Experimental Procedures
A sufficient quantity of water to complete1y fill the mold
was poured into the seàled mold. The plug was then pulled out, allowing
, 1
29.
c
"
1 •
\
',-
FIGURE 2.1 Plastic mo1d' for water and mercury.
("':; ..
\
1 i· r l, , 1
. ! i 1 \
fi ,
Id
30.
l
, ".
,FIGURE 2.2 Plastic mold without coyer showing the runner.
, , i
, ",
p, " " ,
,---' -~--- --, ---- -----
Il
FIGURE 2.3 Dimensions of the plastic mold and direction of flow inside the channel.
(
31.
"
, '.
'j.~ , c
<,<
~ ~ r", ~"
1.25
/ flow
• D 5
1 12.5 25
: ! • .. 5· - -
1.25 " 1..25 \ 5 21.5 5 ~
-34 \
-
~============~1~·5 ~
UNIT= cm
·1 •
"
\
32.
FIGURE 2.4 Tank used for reproducible pouring rates.
J!
c) .,
.'
...
o
1 ,
.. 9
l' 1 , 1 1 1 r 1 1 1
l' 29 1 1 1 1
1 1 1
Il
... . ,
1
/ /
,
•
" ~, 0 17.5 19. 5
17.5 ~ , ,
'/ -1 - 1
19.5 \.
,r,
UNIT= cm
l '
,./
1
f
f-~ 1
II 1 l' 1 ~ 1 1 I-l'
!-'t • 1 t i ~ 1
1 1 l
. (~-)
1 __ - ~ _~_~ ________ :'-~_
..33.
FIGURE 2.5 Friction factor as a function of Reynolds number. 21
r
(
'.
\
-
~ . ! 1
! t , -r '+-
1 -1 0 -u 0 ..... c 0
; -t _ Û l' -\ Z IL. , i
.
0.01
€ 0=0.03
l' (,\
0.001 ~4----....&..--""'-_.a..-............ -"---"'_.....i-~----~-- Ir\ 10 H
Reynol~ s number (Re)
(
( , \ \
... .:.iT§.:i~~~ ... ~ .. ,., ...... , ... "-~~.'U'mr.,,,,,,j~~~'::', . .T_'l;~~~,,,,,,..., _______ ~..t&Z'f~ .. -AliFiVd9-rmœtt: ~Ifi5i)M.WMiUIL-~~~""I.1"~.";:,:".:-~
, \
'i·f~ \':;!i
, .~,
'0< ( ~,>;i :(
\
• t
\'
FIGURE 2.6 Schematic representation Qf two streams of liquid meeting inside a channel. Time increases (from a) to e).
l' .
34 ..
. 1
--, l
" , ,
.~ .. I~
'l.:!â, , ,j ~
'. -,'
il
, 1
, [ f
1
f , 1 ,
l, 1 \
f f, f , i
• i \
i !
'.
...::....
a)
b)
,c)
, 'd) ~ 1
1 , .
e) ~ \ 1
"
; , '
L !, ,
, "
r.
i (J .
1 1
.(
\
\
FIGURE 2.7 Flow visualization for a channel 1.27 cm high. Material: water
, "
Film speed: ISO frames/sec rime interval between prints: 1j'1:S0 sec Time increases from a) to j) Magnification: O.4x
35.
'1 ;
f , 1
1 , i i ,
1 1 ! 1
"
j
" , î 1 , / :
. Ct . r
f ' ~, -f. Ir) iL
o
b
c
C' ~ ..
d
e ~
.\ -
-~
---
<,
/
, 1 1 1
, i ~ 1--1
l
i Il:::_ l
i
, 1
!
1 1
1 1
f
9
h
l ,
J.;.!At~~, .. ~~..,~""""::~~~"1.{, .... ,,,~;~-~~~?.;;;w:,.~~'--40 _._....... • ~,~-----_'_ ---
~_ .... 'ï' <~~:-~~,.,. ~ ,~t,
(
1
: 1
1
, 1
., 1
,
,FIGURE 2.8 Flow visualization for a,channe1 1.27 cm high. Material: mercury Film speed: 150 frames/sec rime inteirV~l between pr1nts: 1/150 sec Time increases from a) to h) Magnification: 0.3x
36~
, ,
.,} ,
! t c
~' 1 1 1
~' 1
"
f f t' ~ ~, ;;' 1. !f :~ J
~, h' L
C
a
b
c
d
e
...,p • 9
!
f
! 1 1-
,~ __ ._ 1
.. ~w'J).Vv.. .--------.. _ .. .,.. Di\I:,
h
.(.
~,
f-f:
r t , t 1 l î· \. t t \ '
FIGURE 2.9 Flow visualization for ~ channel 0.635 cm high. Material: water Film speed: ISO frames/sec Time int~rval between prints: 1/150 sec, Time increases from a) to j) Magnification: O.3x
37.
}"
J 1
1
\
, . .
- . - . . ~, -
" -J"
h
a
.. ' , ~
- ~ .... "' .... --<--, ~ . ~ .. ,
b
c
. .. . . .
~ .
e
! ••• _ .•• " ~-,.,,~ .,.",_k" •• " .. ..".",."'-"....-~ .. "'''111''"~-?'! .. ':1''.,,~_.:''I';f;~''; ..... !:'~""''''-.. ~~t.a.w.~''''''' ___ '._jtA ___ •• _l-'-.-~
. f
9
h
1 " 1 . ~I
J
"
FIGURE 2.10 Flow visualization for a channel 0.635 cm high.
--_ .. _---------------
Materia1: mercury Film speed: 150 frames/sec Tim6 interval between prints: 1/150 ,sec Time increases from a) to h) 'Magnification: 0.16x
,38.
Il
-- -'" ~, ,......... *-&,<J",
_" ..b ~. "':';l:~~
a e
J
" - ~ < -- ,
< ... . .. .. "'. - -. \~
b f
-....... ~ ~ ~ ~ .. - ~ \ '.' : .< .. .. ... ~ .... ' ~ ,W '''-''''r,~ ~ _ .: pt~~!~
--~~ -. . . - - - '
c 9
, ,. --... ~--
..... . ....... . . -' -' .:..:. "':
d h
... <--_ .. _---
c
39~
the 'water to flow ;nto the mold. Mercury (technical grade) was also.
used so as to better reproduce liquid metal flow ,conditions in a real
casting. t, •
Each experiment was recorded using a video tape machine
(model Sony AV3600) at a speed of 60 frames per second. The camera - ,
was located~ for each experiment. perpendicular to the mold wall, and , , '
, was focused on the area ~here the collision ,~f the liquid streams would
probably occur (Fig. 2.1). The experiments were recorded photographically, 1 • 1
and black ink was added to the water ta improve ,the contrast.
The photographs shown in the next section were taken witn a
Locarn 'camera at a speed of 150 frames per second. The watèr and the
mercury appear in white in aIl of these photographs ~ , fi
2.4 Results
The experiments have shown that, under the saroe conditions, , '
wa~er and mercury exhibit similar behavior on meeting'inside a channel,
Le. the two streams of liquid, on meeting, produce a wave and tben
start,backfilling the mold as presented schematically in Figure 2.~. . -
This behavior was always exhibited by both water and mercury, since 1
tlle channel was sufficiently high to allow for the wave formation~ as. '" _ 1 ~ ...
seen in Figure 2.7 and in F,igure~. 8. I~ these figures the channel' is
1.27 cm high. permitting the formation of the wave. -
" When~ channel is not sufficiently high, the collision of
,the two streams is as presented in Figure 2.9 (water) and Figure 2.10
(mercury), in which it can be seen that both fluidsJ-wat~r and mercury, 1>
are as high as the chaJ)Ilel itself, both fluids exhibiting the same
behaviour.
'1
1
l' __ ._~ __ ~.~ •. l
j l-I 1 1
~.l[
/
. ,
\
40.
Before analyzing the dimensionless n~bers calculated and
presented in Tables 2.2 and 2.3, it' should be pointed out that a~ the
runner is of noncircular crQSS section" the hydraulic diameter (0) is
defined as:
D "'!' 4x cross sectional area wetted periméter
(2.5)
The viscosi~y (lI) of mercul;)'" used was 0.015 Poise as rep,orted
elsewhere28 while the suriace tension (0) fOT the fluids are r~orted '30
by lita ~ al.
The velocity Cu) was taken as the \elocity at the channel
entrance and was m.easured based on video rècordings. The character-1
istic length dimension of the system (L) was taken as the height of the
channel. , The friction factor (f) was estimated llsing experimental ,
" Reynolds 'numb~r~ toge~er with the data 21 given in Figure 2.5 which
,correlates the friction factor ,with both the' relative roughness of the
pipe (t) and the 'Reynolds number (Re). As water and mercury were
tested in a plastic mold, the cune taken ~ was that for smooth tubes.
The behavior of the fluids was siDLilar because the dimension-
less numbers presented in Tables 2.2 ,and 2.3' are in the same region.
The Froude numbers are equal for both fluids, while the Reynolds numbers
show tbat wa't.!(r and mercury are flowing in, a turbulent manner (Re > 3,000).
The high Weber numbers show tbat, for both fluids, the inertial forces
1a~e far more important than the surface tension forces. 1
.111 P T' ....... =_h.fi. .IIJ ..•. L._ Lia 1. a
" ' \
n .......
Group .'~ ,
Froude
Reynolds .. ç .-i<
• ~. lI'leber ~
IFriction lFactor, f (Fi~.2.S)
,iii.
!~.,,_ .. ,. ........ .., -""!:" ..... -.tO"""~~ .... -"""'I~~~~c<!" .. '!'I""" ... _,.,., .
TABLE 2~2
Experimental Variables for the Flow of Water and Mercury in a Runner 1.27 cm High
u L p D 1.1. (f, Formula Fluid, (cm/sec) (cm) (g/cm3) (cm) (Poise) (dyile/cm)
2 U - 65 1.27 - - water .. - - - , gL ~
~
mercury 65 1.27 - J - -'\>
puD water 65 - 1 2.03 0.01 \.1
mercury 65 - 13.57 2.03 0.015 , ,
2 Pu D water 6S -; l 2.03 -- 74
a - Il. -• -mercury 65 - 13.57 2.03 - 487
-
l1PfD water -.
pu2l mercury
- - -~_._- - -- - -
\ • .-
Result
'l:r. Fr ..... ;'39
Fr - 3.39
Re - 1.3xl04
. - 5 Re .... 1.2xlO
'"' 1
We - 116 \
We - 239 ..
f "'" 0.0070
f .... 0.0036
,
o 1
\"
0:;;
~ ..... .
1 ;1
~. ri "
~j
""
----;
o
Group
Froude
. , Reynolds
Weber 1 1
Friction ~actorJ f (Fig.2.S)
~
-. ... ..---.-.-....--. ... ~_ . ..,_~I~_~ _",_~~-t~~""-~~""" !l'{!!"::" '!" ... ~, ~ •• ~~ ___ '
-;
1 TABLE 2.3
Experimental Variables for the Flow of Water and Mercury in a Runner 0.635 cm Hi~h-
-. U 1 L- p 1 'D ~ 1 cr
F011ll.l1a Fluid (cm/sec) (cm) (g/cm3 ) (cm) (Poise) (dyne/cm) ~ ,
2 \ u water 60 0.&35
1 - - - -gL c
mercury 60 0.635 - ! - - -1 i
, , -puD ,
water 60 - l 1.13 " 0.01 -l.l i !
i 1
mercury 60 - 13.57 1.13 0.015 -<li<
2 pu D w~ter -60
, 't. - 1 1.13 74
cr mercury 60 - 13.57 1.13 , )- 487
" -
6Pt> water
puZl ,
1
mercury 1 \ < , ,
7
f
-/~-
'·"iflï"'f.'iI"'P_-~"",","",,--------·------· -- -- .. --- ---~ - -- ~ -'--'- ,------ --- --- -- ----- - ------- ----- --- - - --- ----
•
Result
Fr = 5.78
Fr == 5.78
Re """ 6.8xl0 3
Re - 6.1xl04
We ... SS
- 1
We "'" n3 l
f 0= 0.0085
f =: 0.0044
,::.. N •
\
\
Ci "
43.
CUsing the equation for the friçtion factor Cf) an~ its value'
obtained froID the chart (Fig. 2.5)1 ,the 'equation for pressure drop
(âPf) can he derived, whiCh leads to:
(2.6)
The calculation for the pressure drop has shown that, for a channel
1.27 cm high~ it is equal to 6,000 dyne/cm2 in the case of mer'cul)',
',while for water it is equal to 860 dyne/cm2. For a . channel 0.635 cm
high, the pressure drop for the m~rcul)' was càlculated to be equal to
11,223 dyne/cm2 while in the case of w~ter it was equal to' 1,598
dyne/cm2. For· bpth he~ghts of the channel, the frictional energy
losses for the mercury were calculated to be seven times greater than
those for the·water. Naturally, the greater kinetic energy associated , \
with the flow of the denser mercury more than compensated for these
higher absolute losses.
;'
)
\
~
1
i 1·
1
l, (.'
-'
o
1 CHAPTER 3. EXPERIMENTS WIllI LEAD AND LEAD-TIN ALLOYS,
IJ
<.\
1
1 f-I \
, '
C)
\' ( ,
l
oJ
Knowing the kind of behavior which could be expected when
there is a collision of two liquid str~ams inside a chan~el and
knowing the dimensionless number 'which would describe the phenomenon,
experiments with Pb and Pb-Sn a1loys were designed in order to produce
cold shuts on the surface of real castings. Lead and lead-tin alloys
were selected because their low melting temperatures make them suitab1e
for experimental work.
In order to obtain the meeting of two streams of molten metal,
a pattern made of birch and yielding a mo1d (Figs.'-3.1,and 3.2) with
the same simple shape as the plastic mold (Fig. 2.3) was constructed.
A flask was fabricated of oak with, a cope 8.0 cm high and a drag 10.5
cm high. Th~se two pieces of foundry equipment were designed in snch
a way as to allow visnal observation (through a quartz glass window)
of the meeting of the streams. The glass used was 2.5 cm wide, 0.5 cm
thiçk and 15.0 cm long and was supplied by, Lasalle Glass Blowing Co. Ltd.,
AlI the relevant properti~s of the quartz glass (as, obtained from the
manufacturer) ar~ presented in Table 3.1. i
In the 'experiments usjng both cope and drag, the pouring rate
was controlled at the sprue, 50 that the flow speed was varied by ,~,
changing the sprue diameter. ~e sprues use&e tapered (~early 10°),
8.0 cm high, and their minimùm diameters (where the pouring speed was
regplatedl were of six different dimensions~ yielding the pouring rates
presented in the Tables 3.3 'and 3.4 of this chapter.
The molds were made of silica sand~ AFS grain fineness number
140, bonded with 4 per cent by weight of. each of western and southem
J
J
o
(
, 1
FIGURE 3.1 Dimensions of the sand, mold and directions of f10w inside the channel.
\,
45.
, 1
f
1 1
1 , 1
4
wood
.... , • .1 ... "'\:: , .: ... ," •. , '.: ,·.1 :.- ." 1 ;' : ", ,1 • .-..... . ....... \ .... " : ... ~.: ." "I ...... ": ~ ••• '
.' . • J." _ ~ .. . ' ~ ... " sand,' '.' .' .. : . ." '!' ..
" ,
" .
, '. 1 " .
..... t .
4
,;
...... .. j ; .. , ..-.
1 ........... ,.........: .. • 1" ........
___ flow
..
_', ...•. : .:IQIQS5 ... .. ....... J ..
~~ ~~ 5 5 10 5 5
46
\ ...
1 1 \
'. . , ' . " ... '
" .. " . ' .. .. ·.ft. .. ,
' . .. ...... -,/'" .... "', . .. . ~. l'~' • I"
.' , '. . .
4.4
•
UNIT= Cm
"
4
1 6
5
38 12 i'
5
, "
l,. ,
46.
FIGURE 3.2 Section AB of the sand mold ..
f L
1 [ '- o
~: 1
(.
, 1
1
1
1 1
! ! .
,
r 1 ! ' 1
!
------- - --- -
';
1 ", .... ,
! 2.5
, l 1 , 10.5 1 \
j ; ,
4 .4 5 20 5 4 .4
46
, .
UNIT = cm
()
\ \ ~ \ -
1 ! i 1
1
Ji
\ , \
TABLE 3.1
Physical Properties of ~artz Glass
J
Properties Unit
. density g/pm3
coefficient of linear expansion (0 to 1000oC) 1°C
47.
Value
2.203
5.4xlO-7
0.166 ~eat capacity (at 20oe)
~eat conduction (at 20°C) cal/cm-oC-sec 0.003
annealing point
Isoftening point
1
l2l0oC (1483 K)
l6500 C '(1923 K)
bentonites and 4 per çent by weight of water. This fine-grained sand
,~was chosen to produce a smooth finish on the surface of the casting,
'. since the experiment~ were with small castings and the goal 'was to ....
obtain a surface defect.. The water content was controlled with a
"Speedy" Moisture Tester (Thomas Ashworth & Co. Ltd. J Burnley, England).
and aIl sand mixes were mulled for. about 151 minutes after the water was , 1
added.
Since moiten metai cqming into contact with sand causes a
thin layer of clay adjacent to it to be baked, ,the sand mix was recycled T'
• after every 10 castings by adding 1 per cent by weight of each of western
and 'southern bentonites.
All experiments were performed using green sand at the ambient
temperature, and as for'each run the sand was mixed and compacted (using
"
- '~
48.
, <
'}
\ -, FIGURE 3.3 'Flask.
, <
'1
\'
. '
1 , 1 , (
'.
\
"
"
"
\ ~
()
'1'
t l 1
1 l,
1 1 1
1 1
1 i 1 \ !
1 i , 1
, 1 1 L 1 1
1
1
1
1.
t
<
FIGURE 3.4 a) Graphite ladle.
FIGURE 3.4 b) Graphite plug.
l,
,r
.. ) ,
Î
o , , '-..
( / '\
~,
• ------ ...
- ,
'U
, ,
" ~, ,1'
... '
0,
\, ;. .
49.
"
~
,1
! j f
1
r '
()
16 18.5 " a)
L __ ---r-~---_J
" 2.5 " <11=2.51 gj=11 .
~=15
b) --- 1~=4 sa=2r 0
~ . ,
4.5 -/ 24.5 1
29
UNIT= cm
(
50.
a manual bench hammer) in the same way. aIl the molds were assumed to
have approximately the same physical properties.
3.2 Melting Procedures
In aIl experiments. inciuding those \l7i th Pb-Sn alloys, the
metaI was meited in a convJtional manner, U~ing a gas-fired crucible
furnace, and ,-ms superheated sufficientIy to permit handling. Clay-
graphite crucibles were used and the lead employed in aIl experirnents
,."as of commercial purity.
3.3 Pouring Procedures
In order to obtain reproducible pouring rates, a graphite
ladie (Fig. 3.4a), with a 2.S cm dia1lleter hole at the center of the
bottom, was used. The bottom hole was sealed by a graphite cylinder
tapered at one end (Fig. 3. 4b). In experiments with no cope, as des-
cribed later, the pouring rate was controlled aJ this orifice.
The graphite Iadie served as a tundish, and in order to avoid
undesirable premature solidification, it ''las preheated before each
experiment to sooe above the pouring temperature. This procedure \~as
used in aIl experiments, including those with Pb-Sn alloys.
3.4 Experiments
Experiments were performed in an attempt to produce a special
kind of cold shut suitable for scientific analys is. For this J the
defect would have to be perpendicular to the flow veloci ty (i. e., vertical)
and it should occur in a reproducible specified position to allo,'/' for
51.
temperature measurements. This type of defect was found to be very
difficul t to produce and 50 the approach had to be changed several
times. The various types of experiments are described be10w in
chronological order.
3.4.1 Simple Experiments without Ladle
The tirs,t kind of experiment tried \~as to pour mol ten lead
manually into the mold shown in Figure 3.1. The parameters involved
in such castings are presented in Table 3.:? As wifl be seen in Sec-
tion 3.5, the co Id shuts were formed by layers because the pouring
rates were insufficient (due to inadequacies in the pouring practice).
Even when the superheats were varied, the defect continued to be formed "î
in the same way.
3.4.2 Simple Experiments us ing Lad le
The5e experiments were similar to the first ones, the only
difference being the use of the ladle. Its use as a tundish improved
the pouring rates considerably, as well as making these rates reproducible.,
From ~hi5 point on, the ladle was used in every experiment, except for
the experiments outlined in Section 3.4. 7. Al though being reproducible,
the pouring rates were still found to be inadequate for the production
of the desired ~old shut. 0"
The experiments were carried out using lead and Table 3.3
shows the relevant values involved •
• 1
----~- -
/
(
52.
1 TABLE 3.2
Experimental Variables for Experiments without Ladle
-Experiment Superheat Pouring
Temperature (oC) Sprue Height of
Number (oC) Diameter (cm) Runner (cm)
Al 100 427 2.5 2.54
A2 40 367 2.5 2.54
A3 20 347 2.5 - 2.54
A4 50 377 1.5 1.27
AS 50 377 1.0 1.27
3.4.3 Experirnents Using Obstacles
As the experiments performed previously were not useful in
the sense of temperature measurements because they did not produce a
vertical co Id shut, two experiments were carried out using obstacles,
which both slowed the flow and caused splàshing of the liquid metal .
• The obstacles were steel plates 1.2 cm wide, 5.0 cm long and 0.05 cm
thick. They were embedded 0.6 cm in the sand, 50 that the actua1
obstacle height was 0.6 cm, and tney were placed 9.5 cm apart, sym-
metrically to the center of the glass windaw (Fig. 3.1). As the first
experirnent resuIted in cold shuts formed in layers as before, it l'las
decided to place a 'copper plate between the two obstacles ta accelerate
the solidification in the are a wher~ the two streams of the liquid metaI
would meet. This approach also resulted in cold shuts formed as hori- '
zontal layers.
\
l /
'-___ ._ ._...1 ~_.: __ ._, ... ~ - ~ -§ -.....
i,
Ir ~l 1 i
:1 ~ "
" A, ",1 ,.lI ~, !i!
~\l ~
1 , i !
"1
.~
'!; , ' : 1
'"j j
'.\ 1 1
J 11 :1 il 11 il ,j
L' ~~--
, ,"
, 1
,--i
Experiment Number-
81
B2
83
B4
85
B6
B7
B8
H9
BIO L- -~-~-~
'1>
Superheat (oC)
3S
5
3
4
70
5
10
15
100
20 ,- ~ --------_ .. -
TABLE 3.3 r
Experimental Variables for Expériments using Ladle
1
, Pouring 0 S~rue- Height: of
Temperature ( C) Diamet,er (cm) Runner ((cm) 1 1
1
1 !
1. 271 362 ~.S 1 ,
332 2.0 1.27' , 1 1
" 1 1 330 2.0 1.27, 1 1
331 2.0 1. 271 1
397 2.0 1. 27; , 1
332 0.5 1. 27;
337 0.5 1. 27
342 0.5 1. 2~ ;:.
427 0.5 1. 27 1
347 0.75 1. 27 1
- ------ ----- - -- ---~ .. _- -----_ ... _-
1
1
(1)
1 Pouring 1
Rate (g/sec)1 1
230
276
no meeting
288
290
no meeting
no meeting
no meeting
58
115
V1 lJ.l
(
54.
!hase experiments were performed using lead, anQ Table 3.4
shows the values iriVolved.
TABLE 3.4
E~erimental Variables for Experilllents using Obstacles
Pouring Sprue Height of Pouring Experimcnt Superheat Temperature Diameter Runner Rate
Number _(OC) (oC) (cm) (cm) Cg/sec)
"-Cl 15 342 1.S 1. 27 216 . C2 15 342 1.S 1. 27 193 ,
r--
3.4.4 Experiments without Cope
These experiments were designed to reduce the flow rnomentum
(by reducing the head of metaI) in an attempt to produce a vertical
cold shut. As the cope was npt uSed, the sprue was eliminated 'and the
pou:iing' rate was controlled ,by the diameter of the bottom,hole o~ the
graphite Iadle and by the metal head. Thus, '!:!he pouring rate was varied
by changing tpe quantity of Pb inside the Iadie. The variables invoived
in these experiments are shown in-Table 3.5.
3,4.5 ÉAperiments with a ChilI Bottom'in Half Mold
This Und of experiment was performed to try to solidify one - _.Jt
stream of metai before the other could meet with it. In order to
achieve this, a coppeT plate 5.0 cm wide and 0.3 cm tbick was placed
in the path of one of the two streams on the surface of the channel.
, ,
l' l'
55.
TABLE 3.5
Experimental Variables for Experiments without Cope
, 'P~uriJlg Height of Metal Pouring
Experiment Superheat Tempera ture _ Runne.c Weight Rate Number (oC) (oC) (cm) (g) (g/sec) ,
- - - - - - - - - - - ---Dl 70 397 1.27 4167 220
D2 20 347 1.27 2155 no meeting
D3 30 357 1.27 2126 - ,
D4 20 347 1.27 1531 no meeting
DS 20 347 1. 27 2070 I}o meeting -- - - - .- - - - -D6 10 337 , 1.27 2778 -- -
-
This plate extended fronl, the point of pouring to a point halfway around
the entire channel. The copper. acting as a chilling agent, would
solidify the metal quicklY on its side, 50 that the liquid stream
meeting the a1ready solid metal wouid fOrIn the desired vertical defect.
As. the cope was not used, the pouring, rate, as before. was changed by
varying the quanti ty of lead inside the graphite ladie. The relevant
values involved in such experiments are presented in Table 3.6, and the
absence of pouring rates is explained in Section 3.5.5.
/ ~ 3.4.6 Experiments using SoUd Inserts
li These experiments were designed to allow temperature measure-
( ment ~uring cold shut formation by placing ,a soUd in the 'matal stream.
\
" ~-~--... j"- -~-::--:::----
(
If
(p TABLE 3.6
'E:q>erimental Variables for Experiments with a ChilI Bottom in Half Mold ,
56.
Pouring Height of Metal Pourin,'J Experiment Superheat Temperature Runner Weight Rate
Number - (oC) (oC) , (cm) (g) Cg/sec)
El 20 347 1.27 2268 -
E2 10 337 1. 27 2041 no meeting
E3 15 342 1. 27 2098 no meeting
E4 15 342 1. 27 2495 -
A new geometrical simple pattern was developed 50 that the mold would
have th'e:shape shown in Figure 3.5. Insi~e the runner, three special '1
sa~ples of solid metal (Fig. 3.6), located in proper places (as shown . in fig. 3.5)', were embedded in the sand with steel pin.s. The solid
1
samp~~ had the same composition as the liquid which would be poured ,,-, .
oVer it and was made by rolling the metal until the desired thickness /
, '~--was reached. The 3.0 cin long plate was then bènt to obtain the final
shape (Fig. 3.6).
Since a cold shut would be formed if the solid ~ample did
not rernelt, it is Cle~that the surface condition of the sample -
which does influence rem ting - should have an effect on cold shut .
formation. !WO kinds of surfaces were tested. Surface B (Table 3.7)
. is' an oxidized surface. To obtain, this, the Pb sample was heated to
o 0 250 C (150 C for Pb-Sn alloys), kept at this temperature for 20 minutes
57.
1
~- - - - -- ---. FIGURE 3.S Sand mold for experiments using solid inserts.
(
".' ... " 1 :-. '. , . ..' ...... . ,; --. ~
..... "" :.: • •• "C .. • .'
... ' :" .... .. ":". -;
• ",' .1 ."~ ..... ' ..
.. ..... ..... ' .. ,;. .........
14.5
/
- \ .. " ~ .. ,"
'. \ .. .. :. ..,. •• ":. 1 ". .:
1 1
4.5 29.5 4
38
point of pouring
30
13
! ·~;:i::.:.~t;~. [;:}y.:~~~,t;tr:;",G:;· :~D:::;Y il5
UNIT = cm
>,
FIGURE 3.6 Two solid samples as placed on the channe;t.
i \
\
\ ..r-\
/
\ i
) , , /
1
58. '
1
1
2
UNIT = cm
t .'
(
.,
,-..,..
~
I~
TABLE 3.7
Experimental Variables for Experiments using Solid Inserts
- -
Pouring Metal Sample Experiment Metal . Superheat Temperature Weight Thickness
Number Composition (oC) (oC) (g) (cm)
FI Pb 100 427 3650 0.2 F2 Pb 1Où. 427 3650 0.2 F3 Pb 20 . 347 3650 0.2 F4 Pb 20 347 3650 0.2 F5 1'b-- 60 387 3650 0.2 P6 Pb 60 387 3650 0.2 F7 Pb-19% Sn 60 340 3400 0.2 F8 Pb-19% Sn 60 340 3900 0.2 F9 Pb 60 387 3750 0.2 FIO Pb 60 387 3650 0.2 FU Pb-19% Sn 60 340 3500 0.2 Fl2 Pb-19% Sn 60 340 3650 0.2
,
- FI3 Pb 100 427 39QO 0.2 Fl4 Pb 100 427 3500 0.2 FlS Pb-19% Sn LOO , 380 3000 0._2 F16 Pb-6!. 9% Sn 100 283 2600 0.2 Fl7 Pb-61.9% Sn 75 258 2500' 0.2 FlS Pb-61. 9% Sn 50 233 2600 0.2-
-- - -_ .. _----- - ---
-'
/' -,"-. , .. ~;:;; ... ..,,j..... • /
. Surface
Condition
C B B C C B C ~ . B C B C ,
B B B B B B B
------ -
e
1
•
A.
-- -
U1 ~
(
,/ ,
60.
and then cooled in air. Surface C (Table 3.7) was obtained by polishing
the satflple wi th a 600 silicon carbide paper. l ,
A Pb-19% Sn alloy was used in othis kind of experiment because
i t has the largest freezing range of the Pb-Sn system ('Fig. .3.7) and , "
the mode of sOlid,ification should play an important role. Experiments
\'lere aiso performed using an alloy of eutectic composhion.
3.4.7 ~xperiments qsing a Stepped Mold
Thes'e Qxperiments were designed to de termine the effect of
the splashing of the liquid metai on the cold shut formation. \' new
pattern was huilt to produce the mold shown in Figure 3.8. The graphite
ladle was not used in these experiments which were performed with lead
and in which thè metal was poured into t,he mold at its shallow side.
Table 3. B gives the experimental variables. f:
TAI3LE 3.8
Experimental Variables using a Stepped Mold
Experiment Superheat Pouring (oC) Number (oC) , Temperature
,
Gl 1S 1
~ •
G2 150 D . 'G3 2S 352
, . 1 ./
( ,
~--'. I ____ ~~------------~--~----------------
61.
1-
FIGURE J. '7 Pb-Sn Phase Diagram.
" t' ;4
!
~e~ .' "'.l" 1:.. _
I ________ ~--------------~~I,--------------------------
, " - '.
)
\ ,
" 300 L
u 0
w 200 0: :::> t-< 0: W 0.. 100 ~ a+ f3 w t-
0 Pb 20 40 60 80 Sn
'. ,..," WEIGHT PERCENT Sn
( l '
/ ) 62.
FIGURE 3.8 The stepped mold.
-, . . ,
",' ,"
. ~: .... - .. .. 'Or : .. : ".
'. ... -.. ." : .. ' , .. ~ . . . . ' . , . ! .... " ,;. ....... _~
: ..... , . "
~'. ' . . Jo .. :. . ... -: . ~
. " .. ......
14.5
'.'
.-.
.. .. . ,
" ., . t
.. , o· ... .' . . ..
.. j • ~
"
", .. : .. ,. .... .... ~ ..
.~ , ..
't : .. ... " . "
.. . ; . . '. ~ .. · \
' . · 1.5 2 2
38
point of pouring
'. '.
'. .
... ' · .. ",,'.
", ' •• -.1..&,..----. ; t • l... .. ... <4 ... : ... _,'
... 1 1 .... ".... .. .. "" • .,,'
'.
r. .~
~ ...... ~', :' " .. " .... ., .. '.:
~ ,. '. ' . -. ""
.'
4
,,:-" . '. ., ~' .....
li· "
"
: . "
. ,
14
" , ", " ," .. '.
'. :
"
,~ . . 13
4 "
. , 1-0--
, .'
. . . ," ..
13
c !r-~
I-J.. 1
1-0--
• .... 1_ ..... _1 "fi ... ,
.... ", .... " .. '", , " ... : O-"d'-: "'!", : .... 1 .. "._ " .. : ....... .. ,' ' .• -' '. san . :.-: . • .. 0: ",' -.:,. _. ", " '
.. • 1 ..... 1
, :.. !:. ~ "'~ : .. ...... .'" ... . . .. ,. .. ....... .. .,.... "',. : 1,,".1 •• , .. "' .. " fi ' ..
\ . '.' • .. l' ....... ,
........ ; 1--.... -
2
.. , .. 1 :- '. :'.. .,.... t .. '..... " ~ .. , • '. " 1 • ,. ", ..... Or .. ".' •• . . ~>.~~.: \~ =.', ;:'(. ~.:..~.:); >\ .~~. ':':: .. >:.::~.~: ~"':' .~.: ':'. ~ ~:, :'-:~)~
..' .... 1 • 2.5 . .
UNIT ~m
30
7.5
63.
3.5 Results
As previously mentioned, the type of experiment was changed,
when the results were found ta be unsuitable for this stndy. Results
will be presented separately by type of experiment.
3.5.1 Simple Experiments without Ladle ~
These expe+iments, when the molten metal was poured manually ) , !
into the mold, resulted in discontinuous pouring rates as weIl as pouring
rates which varied from run ta run. As no vertical defects were formed,
.~ the runner height, for the last two experiments, was reduced ta half;
however, suitable cold shuts, were still not produced. In a11 experiments
the cold shuts were formeâ as horizontal layers by liquid metai flowing
over the already frozen metaI in contact with the glass window. The
typical defect formed is shawn in Figure 3.9, which is a result of
experiment number AS (Table 3.2). The photograph shows the location
whex:e the two liquid streams met. The ,col.lision produced a wave which
froze on the wall, forming a cold shut which outlined the flow pattern
(indicated by the\arrow,s in Figure 3.9). The cause of the formation
of this layered defect could be the inconsistency of the pouring due
to the human factor. Thus, the graphite ladle was used ta make contin-
uous pouring possible and a1so ta increase the pouring rate. The
pouring rates are not shown in Table 3.2, because they were discontin~ous.
3.5.2 'Simple Experiments using Ladie
The use of the lad1.e did, infact, standardize the pouring
rate but it still was not useful in promoting the desired vertical type
!
1 1.
, -
\ \
. '.
FIGURE 3.9 Typical cold shuts formed in experiments without ladle (superheat: SODe) • Magnification: 1.3x
-----~ .. _-----~ -.
--------~~ ~.~------
flow directions
(
65.
of surface defect. Layered cold shuts continued to be formed exactly
as before. Figure 3.10 (experiment number 82, Table 3.3) and Figure
3.11 {experiment number BS. Table 3.3) show that the cold shuts formed
in experiments where the ladle was used' had the same appearance as
those formed when the ladle was not used. It is wo~h noting, by
c~mparing Figure 3.10 wi th Figure 3. ~ l, tha t the ,superheat did not
make any noticeable difference in the appearance of the cold shuts.
The same cannot be said about the pouring rate. Low pouring rates
(58 g/sec). even at high superheats (lOOoe), produced deeper defec~s
(Figure 3.12, experiment B9, Table 3.3).
These experiments were also recorded (thr~ugh the quartz
glass) by using the video tape machine. In this way the pouring rates
could be ca1culated and the flow behaviour could be analyzed more
carefully. The behavior of the liquid metal was 'si~ilar to that of
the water and mercury presented in Chapter II. The two streams of
liquid Pb .collided and produced the same kind of wave (Fig. 3,13).
Figures 3.13a and 3.13b show the solidified stream (dark. indicated by
arrows) in contact with the glass window, the white line being due to
light reflection. The7e was a small amount of leakage between the
glass and the sand (visible at the right end of the window). but this
did not affect the'results obtained. Figures 3.l3c to 3.13e sh~w.
beyond the solid metal (dark). that the molten meta,l produced the s~e
wave (white, indicated- br arrows) as th~ water and mercury on'meeting
inside a channel. Photographs 3.13f to 3.130 show that, once the liquid
metal has touched the glass (mold wall). it .solidifies instantaneously.
the metal freezing from the point of contact progressively outwards in "
aIl directions in th~ plane of the window. The~e experiments have shown
~!. I ............................. ~.·_._.~.~.·~.a. ___ ... ~ .... '~ ... :.' .... ________ .. ______ .... ______ .. ________ ... ~
FIGURE 3.10 Typical cold shuts formed in experiments using ladle (s\,\perheat: SoC). Magrlification: 1.3x
, "FIGURE 3.11 Typical cold shuts formed in experiments using ladle (superheat: ,700C). Magnification: 1.3x
66'.
, .
------1~... "CI
flow
/..
;
... flow
(
FIGU~E 3.12 TYP~cal co1d shuts formed pouring rate (superheat: Magnification: 1.2x
/ j
- -- -'
in experiments using low IOO°C) •
67.
.,
l' 1
"
--------~.~ ~~~-------
flow
._-~-
, \.
(
FIGURE 3.13 Flow visualization for a channel 1.27 cm high. Material: Pb (commercial purity) Film speed: ISO frames/sec ~ime increases froID a) to 0) Magnification: 0.6x
'\
\
'\
d
68.
-~~_' n __ ~~,;.;.~.: •• (:-
'= --
a e
b f
·1;~ __ ~)!IJI!i.",.~i .. '---.....
c 9
~'~t~~' Ir~ .. ",",
1.
, ,. .:":"
1 d h
t
\ "
69.
FIGURE 3.13 Continuation. \ ,
1
i
c
F
a
)
J m
.-1
k n
" "-'
o
1
70.
that the water system and the liquid Metal system are similar when two
streams of the same fluid (either water or lead) meet inside a channel.
The similarity Was achieved because the dimensionless numbers for bath
systems were kept close or in the same region as shown in Table 3.9.
The hydraulic diameter (0) for the lead system was calculated using
equation (2.5) as was done for the water and Mercury systems. The
velocity Cu) was estimated using the following formula:
(3.1)
where Fe is a correction factor taken as 0.26. This value was obtained
by comparing theoretical calculat!9ns with experimental results for
water and mercury. This had to be done because the opaqueness of bath
the sand and the graphite ladle did not allow for video tape recording.
The viscosity of lead used was 0.025 Poise as reported
elsewherel2 , while it5 surface tension was reported by Iida et al. 30)
The friction factor éf) was estimated using'the ch~2î~~hown in Figure 2.5. For its use, it'was assumed that the absolute' roughness
(E) of the sand was in the same range of that of the con crete reported
by Geiger and Poirer2~ (E - 0.02 in). As the value of D is~.03 cm
whi'ch is equal to 0.8 in, the relative roughness (e:jD) of sane! was taken
as 0.03. For this curve, with Re = 3.8xl04, the value of f obtained
was f .",. 0.015 (Tiible 3.9).
Table 3.9 shows that the Froude number for lead is not much
different from that for water and mercury.' The Reynolds number for the
thfee fluids shows that aIl of them are flowing in a turbulent manner
1
~ ...
Group
Froude
!Reynolds
Weber
Fanning Friction Factor,f ,
: ' . Cl
,
f"2'\ . , 1
TABLE 3.9
Experimental Variables for the Flow of Water, Mercury and Lead in a Runner 1.27 cm High
u L p D ~ cr Formula Fluid (cm/sec) (cm) (g/cm3) (cm) (Poise) (dyne/cm) Result
" <
-2 water 65 1.27 - - - - Fr =0 3.39 u mercury 65- 1.27 Fr = 3.39 - - - - -gL lead 42 1.27 - - - - Fr = 1.42
, 4 water 65 - 1 2.03 0.01 - Re = 1.3xl0 puD mercury 65 - 13.57 2.03 0.015 - Re "'" 1. 2xlO5
..... lead 42 - 11.3 2.03 0.025 - Re """ 3.8xlO4 -2 - water 65 - 1 2.03 - 74 We ..,. 116
E!LQ. mercury 65 - 13.57 2.03 - 487 _ We ==0 239 --cr lead 42 - 11.3 2.03 - 453 We .... 89
1
6Pf~ water f ..,. 0.0070 mercury f ..,. 0.0036
pu2l lead f = 0.015 . /'" - "-
J-
"
'-J ......
<>
72'.
, , (Re> 300Q). The Weber number shows that, for the three fluids studied,
the inertial forces are much greater than the surface tension forces.
Using equation (2.6) and the value of f obtained from Figure 2.5, it
,1 was fouhd that the pressure drop CllP f)' in the case of lead, for a 2
,runner 1. y cm high., is equai to 8,690 dyne/cm. ~is value is even
greater t1an the pressure drop for mer~ury (Secti~~' 2.4) which means
that, among the fluids used, molten lead loses mot.~ energy during flow:
Although losing much less energy than,ihe other fluids, the ll.P
water relative 1055, ~, is similar. As such, water is an adequate p
model for molten metal meeting ,inside a channel since the three dimen-(\
sionless numbers cal<"ulated (Fr, Re and We) are also in the same region
as those for lead and mercury.
Mercury has a steeper,advancing wave profile than the ether
fluids (Figs. 2.7, 2.8 and 3.13) probably because of its non-wetting
characteristic.
Another phenomenon observed was that, for castings using a
sprue diameter equal tQ. or greater than 1.0 cm, a surface defect always . ,
appeared at the bottom, exactly where the collision took place. This
defect (Fig. 3.14, experiment number B2) seems to be an erosion scab
(Section 1.1) which was formed' due to turbulence in the flow. "
Aluminum was aiso tested in this kind of experiment, but the
quartz glass did not restst ~he high temperatures and cr~cked.
Four eXferiments did not produce cold shuts because both
streams solidified befere meeting. Expe~iment number B3 (Table 3.3),
had too Iowa superheat and experiments number B6, B7 and B8 (Table 3.3),
had, too low peuring rates which caused solidification in the sprue.
2
'~
-8
\
FIGURE 3 • .14-~ Typical defect at the bottom of the samples when sprue dü1meter exceeded 1. 0 cm. Magnification: 1.0x ---
..
73.
. \
1 l '
1
~,I
I~
.. flow
(
(
l' ,
74.
Raising the superheat (experiment B9, Table 3.3) avoided this stoppage
but did ~ot prevent deep layered cold shuts (Fig. 3 .. 12).
3.5.3 E~ériments using Obstacles
Since the use of the ladle did not produce results which
were amenab1e to temperature measurements, experiments were tried using
obstacles to dectease the pouring speed as weIl as ta cause splashing
of the liquid metaI. These two experiments, produced the same wave
formation, and again the cold shuts were formed in horizontal layers.
It was thought that the flow momentum was tao high, thus preventing the
formation of a vertical cold shut. Therefore, the next step was to
decrease the flow momentum by eliminating the cape (the upper part of
the mold). \
3.5.4 Experiments without Cape
The elimination of the cape did not contribute to the forma-
tion of vertical cold shuts. The defect was again,formed in horizontal /"
layers and the same wave as before was 'produced (Fig. 3.15, experiment
D G.bl e 3. 5) • Three exp erim en ts (D2. D4 and 05. Tabl e 3. 5) . wi th a
superheat of 200C did not allow the meeting of the two streams. Experi
ment D6 (Table 3.5) with lo~er superheat (IOoe) allowed the stre~ to
collide due to 'the greater head of metal. The pouring rates for experi-
ments number D3 and D6 do not appear in Table 3.5 because the strea$
were not adequately v~si~le in the video tape.
"I.. • - ... f ..... _ ~
(
75.
3.5.5 Experiments with a'Chill Bottom in Half Mold i
This experime,ntal approach proved to be more adequaté than 1
aIl others previously iried. The copper plate solidified one of the
streams, so that when the liquid stream met the sol id one, a cold shut
was formed at the junction. This can be seen in Figure 3.16, which "
shows the bottom surface of the casting re~ultini from experiment
number E4 '(Table 3.6). The shape of the 'stream\;.!.s clearly visible.
Experiments number E2 and E3 did not produce the meeting of the streams
due ta the low head of metai while the pouring rates of experiments
number' El and E4 are not shown in Table 3.6 because the video tape for
those experiments was inadequate.
Although this kind of experimen~ yielded better cold shuts, , i
temperature measurement at the defect remained a problem due to the
uncertai~ty in predicting the exact location of the cold shut. In the
next ~~~ies of experiments solid pieces of metal were placed in the
liquid stream to produce co Id shuts at a predictable location. This
approa2h elim~nated the problem ~f temperature measurement.
3.5.6 Experiments using Solid Inserts
This kind of experiment overcame the pro~lem of the tempera~
ture measurement because it provided, in advance, the poin~ where the
liquid stream would meet the solid metal as weIl as allowing for varia-
tians in tne surface conditions. Varying the superheat, the surface
condition and th~ alloying element, several experiments were carried 1
out, as shown in Table 3.7. After each expe:Hment~ the sample was
sectioned at the three positions (l, 2 and 3), shown in Figure 3.5.
FIGURE 3.15 Typical co1d shuts formed in experiments without cope (superheat: 70°C)., Magnification: 1.Ox
FIGURE 3.16 Typical co1d shuts formed on the bottom surface of the sample (superheat: 15°C). Magnification: 1.0x
76.
,{
flow • 1
n '
• CI
flow
c
77. '
The surfaces of each section were prepared metallographically by wet
grinding on a silicon carbide belt (grit 80). ' Then, the specimens
\'1ere ground on silicon carbide paper of successively finer grades
(gri ts 220, 320, 400 and 600), and finally were poli shed on a polishing
wheel using a metron cloth impregnated with an alumina suspension.
Coarse polishing was done using 5 micron alumina, and 0.3 micron
alumina was used for the final polish. The specimens, once polished,
were etched, \~ith the time of etching depending on the amount of the
alloying element present. Pure lead was etched with a mixture of equal
proportions of the following solutions: 23
Solution A
15 g of ammonium molybdate
100 ml distilled water
Solution B
6 parts nitric aeid (conc.)
4 parts distilled'water
The Pb-Sn alloys were etched using the following solution: 25
1 part nitric aeid (cane.)
1 part distilled water "
Comparing, for instance, the results for experiments number
FS and F6, it can be seen that, as is expected, fol' the same superheat
, {
(~
\
78.
{60oC) the surface condition influenced the remelting of the sample,
therefore affecting the cold shut formation. For low superheat (20oC)~ , ~/
as illustrated by experiments number F4-'and F3 (Table 3.10), the sur
face condition had only a small effect on the cold shut formation.
Table 3.10 also shows that the liquid metal becomes cooler as it flows
towards the farthest parts in the mold. Its capacity for remeiting the
solid is progressiveIy lost downstream, and hence'the farther the liquid
metal is from the point of pouring, the higher is the probability for
cold shut formation.
The effect of the superheat on the remeI ting phenomenon is "', also shown in Table 3.10. Comparing, for inst~ce, experiments number
,~
F3, F6 and F2, i,t can be seen that, other conditions being constant, --:
streaJ)ls with higher superheats have a greater ,~apacity for melting the
solid pieces.
The influence of the alloying element, i. e. the solidification
characteristic, on the remei ting process is' best shol'ffi in Tables 3.11
and 3.12, which separate the experiments according to surface condition.
For the same superheat (experiments number F5 and FU, Table 3.11), the
Pb-19% Sn alloy shows greater resistance to the remel,ting phenomenon
than the unalloyed lead"and this 1s confirmed in Table 3.12 (experi
ments number F6 and 'F12). Table 3.11 also shows that, the superheat
being constant (experiments number F5 and Fp), the effect of the , ;1
alloying element becomes greater as the liquid becomes cooler, which
is also confirm~d in Table 3.12 (experiments number F2 and FIS). The
eutectic alloy (Pb-61. 9% Sn) has a lower resistance to remelting than
the Pb-19% Sn alloy, as can be seen in Table 3.12,(experiments number
. (.
~ H
U r !, ,
"
" il i' ~ M
f \'
~ " " "
i 't
1 ~.
! ~! 1 1
1 ï 1
1
1
1 • 1
1 1
~
L,. il
,,~~ ,- ........ _-- ............ ---._..- ~----_.-
n . '-
... ~--'?
"-
~
TABLE 3.10
Schematic Diagram of the Reme1ting Phenomenon
IExperiment Superheat .~ Number Metal (oC) - Surface 1 2
Pl Pb 100 clean '----' L.--.':I
-1F2.F13.F14 Pb, 100 oXidized 1----1 ~
-FS,F9 Pb 60 clean '----' ~
F6.F10 Pb 60 oxidized c::..t...::J - ~
F4 , Pb 20 .
clean ~ r:!lS . ... dIb c::IT1 P3 Pb t c'"""""~
20 oxidized .,
P7,Fll . Pb-l9% Sn . < 60 c1ean I:..--..:::J ~ 1 Jl.6 c:!Jb F8.1 F12 Pb-19% Sn 60 - oxidized
FIS Pb:'19% SrF 100 oxidized L---.J L--:J
F16 Pb-61.9% Sn Ibo oxidized L--J L--...J -F11 'Pb-61. 9% Sn 7S oxidized L--.J >
I:..--..::J . . Fl8 Pb-61.9% Sn SO oxidized ~ ~
. -- ~ --
LEGEND; L--J - .... cOJllplete remelting of top; c:::J...:::J = partial remelting; cflb ".,. no remelting
.',
e
3
C-J.-:J
c::::::!J..!:::
r:::t=J , ~
~ dI1
, JJ1, ~ t::!lb I:...L:J
d1b c:!iS
~
'-1 ID .'
. (
, '
, { ,
1
, , i, 1 Î
,
,
c
TABLE 3.11
chematic Dia ram of Remeltin for Clean Sa les
Experiment Superheat ~os~~ Number Metal ~ (oC) Surface l 2
FI Pb 100 clean L--..J ~ "
FS,F9 Pb 60 ca.ean L--J c....J....:J
F7, FU Pb-19% Sn 60 clean ~ dlb F4 Pb 20 clean -c::!i!:::J cIT1
LEGEND: as per Table 3.10
TABLE,3.12
Schematic Diagram of Remelting for Oxidized Samples
Experiment Superheat ~ Number Metal (oC) Surface 1 2 ,
P2,F13,fl4 Pb 100 oxidized ~ C-..L..:J
FIS Pb-:19% Sn 100 Oxidized ~ t:..--..:J
F16 Pb-61. 9% Sn 100 oxidized L-......J L--....J
F6,FIO Pb 60 'ox~dized c....L...:J c:::'J..::J
FB,Fl2 Pb-19% Sn 60 oxidized ~ ~ Fl7 Pb-61.9% Sn 75' oxidized l...--J t:....--:J
FIS Pb-61. 9% Sn 50 oxidized c...,.....:J c::Ub F3 Pb 20 oxidized r::ITk t::ITS
1
LEGENDI as per Table 3.10'
BQ.
3
t::..L.:J r
~
~
cfl:b
3
~
dlb c.......L..J
c:Ub c1l1 c!Ib c::!lb dI1
c
81.
FIS and FI6). The behavier af the eutectic allay, in the sense of
resi~tance te remelting, is similar ta that of unalloyed lead, while
the Pb-19% Sn alley, due to its làrge f~e~zing range (Fig. 3.7),
presented a much greater resistance to the remelting process. 1 1
A samp1e which was not remelted is shewn in Figure 3.17
"(experiment number F9, Tables 3.7 and 3.10). The structural differencesi
are clearly seen with the discontinuity being weIl defined (indicated
by arrows) in this sample of lead. Figure 3.18 shows an almost entirely
remelted sample of lead (experiment number F14, Tables 3.7 and 3.10).
Al thougb the cold shut here is formed in only a small part of the sample,
the defect is still weIl defined, and is seen in the region indicated _
by the arrows. For the eutectic composition, the defeet is again weIl
defined, as can be seen in Figu,re 3.19 (experiment number h8, Tables (
3.7- and 3.10). A closer view (Fig. 3. 20) show~ the structural differenee
between the two sides of the co Id shut. The Pb-l9% Sn alloy yielded
a diseontinuous cold shut. as seen in Figure 3.21 (experiment number
FIS, Tables 3.7 and 3.10) and in,Figure 3.22, probably because of its
~arge freezing range.
3.S.7 experiments using a Stepped Mp1d
These last three experiments were des'igned te confirm that '
once splashing of liquid metal has occurred, a cold shut will probably
be formed. Figure 3.23 (experiment number G3, Table 3.8) shows an
example of a cold shut formed bymetal splashing at the bottom surface
of the last step of the sample. At'higher superheat (7SoC), the cold
shut is a~so formed as shown in Figure 3.24 (experiment number Gl,
! . !
, l,
c
, ,
FIGURE 3.17 Typical structure obtained from experiments using inserts (not reme1ted). Magnification: 3.4x
\FIGURE 3.18 Typica1 structure obtained from experiments using' inserts (almost totally remelted). Magnification: 3.4x,
82.
--__ ~l
" /
--------_._-- .. ....
. ,
,r i
f , ,
1
:,ff
(
FIGURE 3.19
..
1 1
83.
Typical co1d shut formed in a1loy of eutectic composition. Magnification:' 3.2x
FIGURE 3.20 Structural difference in both sides of cold shut for eutectic ,(not etched). Magnification: 20x
(
1
r
,-
, ,
:1
-'
(,
r-I ,
"
c
FIGURE 3.21 Typical cold shut formed ih Pb-19% Sn alloy. Magnification: 1.5x
('
FIGURE 3.22 Structural difference in bo'th sides of cold shu't for Pb-19% Sn an'oy (not e'tched). Magnification: 20x
\
, 84.
( /
','" .
/ \
~ ,
~~
i i ~ .
'-
, ' i
lI
(
FIGURE 3.23 Bottom surface of sample from stepped mold. Superheat: 25°C, Material: Pb Magnification: 1.35x
FIGURE 3.24 Bottom surface of sample from stepped mold. Superheat: 75°C Material: Pb Magnification: 1.3Sx
85. '
.'\
Ir. , '\
.... ,
J.
Table 3.8). o At low superheats (25 C), in stepped molds_ the formation
of cold shuts by liquid metai flowing over'solid metai is more likely
to occur, and this is confirmed by Figu~e 3.25 (experimept number G3,
Table 3.8) showing the side of the sample, where the layers of metai
are clearly visible. At higher superheats (150°C), the defect still
occurs but is less visible, as is seen in Figure 3.26.-{experiment
number G2, Table 3.8) •
,\
--- ----_ .. _--
1 r f ,
r'
1
, FIGURE 3,25 Cold shuts formed at the side of samples from stepped mold. Superheat: 25°C Material: Pb Magnification: 1.25x
FIGURE 3.2ç Cold shuts fOïrned at the side of samples from stepp~d mold, Super eat: Materi Magnifica . n: l,4x
c ,
87',
~"""-"~<t~~2"t ;JI!'-"~-~~,;~.lTh."b\':.";~~&illiI. l tiîn.;~;"~;~..-QfjjH.<"'J'1L:R' .. ~.~_~~",,,,~~":"~~~_~._~.~_ ........ ~ .. .-" __ _
" \
.. '
•
" . ,
1\. ...
j 1 1
1 ! r
i 1. •
t r 1 I-r f
c
C>
CHAPTER 4. HEAT TRANS FER MODEL
/
: '\.
{} ,.'
-- ---,l.'
c
The mathematical model presented in this chapter was
developed to investigate the phenomena which occur when two liquid
88;
metal streams collide. As presented in. Chapter 3, it was determined
that the necessary condition to promote significant cold shuts was to
have il satellite fragment of the approaching stream freeze ahead of , ,
the :main liquid flow, and this phenomenon was simulated by, placing in
the mold a solid' piece' of the same J!letal and allowing the parent liquid
to overflow it. As such this represents an unsteady state heat transfer ,1 .
,problem which ca~ he' solved, for the appropriate boundary and ,initial
conditions, by various numerical algorithms. The method used in this
study was chosen because of its mathematical simplicity and also
because it can be programmed without much difficulty on\ a high speed
digital computer. In this method, called the explicit finite-difference
technique, once t~e initial temperature distribution is knownJ~,thè ,1.~
calculation :proceeds directly from one time increment to 'tlY.e next until
the témperature distribution is calculated at the desired final state.
4.1 Definition of the Problem
'" The problem to be solved can be summari~ed in the following
way: a solid metal in a sand m,old is instantaneously heated by a liquid
metai (both solid and liquid are of the same' met(l.) which is brought
in contact with it. Depending on certain variablés influencing the heàt
tnmsfer "proces's, the 50 lid piec~ may or may not be remel ted.. If the
__ solid is entirely remelted, a cold shut i..s avoided. If ~pt, a cold 1 f'
shut is formed • ...
,;,
\
'j . .....
\
c
89,.
4.2 General Equations
The unsteady ~ta'l=e heat transfer problem stated in Section 1
4.1 can be solved' by solving the general partial' differ~tial equation
for heat condition given by:21
+4(~:~
where k pep
thermal di~y T temperature
x,y,z = spatial variab~es . q heat generation pel' uni~ of volume
1
P ,density
c p heat capa ci ty
k thermal conductivity
t time
In the'absence of heat conduction in the 2
ZT y(L - 0) and in the al
(4.1)
z(~- 0) directions, and in the absen~ a2:2
of heJ.t generation (q .... 0),
equation (4.1) 'simplifies to:
/ f
, The situation representing t~e contact of the liquid metal,
with the solid metal, at time t - 0, i5 outlined in Fig. 4.1, which .
depicts, in schematic form, a crosS section of a sand mold with a soUd
piece of metal laying on it.
~ ,
,~> ,.,,," .i'~»"""","'h;;"';";~~,;"~~~~_ii~~:ffifè1îJitt·::[email protected]:t~?~~~~,:·.",;),-
, '
" , , .
r
f , 1 i 1 ; r.-, '
1
\'
c
(1
Î
, f
/
! 1
FIGURE 4.1 Schematic cross section of the mo1d.
90.
J '1
, "
(
6
: '
, , '
.' ". .
" '
, " , . . "
"
q N x
.... " ,. , ... - . t ... ..
, " , :
0 ..... )(
, , ~ . ,
1
'0 Il )(
8 1
t )(
" , "/
,
, , " . :- ' , ' • , t .... 0 .. : ' . , ' , . ". '. " ..
, , .. " ,
. . •
'" 1 ~ Of.
'-'
, ' , '. , , .' .. . , ,
, : ." .. " · - . ' . . ..
, ' . " ..... "., .. , ".' . .,. '" . ... .. .~
" .. ".. • .-.. 1 ~, .-, , .. , • 1 ~ \ J, .J, l' ........ ," ., .. 1 i .' 1 ....
~~~~'~'-'~'~'-'~'~'-'~'~'~'--'~"~'--'--'-'--'-'1r'"'~'~'~''' , , .... , ... , ,
)( ;)
u. .... 0 lU
:I:
, " '"
'." .' ....... "
, " , , .
, , '. " .. ..
, '
0 -CI)
~ "'0 .-~ ~
~
..
)( ;)
u. .... 1 '
0 Q)
J:
)( ;)
u. .... 0
'Q)
:I: •
-~
)( :J
U.
.... 0 Q)
:x:
... , t ,
" ,
, .
, , , " . , J
. 'l' , ,
: l' . 1 .. • :. ,
· r " ." 1 ... • ,. . .,.... ..
, .. " , # ... ' " ... , , .
e, .. f . ,
, .. · " , 'of ..
. , .. ..... ." 1 "." -ë #. ,' ..
.. '.... c: ,,,,1 ' •• ' •• .' .. " .. ' 0 ,. -, ,
.. , " .. ' .. ' V'J ' .. ' .. , , ".. ...,.
, " ":~. :~": ~ ::, ','
, .
: ... .. .. , , , : ....... : . ,
, - , . ,
" , ,
, .. , . ,
"
'., .-.,," .. ' " .
. ',1;" . , , , .
, -'- t ..
:-' , '
.. . .. . .. " .. "I ••••
" .-
"
, , " .
, t .' , ..
, , , •
'\
• 1
." 1 . "
"
, " l "
. ,
" " ,
. .' .' ~ .
! , , 1
! t ~ .
91'.
The appropriate' partial differential equations for the mOld"
sOlid, mushy and liquid regions and presented below:
a) mold
- co < X < 0
a2T
amold ax2 aT at
o < t < tf' l - lna
b) soUd metal
f' !I
c) mushy
, "
O<x<x . - - solldus
a2T aT
asolid ax2 - at
\
xsolidus < x <.x1iquidus
aT at
'O<t<t . - final
o < t ~ tfinal
J d) liquid meta~
X <x<x .\ O<t<t liquidus center llne - final
(4.3)
(4.4) .
1
(4.5)
(4.61 '
, .
1
1 1
( )
! î1
>,
f" 1
\ \
! ' t 1
1 , t
J
4.3 Initial and Boundary Conditions i
These partial differential equations are to be solved using
appropriate initial and boundary conditions. Before pouring liquid
metal into the mold, the temperature of the mold 1s ta ken to be unifarm
and, equal ta To:
t """ 0
T T o
- co < X < 0
, 1 (4.7)
The temperature of the solid piece of meta1 is taken to be
uniform and equal ta T : o
t .... 0 o < x ~ x1,0
T - To (4~ 8)
The bu1k temperature of the 1iquid metal is taken ta be
uniform and equal to Tbath :
t == 0 x1,O ~ x !. x2,O
T .... Tbath (4.9)
There is no mushy region at t - 0:
t - 0
(4.10) j
-1
} .J
1
J
,
1
f
i ( 1
1
1 t'
1
,r c
< •
,1 •
93 ..
o
The mold is assumed to be semi-infinite in the negative
x-domain with surface temperatures equa1 to T : o
o < t < tfo' 1 - lna
T - T ' o
x - - (li)
(4.11)
The heat' flux from the casting side to the interface is
equal to the heat flux from the interface into the mold:
0 < t < t f " x >= 0 - Inal
êTmold aT -Jsnold k 0
castIng
(lx castIng (lx (4.12)
AIso, to allow for the thermai-resistance_of_any air gaps
between the sample and the sand:
where:
o < t < tf' 1 - Ina
j ,
T* . cast1ng
o
( 4.13)
T* 0 .,. temperature of the casting surface in contact castIng
T* mold
with the môld
- ,temperature of the mold surface in contact with
the casting
- thermal resistance due ,to air gap
---_._---~-~------
"
1 \
"
94~
The .temperature at the interface between the soUd and mushy
region of the alloy is ~aken to be constant and equai to the solidus
temperature:
o < t ~ tfina1 x - xsolidus
T - Tsolidus 'I! (4.14 )
-", The temperature at the interface b\tween the liquid and the
mushy region of the alloy is taken to be constant and equa1 to the
liquidus temperature: .
, o < t < tf" l' - ;r..na
x .... Xliquidus
T - T liquidus
J
The amount of metai being solidified (o~ meited) is dependent
on the difference between the heat fluxes from the bulk Iiquid metai
to the solid/Iiquid interface and from this interface into th~ body of
the solid metal:
q" + HF m" c: - k • aT 1 conv solJ.d dX x D x solidus
(4.16)
• where
, ·11 heat flux due to convection from liquid to the qconv -
freezing zone . m" - amount of metai being solid1fied (or melted)
HF - latent heàt of fusion
mAi. :u:
, , ,
. , 1
; ,
î" "
1
1 1
l'
" ... \-
95.
The ~eat flux, q~onv' dep~nds on the heat transfer coefficient
as weIl as on the superheat:
(4.17)
where h .... heat transfer coefficient
4.4 As sumpti ons
The explicit method used in this study to solve the heat
transfer problem invoived the following'assumptio~s:
i) The metai was assumed to be an alloy because even
unalloyed'metals contain a ,certain amount of im~urities resulting in a finite melting range ..
ii) It was assumed to'have an air gap between the metal and
the mold ,which provided a resistance to the heat flow.
iii) Conduction through the side wall was ignored as was
radiation from the liquid surface to the ambient because
both would not influence the results during the pertinent
eatly stages of the hœt flow.
iv) The heat flo~ was taken'to be uhidirectional.
v) Latent heat was assumed to be absorbed in a linear manner
~ between the solidus and liquidus temperatures of the
c
alloy. This as·sumption was ~de to simplify the model. ç
The latent heat was accounted for by assuming an arti-
ficiall)vhigh specifie heat over the range of the mushy / .l ,
zone. This was achieved by defining the heat capacity,
as in equation (4.18):
....
" "
.
(- )
'.
\ c
96.
, HF C , (4.18)
p,m (TL - TS)
where Cp,m heat capacity of mushy zone
HF "
la tent hea t- of fus ion
TL - liquidus temperature
TS .". solidus temperature
4~ 5 Explïcit Finite-Difference Technique
In order to apply the explicit method, ,the system being
studied was divided into a series of finite volume element The,
nodal points were located at the centres of (Fig, 4. f)
and a heat balance was performed in them.
requîres that the temperature gradient between adjacent n
be asslJmed to be linear as well aS the material within ea node be
assumed to hav:e both uniform temperature and thermophysi al properties.
Nodal point number one was 10cated at the mold/ambient i terface, the
other nodal points having încreasing numbers toward the ce
of the system. Nodal points number one, five
haU nodes since they lie on boundary lines.
A h~at balance' was established qver the finite elements as
given in eguation (4.19):
" heat input - heat output .... rate of heat accumulation (4.19)
,This equati,on (4.19), applied to nodal point N-, yields the following
relation wr\tte~ in numerical notation:
,1 1 /
1 J 1
i \
1
i Î
1
f_ r
!
1
1
1
t .!
i
1
o
.'
97.
( J
, ,
.. ,
. FIGURE'). 2 Network of nodal po.ints.
c
(
1· âx -1
ct -- --- Unit
30 /
29 /
/ /
Heat /
1 / Flux 1 /
1 / /
Liquid 1
12
I~X 1\'
,/
11 / /
/
/ /
10 .-
I~X ;
/ .. " ! r
9 /
/, /
l',
Solid 8 '/ /
/
"
7
6 " / /.' , / f
/
5 .-/
4 /
",
lAMX " , /
Mold .-3 " ,
" 2
r 1
/('.\
(
for
"
where
,1
'C
I<N<S, and
\
p C (âx . âx • 1) .... P
. At·
6 < N < 30
Rearranging equation (4.20), it follows that:
98.
..... (4.20)
.... ~(4.21)
TN - new ternperature at time t + 'At at n~dal' point N
TN - - t~mperature at time t at noda). point N
.= temperature at time t, at nodal point N+l
TN
_1
== temperature at time t at nodal point N-I
~,N+I
~,N-I
kN,N+I
~,N-l
At
p.
Cp
lIx
kN,N+I • lit
P Cp Ax2 .. (4.22)
kN N-l .' lit -, ' (4.23)
"""
-----
C Ax2 P P
equivalent thermal
points N and N+ l ,
conduetivity between no4al
equivalent thermal conduètivity between nodal
points N and N-l
time, incremtmt
density of node N
heat ~apaeity of node N
nodal point, spaeing
....
.'
j
l
" ~
-'
)
, '
, !
1 , r
1 f' t
c
99 ..
The equivalent thermal cond~ctivity ~etween nodal points N
f and N"'I, for instance, i,s given by:
(4.24) ,
, for and 6 < N < 30
Applying 'equation (4.19) to nodal point 1 .. yields the fo1-
lowing equation:
(4.25)
Transforming equation ~4.2S) into finit~-difference form, yields:
(4.26)
wheré' ,- Tf , -1- _ ,new temperature at time t + lit lit nodal point 1 '-,
Tl r temperature at time t at'nodal'point 1 " ..
f
T2 . - temperature at time t at nodal point 2
'-
TAMB - ambient temperat\lre
(
,
1 1
1 l ' ! t 1. l
1 f . L
'.
100.
(4.28)
k2,1 - equivalent thermal conductivity between nodal points
2 and 1. In this case, k2,1 - kSAND .
h ,. AMB heat transfer co~fficient for the ambient
... tJ.1x as shown in Fig. 4.2 ,
• l , Performing the heat balance given' in equation (4.19) to'nodal . ,
point number 30, yields the following equation:
..••• (4.29)
The first term in the above equ~tion has a negative sign because the
temperature difference in parenth~ses should be. equal to (T:n - T 30) ,
but as 30 is the last nodal point and i t is the center line of ,the
system, T31 is equal to T29 •
where
Putting equation (4.~9) in finite difference form, it becomes:
/ \J'
(4.30) \
T30 - new temperature at Ume t + At at nodal point '30
T30 - temperature at time t at nodal point 30
T29 - temperature at .time t at nodal P()int 29
, C î
,"
j
~ .'1 l
(
, ,
1 1
J f l, ,
f <
1 i'
1 C~ .
If ~ ~
101.
M - (4.31)
k30 ,29 - equiva1ent thermal conductivity between nodal
points 30 and 29 and is giv.en by:
2 • k30 • k2'g k30 + k 29
, (4.32)
\
Applying the haat balance represent!d by equation (4.19) ta
nodal point 5 yields:
, PINT(6X / i
kS 4 (Ilx 1) --=' =--tJ,-x--(T 5 - T 4)
tJ.x p Cp(r 6X 1)
Transforming tne above equation, gives:
T' .. TSÜ - 2H1NT - 2M} + 2H1NTT6 + 2MT4 5
'\
where T' - new temperature at time t + Ilt at nodal 5
TS temperature at time t at nodal point 5
T6 ... temperature at time t a t nodal point 6
T' - temperature at time t at nodal point 4 ,4
HINT hINT Ilt - p Cp ,tJ,x
. \
(4.33)
(4.34)
point 5
, , i,1 1) t' • t 1
(4.-35)
Il
} .. _______ .J
( 1 '- -
. '
c'
\ \
(
1
/
102.
M - (4.36)
hINT ..,. heat transfer coefficient for the metal/mold interface 1
hx AMx as shown in Fig. 4.2-
kS 4 - equtvalent thermal conductivity between nodal points 1
5 and 4. In this case, kS,4
App1ying equation (4.19) to nodal point 6, gives:
k7,6(LlX 1) --"':'-A-x--(T7 - T6) - hINT(llX • 1) (T6 - T5>
p Cp ~x • /}.x 1)
(4.37)
. The above equation transforms into:
where T' 6 ....
T6 ==
T7
TS
M
•
new temperature at time t + b.t at nodal point ..
temperature.at 1
temperatu:re at
temperature at
k7,6 llt
P C llx2 p
hINT ~t
time t at nodal point 6
time t at nodal point 7
time t at nodal point 5
(4.38)
6
(4 ;'39)
(4.40) , 0
;.,.~~~~4~~~~ÙA:'JP't,Rt .. r _'1 ! .. ,~I~JF d, •. . ;.l~ij!~,.".,,,,,,J .. .,. L
i
1 1
! 1 1
1
-)
1
l 1
, .'
, ,1
! 1 1 1
, .
k7,6 - equi valent thermal conducti vit y between nodal
points 7 and 6, and is giveri by: ,,r--/ ~
103.
(4.41)
The modulus"M, as 'presented in 'equation (4.21), can have two
values ~ N+l and ~ ~-l' The first corresponds to the heat flux , , . entering nodal point N from nodal point N+1. The secOIld corresponds
to the heat flux leaving nodal point N and going to nodal point N-I.
The numerical values of these moduli are dependent on the phases present
.and are applied to nodal points 6 < N 2. 30.
For the solid regJon of the a11oy, the modulus M is given by:
(4.42)
where kg -- thermal conductivity of solid alloy
Cp,s - heat capacity of solid region ,
For the mushy region, the value or M is:
km àt ' J
~ 2 (4.43)
p Cp,m t.x
where km -- thermal conductivity of mushy region 1 \
C p,m - heat capacity of mushy region
, , . , .
"j
1 .~
l
i 1 , 1
!. i ' • l
> ! ,
l04~
.. As pointed out in Section '4.4, L is assumed to be arti-p,m
ficially high in 'order to take into account the latent heat of fusion
of the aUoy. Equation (4.18) defines the C value. p,m .
, For the liquid region, the modulus M is given br:
Ml 1.sl ~t ...
2 P Cp,l Ax
(4.-44)
where kl thermal conduct~Y of the liquid a110y
Cp,l "'"' heat capa ci ty 0 the liquid a110y
'1 '
The p'ossibility of two adjacent nodal points being in regions
of different phases was taken into account 'by using the proper values , .
of the modulus M. When nodal point N is in the solid region and the
adjacent J;lodal point is in the mushy region, the modulus M is given by:
where
Ms,m
k s,m
.C P,S
...
-=
ks m llt ' .
p C llx2 p,s
(4.45)
2 . ks . km . , (4.46) k + k
5 m
thermal conductivity of solid alloy
thermal conductivity of mushy region
heat capaci ty of solid a110y
When nodal point N is in the mushy region and the adjacent
nodal point is in the sôlid -region, the value of M is:
, ; ,
( }
\ \. \
1
1
1 1
1
1 r ~
i:
f ~ r [
f l t, (,
e<
t ., \ (! , r ,
/
M . m,s - (4.47), . p ~ frx2 -p,m
, where Cp,m - heat capacity of mushy region
and ks m was given in the equ~tion (4.46). c ,
, When nodal point N is in th~ ~iquid regi~n and the, adjaçent
nodal point is in the mushy region, the modulus M is gi~en by: '
M -k1,m .6t
l,m p C [).x 2 1 j p"l
(4,.48)
2 . kl • k where k1,m
m -=
k -+- ~ 1 (4.49)
kl thermal conductivity of liquid alloy
k thermal conductivity of mushy regiop. m
C ,p,l heat capaci ty of liquid alloy
When nodal point N is in the mushy region and the adjacent ... , . nodal point is in thé"1iquid region, the modulus M is expressed as:
~,l - (4.50)
where Cp,m - heat capacity of mushy region
and k l is given in ,equation (4.49). ,m .
The presence of a thermal resistance between nodal points 6.
and 5 acts to transfo~ the dimensionless number M (equation (4.21))
into HINT Aequation (4.34)~ and equation (4.38)). For modeJ,ling purposes
IRIII . m
, .. l' , i 1 , 1
1
! l' 1
i 1
1 1 i
1 \
)
106.
it is assumed that the thermal resistance is of negligible thickness
and heat 'capacity. The value of Cp in equation (4.35) i5 equal to the ,
heat capacity of the mold material Whil~ the value of Cp in equati~n
(4.40), ~s well as in equation (4.39), can be equal to Cp,!' Cp,m or
Cp,s' symbols Which have already been defined.
"'4.6 Stability
Th~ accuracy of the solution of the explicit method is deter-, r' ~
mined by the. values of ~t and 6x, because these two variables control
the value of the modulus M. Decreasing the value of M irnproves the . accuracy of the solution by converging the finite-differencè method. 24 ,25
~Basically, to obtain stability, the coefficient of TN (ternp~rature at
time t at nodal point N) mus~ be non-negative. As the values of M
varied depending on the phase where the nodal point N was located, the
values chosen for ~t and ~x to impart accuracy to the results were:
O.QOl second for the time increment, and O.O~ cm and 1.9 cm for the
nodal point spa~ing in the casting side and in the mold side,"respectively. , As determïned' by other authors 25 , 26, increasing' the number
1
of nodal points increases the accuracy of the model, while 6t has a
relatively small effect on the solution.
4.7 COmputer Model
A program, written in the FORTRAN computing language and
executed on an IBM 370/158 digital computer, was used to solve the finite
difference equations presented in Section 4.5. ,It began by setting the
ternperatur~l.stribution ~nd the modulus M with their ,initial values.
\
" 1
, i ' ,
i 1 1 .
1
1 ·-~~'~~'.~~~~';~·W~?~H_,,~~~.~~~~"~!~~~~~~~~~~3_. __ ~~~.~~~~-_'~~~~~~-~-~~=--·-1
( " '-
, , ' ,\
1
i 1
f,
t
1 t. r t C' f r ( ~
!,
107.
Then, temperature profiles were computed in a stepwise procedure for
successive ~t time steps. Obviously, for the calculation of the next
temp(lrature dis'tribution, the phase ,~sting in each n~~a~ point was rI' "
checked to allow for the' use 01: the oper ,data. Such ~ computer pro-
gram, calculating the temp~rature 'stribution throughout the system
(mold ~nd casting). allowed
solid wi!,l he remelteq, for each data set.
FORTRAN (Gl) compiler and it is listed in Appendix A along with aIl
the symbols involVed.
The thermophysical properties for the Pb-Sn alloy and for the'
pure 1 d d · T bl 4 l' ' d b Ch." d G h' 27 ea , presente l.n a e ., are reporte y - l.esa an ut rle ,
the only'exception being the thermal conductivity of the mushy zone
which was estimated ta be between tha~, for tp_e Üquid and the soUd.
The heat capacity and the thermal conductivity of sand are given else
wher.e28 as 0.2 cal/gOC and 0.002 cal/cmoe sec, respectively, while its
den;ity, is rep~rted by Paschkis 29 as being 1.6 g/cm3• The heat transfer
coefficients for'the ambient and for the metal/mold interface were
28 chosen in reasonable agreement with reported values and were taken
2 0 2 0 • as 0.0015' cal/cm C :.sec and 0.01 cal/cm C, sec, respectively.
When the Metal 'was assumed ta he pure lead, the liquidus
temperature was selected ta be 327°C (600 K) while the solidus tempera
ture was tak~n as 326. 90 e (599.9.K).
4.8 Experiments fpr Temperature Measurement
Experiments for temperature meas~rement were carried out ta
check the accuracy of thé heat transfer model. ,!wo chrpmel-alumel
. ,
"
"
1 "
1
1
1
ï
i
t,
1 ft
1 , f f; t,
(
, ..
108.
TABLE 4.1
Thermophysic-al Prop'erties used in Heat Transfer Calculations
0
./ . Pro pert y Phase Sand Pb-19% Sn Pb ,""
-) , '
,
densï'tv (lZ/cm3) . ,
1.6 U.":r 11.3
" <,\ t; 1)
la~nt heat (cal/lZ) solid - , 5'.54' , .'\'" 5.6'
" .,.' ... l , ..
" , ,0~O387" ~O ~ 0387 heat cagacity liquid - ',~ : ;'f -, <
- ' " (cal/g' C) , \
, ,-
0'.03 solid 0.2 0.0'3' , . .
"
thermal conducÙvi ty liquid - 0.039 " '1 0.039 (cal/cm Oc sec) 1
solid 0.002 0~O83 0.083 , ,
mushy - 0.06.1 -
thermocouples were placed in èach of the three sampl'es embedded in-ihe"
mold, as shown in exaggérated forro in Fig. 4.3. Two other type K
(chrom~1-a.1umel) thermocouples were also piaced in the bath in front
of the first and the third samples, as seen in Fig. 4.4. Each of the
eight thermocouples was checked for accuracy br immersing it in boiling
water. Only thermocouples ,which gave a reading within ± 2°C of the
\ expected value were used in the experiments., -The thermocouples were
connected to a micro-processor (seen in Fig.- 4.3 and in Fig. 4.4) which
served as an interface, between them and the IBM/370 computer'. The
" micro-processor registered a temperature reading each tenth of a second -
for a duration of 50 secot:lds.
, l \ i
109'.
( )
; ) 1 ~/ , 1 f"
i
FIGURE 4.3 Positions of thermoêouples inside the, sanlples.
J
; ; , ~
1 1 J
Cl i
(
· . r' " .. :
... ~.. ..
· " . . " .-.. ' . ..... ,
'. "
, ......... '.~ ','
"
.......... "
" . " ' .'
:,. '" " ..... ,"
'.
' ..... . ,
'.
'. " ., ' ,'~
: , "
" '.
"
. . .. .. : '" .... , " ' .. '
\
........ : . - .... . , :
.' . . , · " " . .. ' .... ., .. _t . -., .
. .... . ". ' ..
. " . " . . -, .. ' ......
..... ............
\ .. ' ...... ., ,.1 ..
"
",
'.
Micrg
Processor
1·."" ..
Thermocouole
" . '\ ....
'u .:.,1 ','oP ~.: . '" .'J. ~~I ", " •...
-:. ... : •... , , '., .. ',:~\ ".~ .. , l' 0, o' , .. -......... ,
101 .j
:' • ,#. •• ; # : ,',
•• \-" :-.. J.'.... :,' ,', \ .. " Of ~ . ' l, \'," '\ .. ;,', , ......... -1 :
~: ... ' .. , :): ~"," .. ': '( :~~',;: .~ ,,~. ',<~:\'
) \ III ",,: ••• .: ,:.
/" "."
",;~~:,,:,'; ",' ~ , .. ~< I~;~~.~~,:~,~'::':".' .. ,,,' .; ':::
... "
" . ,
. , '. , .: . . .--:.
.; . "." . . . .. " .
;. ..... ' ... ' ; '.. -:' ·r .. -.. -.. .: ! , : . . . " . .' ... ,. , .'
'. '.: ' " '-: .:. ;.':, ,:' ::'" :: ~"'.' ..... :: . , .Sand ....... -"'J.' •••. O' ,.'. " .. ., . . .. '... .\ ........ ... ,. 1· ..... "' .. , .. ~ ...
-. '. ~ ... , .. " .... • .. .' l ' •• " .... : :' 1"
........ • ... .. . ' 1" ... ,.": .. \ .' .. " ' .. " . . .. ,
.. " ...... .." .1
'.. .. " '\., : : " .. ' . .. " 1 • .. .- ,"
" . ...... .' ~
) /
", " .......
110 ..
(
FIGURE 4.4 Positions of thermocouP.les in the bath.
(
(
,.
,r'
)
Micro
Process,or
Point of Thermocouple
.
..
:: :, :::. ':' :: :; ~ : :.',~':,:,,: ,'-, ,. .......... .. . .. .... '" • , • III • ." •• ' •••
: :- ,. .• t : 0. , " .' . ........ '. , "
" • ". 1 1 ••• ,_
; " .. '- . . , Lor-. -----:-1-'0-'""--'--......... -......... :. < .. ',' f. : ~ :'. ' ...
....... : ........... ,'0. ,. :~'.:~ : ...... : ............. I~~·- .. "0'''_._ '.,,'" :.; •• -• • • .. : .... III :_ ',' ~:., ...... ... .. .. .. '", •
, . . ! ,
• ; . " . .. .
J" • ~, • ,. :" ..
' .. ', .... " '
", .' , '. ,
. ' . '1 '1
"
. ~ ..... . .... " ,
•• '" 'II. : ,.: : :
o
\
.'. ,.,. . , ..... .., ,,, •. '.... . " .... _ .... . .., . ;."il
• ~- t •• ~ ... "\ -;; ... ,. .. '" ""," .
" " . " . , '. iJ .. ,' ..... " , . .. of .. ".. .... 1 '.
" . . \ .. , ... " .... -• " a, ....
."" ~ "'. ~.. ." .\ ' .. .. , S~'ndt~, ;.: " .!. ..'.: .. :. • •
." .... , ., .. . ' ... , . ~ ... ,. .... .:.:":' ;. ,. ... " . - . ":. .."
, •• , ..... -lOt •••• ~ ..... '11 ... ,,: • .-.-
.. -. l'.' " ~ t. : ... ,.' ~.'" ' .. ' , '. , . ..: ... '.:. :'.' .: ...... :" .",.
.. .. '.: ; ,. .' .' .. '; .. ::~: . .':; .... ::. :',,:' ... ~.'
, .
, . , .' , .
J
,,1
, fi,
(
• 1
, ' i
"..' ,
o
'.
o . Experiments using oxidized samples and 100 C of su~~rheat
'.
'were performed with Pb (experiment number F14, Tables 3.7 and 3.10)
'and a Pb--19% Sn alloy (experiment numbeJ: FIS, Tables 3.~ and 3.10). , , :
<
The results fro~ these experiments were compared with tHose from the
model and are presented in the next section.
4.9, Resul ts
:-Defore presenting the results obtained it should be pointed '
~t how the bath temperature, at the time when the liquid metaI contacts
the sol id metaI, was .:esti~ted. The only way found to deterJOine these
temperatures for the ,three d~f~erEmt~ positions ;n tbe runner, was ~y the use of percent ages of the superh~at. Difficulties ari~e because
while the Ùquid metai is flowing in tne mold, a sol~dified 1ayer begins o '
to grow from the 'mold wal+ toward the center of the casting, thus
changing the pertinent values for the heat transfer and thereby affecting
the amount of heat lost in the runner 'during the f10w of molten metal.
The thickness of this solid layer changes wi th time, bein,g dependent
on many other variables such as superheat~ mold properties, etc. J, and
this makes it vèry difficult "to calculate its numerical value,
The expedmental results for the thenocouples in front of Q
Il,
the first and third samples (~ig. 4.4) are prèsented in Fig. 4.5 and
4.6 for Pb and in Fig. 4.7 and 4.8 for the Pb-19' Sn alloy. The
numerical values involved are shown in Table 4.2 in which position 1
means that the thermocouple was in front of the,sample at position l,
and ~e same applies to the themoeouple a~ position" 3. The percenta~es
of thtt superheat were obtained 'br subtracting the liquidus temperatures',
. , .. " l~
" ~.!' •
J'
,
i J j 1\
i " )
"
~ t .' • ,f ~ .R ~\!.
,li ~
'1 ' ,.
( ..}"""" : ,
/
, , t
l ' i
~ 1-
1 r !.~
\ l
1 , t
"
FIGURE 4.5
. '
, 1
"
/
Relationshi~tween bath temperature in front of position l/and)time. Material: Pb. Superheat: loooè.
,
/ " '
" 1
/
\ )
Il
, -, ,i "'t • i l
" , -~
t ,,.
~ , k
Î 1
! , ! 1 i 1
l
( \ , "
\
1 _ 1120
\,
/ 1
\ 1 Y
, '" 1 350
, .1
" 1 / '\
1 '-,. f
;~
t ':
[ t! ,....
1 u .280 0
l ...,
t I.LI a:: ::>
1 1- ' 210 ~ . CC , r a:: f. IJ.J t a.. 1 l: , ! IJ.J ' .
1110 ,
\
l- i
Gl.
70 ') . toi. ! .. 1
~ J A
'1 ,1 1.
'!"
.1 0 10 20 90 qO 50
" TI HE SEC~NOS 'f '" "
1 ( . . - --..: .~ ~.-
·c~ ,
-.. .- " .; r 1 ,--~-. 1 l-..... - .
, { Ifuo
ù' J' .
'ftl. II1II,. 1 _iiii. 1 Il •• L .. , .. ' u , ,
,/
\
t· î !
! '
Il
(
/ {
)
)
FIGURE 4.6 . Relationship between bath temperat\lre in front of', : position 3 and time. Material;: Pb., Superheat' = 1000C.
(
113;0
"
1 J J
j. ! 1
1
( i J
, "
q20~------~------~------~-------r-------'
350 '
f [
t ,..., ) u 280 0 .-
r. W ~ ex: !
f ~ ~, /- 210 , .~ a: , - a:
fi ~ ? •
W 1
Q.. 4 w· lYO '/-
f'
fi '. 70 \
o 10 20 30 110 50
liME SEC~NOS
o l' '-- ...
. -,
__ Wl._UY::1. __ , _____ ....... ______________________ ..... ____ IE! ..... _~z.vùJ ..... ,Çt ...
, -t
'.
(
1
o
l' , (
)'
. )
' ..
FIGURE 4.7 Relationship between bath temperature in front of position 1 and time. Material = Pb-19% Sn. Superheat =, 100°C.
\
114.
.f
,
! ;
1 l
(
" .. , ~I>.
"" 1120
"
" '
"' 350 t
, , ! , r i i 1
f -f
U 280 ,~, ~ ,
f ) ; l.LJ '\
f a: ::;) r 1- 21~ 1
f a: 1 a: s. ! W , Cl.. . !
t x: 1
r l.LJ 1110 "'1-
\
l, ~
'~ .. l ' lü ~-'.
'.
-' ; \ .
0 la 20 30 "0 50'
TIME SECONDS
... "
.. i " 1 .- .-' ~ ",'- .------- _::...... -i ... - .... -- . .: ..
.. ,
=-
(
\
o
II' 11
, .
FIGURE 4.8 Relationship between bath temperature in front of position 3 and time. Material = Pb-19% Sn.
,Superheat = 1000C.
'C ~ .
( , \
115.
",
l~
;
l
1 ~ '\
r 1
i i !
,:
f . , . { 1
, ~ , f f i' ~ l, ~ ~-
, f
,~ . . . ... " ... -_ .......... _ .... __ ....................... ,. , ...... _.u ... · .. ~ ._ ......... _ •...... . ~... .... ..... .., ~ "- ~ ~ .. .............. 't... .... •. H _t. " ...... ... ~
( J
~20--------~------~--~------------------~
350
- ,
U 0 -LU, a: => J- 210 a: . a: lJJ a.. ~
" l.ù . J-' l~Q
\ f>' -\
1
o 10 20 30 50
TIME SECONDS l
.0 '. .., ~ r' .. ~ .. _""-',,- .. _ ... --"- ..... -- -- - ..
~~ .. .-___ .. lIImilln ____ .... ______________________ ~_
" L
1 ~ • i
1.
!
1
1 'f
t 0
1 i
( )
, ,
o
1.16.
3270 e (600 K) for Pb and 2800 e (553 K) for the Pb-I9%, Sn 'alloy, 'from , ,
the temperature readings obtained in ~e respective positions. Since
the initial superheats were of t~ order of IooOe, those values as per-
o centages were found ta be 82% for position 1 and 48% for position 3.
'The percentage for posit,ion_ 2 was estimated- to be between those for
position 1 and position 3, therefore 65% was the value used . . "
TABLE 4.2 . " Experimental Values of Temperature Measurements
, l
Experiment Superheat Temperature Percent age .' Number Materiàl (oC) Position Readings (oC) of Superheat
, If
.' F14 Pb 100 1 410 (683 K) 83 , - ,
3 376 (649 K) 49
-FIS Pb-19% Sn 100 1 361 (634 K) 81
. 3 327 (600 K) 47
4.9.1 Comparison Between E?cperimental and Theoretical Results
The experimental and theoretical results are presented in o
Figures 4.9 to 4.14. The theoreticar' r~sults are for nodal point number
10 (Fig. 4.2); experimental ones'are ,for the thermocouple inserted at , '
the top o~ the horizon~al part of the sample (Fig. 4.3). Figure 4.9
- represents the results obta1ned for position 1 CFig.· 3.5) in the runner
when usih~\P.!lre lead wi:th lOOoe supèrheat. As can be seen, the model
predicts the remeiting of the sampIE, •.
')
(
-,
, '!III
FIGURE 4.9 Comparison pf the experimental and predicted temperature at nodal point 10. ' Material : Pb .
. Superheat : 100°C. Position 1.
.,
•
"
117.
/
( ')
1 -"
T T 1 1 1 ' . 1 1 1 T Cl
.' -J e Î , ,
350 ·623 , • ,~ e .
e e • f- 0 0 0 • • " 327 0 600 - u 0 0 - • 0 - 0
l' u .. 0 ~ -~300 - 1 -573 41
"" ;:) e- Experimental -. ;:) - -t " Pb 0 L. - "" 1 41
t 41 0- Predicted . , a. a. 1
E E 1
l ,! . - .!
; r
J .. , -~ ..
250'fo . 523 '''> Î
J 'l
• ' . 1 1 1 1 1 t J,
1 0 5 10
1 Time (sec)
f ,~
"-i
\
\
() "'-<
.\ ~
\
j ,~
1Ii&lll11. 111U1I_._, 1111 1 .1 ..... _ •. JWJtlEi II Litt! iH: LUi: iil i 01 'E -, . ., .... ~'\-.
,,;
(' ,
\
118.
, .r ' 1
Figure 4.10 represents the results for l?osition l (fig •. 3.5)
in the channel when using the Pb-19% Sn alloy with "IOOoe of superheat.
The ,model predicts reasonably well the temperat!1!e re~hed br that ,
nodal point. Figures 4.11 and 4.12 represent, tl-ie results for position
2 (Fig. 3.5) in the channel when using lead and the Pb-19% Sn alloy,
respecti vely, and both having 1000e of superheat. Again the model is
in reasonable agreement with the experimental results. Figures 4.13
and 4.14 show the' resuIts for position 3 (Fig. 3.5) in the runner when
usi~g lead and t~e Pb-19% Sn 'alloy', respectively, and again both having <
IOOoe of sup~rheat. The theoretical results are again iI} approximate'
agreement wi th the experimental ones.
4.9.2' Predictions of the Model
Sinee. the p'redicted tempe ratures for nodal point 10 (Fig.' 4.2)
located jus't inside the solid ,sample were in good agreement with the , '
va1l:les obtai~ed in experiments 'br means otl thermoc~Ples (Fig. 4.3H it
w,A~ decided to check whether temperature predictions 'of the model
coincided with, remel'Üng ,or the solid {samp1e as determined by\sub~equent
microstructural ana1ysis. The teJ6pe-rature-time curves are shown in
Figures 4.15-4.17, for experiments F3 J FlO and Fi'z (Tables 3.7 and ~.lO),-' ',1
z:especti vely. 1 By comparing Figures 4.15-4. 17 to the resu1 ts pres ented in
Table 3.10 it is 'seen that whenever the sample was remelt ~
predicts a maximulll temperature which was above the ,
and that whenever the sample was not reme1ted, the m9del predicts a
'maximum temper~ture which was below the liquidus temperature.
, Ir .;. QJ ;$,... • Jr
, '
1
119~
{)
FIGURE 4.10 Comparison of the experimental 'and predicted. temperature at nodal point 10. Material: Pb-19% Sn. Superheat = lOOoe. Position 1.
\,
if: \
") ~
~'o
-'>
1
r
, "'~ ? Il
\, " , -'
L ; (l\ ..
1
1 î j
-' - 4- -- --,
"
. /
--
..
o· , .
)
• •
." • -
4- vl o "
.. 1
-!
1
;:,
ê 25 e
! Q.
) E .!.
Pb-19% Sn
-1
'.0 J
,.
> •
"
• Liquidus o
i.
•• Experimental ,.
0- Predicted
5.' 10 Time' ,ec r
~ "
•
"
\J f ..
<.',
'"', '.
.' !
73
--G ';:, -o '-G Q. E .!
, .. ~ !
\ ",
FIGURE 4.11
-
1
1 1
l
\ j .
"
, ,
120.
Comparison of the experillental ~d pred~' t';erature at nodal point l~. Material;: 'Pb. SuperQeat: 10000'.' Position 2.
. ,
\ '
"
,
~~,._r'_~_r __ '_"-RJ~--'-'----'----~-"--_~_~'~Ol~ "'!J~;;t!iO!'I"'f'/~,,\\':~.;rr .... ' \ ' ,
.; ~ . \ '\ .. ( , . '. ' ,
1
()
• ~ ~ , 1
t .,l ~
ç ,1
~{ , :
~,;. " ,It ~
1 , ., . • • • • • • l . J,;: ~
j '" · :1
~
350 - -623 ~ •• %
!/.
" • ~
· ,\ • ' , Melting Point
1
1- • • .. ~ 327 600" Q- - ..,
,0 0 0 e • • 0 • , ~ ,1 0 0
~ .. - -U 0 ~ --.,300~ -573 Il' ,
'!; .-Experimental ....
::) ::l -.. Pb· u , ,0 0 ... · ... \ ,., 0- Predicted· 0
a. . Q. .,. e · E j ~. "'
Il l ....
-
250· .'\
523
1 • i • • . . ' . "
1
O· 5 10 -) .... lime (sec')
. , 1..
III , l'
' . . ' ~
0 "'t"
. (
.' ,
..
; .. _6 .. - .......... """ ..... -- - l,
1 ,1
~ ! ....
-',
o
, ,
FIGURE 4.12 .
..
\ .
/
Comparison of the e~riÎllenta1 and predicted temperatur,e at nodal poïn:t 10. Materia1: Pb::-19\ Sn. Superhea't., =, 100°C. Position 2.
, "
j 1 .
." ) , J
121':'
'.
•
)
... r,
• o \
• • • • 1 . "
)
~ · 1,
t r
,) () '300 t- ·573 ! 1 i"" " , · 1 1 Liquidus 1 .' " · 280 ·t !: 0 553
..... {
~ • 0 0
i , .. ,0 '1 • 0 t- (j1!lIl<. 0 0 ! " . 0 ...... • • ,U •
0 "" J~ · - -~ ~ 2501-... ,·-Experimental
· 523 0 ,Pb -19%5n ... ~ ca D- 0- Predict~d E l-ca . ' ~. ....
1- · , l
1- · N
200t- ·473
1 . • ' '. • .. • 0 5 lQ
lime (sec)
/'
" o J
,
.~.
• · • , .4 _ ; ; d
"-
()
. , \ '
f ~
~ i 1
1 , .
, '
FIG
o . ~ , •
" -'-- 122.
• 1 1
1 i.
\
• +
li
/ ~ ,1
\ ,\
,.
d • <,
. i
-1 . , 1
, \
4.1~ 'Comparison of 'the experimental and predicted temperature a.t nodal point 10. J.1aterial = Pb. Superheat = 100°C. Position 3.
"
1 1
) .~ .
..
•
j " , ~'
~. , l '
\ ,'/ .!
ft, 1
!
(
, ,
"
1 !
J ,1 l
'-
.()
> }
i '. "-, . __ ' i !
"
i
,f
t
\
. >
1 f'
(,
' ,
"
i!
r .
350'-
.... • 0 1-..
!. Pb E 1-
. .! 1-
2~O~
L
(_ o·
, "
"
~ .' .'
..
~ . '.
. . . '''1>
•
.
1 1
, .
.- Experj~ental
o - P~ed j ct~d
J.
1 . . 5.
Time (sec)
'''t
.p
-1 1 ,1
.
·623
, .
.
·523
. • -10
..
"
-! :;) -a ... 4J 0-E li) ....
) \
, , .
, 1
" '1
~ ,
:j 1 , ~ , ,
"1 !
f
,
·1 l,
l' t 1
• 1
.'0
1 , ,
" , , ."~
,. '
~
, . ,
J , q
FIGURE' 4.:14 Comparison of the experilii&ntal and ptediet~' temperature at nodal point 10. Material: Pb-19' Sn. Superheat: 100°C. ~ Position :3.
, "
l'
1
" '.
"
. . . , .... ""'-~~ .... _~:.,'~~_.~~.~"' ~-~~~: .~ .. I_!!'!.'~~~ ... ~.,.;!!II. 1I!I·1!":'l"-:,3.Nlgl.tl!lkltu.liL_ •• lDl~.S.j.Jtt.1i2.I ___ ... -----~- \
, ,
"
1 '
, 1
. " , ,
7" ,,' 't',
" \\ " J,:
~ ii\ •
",i '(
• \.... __ / 1 , . "
"~.~._._,_~~_"",,,,._,.,,, ... !."*_",,,,,,,~~~.,~,,,,, ••• ,.~~f·C,,, .. '-~l>~, l " " " ,- , " " "
\
\, ,
, \, '
, ,,'
• 'T , . , Ir l , 'l' 'T 1
,. · 300 ~ ·573
" . r ~ · 280 1
liqu~du; 553
~ • • 0 0, 0 - ~ .. ' 0 • 0
U • 0 0 ·
fi • -- '. • 0 ~
• 250- 0 • • ·523 .-... tJ ::) . ... -' :;, 0 d ... ... · 0 0 .':'"Experimental ... Q.
Pb-19% Sn al
E ~ Q.
il ,! · E 0- Predicted ,!
i. · ..., '. (
1- · ...
\ . 2001- · 473
• .. < 1 • 1 ~ • • • 0 5 10
lime (sec) ~ , "
.~
p
l' l ,
... (
,-' ,.
0. j' 1
--.~---~~
"
\ 1 1
-.. ~ .... ---.--~- ~', --;::-,-""':'.:-----...-------
, ,
1 Il
1·
.'
o
" '
FIGURE 4.15
, ,
SiIi!$i,;C"'fiii+'·
1
'l' ~ Predicted temperatures at nodal point 10 at difterent 'p~sitions in the ~ld. Material: Pb. S!:1perheat: 60°C"
. ,
. '
, ,
0- Position 1
Pb \
.- Position 2
A - Position 3
Melting PO,int
0 0 0 0 0
0 • . ' • 0 • 0 - ., 0
~ • À À A .' • -' A ' ~ - 573~\ ! r. " .; -300 A ... A :) .... A '~ 0
' .... . .. .. A G) '"'" 0. C-
e e .. CIl .... .... ~
l ,
~ - "
0 S 10 Time (sec)
/
1 \
\ \
0
? _1 ____________ ~ ______ ----------.. __ -----------
, ,
,
" . • l'-" ·'-'·_·-~-·-·_._'--'-----'''''--_''i.,."'''!111!4!!>lIi! ... *,,,,~\~;;;ç:;ei,~;t"~~ , . '"
'0
1 .'
),
It/,b
'\.
0 ~'
, .
,.- .,
FlGUR! 4.16 Predictel~~eratures at nodal poi~ 10 at different positiOJa' in the .old; Material: Pb-19\ Sn. Superheat = 60°C. ~
\.
\
t '"
~ , ,1 ! ' ,",'
~
"
125:
. J
'- ,
l,
..
,.~'
1
.. .-'t"'''t'il.l!':,
--1 - - -- '" _-""--'" "~~.J"If'I""'.,.,A~iS-~~~.q ,~ ~~",.~~\'; .. ,,'l'\.~'
t J
j 1 . { .. \ \
1 ~ "
• i
Cl ~ " .. \ ? i '- . \
. , 1
r ", {}
l .. ! " s l ., , } , • • • • " . , •
1- o~ Position 1 · -
300~ P.b-19 % Sn .-Position 2 ·573
J , ~ - Position 3 ~ r- ·
liqu' us 280 553
$ f
... · 0 0 0
0 0 0 - 1- 0 · • • • u' • 0 pa -0 • 1 • ~ ,- • • e 2501- 0 • • 523 .. "" ~ ..
Il. A A :» .. • A ... 0 l- ll. lJ.. 0 "" lJ.. ..
"CI Il. e 0. A o.' , ,E l- ll. · E ~ e .(
1 .... .- ~ ·
., "' ....
'"' · 200 ~ .: 473 ~
~ "
• . . • ' . .. --' • . 0 5 10 ,- Time($ec)
J fi>
,> '""'
....-() '"
'" • .
'jI
/
, "_,,-·;;,,m~Uti'tt_AJiMJ!~ ... :%!!! .. _ .... _ JI ç
,"., " .. - ~ ... -_ ...... ,~ ~ .... -"
"
o
J
'/ /
"
..
" . ,
\
.
. "
.\
,
"
1
*
. '
" ,
, '
.. 126~
(
, 1
r, L
"\h. '%-..J • , Iir, ' ?'fC'.
PIGURE 4.17 > Prèdic~ ~emp~ratures ait nodal point' la ~t different, . - ' , ,~sitions~oht. . Ma7~:, ~ Pb ... ~:,erheat • 20°C. " J' ,i"
~ " .... , . '" \
, ..
, . t ': ',: /
• , 1 ~
...
1
. , " '
, "-___ ___________ ._. ____ """""J,JFft ..... ___ .............. ,_ ...... =m'" ........... t! ........ ~ .... 4.~ il •• • $tV..,..:Qc::e&flP.1'i',~iJ$lJilf';IJ)'!
ü
". ,\ \
'1, 1
"
i ~ O-Position 1 ,
",' " Pb .-Position 2 ,
350 ~ 1 .. 62~ • . " ~ ~J"
.. '~ - 05lt.,on 3 '" .
# 327~ Melting Point ,
'600
, , . - )
~ ~
~ . " .. 573 -G
, .. ;1 -a .. G , et' E G
: t-
- "', 'c,:) , • 0 -G300 ~ 0 0 '" .. "-
j v ;1 ! ~'J 0 ...
ï " 0 ~' 0 Â, .. • ,0
! ! 0 1 lÀ
E • '0
,! A • 1 0 l' A • 0 t "Â ,. 0
a . •
A • 1- A
Â
2501- -523 , . . . 1 • • ..
0, s 10 rime (sec)
/' ...-'
',1 * 1 G \) -\ .(
r .. ,r 0 '.
r
) ...
.)
~'t.,. ;~L ____ .. ' .. 'ï~.
!
1 , 1
!" ,
o
127 ..
if 4:9.3 Effect of Solid Temperature and Superheat on COld)Shut, Fo~ti~
" ["> ,
In reai castings when liquid metal meets solidified metal, , j) ~ •
the temperature of the solid metal is DOt usua;1ly equal ta ambient ;.1:
temperatu~e as considered thus far in the present model and in the ..:
, '-.,
.experiments. The next step in using the model was to 'determine, for \
each position in the runner; the effect of the temperature of the solid ,
on the superheat necessary to avoid cold shUts. The critical conditions ,
obtained for lead in position 1 (Fig. 4.18), position 2 '{Fig. 4.19),
and position 3 (Fig. 4.'20) l the ~ner show that, as expected; ,the
higher the solid temperature, ~he lower the s~perheat necessary to re-
melt the sample (and 50 avoid cold shuts). Thè curves shown ,in Figures
4.18-~.20 show the limlting conditions for cold shut formation. Points ,
above the curves provide castings free from cpld shuts, while values
taken below the curves faci1itate. the formation Qf cold shuts. It 1s
interesting to notice that the relationship between th~ critical super-
heat and the solid temperature.ls almast line~r at solid temperatures
less than or equal to 300oC*(573 ~). For higher temperatures of the
solid, the slope of the cune iDcreases considerably. ~
\ ;~
\
The "same analysis was made on the Pb-19\ Sn aIloy, and the
resulFs are presented in Figures 4.21-4.23 for positions ~73, respectiveIy. 1
. . 4.9.4 Effect of Position in ,the Wold on Col~Shut Formation
As the position in the runner also has a strong effect on
the remelting process because the liquid metal loses $Uperheat down-1 ~
stream, the relationship between the critical superhèat.and the distance
do.wnstJ"eam' in the runner vas analyz~. Figures 4.24 and 4.25 we,re drawn,
• 1 f,
" , . )
,'Ù
\
r 1\ i
, 1
JI /',
(1
" ,
., ~ ..... ........,. ,,~ ... ~ ... .,..., '-""_~"·'r""_ ""~"'t!!" ~ ..... ~..-..;",,,. _ • ., ...... -~~ .... o""~~~"'" ~~""f:f~~~~t?1!"~~~iIlo~,~~~'2~'U"~ ~~'"('1l:i~
" '
1.28;
\ , . ,
presenting th~ curves for various solid t~mperatures. They show for . .
Pb and Pb-l9' s~ a110y th~criti~al superheat,-at~~'eertain'distance in th~ . " Î
~old and 3t, â certain salid temperatur~ Which is necessary to remelt, '
the solid. For instance, Fig. 4.24 shows that, at,20 cm frOm the point
of pOU;ing and with the 501id at 250°C (S23 K)) the minimum supetheat ~
required to remelt the' $olid Pb i5 sooe. f ,
Although the theoretical pr~ictions did not take into ac~ount , '
convection in the liquid and/or ap oxide layer at nodal point 10, the '
computer program is sufficientiy flexible ta allow for th~ir use.' The II'
simple approach use~ 1S shown ta be in reasonable agreement with experi-
mental results.
• l
û
. ' "
"
1 .: 1
. ,
..
.. FIGURE 4.18
\
. , ..
...
./
'W .,
li.
" . ' r ,
Relationship between critical .,superheat shuts and umperature of sallâ sample. Position 1.
."
J'
11&&&
,
to fam cold Material = Pb.
.c"'~1"
; t. 2 UA # 4 lU iL ."UR i ,alé. ct \~ li 0
Il ~ ""
'1-11~ ,
" t f. ~
~,
t l-,
/'
..
('\ C
-u o --o .. .s: ... .. go
V)
~~
323
~o
-'~l
.. .-
i \.-
Solid Te'mperoture ( K )
373 , 423 473
;.
No Cold Shut
--
'Cold Shut
100 150 200 Solid Te~perature (OC)
t
~
~
-52 5'73 .... -,.
~ Pb .. lib
Position 1
..
/'
j 1 ..... --~----.!. "
250 '300
,~~
') ·l
) o ) i-
f i j
,f !
i f l l, l
1
\/ ---- 1 \1
. ·1
.j 1 ~
~
{ " r
( 1 l, , \ f
t 1 i )
1 1
1 1 l
~ ! i r l-
)
e-
# 1
0 " !
f 1
i
,1
/
/f
/ ~ ..... ( !
t
\
\
, . <,
:'
FIGURE 4.19 Relationship ~etween critical'superheat to /orm cold shuts and temperature of 501i4 sample. Material : Pb: Position 2.
(
~, "
/ /
r /
/
.., f
!
"
"
;'
\, \ . \ "
i ; ~ l' L .1 i;
t
'" ,J
t
( ,
,,-,..._ ... __________ - ___ ... ___ ~ T __ ._~.~ ___ _
_____ ..... ..- __ ::;-- _ ..... "' __ .......". __ "' ... "'_ ...... _ ... ~_....,,. .. ~--'f;l<~ ) (~ '.liHl .... ',..,,_ ; s ::4iUJiw4 .... a.#44==Jl~
t..... " ~I 0 Ct \-.
i ~ 1 1
-l .-/ l ,
'1 f --,
-, i
~ "-- .
r ~ j
Solid Temperature (K) 1 •
1 l
373 - ....
}1
:~of · 323 ;;. 423 4-73 523 -573 r • • 1 • i 1 , i i i , 1 1 • 1 • i 1
l -i,
!. ~~
<:: • l - ..
( Pb j " 1
, -------:::.Id Shul Position 2 j, ' j. .' ,t .. ' ,
-~ , <! ( i '0 i
i ; - ~,,-\ ~ 1 ~
JJ-s ~ j
l Cold Shut t
i j .. """"'- ..-'J l
1 ...... 1
f. ~
-JO i _ , , . \,
fIT. .'\. - 1 1 i li
CS'"( r .i.. -- 1 " ~ '1
lm)" - - 150,-~~~~200~-~~25(f---~----30(j-~~-1
50 ~
Sol id Tèmp_ero ture ~oC ) >
'l " ~ -~
~ '- ~ !?
>. ~ ~
.ho 'a." n7 sV t "" =l»>I.u~ .. __ 1 FH? [ ~tWln . t Sr , -i,un' u_ -~. __ . . --.' ~-~ .. "'""'~.-~\"It."...: .... ',.~~'~~' . ":--'
-1
l , 1 l,
131'. i
.. \ -, '
. , ,
.'
\
" l,
, .. r FIGURE 4.20 \. '~I Relationship between critieal SUperB~' t,to.fo~ cold shuts and temperature of soUd sample.. terial = Pb. ,Position 3. . ' " .
.1
, t "
'.a ' "
\
·0. l ,
- 1
'0 '~.
\ ' 4~. ______ ....:..--:.. __ _
~,~'1":~"" ~~~"l"'"~! JlQCS@QlUZWZ " .. ~.-. _U-~"'L~,_~"IIe''litl. __ ~~~ ___ ~_..-__ ..... ~
o "Q't
"........
F
! ~ !
1 1 • 1 1
( f
Solief. Temperature (K) " " 0'1 j
323 373 423 473 523 S73 1 > 1
~rI > Pb> 'll1 J. ~ -. 1 J, r ~ No Cold Shut Position 3' _ l,
5 ~
<> i ~ l' . -l .. .
> / 2 > ( ~
~ ~ Cold i ., "" ~ "
~ Jl 50r -- "'-1 r . ~ 1
~ ? \5q 100:' 15~ 200 250 300 ~:1 . Solid Temp~ratltre (OC) .~
~~
1 f ;~ ,
~ no/rter i&tW'tlkh Il ,a1m:r~~1*f.".=.otll\wo"'~\.,.lr...;'l..";)'""~'-'L<t.{J'~""-~II' n'41~ ........ ~_~ • "!l-~'~.c..L~~:t,","o;A:~"_"",~~ . - .. ft ~ ~. ~ ~-,!J.. ~ ::':\oI:~" ..{'_' .t" ~ ~"'J~t'~ .., .r t b. "t • sr ", ....... - -pt' / _ .'~ . .:;.m-:.>\ _ • , _
:~ - ,,-'"
i' L
o
o
..
! ?
/ ,
1 1
1
, .
. ,~~.
FIGURE 4.21 Relationship between critical superheat to form cold' sbuts and temperatur.e o~ solid sample. Material: Pb-t9\ Sn. Position 1. .
"
'.
,\
\
J
132. ,
1 •
L
f
t',i .. ~
1
•
.-'
-.U o· -.. o • .I! ... .. Q. :;:,
t/)
" III
-0
/
323 - 373 -
Pb-19% Sn
/,
50 o 100
__ • __ ~ ............... __ ~_ .... __ "'-~,.,.j.,.."""''''-'"''''''''''*''''C:'''~> ~~_.G."_ ( ~_ _,_~ ... __ ........
Solid Temperature (K)
423
G , "/
No COld-~~
Cold Shut
\ 150
P~sitiQn 1
/
~
'0-
Solid Temperature (OC) \ \
....
--473
\ *'
200
•
--------
-
..-...., t -
523 -
250
.1. _r,sp' t . ; en ft t lil.hWI,iI • .ra» zn hm',. _11_51.. . RU.,'.' "<;,:,. .... ~'jœ ...... _f'; ... ''''"...::;·"...c::. •• ~.,;, .... ~'l.''''''"f~~'''''_ .. "'"";';;:'IA.~j'l"..JI'~f-;l"*" .;,: •. "
~ l
l 1 -)
1 i J ,~
~
l ~
l ~ .~ . .'
'. ". ;'-
~ -1
1 '1 ,
ù
\ ,
1
, 1
• •
..
..
".
FIGURE 4.22 R~lationship between critical superheat to fprm cold shuts and teaperature of solid sample. Material = Pb-19\ ,Sn •. Position 2~~ l, '.
.",
'.
""
" . . , , .
.' / .
$
133~
J
f".,
'1 • ~ 1 }
. ,
\'
.f'
1 {
-u o .--i J:. ~
-
., .. a. ::J
cl)
~ ...
.,
....L " •
'0 ?
V 323 37~:
~)
JO.
\ .. 50 100
'" ..
__ ~_ ~ __________ ~_~..-r>'<",. ... -~.~_ ........ ~~~aL en t 4 ~_. Il USd §;$lA. 4M3 4 l ~_
(\. ·0 r
)" Id -TPmp.r~( K_ ~""
, 423 .)' 473' . . 523 ' .•
-...... Pb-19~ S.n
No Cold Shut Position 2
J ~
Cold Shut
\. '} t
,\
" ...-1' . '
150 200 250 SoUd Temperature (OC)
, . '
. 1 j !
~ l f 1
\ i
·1 ~ l .' j 1
l ï f
l i .
i ' l
... j r ,
·l . '1
/-~--.
t ~ ,~ '!
t . III pra 7 _- nu. Ulm? Il' Il iii ~ J,""" 1 r) JI --.----.p ... -,,- ____ 1. ·--'--..... --:;:;---)~.,.:"e*'tttlO:T\;ii "HriIt_f)"'ji'Ctl~!
;-'r Cd
O· (
.'
".
• .1
.'.
•• 4*
"
/
\
FIGURE 4:23 -
. '
/
, \ .
.«;aM d L '.,....,...."4",,, " JU a &U
(
1 "-
, " J
\ /
'\ ~
.. """ .
Relationship betw,en critical superheat to fora cold shuts and teçerature Qf so!id sample .. ~teria! = Pb-l9'- Sn. Position 3 •
'. •
, ... , . /
,'10
\
~ "1"
, ' ,.,. , 1 ~
134. \,
..
" '
ij JJ' tl
i~1." ..\' :--
t-: l:q t~ / f2~1
t~ " ~ i(,.· t·: ~;. ,
cP -- 100 B . ..c te 0-
.::) &1)
5
') --'
l -323 ~~ 373
'-
Î /'
~
50 lpO
# 1 U= [!LÀ 0&\
" tt 0
:. ,\
~
SoUd Temperature (K)
423
No Cold Shut
Cold Sfiut
..".
150 Solid Temperature (OC)
--..
~
/'
....
473
Pb-19% Sn
Position 3
AI
200
. .
523 .
"
.-250
1
1·
(f, J
"""
.1
1 ·1 !
1 1
1 e 1 .
! 1 ~
î ' " "'" "iii'" l .. ,-".-_ .. r ......... _"_Milj ...... ~ sm Pd l' , rœmtsN?1 1 . . NI PC .. nt "_Sll
i "/ ,. =
. !
o
'0 ~~.'
, ..
... III.. IST ft
f
1
, ,
. '
,FIGURE 4.24 Relationship between critical superheat ,to form cold, shuts and position in the mold. Material: Pb.
, .
0' ",
,:.', ii ,j
135.
\
\.
1 i 1 i
r 1
o J
Curve So'lid " "l
150 t \
i~ # Temperature (OC) Pb
1 l 50 ' 2 100 3 150 4.- 200
:~
~ 5 250 ,
J 6 300 7 320 -" c
j
. r
1
l -0
l' 4J .t: ... 4J
" a. ::>
V) . 'tt,
l , . '
, '
15 20 25 ,) Distance fro(Point of Pouring (cm)
• o
,1
1 ! 1
1
1 rI
. 1
", . , . '
. } ~ ,. - , , • 1., , •
, - ~:--~, " , ". u._ ~n_"",_>_ ... ~ . ...,..,.._~ ---~""'_,.~...w',., .... _~ •.• """.,._ ""' ..... ~."'_,~!""".,,':;fi"l<'l\;\~!,""1
..
FlGURB' 4.25
.: r"
o
, (
f , .
Relationship between 'critical superheat ~o form cold shuts and positio~ in the mold. Material = Pb-l9' Sn .
\1'"
136.
,
t
, 1
1 1
1 1· ' l
l'
1
i
o ,. J
J'
150
cP - 100 ,g .&. 'Q)
0-;:)
CI)
1
Curve #
l
2
3
4
5-
6
Solid Te,mpérature (~C )
50
100
150
200
250
270
. -, <
, Pb-19% Sn
20 25 Distance from ~ni .. ~ Pouring tcm)
'.
\,
1
. \ . f (
o
o
•
, , l'
CHAPTER S. OISCUSS ION
)
1
. 1
..
'j
1
<\
1 \ , ~,
o
=
, , ... ",') -~ .. " .... - ...... "t<-~ "~1i"'i '~-L~.T'" i'''·\l~'·f'IL·'='''''''''·' '~""-,!,~~.tll·,,-~' ""';~ t'- , .... ~-,'
137.
As 'it was. found that the major aim of the few works enc~te"l'ed
in the literature was ta determine methods to avoid cold shuts, this " '
"" study was undertakerl in an attempt to determine the mechanism of fo~a-
tian ,of such casting defects.
During the course of the experiments it was, found to be very " \1
. difficult to p~oduce a suitable vertical coldt/ shut. ~This kind of special o ,
defect seems to be formed only'under a very ~pecific set of cçmditions
whiéh are unlikeiy ta occur in practice. ' In addition, not knowing ,in
advance the exact place where th~' ;col<1 shut would be formed made the
pr~uction of an appropr}ate defect even more difficult. The use of
solid inserts overcame the difficulties and it allowed for temperature
measurements. '.
5.1 Mechanism of Cold Sh.ut Formation ,
, From the experiments carried out in this study, it l'las found
that cold .Shu~, originate whenever a liquid metal meets a solid metal,
and in addition only when the liquid does not have suifident thermal
énergy ta remeit the solid. This 15 shown schematicalaly in Figure 5.1.
The liquid flowing over the solid fo~; instantaneously, a solid shell
(Fig. S.la). At tl > 0, heat flowing, from the Iiquid toward the salid,
through the shel1, partially remelt5 this shell (Fig. S.lb). At t2 > tl,
if the hea~ transported through the shell is not sufficient; to remei t...: b,oth the shell and the solid, then cold Shut5 are formed, as'shown in
Fig. S.le,' If the the~-l energy is sufficient to compietely remelt
the sheU and the solid. then the formation of cold shuts ,i5 a.voided . i\ .
(Pig: S.1d). 'nIis explana.tion i5. in agreement ttith that lihiçh was cfound
" "
•
.J
o
.. 1
t 1 1
1 1
J
' ..
. .
,0
..
.. '
'( ,
F'IGURE 5.1 Schematic diagram of cold shut formation.
\ 1
138.
.,'
. .
\ ' ,
." i i "
, ! . { ,
• l '
, 1 t i ~ f
o
, ,
a)
b)
cr
.. d)
Liq",id ? .
. z;::~~~ t=O
.. '
Mol<l
liquid
~Sh~l~ Soltd .
Mold J /
Solid
< ~Id
Solid
Mold
Cold Shut / . , t=12 -
t"'t - 2 \ ,
1 \
\
t ! ~
l 1 1 1
c)
.,
139.
IY ! . ,8 ' , by Gorbachev and 23.tkov., (Ou~,pter l, Section 1. 2 .1)' in studying the
elimination of soft structur'es, in white iron. The solidified eddy, " ,
in their case, corresponds to the solld insen used in this study. 1
" 5.2 E~fect of Superheat and Alloy COmposition 'on Cold Shut Formation , .
As already mentioned, since there is a solid portion in the
'.. . mold, cold shut formation ~epends on the amoynt of neat which will be
"---eXFTacted, from the 'liquid by conduction through the solid. Therefore,
the remelting of the solidified layer'is strongly dependënt on the
superhe~t at which the liquid meets the solid. Lillieqvist lO has shown, \ '
this, (fig. 1.12) and Figure 5.2 shows that .• for pure lead. the Pb..l19% Sn
, a11oy, and the Pb-61. 9\ Sn aHoy J ther~' is a c~rtain superheat above, ~
which the formation of co Id shuts is avoided. The data used in Figure
5.2 we~e obtained f~om Table ri5.l0 (oxidh.ed samples only) and the super
heats ~ere calculated as bein1 82% for position 1, 65% for position 2,
ana 48% of the-i~itial sup~eat for position 3 in the channel. Figure
5.2 also shows that •. unlike for the effective superheat. the colnp.?sition
of the a110y (as reported by Kvasha, ~ !l.~) does not have a notice~ble
influence on the remelting process, a1though the alloy composition
,influences the final aspect of the cold shuts. aS,will be seen Iater.
In Figure 5.2 the dotted line5' represent the unknown li.mi.t criti'cal '
values for the formation of cold shuts and, fOr the alloys studied, 'it
was found that the minimum effective superheat necessary ta. avoid j:he ~
~ormation of cOld, shuts is so~ewhere between sooe and 60°C. It should
be pointed out here that these vàlues were 'obtained when r~eI1:ing a
solid sample of metal at the'ambient temperature. In pr~tice the
. '
.,
,\
"
j, 1
-1
, "
1 , ..... 1
1
~
o
, , . _"QI .... ,.*" __ .~ lI!!i6IGW"",.~t~!QJ .. ;tW!!_~.\1IOd*l"Af!P\t.''',!lilf;·W~~
"
" .
..... .
,.
.. ,FIGURE 5.2 RelatiQRship between effective superheat, alloy
compos~tion and occurrence of cold shuts.
\
\ , ; ,
r ;l, t
140.
J,
. ,
1
o * ..
f
~ 80~
u 0 -, ... -< w 60~ J: Ct! w Q. :) CI)
40 1-w
.' > t-U w "- 20 "-w
, "
\
1 ' .,
1
, " 1 1" 1
0 .'
~ -~ ....... _----,."'-'.,,- --~-~~~~------_ ... _~ ~ -~- ., -< < '
\
'. .
• • • No Cold Shut
fi • • --------- .... ~ ......... .... -........ --rr-.- -8- - ~- - -_:..-:- --8-,
a a 0 ... 0
Cold Shut 0' a 0
0
.g 0
• -~' • 1
Pb 20 40 60
WEIGHT PERCENT Sn
~
, \
80
Q j, .. i
:; ! '\
.. -
.
-
~ l~
<t'
1
. ,
, , • '"
141.
effective superbeat necossary to avoid the formation of the aefect
shou1d be much' lower than t~at p~esented in Figure S.2.
The ~~loy composition influences the aspect of the co Id shuts
by affecting the mode of solidification,' This i5 done in the following
vay: To completely remelt the solid Insert it was found that, for the \'1
ùnalloyed lead ~(for the Pb-61.9\ Sn ~110~ (eùtectic ~omposition) -
wltich have a c";'~en'I: .eltmg point'~ it was necessarY ~ ~: solid piece of metal above the melting point, as shown in Figure 4.11 l •
I~
Figure 4.13, and Figure 4.15. In both cases, the solid/liquid inter~
face is planar, as outlined in Figure 5.3. On the othe~ hand, for. th~ , .
Pb-19\ Sn allay, which, has the la1."8er freezing range (Fig. '3.7), the
solid ins~rt, when heated to withïn the mu5hy zone (Figs. 4.12, 4.14
and 4.16), i5 partial1y remelted. This ~esults in the cold shuts
presented in Figures 3.22 and 3.23, which are neither as visible nor . ~
as conÙnuou~ '~s thos'e presented in Figures 3.18 '(unall'oyed lead), 3.20
and 3.21 (the fast two both for the Pb~61.9% Sn a110y). The' partial -
remelting of the solid surface is possible due ~o the mùshy zone, being
a mixture of solid and liquid portions of meta!. In this case, as is \
, well known, the solid/liquid interface i5 no longer planar, becoming
dendritic, as' shown in Figure 5.4. 1
S.3 Sffèct of Syperheat and Head of Metal on Misrun
A misrun is an exaggerated form of S'hv.t and it r~ers. to' .
,castings in which the molten metal do es not penetrate all parts of the; . "
m.oId. Misnms are mainly due to a lack of fluidity in the métal, and ," "
\ , this uSually occurs because the meta! is poured at too low. a tempex:ature.
"
Mt.l'. ) ... '
o
FIGURE 5.3
Il
, f ~ PlGU&B 5.4
î ), 0 .. '. " . t.
.' , \ .
,"
(101 .. 1' • W •• Il;. IN .1 ... uu
J
" "
\
/,
Schematic diagram for the remelting of an unalloyed metal.
Scheeatic diagram'for the remelting of a large freezing range, a11oy.
..
l '
..
, , -, , . l'
,
;ij'
) il ,~
1 1 i
t 1
, f 1
.1 1
l
-.."It,......,.~"'f>'~ , ..... '~"""t'l~~/,.--__ W ... __ .. ""' ... + ....... r __ _
, ,
, , r.. l' '~~""'~"'f "';>I~ltt~t~~-;
_ ....... 'Io:!!.~~'~It~'H~~~~~'!!.'"'"_~~~_~<'"ttW~~P!~ .. !::~~~(~'1~t~ .. "fJ;'~t~~~t i~ • ., ,-' •
o
..
o
o
" '
"
143.
It w~ found in this study that the head of metal also'has
a r~lative influence on the occurrence of misruns. A careful analysis .', ' 0
of Tables 3.5 and 3.6 shows tha~t a superheat ,of 20 C, the weight
of ~olten lead in the ladle must be greater tha~, say, 2200 ~ to
avoid a misrun (no collision of the two,liquid streams). Plotting the , ' ..
data fro~ those two tables yields the results shown in Figure S.S.
Although the numQer of experiments was,not sufficient to allow for a
final conclusion; it can beJseen that the amount of lead (head of metal)
and thè superheat are the two factors which allow one to ~pecify when à
misrun will occur. Assuîning that the dotted Une lies on critical
values of both variables (head of metal and superheat), ,then experimenta~ . , ~'\ '.
values taken above the line will provide a casting ~ere the two streams
will collide, 'while valu~s taken below the line will result in the
.liquid streams not meeting • . ,
5.4 Effect of Position in the Mold on Cold Shut Formation
The influence of the position 'in the mold on cold shut forma
tion, ,shown in Figures 4.26 and 4.27, .can be explained on the basis of
superheat. In fact, these positions mean effective superheat, since
the mo~ten metai loses heat as it flows in th~ mold. In other words,
the distance f1"OII' the point of pouring inside tpe- runner 15 inversely 1 • '
proportional to the effective,superheat - which was found tl) be per-'." , centages of the initial superheat for,different positions in the mold
~t 1Ihich th. !iquid •• tal _che. that poJ as l.5 presente<! in
Pigure 5.6.
o
(
l 1 1
FIGURE 5,.S
0,
/
..
Relationship between the head of metal, the superhe~t and the occurrel1ce of mïsruns.
"
1 \ .
. 144. ' \
1
1
. t
.J
t. 1
1 r ! 1
1
o )
J
G,
\
3000~
!.-Is-
; ~ 2500 ':" ,.0 0.., ) u.. (' 0 ...... Z
.::) 0 ~ .(
2000r-
1500 ~
, \ r--\ ., \ 1
\1 \ ~'
\ . \ \
if
\ ,
\ \
, ". , , No Misrun
1
o ,
o o
MiSTun
l',
10 .'
o
o
•
, . " " "
30
SUPERHEAT {oC)
-
-, "
-.... - .
-'_1
50
. '
.(j
/~,
o
•
, ,
FIGURE 5.6 Relationship between position in the mold and the superheat at Wbich the liquid reaches the position (which is expressed as percentage of the initial s~perheat). .
. ,
. ,
14?.'
\ . '
, l,
" .
(, Q-I J
, .
1
~ , . t f 1
.. " ..
t- 80
1 « w
'. ::t
\ .! IX w
1 0-:::> ~ ( CI)
1 U-
0 w
40 , ( ~
;! • !
Z W ; U i. IX 20 w a..
lS 2S
DISTANCE FROM POINT OF POURING (cm)
o
{
o
146.
5.5 Effect of Pouring Rate on Co1d Shut Formation
Figures 3.1Ô a~d 3,.11, resu1t~ng fr,om ~eriments number B2'
and BS (Table 5.3) respectively, show that, for similar values of 1
~ ... - fi> 0 pouring rates (276 g/see and 290 g/see), 10 C i5 not a 5ufficiently
high superheat ta avoid, the formation of a co Id shut. Decr~asi~g the
pouring ra~e ta 58 g/sec and increasing the superheat to IOOoe (experi
ment number B9, Table 3.3) caused the formatiort of ve~,deep cold shuts
(Fig. 3.12). This means that the increase in superheat did not compEm~ \
sate for the decrease in the pouring rate, and that the 'formation of
col~ shuts is a{fected by~t~ the superheat and the pouring -rate.
As already stated, 'the remelting o~ the solid formed is
strongly dependent .ôn the ~mount of ?eat carried br the liquid m~tal.
Actuaily, th~ effect of PJr~ing rate o~ eold shut fo~tion represents
the influence of the effective superheat on the derect formation. In ,
other word's, ro~ pouring rates }ignifr that the superh'e9.f. at which the
molten ~etal ,~eets,the solid already formed i5 also low, as the liquid , ,
metai loses heat while flowing in the mold. On the other hand, for
higher pouring rates, the heat losses are much'lower than those for
lower pouring rates, and then the effective superheat is substantia!ly
higher.
, 1
, <'
1 l
o
\.
f ,
+' Cl
'1 ,
CHAPTER 6. CONCLUSIONS AND SUGGÈSTIONS FOR FURTHER WORK 'q
, ;'
1
/
)
"
o
1
.. W, .. JiI!J!&
l' i \ '
l !
l ! 1 1
1 ~
, ~
t'
1 ~ ,
, 'j , ! 1
. 1 1
1 l,
C)
. )
• • _~., ~ ....... " _,_-...... ~ '-' ," .... _'lit ~'r1I"'" - 1 ~ "
. , '
147.
6.1 Conclusions
Some conclusions which can be drawn fram the present work
are given below .•
1. Cold shuts are formed only when ,one of the streams of '
metai is already solid at the time when the two streams tj
collide, and even then only when the liquid does not
have sufficient energy to completely remeit the salid.
'2. The meeting of two streams of liquid metal has a high 1
probabili ty of forming cold shuts because the collision
splàshes molten metal which solidifies when it comes in
contact with the mold. This solid can be the origin of
a cold shut.
3. An oxide film on the surface of the solid stream will
favour the formation of the defeet sinea this film makes
it ~ore difficult to remeit the solid.
4. Cold shut formation 15 strongly depandent on the effective
superheat, and this can be eontroiled by a, combinat ion of
the pouring rate with the superheat at pouring. f . 5. The appeatance of the cold shut 1S affected by the mode
of splidifieatlon (alloy comp?Siti(;m). ,',
6. The farther the liquid metai i5 from the point of po~ring,
the higher i5 the probability for cold shut formation. \
7. Water i5 an adequat~ fluid for simulating the collision
of two streams of molttm me'fàl inside a channel'.
8. It was verified throush experiments on an idealised system
(-) that the occurrence of cold 5huts cou Id be predicted from
,IJ, '
.. ~ '; t (
1
; 1
• i •
1 1
, -' ... --ott'" IT"'~"\'~, !~"f1o'~."~' .'ft. .... """.~~,~~. ";.1~"'""Y"~"""*-~'~ ~--, ..... ,~tI'l",.",,"-r;'.rrf"'1'·~·~~1-"'·'; ,,,. lt.,,,·-Httf~'~t""'l-'\,",,"""I-pr;<";'~lh - J." ~{,"("";;I~"'''''-I-'.''''f!-f'''I'1'\.'''' ~'r~' , ~i''/ '-~:>~~~}1"""
, t
148.
firs~ princip les using t~e heat transfer model presented
in the text.
6.2 Suggestions for Further Work
From the results obtain~d in this study, it is thought that
the following investigations would lead to a better understanding of
-cold shut formation •
1. ,The use of other a 110ys , should be tried to verify the
res~lts obtained in this work for lead and lead-tin alloys.
2. Th~ use of heated ipserts in futur.e experiments woul~
supply more precise data ta 'check the heat transfer model
developed here.
5. The heat transfer model cou Id be expanded to two dimen- '
sions for more accurate remelting predictions:
4. An inve~tigation of th~ relatiqnship between pouring rate,
superheat and the occurrence of cold shuts would be valu
able ànd shed more 1ight on ,the formation of this type of
defect.
\. p ,
...
o
, "
, "
j'
~
i, l'
t, 1
o
)
, .
APPENDIX A
Pt.ogramming J
\
""1 j
j
L-
, ,
: ~ ,
". j .)
1 l 1 ';
, .. ~
; .. , • ,d.Ù'i..ol>., ... t'''!' ~ ,~-. ... HI'--'{ ..... \
\,1' ~~ .. -, ......... ~'~ ..... "'t",.,..~!:"<"'-,.!1"~,., ... ~ "i.-.. .... .......-............-"l-~_~~~.'I"i":'t~J "!il'" 'f'/!!rt""":."~'!I""'~I""I'1"""'~~·"'~~t'i'i'\.""'~~~~~~~'\."\Of~' '" 1
. , .. ,
149.
o LIST OF SYMBOLS FOR mE PROGRAMME
XTL liquidus temperature
f ' XTS solidus temperatur~
f, VT pouring temperature {' '"
i ,. XTP temperature' of solid metal 1 1
'.' , j~ t
MT total time , v (,
, ~ , ,;
NI key for the use of convection 1
t F factor for convection
~' CML thèrmal conductivity of liquid metal ~
, ~ /.
00 thermal conductivity of solid metal t !
CMM thermal conductivity of DlUshy ; zone 1
).'
! CMO thermal conductivi~y of mold ( , /' {.
heat capacity of liquid metal 1 HCML 1 i \ HCMS heat capacity of solid metal 1
1 HCMO heat eapacity, of mold.
RO l ' density of metal 1
ROMO density of mold 1
HF J latent hea t of fus ion for the· metal (
HI heat transfer coefficient at metal/mold interface
HAMB heat transfer coeffic~ent for tlie ambiet:lt
AT aJlbient temperature
XTM initial temperature of 'the JIOid
DT iteration time
DX nodal point spacing in the metai side . \
C} :
i'
\
\ .
1 ,)
!
f 1 1 1
1
0 · DMX
W,Ci)
T(i) ~~ ... ~--- -. ..........
~
•
nodal point ~
temperature
temp e rature
, -
6
150 .
.... /
" i' t~
~
i '-of nodal point i at time t .,
of nodal pOint,i (
at time t + 11t
1 1": i
, 1
" .
1
/ 151. '
o
SOURCE LISTING
1 OF , PROGRAM SAND 1 !
! (y ,
1
() i
f <:
Developed by
~iz Augusto Siqueir~ Bittencourt
McGill University 1979
-. , ,1
1
1 1
f
... 0 f . -..... l'
.1 ) " -1:-
1 fi' \ >
( , ~ ,
Ct
, . .
0,
, , , \ J" <% ..... "."'.. ?' ~'~"",~~""'''I)l'f
!~~'!--J~_tl-'''<YN'~'''_'''''I''\P''''''''''·-''''''~rl:''' .. _.~""~ __ , ..... ~~"Ir;;""",,,~~p~~~~\Ir''m''~'l'''tC'ilJ;l#"W'"ni~~'f('VV~""'t!l!"<".ri'i"'~""~~fl"'i>i~"i-;V, '"' f~ \ r 'I~
\
DIMENSION T(35),W(3S),B(ôO), RE'AD(9,*) XTl, X~, VT ,XTP,MT,iU, F ,CML, CMS, CMM,CMO,
*HCML,HCMS,HCMO,RO,ROMO,HF,H1,HAMB,AT,XTM,DT,DX,DHX DO 5 1=1,5 TO )=XTM
5, W( l )=XTM COXI=CMS
',ROXI=RO Xc=o.o HC~M=HF/(XTl-XTS) CHL1=CHL*F XS=RO*HCMS*DX XL=RO*HCMl*DX XH=RO*HCMM*DX . XMMl...=CML*'DT 1 (XL*DX) X1"=XMML XMML1=XMML*F XMO=CMO*ROMO*HCMO XML=CML*RO*HCML XML'1=XML*F XMS=CMS*RO*HCMS XMM=CNM*RO*HCMM XOXI=ROXi*HCMS*DX • HCL:;: (1.+ GRT (XMO/XMU ) *HI , HÇS=(l.+ GRT(XMO/XMS»*HI HCM=, (1. +SGRT (XMOIXMJp) ) *H1 <,
HML=(l.+SQRTeXML/XMO»*HI ,HMS=(l.+SGRT(XMS/XMO»*HI HMM=(l.+SGRT(XMM/XMO»*HI HL1NT=HU<ItT IXL HSINT=HI*rtT/XS HMINT=HI*DT/XM XM01=ROMO*HCMO*DMX HLMO=HI*DT/CROMO*HCMO*DMX) HSMO=HLMO HMMO:;::HLMO HAMB=HAMB*DT/(ROMO*HCMO*DMX) XMMO=CMO*DT/(XM01*DMX) CLM=2.*CML*CMM/(CML+CMM) ,CLM.l=2.*CMLUCMM/(CML1+CMM) CSM=2.*CHS*CMH/(CMS+CMM) '~ XLM=ClM*DT / (XM*DX)X2=XLM XLM1=CLM1*DT/(XM*DX) !
CSL=2.*CMS*CML/(CMS+CML) CSll=2.*CMS*CHL1/(CMS+CML1) COXIS=2;*COXI*CMS/(COXI+CHS)
, "
'"
\
"
.. ."
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\
rI
u,
l
1
l ' 1 ~
. '.1: , -
(
t f
1
,,~~" ...... ~.,...,,..(,o- -.~~'~~:..-"~ ............ ~- .~.,.~~ __ ,,,,_.,~~_ ._ ..... {""""V'.,~.r~.,., ... ...,.~,. .. ~' .... " ; --"1'1""..,..,.....,.--"1}."'~~~~""'f'fI".!'~"" .,..~..- ....... ~ .... ;-}, ...... J~~.~., ~"'1tl11i:"~",,.p\,~~.:"ï'· "'"
o
l'
\
0 ..
,COXIL=2. COXI*CML/(COXI+CMl) . COXIL1= '.*COXI*CMLlI(COXI+CMU)
COXIM= .*COXI*CMM/(COXlfCKM) XOXIL COXIL*DT/eXOXI*DX) X5=)(' IL \ XOXI 1=COXIL1*DT/eXOXI*DX) xc S=COXIS*DT(XOXI*DX)
----~XIM=COXIM*DT/eXOXI*DX) XSL=CSL*DT/(XS*DX) X3=XSL XSL1=CSL1*DT/(XS*DX) XSM=CSM*DT/(XS*DX>. XMMS=CMS~DT/(XS*DX) XMLM=CLM*DT/(Xl*DX) X4=XMLM XMLM1=CLM1*DT/eXL*DX) XMMM=CMM*DT/(XM*DX) XLS=CSL*rrT / (XL*DX) X6=XLS XLS1=CSL1*DT/(XL*DX) XMSM=CSM*DT/(XM*.DX) ~ HX=HLMO DO'7 1=6,10 T<q=XTF' Wq)=XTF'
7. CONTINUE SH=VT-XTt. HF=HF+HCMLlkSH DO 10 I=l1, 30 nI>=VT W(I)=VT
10 CONTINUE Il( 1) =XMML B(2)=XMMLl B(3)=HLINT B(4)=HSINT B~S>=HMINT B(6)=HLMO B(7)=HAMB B(8)=>,<MMO B(9)=XLM B(10)=XLMl B(l1)=XOXIL IH 12) =XOXILl B (13) =XOXIS B<14 )=XOXIM B( 15)=XSL
. J Hg, z_rE5zst -- z- sœ- =
153.
"
1
1
,1.
'. " !.:'~'~ '-'
0 B(16)=XS~1 B(17)=XSM B(18)=XHMS
, - B(19)=XMU1 !I(20)=XMLMl IH21 )=XMMM
, !I(22)=XLS B(23)=XLSl B(24)=XMSM B(25)=HX B126)=2+*CXMML+HliNT) B(27)=2+*(XMML1+HLINT)
, f B(28)=2.*XMML . B (29 ,) =2. *XMMLl !I(30)=2.*(HX+XMMO) El (31) =2 + *XMMO
f B(3~)=2.*~XMMO+HAMB) <~ B(33)=2.*<XLMtHMINT)
B(34)=2.*<XLM1+HMINT) B(35)=2.*<XMMMtHMINT) B(36)=2.*(XSLtHSINT) B(37)=2.*(XSL1+HSINT) B(3B)=2.*(XSMtHSINT) B(39)=2.*(XMMS+HSINT) B (40) =XMML,+XMLM B(41)=XMML1+XMLMl B(4,2)=XLM+XMMM B(43)=XLM1+XMMM B(44)=2.*XMMM B(45)=XMML+XLS B (46" =XMML1+XLS B(47)=XLM+XMSM B(48)=XLM1tXMSM
, B (49) =XMMM+ XMSM B(50)=XSL+XMMS Il (51) =XSL1tXMMS B(52)=XSM+XMMS B(S3)=2.*XMMS ~~-~---B(54)=XOXIL+XOXIS ~-
--~ B(55)=XOXIL1+XOXrS --~ .... B(56)=XOXIM+XOXIS B(57)=2.*XOXIS WRITE(6,6) (BO),I=1,57)
6 FORMAT(25(10X,F15.7/)//3Z(10X,F15.7/)//) DO 1500 JK=l,MT DO 1000'JN=1,1000, IF(T(6)+LE.XTL) GO TO 60
:>-
0
\ .
-' -/
~ , ~~
\
a
154.
"
1
, \
. , \
. '
.., .... ~ ''''''~':~''''''''-'''~''~''''''''~\t~.'''''''''''Pt';'\~''i,,:'''',,;!!"''''r·.<f''J''',,''~\~ .... ~ • i''' '~"Ifi;'
-v"'_/ J , 1.
l 1 t 155. ' '
;. " ~ "- ",
1 ~ /f' : .. , ~ ---- j l ' 0, , ~ -, -- -
C TEMPERATURE IN THE CASTING 1 15 T(6)=(1-Z*XMML-2*HLINT>*W(6)+Z*XMML*W(7)+2*HLINT*T(5) 16 T(~)=(1-2*XMML)*W(7)+XMML*(W(8>+T(6» 1 17 TCB)=(1-2*XMHL)*W(S)+XMML*<W(9)+T(7» 18 T(9)::::(1-2*XMML>*W(9)+XMML*(W(10)+TCS»
1 19 T(10)=(1-2*XMML)~WC10)+XMML*(W(11)+T(9»
C TEMPERATURE IN THE MDULIt 44 CONTINUE
l' : T(5)=(1.-2.*~X-2.*XMMO~*W(5)+2.*HX*T(6)+2.*XMMO*W(4) i (' J=6 , r- l'
, DO' 40 1=2,4 l
t 1 , K=J-1 , "
r ~' N=I\+1 , M=K-l
i 40 TCK)=(I.-2.*XMMO)*WCK)+XMMO*(TCN)+WCM»
" T ( 1 ) =(!. -2. *XMMO-2 .,*H0MB) *W (IV +2. *XMMon (2 H2. *HAMB*AT VO 50 1=1,30' ,
t W<I)=TC[) (, '--/,
t 50 CONTINUE .
XC::;:XC+DT t GO TO 1000 r 60 CONTINUE f ! ,;-
1 IFCT(6).LT.XTS) GO TO 70 ;, ·IF<T(7) .LE.XTL)GO TO 75 !. 1 'C T6=M ' T7:::.1.,.
- f T(6):::.(1.-2*XLM-2*HMINT)*W(6)+2*XLM*W(7)+2*HM1NT*T(5~ ,
! GD TO 80 , 1 • 1
C, T6=M T7=M . 1 75 T ('6) = <,l-2*XMMM-2iHMINT) *W (6) +2*XMMI1*W (7) +Z*HMINT*T (5)
GD TD SO !; .. .
70 IFCT(7).LE.XTL»)GO TO 90 (~. C T6=$ T7=L
T (6 )=( 1-2*XSL-2*HSINT) *W( 6) +'2*XSL*W( 7) +2*HSIN~*T (5) GO TO 80 . .
90 IF(T(7).LT.XTS) ~O TO 100' ,- , C T6=S T7=M ! .
J T(6)=(1-2*XSM-2*HSINT>*W(6)+2*X5M*W(7)+2*HSINT*T(5) GO TO 80 ,.,;
C T6=S T7=5 , 100 T(6)=(1-2*XMMS-2*~SINT)*W(6)+2*XMM5*W<7)+2*HSINT*T(5) 80 IFCT(6).LT.XTSYOO TO 150
IF(T(Î) .LE'.XTL) GO TO 160 /1;.
C T6==M . T7=L T8=L
~ T(7)==(I-XMML-XMLM>*W(7)+XMML*W(B)+XMLM*T(6)
r GO'TO 300 1 160 fF(T(S> tLE.XTL) GD TD 170
C T6=M' T7=M T8=1.: \
1
0: . '/1:
\ ft· ~ 'tl
1
~ ,./ .' .
1 156,.
-~.
(j
T(7)=(1-XLM-XMMM)*W(7)+XLM*W(S)+XMMM*T(6) GO TO 300
C T'~=M T7=M' TS=M . '170 T(7)=(1-2*XMMM)*W(7)+XMMM*<W(S)+T(6»
GO TO 300 150 IF (H7) .LE. XTU GD TO 180
C T6=S T7=L. T8=L T(7)=(1-XMML-XLS>*W(7)+XMML*W(8)+XLS*T(6) GO TO 300
180 ,IFCT(7).LT.XTS) GO TO 19Q J' IF(T(S).LE.XTL) GO TO 200 .' l C. T6=8 T7=M' , T8=L \ t
T(7)=(1-XLM-XMS~)*W(7)+XLM*W(8)+XMSM*T(6) \ t GO TO 300
C T6:.::8 T7=M TB=M 200 T(7)=(1-XMMM-XMSM)*W<7)+XMMM*W(S)+XMSM*T(6)
GO TO 300 190 IF(T(S).LE.XTL) GO TO 210
C T6=8 T7=8 TS=L T17)=(1-X8L-XMMS)*W(7)+X8L*W(S)+XMMS*T(6)
1 GO TO 300
210 IF(T(S).LT.XTS) GO TOh220
!. C T6=8 T7=8 T8=
'T(7)=(1-XSM:XMMS)*W(7)+XSM*W(S)+XMMS~T(6) \, GO TO 300 ') C T6=8 T7=8 ' T8=8 220 T(7):(1-2*XMMS>*W(7)+XMM8*(W(S)+T(6» 300 IF(T(7).GT.XTL) GO TO 17
IF(T(7).LT.XTS).' GO TO 400 " IF(T(B>.LE.XTL) GO TO 320
C T7=H T8=L T9=L T(8)=(~-XMM~-XMLM)*W(8i+XMML*W(9)tXMLM*T(7) GO TO 500
,320 IF(T(9).LE.,XTL) GD TO 330 C T7=M T8=M T9=L
T(8)=(1~XLM-XMMM)*W(S)+XLM*W(9)+XMMM*T(7) GO TO 500 '
C T7=M T8=H T9=M 330 T(8)=(1-2*XMMM)*W(8)+XMMM*(W(~)+T(7»
GO TO 500 400 IF(TCS>.LE.XTL) GO TO 410 il
C T7=8 T8=L T9=L l T(S)=(1-XMML-XLS)*~(8)+XMML*W(9)+XLS*T(7) GO TO 500.
410 IF(T(S).LT.XTS) GO TO 430 IF(T(9).LE.XTL) GO/TO 420
C T7=8 T8=H T9=L ,
O.
. ....... , .
.0
1 1 1 1
< ~
0
C
C
C
C
420
430
"'-,
/ , J
T(B)=(1-XLM-XMSM>*W(S)fXLM*W(9>fXMSM*T(7) GO TO 500 T7=5 T.8=M T9=M , T(8)=(1-XHMM-XHSM>*W(B)+XMHH*W(9>+XMSM*T(7) GO TO 500
. IF(T(9).LE.XTL) Ga TO 440 T7=S T8=S ' T9=L T(S)7(1-XSL-XMMS)*W(B)+XSL*W(9)fXMMS*T(7) GO TO 500
440 IFCT(9).LT,XTS) Ga TO 450' . T7=S TB=S T9=M . T (8)= (l-XSM-XMMS >*W(8 > fX8M*W( 9 >+XMMS*T (7)
GO TO 500 , T7=S T8=S T9=8 1 450 T(~)=(1-2*XMks>*W~8)+XMMS*(W(9'fT(7) )
. 500 IFCT(B).GT.XTL) ~O TO.18 . IF(T(B).LT.XTS),GO TD 600 IFCT(9).LE.XTL) GO TO 520
C T8=M T9=L Tl0=L T(9)=(1-XMML-XMLM>*W(9)fXMML*W(10)+XMLM*T(B) GO TO 700
,
520 I~(tCl0)~LE.XTL) GO TO 530 C T8:::H T9=,/1 .Tl0=L
Tb 9)= (l-XLH-XMMM.>*W (9 >+XLM*W (10 HXMMM*T( 8) G To 700 '
C T8=M T9=M T10=M 530~T(9)=(1-2*XMMM)*W(9)+XMMM*(W(10)+T(8»
GO To.700 600 IF(T(9).LE.XTl),GO TD 610
C T8=S T9=l Tl0=L T(1)=(1-XMML-XLS>*W(9)+XMML*W(10~+XLS*T(8)
GO TO 700 610 IF(T(9).LT.XTS> GD TO 630
IF(T(10).LE.XTL) GO TO 6?0 C T8=S T9=H Tl0=L
T(9)=(1-XLM-XMSM>*W(9)+XLM*W(10)+XMSM*T(B) GO TO 700'
C' TS=S • T9=M T10=M 620 T (9):: (l-XMMM-XMS'M~,*W (9) +XMMM*W (10 )fXMSM*T (8)
GO To 700 <-.. 6;30 IF(T(10>.LE.XTL) GD TO 640
C T8=8 T9=5 ' T10=L T(9)::(1-XSL-XMMS)*W(9>+XSL*W(10>+XMM5*T(8) GO To 700
640 IF(T<10) .LT.XTS>. GO TO 650 - C T8=5 T9=S T10=/1
T(9)=(1-XS/1-XMMS)*W(9)+XS/1*W(10)+X/1M5*T~~)
i g
- ~ , \ JI
151.
f ' ! ' l~ 1
1 ,1
1
1
o
(")
, ' , ' .. "
/, - ~.~, ...... ~-
o
111
GO TO 700 C T8=5 '9=S T10=5
650 T(9)=(1-2*XMMS>*W(9)+XMMS*(W(10>+T(B?' 700 IF(N1.EO.0) GO TO 705
IFCJK.EO.l.AND.JN.LE.Nl) GO TO 710 ,70S XMML=Xl
,
c
c
C
c
c
c
,c
c
710
720
820
830
800
810
825
835
840
.>
XLM=X2 XaXIL=X5 GO TO 720 CONTINUE XMML=XMMLl XLM=XLMl XOXIL=XOXILl CONTINUE' IF(T(9).GT.XTL) GO TO 19 IF(T(9).LT.XTS) GO TO 800 IF(T(lO).LE.XTL) GO TO 820 T9=M 'TI0=L (~ Tl1=L T(lO)={1-XMML-XklM)*W(10)+XMML*W(11)+X~LM*T(9> GO TO 850 _______ ~----------- r_ - ,
IF(T(11).LE.XTL) GO TO 830 T~=M 'Tio=M Tl1=L T(10)=(1-XLM-XHMM>*W(10)+XLM*W(11)+XMMM*T(9t GO TO 950 T9=M TI0=M Tl1=M T(10)=(1-2*XMHM>*W(10)+XMMM*(W(11)+T(9» GO TO 950 IF(T(10).LE.X1L) GO TO BiO T9=S TI0=L Tl1~L , T(10)=(1-XMML-XLS)*W(10)+XMML*W(11)+XLS*T(9) GO TO 850 IF(T(10).LT.XTS) GO Tp 835 IF(T(11).LT.XTL) GO TO 825 T9=p" TlO=M Tl1=L T(10)~(1-XLM-XMSM)*W(10)+XLM*W(11)+XMSM*T(9~ GO TO 850 T9=S TlO=M Tll=M, _ T(10)=(1-XMMM-XMSM>*W(10>+XHMH*W(11)+XMSM*T(9) GO TO 850 IF(T(11).LE.XTl) GO TO,840 T9.=5 TI0=OXI Tll=L T< 1'0) = (1-XOXIL-XOX15.) *W (10)+XOXIL*W (11) +XOXIS*T( 9 > 130 'TO 850 - - , IF(T(11).~t.XTS) GO TO 845 T9=9 TI0=OXI Tl1=M T(lO)=(1-XOXIM-XOXIS)*W(10)+XOXIM*WCll)+XOXIS*T(9), GO TO 850
",
.'
, 158.
i , l' 1
1. 1
c' T9~~T:i-6=OX'I T11=9 --- - -845 T(10)=Cl- *XOXIS)*~(10)+XO~I9*CW(11)+T(9)~ 850 CONTI~ E' ,
c
tlO 2000 NM=11, 30 Kl=NM-l K2=NM+l IFUCK1).LE.XTU GO TO 2001 DO 2050 N~=11,30 ' K3=NK-l
~NK+l ' IF( NK .EG. 30) W(/~ )=T<K3) T(NK)=(1-2*XMML>*W(NK)+XMML*<W(K4)+T(K3»
2050 CONTINUE GO TO 3000 )
2001 IF(NM.EG.30) WCK2)=T(Kl) IF(NM.GT.11~·Ga4TO 2002 IF(JN.GT.Nl) GO TO 2002 IF(,K.GT.l) GO TO-2002 IF(N1.EG.0) GO TO 2002 IF(JK.EQ.1.AND,JN.LE.Nl) GO Ta 2004 GO TO 2Q02
2004 CONTINUE XMML=XMKLl XLM=XLMl XSL=XSL1 GO TO 2003
:!002 XHML=Xi· XLM=X2 . XSL=X3
2003 CONTINUE
"
IF(T(Kl).LT.XTS) GO TO 2100 . . IFCT(NM) .LE.XTL> GO TO 2200
TK1=M tNM=L TK2=L ,T(NM)::(1-XMML-XMLM)*W(NM)+XMML*W(K2)+XMLM*T(K1) GO TO 2000
2200 IF(T(K2).LE.XTL) GO TO 2220 C TK1=M TNM=H TK2=L
T(NM)=(1-XLM-XMMM)*WCNM)+XLM*W(K2)+XMMM*T(K1) (30 TO 2000
C' " TI<-1=M _ TNM=M TK2=M 2220 T(NM)=<1-2*XMMM)*W(NM)+XMMM*<W(K2)+T(Kl»,
GO TO 2000 \ 2100 IF(T(NM).LE.XTL) GO TO 2120
C TK1=S TNM=L TK2=L ·T(NM)=(1-XMML-XLS)*WCNM)+XMML*WCK2)+XLS*T(Kl)
GO TO 2000 2120 IF<.TtNM~,.LT.XTS) GO TO 2130 .
"
159.
, î ~ .
. '
IF(T(K2).LT.XTL} GO TO·2140 C TK1 c S TNH=H TK2=L'
T(NM):<1-XLH-XHSM)*W(NM)+XLM*W(K2)+XMSH*T(Kl) GO Ta 2000 1
C TK1=S . TNM=M TK2=M y 2140 T (NM)::: (l-XMMM-XMSM) *W( HM) +XMMM*W fK2HKMSM*T (tH)
GO TO 2000 , 2130 IF(T(K2).LE~XTL) GO TO 2150
C TK1=S TNM=S . TK2:::L T (NM) = (l-XSL-XHMS) *W('NH >+XSL*W (K2 >+XMMS*'T (Ki) GO TO 2000
2150 IF(T(K2).LT.XTS) GO TO 2160 C TK1=S TNM=S' TK2=M
T(NM)=(1-XSM-XMMS>*W(NM)+XSM*W(K2)+XMMS*T(Kl) GO rp 2000
C TK1=5' TNM=S T1\2=5 ' p •
2160- T'NM)=( 1,",~*XMMS)*W(NM)tXMMS*(W(K2>+T'(Kl» 2000 CONTINUE~
'XMML=Xl ~ X'-:M=X2 XSL=X3
. XOXIL=X5 3000 'CONTINUE
?OO GO TO 44 1000 CONTINUE
WRITË(6,55) XC,(T(I),I=1,30) 55 FORMAT(2X,F10.4//10(3X,F5.0)/10(3X,FS.O)/
*10(3X,FS:O)/1> 1500 CONTINUE
950 CALL EXIT ENII
160.
1 i { , !
, ,
l' J
\
~ t f
~
, ! . \
! 1
Cl
o
ili Ir i~, çg
...... or T
}
, REFERENCES
1. Anàlysis of Casting nefects. AFS, 1974.
2. Logan, T.: "Casting from the user' 5 standpointIf • AFS Transactions, Vol.65, 1957, 97-9~.
161.
3. Heiner, R.W., Loper, C.R. and Rosenthal. P.C.: metal 'casting, McGraw-Hill Book Compan1, 1967.
Princ:i.p1es of .1'0
'~,~\
4. Davies, G.J.: Solidifica~ion ~d casting. Applied Science, 1973.
S. Beeley, P.R.: Foundry Technology. John Wiley and Sons. 1972.
6. Taylor. H.F., Flemings, M.C. and Wulff"J.: Foundry engineering, John Wiley and Sdns, 1959.
7. Metals Handbook, Vol.S, part B, Melting and Casting, 8th edition, ASM. }
8. Gorbachev. I.A. and Zhukov, A.A.: "Elimination of soft structures in the white iron layer on castings", Russian Castings Production, n. 7, July 1975, 277-278.
9. tvasha, F.S., Lakedemonskii, A.V., Vasile'v, V.A. and Saikin. V.T.: "The mechanism of lap formation on the surface of iron castings",
~ Russian/ Castings Production. ,Il:. 10, October 1968, 443 .. 444.
la. Lillieqvist, G.A.: "Influence of tempet;ature on fluidity and surface appearance of steel castings", AFS Transactions. Vo1.58, 1950, 261-269.
1) ,
Il. Higg~ns, R.A.; Engineering Meta lurgy, Part II, Meta}lurgical Process Technology, Hpdder and Stoughton, 1974.
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