Page 1
Metal Casting F orm ula Sheet
Solidification Time
• Ch v orino v’s R ule : Time for complete solidification of a casting.
t
s
= C
(
V
A
)
n
where t
s
is solidification time ( s ), V is v olume of casting (m
3
), A is surface area of
casting (m
2
), C is mold constan t (s/m
2
), n is t ypically 2 for sand casting.
• Mold Constan t (C ) : Dep ends on material and mold prop erties.
C =
?
m
L
k
m
(T
m
-T
0
)
where ?
m
is metal densit y (kgm
-3
), L is laten t heat of fusion (Jkg
-1
), k
m
is thermal
conductivit y of mold (Wm
-1
K ), T
m
is melting temp erature (K ), T
0
is initial mold
temp erature (K ).
Riser D esign
• Riser Solidification Time : Riser m ust solidify after the casting.
(
V
A
)
riser
=
(
V
A
)
casting
• Caine’s Metho d for Riser Sizing : Empirical relation for riser v olume.
X =
V
riser
V
casting
=
a
Y -b
+c
where X is freezing ratio, Y =
A
casting
/V
casting
A
riser
/V
riser
, and a,b,c are material-sp ecific constan ts.
• Riser V olume for Cylindrical Riser : F or a cylindrical riser (heigh t = diameter).
V
riser
= pr
2
h, A
riser
=2prh+2pr
2
where r is radius (m ), h is heigh t (m ).
Gating System
• Bernoulli’s Equation for Flo w : Applied to gating system design.
P
1
+
1
2
?v
2
1
+?gh
1
= P
2
+
1
2
?v
2
2
+?gh
2
where P is pressure (Pa ), ? is metal densit y (kgm
-3
), v is v elo cit y (ms
-1
), h is
elev ation (m ), g =9.81ms
-2
.
1
Page 2
Metal Casting F orm ula Sheet
Solidification Time
• Ch v orino v’s R ule : Time for complete solidification of a casting.
t
s
= C
(
V
A
)
n
where t
s
is solidification time ( s ), V is v olume of casting (m
3
), A is surface area of
casting (m
2
), C is mold constan t (s/m
2
), n is t ypically 2 for sand casting.
• Mold Constan t (C ) : Dep ends on material and mold prop erties.
C =
?
m
L
k
m
(T
m
-T
0
)
where ?
m
is metal densit y (kgm
-3
), L is laten t heat of fusion (Jkg
-1
), k
m
is thermal
conductivit y of mold (Wm
-1
K ), T
m
is melting temp erature (K ), T
0
is initial mold
temp erature (K ).
Riser D esign
• Riser Solidification Time : Riser m ust solidify after the casting.
(
V
A
)
riser
=
(
V
A
)
casting
• Caine’s Metho d for Riser Sizing : Empirical relation for riser v olume.
X =
V
riser
V
casting
=
a
Y -b
+c
where X is freezing ratio, Y =
A
casting
/V
casting
A
riser
/V
riser
, and a,b,c are material-sp ecific constan ts.
• Riser V olume for Cylindrical Riser : F or a cylindrical riser (heigh t = diameter).
V
riser
= pr
2
h, A
riser
=2prh+2pr
2
where r is radius (m ), h is heigh t (m ).
Gating System
• Bernoulli’s Equation for Flo w : Applied to gating system design.
P
1
+
1
2
?v
2
1
+?gh
1
= P
2
+
1
2
?v
2
2
+?gh
2
where P is pressure (Pa ), ? is metal densit y (kgm
-3
), v is v elo cit y (ms
-1
), h is
elev ation (m ), g =9.81ms
-2
.
1
• Con tin uit y Equation : F or steady flo w in gating system.
A
1
v
1
= A
2
v
2
where A is cross-sectional area (m
2
).
• P ouring Time (t
p
) : Time to fill the mold.
t
p
=
V
mold
Q
where V
mold
is total v olume of mold including riser (m
3
), Q is v olumetric flo w rate
(m
3
s
-1
).
• Chok e Area (A
c
) : Minim um cross-sectional area in gating system.
A
c
=
V
mold
C
d
v
2ght
p
where C
d
is disc harge co e?icien t (t ypically 0.6–0.8), h is effectiv e head ( m ).
Shrinkage and Allo w ances
• Shrinkage Allo w ance : A ccoun ts for con traction during co oling.
Shrinkage Allo w ance= a?T
where a is co e?icien t of thermal e xpansion ( K
-1
), ?T is temp erature c hange (K ).
• Shrinkage V olume : Reduction in v olume during solidification.
?V = V
liquid
×S
f
where S
f
is shrinkage factor (e.g., 3–7% for metals lik e steel, alumin um).
• Mac hining Allo w ance : Extra material for mac hining (t ypically 1–5 mm).
Casting Defects (Key Relations)
• Gas P orosit y : Caused b y gas en trapmen t; minimized b y prop er v en ting.
• Shrinkage P orosit y : Con trolled b y riser design and directional solidification.
• Misrun/Cold Sh ut : A v oided b y ensuring su?icien t p ouring temp erature and flo w
rate.
• Sand Inclusion : Minimized b y prop er mold preparation and sand qualit y .
Key Notes
– Use SI units: V in m
3
, A in m
2
, t in s , ? in kgm
-3
, P in Pa .
– T ypical v alues: C v aries (e.g., 0.5–2 s/m
2
for sand molds), S
f
(e.g., 7% for alu-
min um, 3% for steel).
2
Page 3
Metal Casting F orm ula Sheet
Solidification Time
• Ch v orino v’s R ule : Time for complete solidification of a casting.
t
s
= C
(
V
A
)
n
where t
s
is solidification time ( s ), V is v olume of casting (m
3
), A is surface area of
casting (m
2
), C is mold constan t (s/m
2
), n is t ypically 2 for sand casting.
• Mold Constan t (C ) : Dep ends on material and mold prop erties.
C =
?
m
L
k
m
(T
m
-T
0
)
where ?
m
is metal densit y (kgm
-3
), L is laten t heat of fusion (Jkg
-1
), k
m
is thermal
conductivit y of mold (Wm
-1
K ), T
m
is melting temp erature (K ), T
0
is initial mold
temp erature (K ).
Riser D esign
• Riser Solidification Time : Riser m ust solidify after the casting.
(
V
A
)
riser
=
(
V
A
)
casting
• Caine’s Metho d for Riser Sizing : Empirical relation for riser v olume.
X =
V
riser
V
casting
=
a
Y -b
+c
where X is freezing ratio, Y =
A
casting
/V
casting
A
riser
/V
riser
, and a,b,c are material-sp ecific constan ts.
• Riser V olume for Cylindrical Riser : F or a cylindrical riser (heigh t = diameter).
V
riser
= pr
2
h, A
riser
=2prh+2pr
2
where r is radius (m ), h is heigh t (m ).
Gating System
• Bernoulli’s Equation for Flo w : Applied to gating system design.
P
1
+
1
2
?v
2
1
+?gh
1
= P
2
+
1
2
?v
2
2
+?gh
2
where P is pressure (Pa ), ? is metal densit y (kgm
-3
), v is v elo cit y (ms
-1
), h is
elev ation (m ), g =9.81ms
-2
.
1
• Con tin uit y Equation : F or steady flo w in gating system.
A
1
v
1
= A
2
v
2
where A is cross-sectional area (m
2
).
• P ouring Time (t
p
) : Time to fill the mold.
t
p
=
V
mold
Q
where V
mold
is total v olume of mold including riser (m
3
), Q is v olumetric flo w rate
(m
3
s
-1
).
• Chok e Area (A
c
) : Minim um cross-sectional area in gating system.
A
c
=
V
mold
C
d
v
2ght
p
where C
d
is disc harge co e?icien t (t ypically 0.6–0.8), h is effectiv e head ( m ).
Shrinkage and Allo w ances
• Shrinkage Allo w ance : A ccoun ts for con traction during co oling.
Shrinkage Allo w ance= a?T
where a is co e?icien t of thermal e xpansion ( K
-1
), ?T is temp erature c hange (K ).
• Shrinkage V olume : Reduction in v olume during solidification.
?V = V
liquid
×S
f
where S
f
is shrinkage factor (e.g., 3–7% for metals lik e steel, alumin um).
• Mac hining Allo w ance : Extra material for mac hining (t ypically 1–5 mm).
Casting Defects (Key Relations)
• Gas P orosit y : Caused b y gas en trapmen t; minimized b y prop er v en ting.
• Shrinkage P orosit y : Con trolled b y riser design and directional solidification.
• Misrun/Cold Sh ut : A v oided b y ensuring su?icien t p ouring temp erature and flo w
rate.
• Sand Inclusion : Minimized b y prop er mold preparation and sand qualit y .
Key Notes
– Use SI units: V in m
3
, A in m
2
, t in s , ? in kgm
-3
, P in Pa .
– T ypical v alues: C v aries (e.g., 0.5–2 s/m
2
for sand molds), S
f
(e.g., 7% for alu-
min um, 3% for steel).
2
– Ensure riser solidification t ime exceeds casting time to a v oid shrinkage defects.
– Gating ratio (sprue:runner:gate ) v aries (e.g., 1:2:2 for pressurized systems).
– Chec k mold material prop erti es (sand, metal) for accurate C in Ch v orino v’s rule.
3
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