SME
Manufacturing Processes
Casting and forming
Use this for “A 10 cm steel cube is sand cast with B = 2 min/cm². How long does it take to freeze?”
Diagram
M
=
V
A
=
1,000
cm³
600
cm²
=
1.67
cm.
Chvorinov: t = BM² = 2 min/cm² × (1.67 cm)² = 5.56 min.
Mould cut open; casting and riser to one scale.
This is an example. Type your own values to start a new problem.
M (cm)
=
V (cm³)
A (cm²)
t (min)
=
B (min/cm²)
×
(
M (cm)
)
2
Formulas
M
=
V
A
1.6667
=
1,000
600
t
=
B
×
M
2
5.5556
=
2
×
1.6667
2
Assumptions
•
Chvorinov’s rule with n = 2: the freezing time grows as the square of the modulus V ÷ A.
•
A is the surface the casting loses heat through to the mould; a 10 cm cube has A = 600 cm².
•
The mould constant B depends on the metal and the mould; about 2 min/cm² for steel in sand.
Step-by-step
WE KNOW
V = 1,000 cm³, A = 600 cm², B = 2 min/cm²
FIND
casting modulus (M), solidification time (t)
Step 1 · Find casting modulus (M)
Use M = V ÷ A
The modulus is the volume over the surface it loses heat through.
M
=
1,000
600
M
=
1.66667
cm
Step 2 · Find solidification time (t)
Use t = B × M²
Chvorinov’s rule: the mould constant times the modulus squared.
t
=
2
×
1.66667
2
t
=
2
×
2.778
t
=
5.5556
min
Check
Put the numbers back in. Both sides should match.
1.66667
=
1,000
600
✓
5.5556
=
2
×
1.66667
2
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
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