SME
Manufacturing Processes · Problem type
Size a riser
Use this for “A 10 cm cube casting (M = 1.667 cm, B = 2 min/cm²) needs a side riser with H = D. How wide?”
Diagram
Chvorinov: tc = BMc² = 2 min/cm² × (1.67 cm)² = 5.56 min.
The
riser
must
freeze
last,
1.25
×
as
long:
Mᵣ
=
√
1.25
×
1.67
cm
=
1.86
cm;
with
H
=
D
its
M
is
D
6,
so
D
=
11.2
cm.
Mould cut open; casting and riser to one scale.
This is an example. Type your own values to start a new problem.
Mᵣ (cm)
=
1.25
×
Mc (cm)
D (cm)
=
6
×
Mᵣ (cm)
B
Mould constant
example · min/cm²
tc
Casting freezing time
calculated
tᵣ
Riser freezing time
calculated
Formulas
Mᵣ
=
√
1.25
×
Mc
1.8634
=
√
1.25
×
1.6667
D
=
6
×
Mᵣ
11.1803 = 6 × 1.8634
tc
=
B
×
Mc
2
5.5556
=
2
×
1.6667
2
tᵣ = 1.25 × tc
6.9444 = 1.25 × 5.5556
Assumptions
•
The riser must stay liquid 1.25 times as long as the casting, so it feeds the casting as it shrinks.
•
Both freeze by Chvorinov’s rule t = BM² in the same mould, so they share B.
•
The riser is a cylinder with height equal to diameter: V = πD³ ÷ 4, A = 1.5πD², so M = D ÷ 6.
Step-by-step
WE KNOW
Mc = 1.6667 cm, B = 2 min/cm²
FIND
riser modulus (Mᵣ), riser diameter (D), casting freezing time (tc), riser freezing time (tᵣ)
Step 1 · Find riser modulus (Mᵣ)
Use Mᵣ = √1.25 × Mc
Time
grows
as
M
2
,
so
1.25
times
the
time
needs
√
1.25
times
the
modulus.
Mᵣ
=
√
1.25
×
1.6666667
Mᵣ = 1.118 × 1.6667
Mᵣ = 1.86339 cm
Step 2 · Find riser diameter (D)
Use D = 6 × Mᵣ
A
cylinder
with
H
=
D
has
M
=
D
6
.
D
=
6
×
1.86339
D
=
11.1803
cm
Step 3 · Find casting freezing time (tc)
Use tc = B × Mc²
Chvorinov’s rule for the casting.
tc
=
2
×
1.6666667
2
tc = 2 × 2.778
tc = 5.55556 min
Step 4 · Find riser freezing time (tᵣ)
Use tᵣ = 1.25 × tc
The riser freezes 25% later than the casting.
tᵣ = 1.25 × 5.55556
tᵣ = 6.9444 min
Check
Put the numbers back in. Both sides should match.
1.86339
=
√
1.25
×
1.6666667
✓
11.1803 = 6 × 1.86339 ✓
5.55556
=
2
×
1.6666667
2
✓
6.9444 = 1.25 × 5.55556 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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