Casting
Exam Duration: 45 Mins Total Questions : 20
Casting process being expensive, used only where small number of intricate and highly accurate parts are to be manufactured is
- (a)
die casting
- (b)
centrifugal casting
- (c)
investment casting
- (d)
Any of these
A cube of side a and a solid has diameter d. They are made from same material. The ratio of their solidification time is
- (a)
a2d2
- (b)
\(\frac { { d }^{ 2 } }{ { a }^{ 2 } } \)
- (c)
\(\frac { { a }^{ 2 } }{ { d }^{ 2 } } \)
- (d)
\(\frac { a }{ d } \)
We know that
Solidification time
t∝\(\left( \frac { V }{ SA } \right) ^{ 2 }\)
or t=k\(\left( \frac { V }{ SA } \right) ^{ 2 }\)
tcube =k\(\left( \frac { { a }^{ 3 } }{ 6a^{ 2 } } \right) ^{ 2 }=\frac { k\times a^{ 2 } }{ 36 } \)
tsphere =\(k\times \left( \frac { \frac { 4 }{ 3 } { \pi r }^{ 3 } }{ 4\pi r^{ 2 } } \right) \)
=k x \(\left( \frac { r }{ 3 } \right) ^{ 2 }=k\times \frac { { d }^{ 2 } }{ 36 } \)
=\(\frac { { t }_{ cube } }{ { t }_{ phere } } =\frac { k\times a^{ 2 } }{ 36 } \times \frac { 36 }{ k\times d^{ 2 } } =\frac { { a }^{ 2 } }{ d^{ 2 } } \) .
During cooling, a cubical casting of side 40 mm undergoes 3%, 4% and 5% volume shrinkage during liquid state, phase transition and solid state respectively. The volume compensated from riser is
- (a)
2%
- (b)
8%
- (c)
7%
- (d)
12%
Rise provides molten metal during liquid state shrinkage and phase transition.
∴ Volume compensated from the riser = 3% + 4%
=7%
If shrinkage allowance are 0.3 mm/mm, then the internal diameter of the pattern is (given, the cross-sectional area of sprue at the base = 1 cm2, in figure actual size of casting is given)
- (a)
20.6 mm
- (b)
40.6 mm
- (c)
20.12 mm
- (d)
19.4 mm
After shrinking, outer diameter is reduced but internal diameter is increased. So, allowance are added in external dimensions and subtracted from internal dimensions.
Allowance = 0.03 x 20 = 0.60 mm
Internal diameter = 20 - 0.60 = 19.4 mm
Time taken to fill the cavity is
- (a)
169.16 s
- (b)
180 s
- (c)
175 s
- (d)
184 s
Volume of the mould cavity =\(\frac{4}{3}\)πr3
=\(\frac{4}{3}\) x 3.14 x (20)3 cm3
This is the case of top sprue. We know that in case of top sprue, time required to fill the cavity
t=\(\frac { { V }_{ m } }{ A\sqrt { 2gh } } =\frac { \frac { 4 }{ 3 } \times 3.14\times 8000 }{ \sqrt { 2\times 980\times 20 } } \) (Given h = 200 mm = 20 cm, g = 9.8 rn/s2 = 980 cm/s2 )
t=\(\frac { 4\times 3.14\times 8000 }{ 3\times \sqrt { 2\times 19600 } } =\frac { 4\times 3.14\times 8000 }{ 3\times 140\times \sqrt { 2 } } \)
=169.16 s
The area of sprue at the base is 5 cm2. The time taken by sprue to fill the cavity is
- (a)
7.31 s
- (b)
6.32 s6.78
- (c)
6.78 s
- (d)
6.9 s
Volume of the cavity = 60 x 20 x 10 = 12000 crn3
This is the case of bottom sprue. In the case of bottom sprue, time to fill cavity is given by
t=\(\sqrt { \frac { 2 }{ g } } \times \frac { { A }_{ m } }{ A_{ g } } (\sqrt { H } -\sqrt { H-{ h }_{ m } } )\)
Given H= 60 cm, hm= 10 em
Ag = 5 cm2, Am = 60 x 20 = 1200 cm2 g = 980 cm/s2
t=\(\sqrt { \frac { 2 }{ 980 } } \times \frac { 1200 }{ 5 } (\sqrt { 60 } -\sqrt { 60-10 } )\)
=\(\frac { 1 }{ 7\sqrt { 10 } } \times 240\times (\sqrt { 60 } -\sqrt { 50 } )\)
=\(\frac { 240 }{ 7 } \times (\sqrt { 6 } -\sqrt { 5 } )\)=7.31 s
A sprue for avoiding aspiration to deliver liquid iron at a rate of 20 kg/so The density of iron is 7800 kg/m3. The height of pouring basin is 9 cm and height of sprue is 25 cm. The diameter of sprue base is
- (a)
3.55 cm
- (b)
4.55 cm
- (c)
3.75 cm
- (d)
4.75 cm
m = 20 kg/s
P = 7800 kg/m3
We know that to avoid aspiration effect
\(\frac { { A }_{ 1 } }{ A_{ 2 } } =\sqrt { \frac { { h }_{ 2 } }{ { h }_{ 1 } } } =\sqrt { \frac { 25+9 }{ 9 } } \)
\(\frac { { A }_{ 1 } }{ A_{ 2 } } =\sqrt { \frac { 34 }{ 9 } } \)=1.943
\(\frac { { A }_{ 1 } }{ A_{ 2 } } \)=1.943
Volume delivered per second =\(\frac { m }{ \rho } =\frac { 20 }{ 7800 } \)
=\(\frac { 20\times { 10 }^{ 6 } }{ 7800 } \) cm3/s
v=2564.10 cm3/s
From figure,
v=A1 x \(\sqrt { 2g{ h }_{ 1 } } \)
2564.10 = A1 x \(\sqrt { 2\times 980\times 9 } \)
A1=\(\frac { 2564.10 }{ 14\times 3\sqrt { 10 } } \)=19.30 cm2
\(\frac { { A }_{ 1 } }{ A_{ 2 } } \)=1.943
A2=\(\frac { 19.30 }{ 1.943 } \)
=9.936 cm2
Now, \(\frac { \pi }{ 4 } \)d22 =9.936
d22 =\(\frac { 4\times 9.936 }{ 3.14 } \)
d2=\(\sqrt { \frac { 4\times 9.936 }{ 3.14 } } \)
=3.55 cm
The sprue is designed as avoid aspiration effect. The ratio of A1 to A2 is
- (a)
2.08
- (b)
1.58
- (c)
2.5
- (d)
2.00
To avoid aspiration effect
\(\frac { { A }_{ 1 } }{ A_{ 2 } } =\sqrt { \frac { { h }_{ 2 } }{ h_{ 1 } } } \)
h2 = 6 + 20 = 26 cm
h1 = 6 cm
\(\frac { { A }_{ 1 } }{ { A }_{ 2 } } =\sqrt { \frac { 26 }{ 6 } } \)=2.08
Gray cast iron blocks 100 cm x 50 cm x 40 cm are to be cast in sand moulds. Shrinkage allowance pattem making is 1% The ratio of volumes of pattern to that of casting will be
- (a)
1.03
- (b)
1.02
- (c)
1.10
- (d)
1.20
Pattern length =100+\(\frac { 100\times 1 }{ 100 } \)=101 cm
Pattern Width =50+\(\frac { 50\times 1 }{ 100 } \)=50.5 cm
Pattern height =40+\(\frac { 40\times 1 }{ 100 } \)=40.4 cm
Pattern volume = 101 x 50.5 x 40.4 cm3
Casting volume = 100 x 50 x 40 cm3
\(\frac { { V }_{ p } }{ { V }_{ c } } =\frac { 101\times 50.5\times 40.4 }{ 100\times 50\times 40 } \)
=1.03
For a riser \(\frac{d}{h}\)= 1, it is used to feed a casting 20 cm x 20 cm x 10 cm. Volume shrinkage on solidification is 3% for steel and that the volume of riser is 3 times that dictated by shrinkage considerations alone. The riser diameter or height is
- (a)
14 cm
- (b)
13 cm
- (c)
15 cm
- (d)
17 cm
Volume of casting
=l x b x h = 20 x 20 x 10
=4000 cm3
Volume of shrinkage
= 3% x Volume of casting
= \(\frac{3}{100}\) x 4000 =120 cm3
Volume of riser = 3 x 120 = 360 cm3
Given, \(\frac{d}{h}\)=1 for riser
\(\frac { \pi }{ 4 } \)d3=360
d3=\(\frac { 360\times 4 }{ 3.14 } \)=4583.cm3
\(\left( \frac { SA }{ V } \right) _{ casting }=\frac { 2(lb+bh+hl) }{ lbh } \)
=\(\frac { 2\times (20\times 20+20\times 10+10\times 20) }{ 20\times 20\times 10 } \)
=\(\frac { 2\times 800 }{ 4000 } \)=0.4 cm-1
\(\left( \frac { SA }{ V } \right) _{ riser }=\frac { \pi dh+2\frac { \pi }{ 4 } { d }^{ 2 } }{ \frac { \pi }{ 4 } { d }^{ 2 }h } \) (\(\frac{h}{d}\)=1, for side riser)
=\(\frac { \pi d^{ 2 }+\frac { \pi }{ 2 } d^{ 2 } }{ \frac { \pi }{ 4 } { d }^{ 3 } } =\frac { 3 }{ 2 } { \pi d }^{ 2 }\times \frac { 4 }{ \pi d^{ 3 } } =\frac { 6 }{ d } \)
=\(\frac { 6 }{ 7.71 } \)=0.778 cm-1
\(\left( \frac { SA }{ V } \right) _{ riser }>\left( \frac { SA }{ V } \right) _{ casting }\)
But it is not favourable condition
\(\left( \frac { SA }{ V } \right) _{ riser }>\left( \frac { SA }{ V } \right) _{ casting }\) (Riser should have longer solidification time compared to casting)
\(\frac{6}{4}\)≤0.4
d ≥ \(\frac{6}{0.4}\)
d ≥ 15 cm
h=d=15 cm
Draft on pattern for casting is
- (a)
shrinkage allowance
- (b)
taper to facilitate its removal from mould
- (c)
for machining allowance
- (d)
All of the above
In order to facilitate withdrawal of pattern
- (a)
allowances are made on pattern
- (b)
draft is provided on pattern
- (c)
Both (a) and (b)
- (d)
All of the above
Cores are used to
- (a)
make desired recess in castings
- (b)
support loose pieces
- (c)
remove pattern easily
- (d)
All of the above
Shrinkage allowance is made up by
- (a)
adding to external and internal dimensions
- (b)
subtracting from external and internal dimensions
- (c)
Both (a) and (b)
- (d)
adding to external dimensions and subtracting from internal dimensions
The purpose of chaplets is to
- (a)
support the core
- (b)
compensate shrinkage
- (c)
provide binding
- (d)
None of the above
The purpose of gate is to
- (a)
feed the casting at a rate consistent with the rate of solidification
- (b)
feed the casting until all solidification takes place
- (c)
act as reservoir for molten metal
- (d)
None of the above
The purpose of sprue is to
- (a)
act as a reservoir for molten metal
- (b)
feed the casting until the solidification takes place
- (c)
feed molten from pouring basin to gate
- (d)
All of the above
The purpose of riser is to
- (a)
feed the casting at a rate consistent with the rate of solidification
- (b)
act as a reservoir for molten metal
- (c)
feed the casting until the solidification takes place
- (d)
None of the above
The ratio between the pattern shrinkage allowance of steel and cast iron is about
- (a)
2:1
- (b)
1:2
- (c)
1:1
- (d)
3:1
Investment casting uses pattern made of
- (a)
metal
- (b)
wood
- (c)
wax
- (d)
polymer
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