GATE ME 2016 Set 2 — Question 59
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Manufacturing Processes → Casting → Pattern Design & Allowances
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Question
Gray cast iron blocks of size with a central spherical cavity of diameter are sand cast. The shrinkage allowance for the pattern is . The ratio of the volume of the pattern to volume of the casting is _________
Correct answer
1.08 to 1.1
Solution
The volume of the casting () is the volume of the block minus the volume of the spherical cavity.
Shrinkage allowance is given as . This is a linear allowance, meaning every linear dimension of the pattern is times the corresponding dimension of the casting.
Let be the dimensions of the block and be the diameter of the cavity.
Pattern dimensions: , , , and .The volume of the pattern () is:
The ratio of the volume of the pattern to the volume of the casting is:
Rounding to two decimal places, the ratio is approximately .
Shrinkage allowance is given as . This is a linear allowance, meaning every linear dimension of the pattern is times the corresponding dimension of the casting.
Let be the dimensions of the block and be the diameter of the cavity.
Pattern dimensions: , , , and .The volume of the pattern () is:
The ratio of the volume of the pattern to the volume of the casting is:
Rounding to two decimal places, the ratio is approximately .
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