In a polymer extrusion process, some cross-sectional shapes of the extruded polymers are shown. Cross-sections of available dies are also shown.
Which ONE of the following options CORRECTLY matches the extruded cross section with the die opening that most likely generated it?
Note: The cross-sections are in a plane orthogonal to the extrusion direction. Figures are not to scale.

Question

A through hole of 10 mm diameter is to be drilled in a mild steel plate of 30 mm thickness. The selected spindle speed and feed for drilling hole are 600 revolutions per minute (RPM) and 0.3 mm/rev, respectively. Take initial approach and breakthrough distances as 3 mm each. The total time (in minute) for drilling one hole is ______. (Rounded off to two decimal places)

Answer 1

Step 1: Setting up a single rule for die swell:
Extruded polymers are viscoelastic, so they always swell after leaving the die, this is called die swell.
The amount of swell is bigger where the melt is less restrained, that means flat straight faces swell more than sharp corners.
We can use this one rule to test every option directly instead of first working out the shapes ourselves.

Step 2: Testing the options by elimination:
Take option (B), P-1 and Q-2. Die 2 is a plain square hole, so its flat sides would swell more than its corners and the extrudate would come out barrel shaped, not the clean square Q shown in the figure, so (B) fails.
Take option (C), P-3 and Q-2. Die 3 has an oval hole, and an oval swells into a bigger oval, never a perfect circle, so P cannot come from die 3, and (C) fails on the very first pair.
Take option (D), P-3 and Q-4. Again die 3 is oval and cannot give the round profile P, so (D) also fails.

Step 3: Confirming the surviving option:
Only option (A), P-1 and Q-4, is left standing.
Die 1 is a plain circular hole. A circle has the same restraint all around its edge, so it swells equally everywhere and simply grows into a larger circle, this matches profile P.
Die 4 has concave, pinched in sides, like a pin cushion. Because the middle of each side is pulled in, that region swells out the most when the melt exits, and this extra outward growth cancels the concave curve, leaving straight sides. The corners, which are less restrained by the geometry, swell least. The final result is a true flat sided square, which matches profile Q.

Final Answer:
Elimination and direct reasoning both point to the same pairing. \[ \boxed{P{-}1,\ Q{-}4} \]

Show Hint

The Correct Option is A

Solution and Explanation

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