22-Mec-A4 Design and Manufacture of Machine Elements · December 2014

Question 1 of 6: Casting an undercut part — sand mould versus permanent mould

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. National Examinations, December 2014 — 07-Mec-A4, Design and Manufacture of Machine Elements. Three hours, open book, any non-communicating calculator permitted. Six questions divided into Part A (Q1–Q3, manufacturing processes) and Part B (Q4–Q6, machine elements); candidates answer two from Part A and two from Part B, and all questions carry equal value (25 % each). All six questions are worked here.

Reference texts.

S. Kalpakjian and S. R. Schmid, Manufacturing Engineering and Technology — Ch. 10–12 (casting processes and design), Ch. 1 and 3 (structure, cold work, annealing), Ch. 21–22 (machining and tool life).
R. G. Budynas and J. K. Nisbett, Shigley's Mechanical Engineering Design — Ch. 3 (stress, Mohr's circle, beam deflection), Ch. 4 (statically indeterminate shafts), Ch. 16 (clutches and brakes).
R. C. Hibbeler, Mechanics of Materials — Ch. 6–9 (bending, transverse shear, combined loading, stress transformation).
W. D. Callister and D. G. Rethwisch, Materials Science and Engineering — Ch. 7 (dislocations, strengthening, recovery and recrystallization).

it reports a single 5,200 N load and a dimension chain of 750 + 450 + 450 = 1,650 mm that "contradicts" the 2,400 mm overall. Q5 is solved against the drawing, not the caption. Likewise in Q4 the 3,000 lb load is read from the drawing as a horizontal force applied through the bolted plate on the neutral axis, and the section as a 8 in deep I-beam (¹⁄₂ + 3¹⁄₂ + 3¹⁄₂ + ¹⁄₂).

Question 1: Casting an undercut part — sand mould versus permanent mould (25 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

The part is an axisymmetric body whose internal cavity is a wide chamber reached through a narrower neck. That single geometric fact — a cavity larger than the opening leading to it — is what the word undercut means here, and it is the whole question. Whether the part can be cast depends entirely on whether the mould element that forms the internal chamber can be got out again after the metal has solidified.

(a) Sand mould

Yes — the part is readily castable in sand, using a dry-sand core. The external form is a plain body of revolution with no external undercut, so the mould cavity itself splits cleanly on a horizontal parting plane through the mid-height: the cope forms the upper half, the drag the lower half, and both halves draw straight off the pattern without breaking the mould. The internal chamber is then formed by a separate sand core, made in a core box and set into the mould on core prints before closing.

Sand mould: the internal chamber is formed by a collapsible sand core set on core prints; the mould itself parts on the horizontal centreline.

The reason a sand core solves the undercut is that it does not have to be withdrawn at all. A bonded-sand core is deliberately collapsible: the binder is chosen to break down under the heat of the casting, so once the metal has solidified the core loses its strength and is shaken, vibrated or washed out through the neck as loose sand. Its geometry is therefore unconstrained by any draw direction. It may be wider than the opening, re-entrant, or as convoluted as the designer likes, provided only that (i) the core can be supported rigidly during pouring, and (ii) there is at least one opening through which the disintegrated sand can escape.

The practical limitations that remain are those of core engineering rather than of shape. The core must be located by core prints of adequate bearing area, so that buoyancy does not lift or shift it — a core displaced by even a couple of millimetres shows up directly as a wall-thickness variation. Buoyancy is significant: a core is effectively immersed in liquid metal several times denser than itself, and for a large chamber the uplift may require chaplets or an anchored core print. The core must also be vented, because the binder burns off and generates gas that must escape through the print rather than through the solidifying metal, where it would form blowholes. Finally the neck itself sets a lower bound on the shake-out passage: it must be big enough for the spent sand to be extracted, which for this part it comfortably is.

(b) Permanent mould

No — not with a conventional permanent (metal) mould and metal cores. A permanent mould is reusable, and every element of it must therefore survive the casting and be withdrawn intact. The die halves separate sideways and clear the external shape without difficulty, but the internal core is rigid steel and must be pulled out through the neck. Because the chamber is wider than the neck, the shoulders of the core foul the neck on withdrawal: there is no straight-line motion, and no combination of rotations, that frees a rigid one-piece core from a cavity whose entry is smaller than its body.

Permanent mould: the die halves draw sideways, but a rigid metal core wider than the neck cannot be withdrawn.

This is the general design rule for permanent-mould and die casting: every surface must be reachable by a straight draw, so external features need draft and no external undercuts, and internal features must taper towards the opening. The part as drawn violates the internal half of that rule.

Four remedies are available, and a preliminary design should state which one is proposed. The first and most common is semi-permanent mould casting: keep the metal die for the external form, which is where the dimensional accuracy, surface finish and fast cycle time come from, and use an expendable sand or salt core for the internal chamber. The core is destroyed each cycle, so the mould is only "semi"-permanent, but the process retains most of the economic advantage. The second is a collapsible or segmented core, in which the core is built from several pieces plus a central key; the key is drawn first, the remaining segments then move inwards into the vacated space and come out through the neck. This works but adds cost, parting witness lines inside the chamber, and a mechanism that wears. The third is to change process entirely to investment casting, where a ceramic core or a wax pattern is melted and leached out, again giving unlimited internal freedom. The fourth, and the one a designer should always price, is redesign: open the neck out to the full chamber diameter, or split the part into two simple castings joined afterwards, and the undercut disappears along with the tooling problem.

Topic. Mould-element withdrawal as the governing constraint on castable shape; expendable versus permanent moulds and cores.

Key relations. There is no formula here; the governing statement is geometric. A rigid mould element can be withdrawn only if every point of the moulded surface recedes monotonically along the draw direction, i.e. the projected silhouette never grows after the widest section. An expendable core is exempt from this rule because it is destroyed rather than withdrawn.

Why this works. Casting processes are classified first by what happens to the mould, because that determines what shapes are possible. Expendable moulds and cores (sand, shell, investment, plaster) are broken out, so re-entrant internal geometry costs nothing but core-making effort; their penalty is a fresh mould per casting, hence slower cycles, rougher surfaces and wider tolerances. Permanent moulds (gravity die, low-pressure, pressure die casting) buy accuracy, finish and rate by reusing the mould, and pay for it with the withdrawal constraint plus the cost of draft, generous fillets and parting-line planning. Recognising that the undercut is a core problem and not a cavity problem is what lets the designer keep the die for the outside and go expendable only where he must.

Common pitfall. Candidates often answer "no" to the sand mould as well, reasoning that the undercut prevents the pattern from being drawn. It does not: the pattern forms only the external shape, which is undercut-free. The other frequent error is to propose a metal core for the permanent mould "with enough draft" — draft cannot rescue a core whose body is wider than its exit; only segmentation or expendability can.

Source. Kalpakjian & Schmid, Manufacturing Engineering and Technology, Ch. 11 (expendable-mould casting, cores and core prints) and Ch. 11–12 (permanent-mould processes; design for castability, draft and undercuts).

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