22-Mec-A4 Design and Manufacture of Machine Elements · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examinations, May 2016 — 07-Mec-A4, Design and Manufacture of Machine Elements. Three hours, open book, any non-communicating calculator. Six questions in two parts: Part A (Q1–Q3, manufacturing-process theory) and Part B (Q4–Q6, machine-element analysis). Candidates answer two from Part A and two from Part B; four questions constitute a complete paper and all questions carry equal value (25 %). All six are solved here.
Reference texts. Kalpakjian & Schmid, Manufacturing Engineering and Technology (Part A); Groover, Fundamentals of Modern Manufacturing (Part A); Budynas & Nisbett, Shigley's Mechanical Engineering Design, 11th ed. (Part B); Hibbeler, Mechanics of Materials, 10th ed. (Q4, Q5); Norton, Machine Design: An Integrated Approach, 6th ed. (Q6).
Check: two corrections carried through Part B. (1) Q5 prints the shaft modulus as “E = 30 ksi”; a 30 ksi modulus is physically impossible for steel and would make the shaft a rubber band, so it is read as the standard E = 30 × 106 psi (30 Mpsi). (2) Q6 supplies the linkage dimensions but not the cross-section of the levers, so the stress in members 2 and 3 is worked for an explicitly stated assumed section and the required section is also reported. Both readings are flagged where they are used, in the spirit of Note 1 on the cover page.
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.
An alloy with a wide freezing range solidifies over a large temperature interval between its liquidus and its solidus. Because the whole casting is within that interval at once over a broad band, solidification is mushy rather than skin-forming: instead of a sharp, advancing solid front there is a wide zone containing a dendritic network bathed in interdendritic liquid. Three consequences follow, and all three are bad for a casting.
First, feeding becomes very difficult. Liquid must flow through the narrow, tortuous channels between dendrite arms to compensate the roughly 3–6 % solidification shrinkage. The pressure drop required by Darcy flow through that network rises without bound as the solid fraction approaches unity, so the last liquid to freeze cannot be fed. The result is dispersed microporosity throughout the section rather than a single, safely located pipe in the riser, and dispersed porosity is far more damaging to fatigue strength and pressure tightness than a concentrated shrinkage cavity.
Second, the alloy has a large mushy zone with low strength and low ductility at high solid fraction, which is exactly the condition required for hot tearing (part iii). Third, the extended local solidification time coarsens the dendrite arm spacing and promotes strong microsegregation (coring), so the as-cast structure is chemically inhomogeneous and often needs a homogenising heat treatment. A short-freezing-range alloy such as a eutectic or a pure metal avoids all of this: it forms a solid skin, feeds through open liquid, and directs its shrinkage into the riser.
Die casting removes almost every one of those objections, because it does not rely on gravity feeding of a slowly freezing mush. The molten metal is injected into a water-cooled metal die at very high velocity and is then held under very high intensification pressure (typically tens of megapascals) throughout solidification. That pressure does the feeding that capillary flow cannot: it forces liquid through the interdendritic network, collapses gas porosity, and keeps the casting in intimate contact with the die.
At the same time the metal die extracts heat one to two orders of magnitude faster than a sand mould. The freezing range is traversed in milliseconds, so the mushy zone is physically thin even though the temperature interval is wide, the dendrite arm spacing is very fine, and microsegregation has no time to develop. The rigid steel die also constrains the casting geometrically, and the high pressure keeps the semi-solid material compressed rather than in tension, which suppresses hot tearing. Finally, the alloys concerned — principally the aluminium–silicon–copper and magnesium–aluminium–zinc families — offer the strength, castability and die-life behaviour that die casting requires, and their wide freezing range is simply not the controlling variable it would be in sand casting.
Because the as-cast surface layer is metallurgically and mechanically better than the interior, and machining throws that advantage away. The chilled skin of a casting solidifies against the mould at the highest cooling rate anywhere in the section, so it has the finest grain size and finest dendrite arm spacing, the least porosity, and the fewest and smallest inclusions, giving it the highest local strength, hardness and wear resistance. In grey and ductile iron the skin is additionally carbide-rich; in aluminium die castings the fine-grained skin carries most of the load-bearing capability of a thin wall. The skin is also frequently in residual compression because it solidifies and contracts first while the interior is still hot, and residual compression at the surface is precisely what suppresses fatigue-crack initiation and stress-corrosion cracking.
Machining cuts through that skin and exposes the coarse, porous, segregated interior. Sub-surface porosity that was harmlessly buried becomes a set of open pits and stress concentrations on the working surface, which destroys pressure tightness, ruins the appearance of a decorative surface, and can drop the fatigue limit substantially. Machining also removes the beneficial compressive residual stress and may redistribute the remaining locked-in stresses enough to distort the part. Practical corollaries are familiar: leave the as-cast skin on hydraulic and pneumatic castings that must hold pressure, on thin-walled die castings, and on cast iron surfaces intended to run against a mating part; and where machining is unavoidable, provide adequate machining allowance so that the cut reaches sound metal rather than stopping in the porous transition layer.
(a) and (b) Sketch and mechanism. A hot tear is an irregular, intergranular, heavily oxidised crack that opens at a hot spot where the casting is restrained from contracting freely — classically at a re-entrant corner, at the junction between a thin section and a heavy boss, or across a section that a core or a mould projection prevents from shortening.
The sequence of events is as follows. The casting cools and the outer regions solidify and begin to contract thermally. The hot spot is still in its coherent but not yet fully solid condition, with the solid fraction somewhere between roughly 0.85 and 0.99. In that window a continuous dendritic skeleton exists — so the material can transmit tensile stress — but the grains are still separated by thin, continuous liquid films, so the material has almost no ductility and a tensile strength of only a few megapascals. This is the brittle temperature range.
The mould, the core, or the already-solid adjacent sections now impose a contraction strain on this weak region. Because the region is stiff in tension but has no ability to accommodate strain plastically, the strain is taken up by pulling the grains apart across the liquid films. If liquid can flow in fast enough, the opening heals and nothing is seen. If it cannot — and at a solid fraction near unity the permeability of the interdendritic network has collapsed, so it usually cannot — a void nucleates on the film, grows, links with its neighbours along the grain boundaries and becomes a hot tear. The fracture surface is therefore intergranular, dendritic in appearance, and oxidised or discoloured because it formed at near-solidus temperature in contact with mould gases. Remedies follow directly from the mechanism: generous fillets, tapered rather than abrupt section changes, collapsible cores and mould materials, correct riser placement so the hot spot is fed, lower pouring temperature, and grain refinement to break up the continuous films.
(c) Alloys most prone to hot tearing. Solid-solution alloys with a wide freezing range — exactly the alloys of part (i). The susceptibility peaks not at the widest possible composition range but at intermediate solute content: pure metals and eutectics have essentially no freezing range and are immune, while at intermediate compositions the alloy spends a long time in the brittle temperature range with continuous liquid films and poor feeding. This produces the characteristic “lambda” or single-peak susceptibility curve versus solute content. Aluminium–copper alloys near 1–2 % Cu, aluminium–magnesium and aluminium–silicon alloys well below the eutectic, magnesium alloys, and long-freezing-range steels and nickel alloys with sulphur or phosphorus (which form low-melting grain-boundary films) are the classic offenders. Alloys with a eutectic reservoir at the end of solidification — near-eutectic Al–Si, for instance — are far more resistant because that last liquid feeds and heals incipient tears.
