22-Mec-A4 Design and Manufacture of Machine Elements · December 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examinations, December 2018 — 16-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 processes) and Part B (Q4–Q6, machine-element analysis). The rubric asks for two questions from each part — four questions constitute a complete paper, each worth 25 %. All six are solved here, since the set is intended as a study resource.
Reference texts.
Check: every boxed result in this paper, which also carries the independent closure checks noted in each question (moment closure on Q4, volume conservation on Q2, gap compatibility on Q6).
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.
[Figure not reproduced: Fig. S3 redrawn: gas porosity in the upper corner of the tee base, metal penetration on the lower inside diameter against the core, and a dimensional enlargement (swell) at C in the lowest part of the mould. See the official exam paper.]
(a) Why the gas bubbles occur only at that one location. Two conditions have to coincide before a gas bubble becomes a trapped defect: gas must be generated, and it must arrive somewhere it cannot escape. Both conditions are met at the observed spot and nowhere else in this casting. The gas source is the no-bake binder itself — air-set sands are held together by an organic resin (furan, phenolic-urethane or alkyd-oil systems), and when liquid iron at roughly 1400 °C touches that binder it pyrolyses instantly, releasing hydrogen, carbon monoxide and hydrocarbon vapours at the mould–metal interface. The core is the most intense source in the mould because it is a thin body of bonded sand almost completely surrounded by hot metal, so it is heated from every side at once and has nowhere to vent except through its own prints.
The trapping condition explains the location. Gas evolved at the core surface is buoyant in liquid iron and rises immediately, so it collects at whatever is locally the highest point of the cavity. The upper corner in the base of the tee is exactly that: it is a re-entrant pocket at the top of the horizontal run, capped by the cope, with the vertical branch and the gate positioned so that no riser or vent stands above it. Metal there is also the last of the stream to be displaced during filling, so the trapped air ahead of the metal front (mould-cavity air, not just binder gas) is swept into the same corner. Everywhere else, the bubbles either rise into the riser and sprue and escape, or are carried along by the flowing stream until they reach a vented surface. The practical corrections follow directly: vent the core through its prints to atmosphere, add a vent or a small riser over the high corner, use a low-gas binder at the minimum workable addition level, ensure the core and mould are fully cured and dry, and pour hot enough and fast enough that the bubbles have time to float out before the skin freezes.
(b) Factors that produced the penetration defect. Metal penetration is the mechanical infiltration of liquid metal into the pore spaces between sand grains, producing a rough, sand-fused skin that is hard to clean and often has to be ground off. It happens whenever the metallostatic pressure pushing metal into a pore exceeds the resistance from surface tension and from the friction of the interconnected pore network, a competition normally expressed as $p_m > \dfrac{2\gamma\cos\theta}{r}$, where $r$ is the effective pore radius. Every factor that raises the left side or lowers the right side is a candidate cause, and several of them are concentrated on the lower inside diameter of a tee:
The remedy set therefore is: coat the core, use a finer and better-compacted sand at the inside diameter, chill or thin the local hot spot, reduce the pouring temperature to the minimum that will still fill, and lower the head by regating the casting so the bottom section is not carrying the full sprue height.
(c) Factors that led to the enlargement at C. An enlargement of the casting beyond the drawing dimension, at the lowest point of the mould, is a swell — the mould wall moved outward under the pressure of the liquid metal. It is a mould-strength problem, not a metal problem. The metallostatic pressure at C is $p = \rho g h$ with the full head above it, and for a tall tee poured in iron that is easily 25–40 kPa; if the compacted sand cannot resist it, the wall dilates plastically and the casting solidifies to the enlarged shape.
The specific contributors are low compaction density in the drag at that location (again a consequence of a self-setting sand that is placed rather than rammed hard), a binder addition below the specified level or a mix that had already begun to set before it was placed, so it never reached full bench life strength, insufficient cure time before the mould was closed and poured, and inadequate flask support or clamping so that the drag sand could move as a body. A related mechanism that produces the same symptom is erosion or wash: high-velocity metal entering through an undersized gate scours sand from the mould face at the lowest point and leaves both an oversized casting and sand inclusions elsewhere. Distinguishing between the two is a matter of examining the surface — a swell has a smooth, dimensionally displaced surface, whereas erosion leaves a rough scoured face and dirt in the metal. The corrections are to raise the compacted density and cure time, verify the binder and catalyst addition and the sand temperature, clamp or weight the flask against the head, and reduce the metal velocity through the gate.
