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

Question 1 of 8: Intersecting ribs in a cast machine-tool base, and porosity in a cast connecting rod

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

Notes on this paper

Paper format. National Examination, 07-Mec-A4 Design and Manufacture of Machine Elements, May 2014 — 3 hours, open book, any non-communicating calculator permitted. Eight questions on six pages, divided into Part A (manufacturing processes, Q1–Q4) and Part B (machine-element design, Q5–Q8). The rubric asks for three from Part A and two from Part B, five questions constituting a complete paper, all of equal value (20 % each). All eight questions are solved here, because this document is a study resource rather than an examination script.

Reference texts.

Kalpakjian & Schmid, Manufacturing Engineering and Technology, 7th ed. — sand casting and casting defects (Ch. 10–12), sheet-metal shearing and fine blanking (Ch. 16), bulk deformation and hydrostatic extrusion (Ch. 15), fusion welding and weld defects (Ch. 30–31).
Budynas & Nisbett, Shigley's Mechanical Engineering Design, 10th/11th ed. — eccentrically loaded shear joints (Ch. 8), statically indeterminate beams and deflection superposition (Ch. 4), welded joints in torsion (Ch. 9).
Hibbeler, Mechanics of Materials, 10th ed. — combined loading, transverse shear and stress transformation / Mohr's circle (Ch. 7–9).
AWS D1.1 Structural Welding Code — Steel and CSA W59 — preheat, hydrogen control and minimum fillet-weld sizes (Canadian practice).
ASM Handbook Vol. 15 Casting and Vol. 6 Welding, Brazing and Soldering — hot tearing, solidification cracking and riser/chill practice.

Check: Part B is entirely figure-driven. Every number below was read from the printed figures (Figures A, B, C and S7). Two readings are worth stating explicitly so a grader can substitute a different interpretation without redoing the method: (i) in Figure A the rivet group is five rivets in the top row plus one rivet 200 mm below, the lower rivet lying on the same vertical line as the third top rivet; (ii) in Figure B the 67 500 N horizontal force acts on the centroidal axis of the section, so it produces pure tension and no additional bending.

PART A — Manufacturing Processes

Question 1: Intersecting ribs in a cast machine-tool base, and porosity in a cast connecting rod (20 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.

(a) The intersecting-rib problem and its cure

Where two ribs cross, the metal at the junction is bounded by sand on a much larger fraction of its surface than the metal in the plain rib, yet it contains more metal per unit of surface area. The controlling geometric measure in casting is the modulus \(M = V/A\), the ratio of the volume of a casting element to the mould surface through which it loses heat; because solidification time follows Chvorinov's rule, \(t_s = C\,M^{2}\), the junction — whose modulus is markedly larger than that of the ribs feeding into it — is the last region to freeze. It becomes a hot spot. Since the surrounding ribs have already gone solid, no liquid can be drawn into the junction to compensate for the roughly 3–6 % solidification shrinkage of cast iron or steel, and the junction ends up containing a centreline shrinkage cavity, gross microporosity, or — if the surrounding rigid framework restrains the contraction — a hot tear radiating from the corner. Making the ribs intersect on both sides of the flat plate doubles the effect, because two junctions then share the same slab of thick metal through the plate.

The cure is entirely geometric: break the single fat junction into several smaller ones, and never let the local modulus rise above that of the sections that feed it. The three standard modifications, in the order a foundry would try them, are shown in the sketch below.

Figure 1.1 — The intersecting-rib hot spot (left) and three design modifications that suppress it (right).

Staggering the ribs so that no two meet at a common point is the preferred fix because it costs nothing in pattern work and removes the hot spot entirely; the stiffening effect on the plate is essentially unchanged, since a rib stiffens by its own second moment of area about the plate, not by continuity with a crossing rib. Offsetting the ribs on the two faces of the flat does the same job through the thickness. Where a true crossing is unavoidable — a corner boss, for instance — the junction is cored out so that a hole replaces the excess metal, generous fillets replace the sharp re-entrant corners that concentrate the tearing strain, and the ribs are thinned locally so the junction modulus falls back to the rib modulus. As a last resort a metal chill is set in the sand against the junction to accelerate its freezing so that solidification once again proceeds directionally toward the riser.

(b) Porosity in the shank and cavities in the heads of a cast connecting rod

The connecting rod is the classic textbook illustration of directional solidification because it is two heavy masses (the heads) joined by a thin one (the shank). The heads have the largest modulus and freeze last; the shank freezes first and, in doing so, cuts each head off from any external supply of liquid metal. The two reported defects therefore have one root cause and two faces: shrinkage cavities appear in the isolated heads, while the shank — which was itself starved during its own contraction because the gate froze before it did — develops distributed microporosity along its centreline.

Figure 1.2 — Connecting-rod casting: the defects as cast (top) and the design remedies for the heads and the shank.

(I) Remedy for the heads. Place a riser (feeder head) directly over each head, sized so that its own modulus exceeds the head modulus by about 20 % — the riser then stays liquid longer than the casting and feeds the head's shrinkage instead of the head feeding itself; a chill placed on the far side of each head reinforces the effect by steepening the thermal gradient toward the riser.

(II) Two remedies for the shank. First, taper the shank so that its section increases steadily toward the risered head: this creates a continuously rising modulus and hence a temperature gradient along which liquid metal can be drawn all the way from the riser, converting the shank from an isolated pool into part of a feeding path. Second, either chill or deliberately thin the shank so that it freezes distinctly before the heads — the porosity then has nowhere to nucleate because the shank solidifies as a skin-to-centre front while still fully fed — or, equivalently, gate the metal through the shank so that the hottest metal arrives last at the shank and the coldest metal is pushed into the extremities.

Topic. Solidification shrinkage, casting modulus and directional solidification in sand castings.

Key relations. Chvorinov's rule \(t_s = C\left(V/A\right)^{n}\) with \(n \approx 2\); riser criterion \(M_{\text{riser}} \ge 1.2\,M_{\text{casting section}}\); solidification shrinkage of steel and grey iron in the range 3–6 % by volume (grey iron is partly offset by graphite expansion).

Why this works. Every shrinkage defect in a sand casting is a feeding failure: liquid metal contracts on freezing, and unless a still-liquid reservoir at higher modulus is connected to the freezing region, that volume deficit has to appear as a void somewhere. The designer's lever is geometry, because modulus and hence freezing order are set by shape, not by pouring practice. Ranking every section by \(V/A\) and checking that the ranking increases monotonically toward the riser is the whole of the method — intersecting ribs violate it by creating an internal maximum, and a constant-section connecting-rod shank violates it by creating an internal minimum between two maxima.

Common pitfall. Students propose "pour hotter" or "use a bigger sprue" for both parts. Superheat delays freezing everywhere and does not change the order of freezing, so it cannot cure an isolated hot spot; it usually makes matters worse by increasing total contraction. The second pitfall is adding a riser to the shank of the connecting rod, which merely creates a third hot spot to feed.

Source. Kalpakjian & Schmid, Manufacturing Engineering and Technology, 7th ed., Ch. 10 (Fundamentals of Metal Casting, §10.5–10.6) and Ch. 12 (Design considerations for casting); ASM Handbook Vol. 15 Casting, riser design and hot tearing.

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