22-Mec-A4 Design and Manufacture of Machine Elements · December 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examinations, December 2019 — 16-Mec-A4, Design and Manufacture of Machine Elements. Three hours, open book, any non-communicating calculator. Six questions divided into Part A (Q1–Q3, manufacturing processes) and Part B (Q4–Q6, machine-element design); candidates answer two from Part A and two from Part B, and all questions carry equal value (25 % each). All six questions are solved here so the paper can be used as a complete study resource.
Reference texts. R. G. Budynas & J. K. Nisbett, Shigley's Mechanical Engineering Design, 11th ed. (Ch. 3 stress, Ch. 5 static failure, Ch. 6–7 fatigue and shafts, Ch. 9 welded joints); S. Kalpakjian & S. Schmid, Manufacturing Engineering and Technology, 8th ed. (Ch. 15 bulk deformation, Ch. 16 sheet-metal forming); M. P. Groover, Fundamentals of Modern Manufacturing, 7th ed. (Ch. 19–20); R. C. Hibbeler, Mechanics of Materials, 10th ed.
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 figure shows hydrostatic extrusion. A billet with a nose machined to match the die cone is placed in a thick-walled container that is otherwise filled with an incompressible fluid — typically a vegetable or mineral oil, and for very high pressures a light hydrocarbon or a mixture with a viscosity that stays workable under pressure. The ram does not touch the billet. Instead it advances into the container and pressurises the fluid, and the fluid transmits that pressure hydrostatically to every exposed surface of the billet. When the pressure reaches the level required to force the material through the die orifice, the billet extrudes and the part emerges continuously on the far side.
Three features distinguish it from conventional direct extrusion. First, the billet never rubs against the container bore, because a fluid film separates the two; the whole of the container-friction term that dominates the direct-extrusion pressure requirement simply disappears. Second, the same fluid is dragged into the die throat by the moving surface, so the die-interface friction is hydrodynamic rather than boundary and the coefficient of friction falls by an order of magnitude. Third, and most importantly for what the process is used for, the material inside the deformation zone sees a large superimposed compressive hydrostatic stress. Deviatoric (shape-changing) stresses do the forming; the hydrostatic component does not change the von Mises flow stress at all, but it does suppress the growth of voids and microcracks.
The stages drawn in Figure S1 are simply successive ram positions: the billet seated with the fluid not yet pressurised; the pressure built up and the nose starting through the die; and steady-state extrusion with most of the billet consumed. Because the pressure is applied everywhere at once rather than being pushed up the length of the billet, the extrusion pressure is constant through the stroke instead of decaying as it does in direct extrusion.
The advantages follow directly from the three features above. Friction is nearly eliminated, so the required pressure and the ram energy are much lower than for direct extrusion of the same reduction, and very long billets — including coiled wire fed continuously — can be run because pressure no longer scales with billet length. Very large reduction ratios are attainable in one pass, ratios of several hundred to one being reported where conventional extrusion would be limited to perhaps forty to one.
The decisive advantage, though, is ductility. Raising the hydrostatic pressure raises the fracture strain of a material without raising its flow stress, so materials that are brittle in every conventional forming operation — molybdenum, tungsten, beryllium, cast irons, tool steels, some magnesium alloys, and metal-matrix composites — can be extruded successfully at room temperature. The process is also used to clad one metal in another and to produce fine wire from materials that cannot be drawn. Because the deformation is uniform and no dead-metal zone forms at the container corners, the product has a good surface finish, close dimensional tolerance and a uniform, refined microstructure, with none of the extrusion defects (centre-burst, pipe defect, surface cracking) that dead-metal zones and severe surface shear produce in direct extrusion. Tool wear is low, and a wide variety of die profiles can be used because the die is not required to seal the billet.
The process has remained a specialty operation despite these advantages because everything that makes it attractive also makes it awkward to run in a production shop. The pressures involved are of the order of 1 to 2 GPa, and containment at that level demands heavy, pre-stressed, compound-cylinder containers together with high-pressure seals that must survive repeated cycling; both the capital cost and the maintenance burden are high, and a seal failure at that stored energy is a genuine safety hazard, so the equipment must be guarded and the fluid volume kept as small as possible.
Second, the process is inherently a batch operation with a long non-productive fraction of the cycle. The container must be opened, the billet loaded, the fluid replenished and the system pressurised and then depressurised for every billet. The compressed fluid also stores a large amount of elastic energy, and when the billet nose breaks through the die that energy is released suddenly, producing a "stick–slip" jerk in the extrusion that spoils dimensional consistency unless the back end is restrained — which is what led to the fluid-to-fluid variants in which the product extrudes into a second, lower-pressure chamber.
Third, billet preparation is exacting. The billet nose must be machined to seat against the die and seal it before pressurisation, because if the fluid can escape through the die no pressure builds; that pre-machining is an extra operation on every billet. The fluid itself is a problem: its viscosity rises steeply with pressure, it can solidify at the highest pressures, it must not react with or embrittle the workpiece, and it has to be cleaned off the product afterwards. Finally, the process is confined to cold or warm working, because a hot billet would degrade the fluid, so it cannot compete with hot direct extrusion for ordinary aluminium and copper sections, where conventional presses are faster and far cheaper. The result is that hydrostatic extrusion is used where it is the only option — brittle or exotic materials, clad products, very high reductions — rather than as a general-purpose process.
