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.
At low cutting speeds the dominant problem is not heat but friction and adhesion at the tool–chip and tool–workpiece interfaces. The two principal functions are therefore lubrication of those interfaces and prevention of built-up edge and adhesive wear; incidental cooling is secondary because the heat generation rate itself is modest. Fluids used in this regime are consequently oil-based — straight mineral oils, fatty oils, and oils carrying extreme-pressure (EP) additives — rather than water-rich emulsions.
The first mechanism is boundary lubrication by chemically adsorbed films. Fatty acids and EP additives (chlorine, sulphur and phosphorus compounds) adsorb onto and react with the freshly exposed metal to form low-shear-strength soaps, chlorides and sulphides only a few molecules thick. Because the chip is sliding slowly, there is time for the fluid to reach the interface and for the reaction to occur, and the resulting film lowers the shear strength of the junctions so the friction coefficient on the rake face falls. A lower rake-face friction increases the shear-plane angle, thins the chip, shortens the contact length and reduces the specific cutting energy.
The second mechanism is capillary and diffusive access to the interface through the microcracks and the sliding-region gaps at the edge of the contact. The tool–chip contact is not uniformly seized: only the inner portion is a sticking (seizure) zone, while the outer portion is a sliding zone into which fluid can be drawn by capillary action from the chip–tool wedge behind the contact. At low speed the residence time is long enough for this transport to happen, so the fluid can suppress the metal-to-metal welding that builds a built-up edge. Removing the built-up edge simultaneously improves surface finish and dimensional accuracy, because the effective tool geometry stops changing as fragments of the built-up edge break away.
At high speeds the picture inverts. The interface is hot, largely seized, and the fluid has essentially no time to penetrate the contact, so its lubricating role collapses. The two principal functions become cooling — removing heat from the tool, the workpiece and the chip so that the tool retains hardness and the workpiece retains dimensional accuracy — and chip flushing and transport, clearing chips from the cutting zone (critical in drilling, milling of pockets and grinding) so they are not recut. Water-based emulsions and synthetic fluids dominate here precisely because water has the largest heat capacity and the largest latent heat of the practical candidates.
The first mechanism is forced convection and boiling on the tool flank, the shank and the workpiece surface, not inside the contact. The fluid never reaches the seized rake face; it cools the tool body and the workpiece surrounding the cut, so heat conducted away from the interface is removed rapidly and the steady-state interface temperature drops. Where the surface is hot enough for nucleate boiling, the latent heat of vaporisation makes the local heat-transfer coefficient very large, which is why a flood of emulsion outperforms a mist or a straight oil on the same operation.
The second mechanism is momentum transfer to the chips and the swarf. A high-pressure, well-aimed jet supplies the force needed to break, curl and evacuate the chip, and in high-pressure through-the-tool delivery it can wedge into the tool–chip contact near the edge and mechanically lift the chip, shortening the contact length. This both reduces the heat partitioned into the tool and prevents the thermal damage and re-cutting that trapped chips would cause. A third, related benefit is corrosion protection and residue control on the finished surface, achieved through the emulsifiers and rust inhibitors carried in the fluid.
(a) Manifestations. Chatter is a self-excited vibration between tool and workpiece, and it announces itself unmistakably. The typical manifestations are: a loud, high-pitched screech or a low-frequency growl that changes with spindle speed; a regular, wavy pattern of marks on the machined surface at a pitch equal to the surface speed divided by the chatter frequency; a marked deterioration in surface roughness and in dimensional and roundness accuracy; visible vibration of the tool post, tailstock or workpiece; fluctuating cutting force and motor current; and chipping or accelerated, uneven wear of the cutting edge, sometimes with a segmented or wavy chip.
(b) Systematic diagnosis. The essential distinction is between forced vibration (something is exciting the system at a frequency it does not generate itself) and regenerative chatter (the wavy surface left by one revolution modulates the chip thickness on the next). Proceed as follows.
First, change the spindle speed while holding depth and feed constant. Forced vibration from an out-of-balance workpiece, a bad belt or a faulty bearing will track the speed; regenerative chatter is speed-dependent in an entirely different way and will vanish and reappear in lobes as speed is varied. Second, measure the frequency with an accelerometer or a microphone and compare it with the spindle frequency and its harmonics, the tooth-passing frequency of the drive gears, and the natural frequencies of the tool, tool post, workpiece and tailstock centre. A chatter frequency close to a structural natural frequency and unrelated to any drive frequency confirms regeneration. Third, measure the pitch of the marks on the workpiece and back out the frequency from the surface speed as an independent check. Fourth, reduce the depth of cut progressively to find the stability limit; a sharp threshold in depth of cut is the signature of regenerative chatter, since the stability lobe diagram is a boundary in depth of cut. Fifth, stiffen and re-check one element at a time: shorten the tool overhang, support the workpiece with a steady rest or a live centre, tighten the tool post and gib clearances, and check the bearing preload. Finally, examine tool geometry and wear — a large nose radius, a small approach angle or a worn flank all increase the width of cut and the process damping, and a rubbing worn flank is itself a classic excitation source.
The ideal (geometric) roughness of a turned surface produced by a round-nosed tool is governed by the feed and nose radius:
$$R_a \approx \frac{f^{2}}{32\,r_\varepsilon}, \qquad R_t \approx \frac{f^{2}}{8\,r_\varepsilon}$$
where $f$ is the feed per revolution and $r_\varepsilon$ the nose radius. Roughness therefore varies as the square of the feed and inversely as the nose radius, and those are the only two geometric levers available.
(a) Process change: reduce the feed. Halving the feed cuts the ideal roughness by a factor of four. It is the fastest and cheapest remedy. The unintended consequences are a proportional increase in machining time and cost, and — more insidiously — a risk of dropping below the minimum uncut chip thickness set by the tool edge radius. Below that threshold the tool ploughs and rubs instead of cutting, the specific cutting energy rises steeply (the size effect), the surface is smeared and work-hardened rather than sheared, tool flank wear accelerates, and the finish can actually get worse. A very low feed also reduces the process damping and can push a marginally stable set-up into chatter. A useful secondary process change is to raise the cutting speed, which suppresses built-up edge and usually improves finish, at the cost of shorter tool life through the Taylor relation.
(b) Tool change: increase the nose radius (say from 1 mm to 2 mm), or better, fit a wiper insert whose large-radius trailing flat sweeps the feed marks flat and delivers the finish of a much smaller feed at the original feed rate. The unintended consequences of a larger nose radius are that the width of cut, the radial (passive) force component and the ratio of radial to tangential force all increase. That deflects a slender workpiece, producing taper and barrelling, and it lowers the chatter stability limit — the very failure mode most likely to be causing the poor finish in the first place. A larger radius also increases the tendency to trap heat at the edge. A wiper insert avoids most of this but demands a rigid, well-aligned set-up and is intolerant of run-out. Sharpening the edge or applying a smooth coating is a further tool-side option that reduces built-up-edge tendency, at the cost of edge strength.
