22-Mec-A4 Design and Manufacture of Machine Elements · Undated paper

Question 1 of 6: Grinding wheel grade, workpiece burning, and acting hardness

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

Notes on this paper

Paper format. National Examinations, May 2019 — 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; all six are solved here. All questions carry equal value (25 %).

Reference texts. S. Kalpakjian and S. Schmid, Manufacturing Engineering and Technology, 7th ed. (Part A: Ch. 16 sheet-metal forming, Ch. 26 grinding); M. Groover, Fundamentals of Modern Manufacturing, 6th ed. (Ch. 20, 25); R. Budynas and K. Nisbett, Shigley's Mechanical Engineering Design, 10th ed. (Ch. 3 stress, Ch. 6 fatigue, Ch. 7 shafts and keys, Ch. 16 brakes); R. Hibbeler, Mechanics of Materials, 10th ed. (Ch. 6, 7, 9 transverse shear and stress transformation).

Question 1: Grinding wheel grade, workpiece burning, and acting hardness (25 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) Yes — the advice is sound, and the reason is the self-sharpening mechanism, not the abrasive itself. The letter "grade" of a grinding wheel describes the strength of the bond that holds the abrasive grains, and nothing about the hardness of the abrasive. A grade "T" wheel sits near the hard end of the A–Z scale: the bond posts are strong enough that a grain is retained even after its cutting edges have worn flat.

That retention is exactly what produces the discoloration being observed. A dull, flat-topped grain no longer cuts a chip; it rubs and ploughs, and rubbing dissipates essentially all of its work as heat in a contact zone only a few tenths of a millimetre long. The specific grinding energy therefore climbs as the wheel dulls — from perhaps 20 J/mm³ with sharp grains to several times that with glazed ones — and because the wheel is a poor conductor and the chips are tiny, most of that energy goes into the workpiece surface. The result is the classic temper-burn signature: oxide colours (straw, blue, brown), a re-tempered soft layer or an untempered-martensite white layer beneath it, tensile residual stress, and, on hardened steels, thermal cracking. The colour is a symptom of an energy problem, and the energy problem is caused by grains that are not being replaced.

Selecting a softer grade fixes the cause directly. In a soft-grade wheel the bond fractures once the force on a grain reaches a modest level, so a dulled grain is torn out and a fresh, sharp grain is exposed. The wheel dresses itself continuously, the specific energy stays low, and the surface stays cool. The general selection rule that follows — hard workpiece, soft wheel; soft workpiece, hard wheel — is really a statement about matching grain-release force to the force needed to cut the work material.

The advice is not cost-free, and a complete answer says so. A softer wheel wears faster, so it holds its form and size less well, needs dressing and replacement more often, and consumes more wheel per part. On a surface grinder producing a flat face, loss of form is a second-order concern and the trade is clearly worth making; on a form-grinding or thread-grinding operation, where the profile must be held for a long run, it might not be, and the correct answer there would be to keep the harder grade and change the process conditions instead — which is precisely what part (b) asks about.

(b) A wheel of fixed grade can be made to act softer by raising the force carried by each grain, and the lever for that is the undeformed chip thickness per grain. A grain is released when the force on it exceeds the bond strength. The bond strength is fixed once the wheel is chosen, but the force is not: it grows with the size of the chip each grain must take. For surface grinding, that chip thickness follows (Kalpakjian, Ch. 26)

$$t_c \;\propto\; \sqrt{\frac{4\,v_w}{V\,C\,r}\sqrt{\frac{d}{D}}}$$

where $v_w$ is the work (table) speed, $V$ the wheel surface speed, $C$ the number of active grains per unit area, $r$ the grain width-to-depth ratio, $d$ the depth of cut (down-feed) and $D$ the wheel diameter. Every symbol that appears under the radical is a knob the operator already has. Increasing $t_c$ increases the force per grain, which releases dull grains sooner, which makes a grade-T wheel behave like a grade-K or grade-L one.

Increase the work speed. $t_c \propto \sqrt{v_w}$, so doubling the table speed raises the chip thickness by $\sqrt{2}$, i.e. $+41\,\%$. This is the strongest and most convenient lever, and it also shortens the dwell time of any point on the workpiece in the hot contact zone, which attacks the burning from the second direction as well.
Reduce the wheel speed. $t_c \propto 1/\sqrt{V}$, so halving the spindle speed also gives $+41\,\%$. Fewer grains pass through the arc per second, so each must take more material. Dropping wheel speed additionally lowers the rubbing velocity and hence the frictional power.
Increase the depth of cut. $t_c \propto d^{1/4}$, so doubling the down-feed gains only $2^{0.25}-1 = 19\,\%$ — a real but weaker lever, and one that raises the total power, so it should be used last and watched.
Dress the wheel more openly. A faster dresser lead and a deeper dressing infeed reduce the active grain density $C$ and leave a rougher wheel face, which raises $t_c$ for the same kinematics and simultaneously opens the porosity so that coolant can reach the arc.
Support the change with the coolant system. Higher-pressure, correctly aimed (or through-the-wheel) delivery penetrates the air boundary layer dragged around by the wheel; without it, the flood simply washes over the top of the arc and the surface still burns.

The mirror image of these rules is worth stating because it is the other half of the same examinable idea: raising the wheel speed or lowering the work speed makes a wheel act harder, which is the correct response when a wheel is breaking down too quickly and losing its form.

Summary — making a grade-T wheel behave like a softer wheel
Change	Effect on $t_c$	Acting hardness
Work speed $v_w \times 2$	$\times\sqrt{2} = +41\,\%$	softer
Wheel speed $V \times \tfrac{1}{2}$	$\times\sqrt{2} = +41\,\%$	softer
Depth of cut $d \times 2$	$\times 2^{1/4} = +19\,\%$	slightly softer
Coarser, faster dress	lower $C$, higher $t_c$	softer, more open

Topic. Grinding-wheel grade versus acting hardness, and thermal damage in surface grinding.

Key relations. Undeformed chip thickness per grain $t_c \propto \sqrt{(4v_w/VCr)\sqrt{d/D}}$; material removal rate $\mathrm{MRR} = v_w\,d\,w$; specific energy $u = P/\mathrm{MRR}$, which rises sharply as grains dull.

Why this works. Grade fixes the force at which a grain is released; the process fixes the force each grain actually sees. Because those two are independent, the same wheel can be driven anywhere along a range of acting hardness by changing the kinematics. Burning is a specific-energy problem, so any change that keeps the grains sharp — a softer bond, or conditions that break the bond sooner — attacks its root cause, whereas simply flooding more coolant onto a glazed wheel treats only the symptom.

Common pitfall. Reading "grade" as the hardness of the abrasive rather than the strength of the bond, and therefore concluding that a softer wheel must cut more slowly. A second pitfall is reaching for a lower depth of cut to fix burning: it lowers the total power but also lowers $t_c$, so the wheel glazes even faster and the burning gets worse.

Source. Kalpakjian & Schmid, Manufacturing Engineering and Technology, 7th ed., Ch. 26 (§26.3 grinding wheel selection, §26.4 grinding temperatures and burn).

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