22-Mec-A4 Design and Manufacture of Machine Elements · May 2015

Question 3 of 6: Grinding-Wheel Grade and Workpiece Burn

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

Notes on this paper

Paper format. National Examinations, May 2015 — 07-Mec-A4, Design and Manufacture of Machine Elements. Three hours, open book, any non-communicating calculator permitted. Six questions in two parts: Part A (Q1–Q3, manufacturing processes) and Part B (Q4–Q6, machine-element design). The rubric asks for two questions from each part, and all questions carry equal value (25 % each). All six are solved here, because this set is a study resource rather than an examination script.

Reference texts.

S. Kalpakjian and S. R. Schmid, Manufacturing Engineering and Technology, 8th ed. — sheet-metal forming, deep drawing, abrasive machining.
M. P. Groover, Fundamentals of Modern Manufacturing, 7th ed. — stretch forming and the flow-curve treatment of forming loads.
R. G. Budynas and J. K. Nisbett, Shigley's Mechanical Engineering Design, 11th ed. — bolted and welded joints (Ch. 8, 9) and brakes (Ch. 16).
R. C. Hibbeler, Mechanics of Materials, 10th ed. — net-section bending and bearing stress.

Units. The paper mixes systems deliberately: Q1, Q5 and Q6 are in US customary units (inch, pound, psi) and Q4 is metric. Each question is solved in the units in which it is set, as the exam intends.

Question 3: Grinding-Wheel Grade and Workpiece Burn (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) Is the advice sound?

Yes, the advice is sound, and the reason lies in what the grade letter actually denotes. Grade in a bonded abrasive wheel is not the hardness of the abrasive grain, which is a property of the aluminium oxide or silicon carbide itself and does not change from wheel to wheel. Grade measures the strength with which the bond holds each grain, that is, the force required to tear a grain out of the wheel face. A grade "T" wheel sits well toward the hard end of the alphabetical scale and holds its grains very tenaciously.

A grain does not stay sharp. As it cuts, its cutting edges wear flat, and those wear flats rub against the work rather than cutting it. Rubbing and ploughing do no useful chip formation but dissipate essentially all of their work as heat in a very thin surface layer. In a soft wheel the growing force on a dulled grain eventually exceeds the bond strength, the grain is torn out, and a fresh sharp grain is exposed — the wheel dresses itself continuously. In a hard wheel the bond holds on to the dull grain instead. The wheel glazes over, the specific grinding energy climbs, and the heat generated per unit volume of metal removed rises sharply. Because surface grinding is a low-material-removal, high-energy process to begin with, and because almost all of that energy ends up in the workpiece surface rather than in the chips, the surface temperature rises until it oxidises and, at worst, retempers or rehardens the layer. That is precisely the discoloration described. Moving to a softer grade restores the self-sharpening action, lowers the specific energy and therefore lowers the surface temperature. Grinding burn on a hard wheel is a textbook symptom, and softening the grade is the textbook correction.

(b) Can the wheel be made to act softer without changing wheels?

Yes, the foreman is right, and this is one of the more useful pieces of shop knowledge in abrasive machining. The distinction that makes it possible is between the grade of a wheel, which is fixed once the wheel is manufactured, and its acting hardness, which is the behaviour the wheel actually exhibits in a given set of cutting conditions. Whether a grain is torn out depends on the force on that grain, not on the bond strength alone. If the cutting conditions are changed so that each grain has to carry a larger force, grains will be released sooner, and the wheel will behave exactly as a softer-grade wheel behaves — it will break down and re-sharpen itself.

The force per grain is governed by the undeformed chip thickness taken by each grain, which for surface grinding varies as

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

where $v_w$ is the work speed, $V$ the wheel peripheral speed, $d$ the depth of cut, $D$ the wheel diameter, and $C$ and $r$ describe the grain density and the chip shape. The relation shows the three levers directly, and the ranking among them matters:

Increase the work speed $v_w$ — the preferred change. Raising $v_w$ increases the chip thickness per grain, so the force per grain rises and the wheel acts softer. It has a second, independent benefit here: a faster work speed shortens the time any point on the workpiece spends in the grinding zone, so less heat is conducted into the surface even at the same total energy. Both effects attack the burning.
Reduce the wheel speed $V$. A slower wheel means fewer grains pass through the cut per unit time, so each of them must remove more material. The force per grain rises and the wheel again acts softer. Lower wheel speed also lowers the rate of frictional energy input directly.
Increase the depth of cut $d$. This too raises the chip thickness and softens the wheel's action, but it should be used with caution as a burn remedy, because a larger depth of cut increases the total energy delivered and lengthens the contact arc. It is the least attractive of the three when the problem being solved is thermal.

There is a further reason why increasing the chip thickness reduces burning that is independent of the grain-release argument. The specific grinding energy falls as the chip thickness rises — the well-known size effect. Very thin chips are cut inefficiently, with a large proportion of rubbing and ploughing, so the energy per unit volume removed is high. Thicker chips are cut more efficiently. Every change in the list therefore reduces both the energy per unit volume and the fraction of that energy that reaches the workpiece.

The practical recommendation for this shop is to raise the table (work) speed first and, if burning persists, reduce the wheel speed; keep the depth of cut modest, dress the wheel before restarting to remove the glazed layer, and ensure the coolant is delivered through the air barrier into the grinding zone rather than sprayed at it.

Question	Answer
(a) Is a softer wheel sound advice?	Yes — a softer bond releases dulled grains, restoring self-sharpening and lowering specific energy
(b) Can conditions substitute for grade?	Yes — acting hardness falls when the force per grain rises
Preferred change	Increase work speed $v_w$
Secondary change	Decrease wheel speed $V$
Use with caution	Increase depth of cut $d$ (adds total heat)

Topic. Grinding-wheel grade, acting hardness, specific grinding energy and thermal damage.

Key relations. Undeformed chip thickness $t_c \propto \sqrt{(v_w/VCr)\sqrt{d/D}}$; material removal rate $Z_w = v_w\,d\,b$; specific energy $u = P/Z_w$, which falls as $t_c$ rises (the size effect); acting hardness decreases as the force per grain increases.

Why this works. A grinding wheel is a self-renewing cutting tool whose renewal rate is set by a force balance at each grain, not by a schedule. That single idea answers both halves of the question. Part (a) changes the bond side of the balance, part (b) changes the force side, and either one restores the same self-sharpening behaviour. It is also why grinding is the one machining process where a "harder tool" is often the wrong answer: hardness of the abrasive is already far above that of the work, so the binding constraint is not the ability to cut but the ability to shed grains that have stopped cutting.

Common pitfall. Confusing grade with abrasive hardness, and therefore concluding that a softer wheel will "cut less well". A second pitfall is answering part (b) by reducing the depth of cut. That does reduce the total heat, but it makes the wheel act harder, not softer, because it lowers the force per grain — so it is the wrong answer to the question actually asked, even though it may reduce burning in the short term.

Source. Kalpakjian and Schmid, Manufacturing Engineering and Technology, 8th ed., §26.3–26.4 (grinding wheels, grinding temperature and burn); Groover, 7th ed., §25.1.

← Question 2 Next: Question 4 →