Why a Disc Diameter Is Really a Speed Limit

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It does, and the first thing it bears on is not cutting at all. It is the speed limit. Diameter and maximum speed were never two independent specifications you get to choose between, because the thing a disc is really rated for is how fast its rim is allowed to travel, and the revolutions a minute printed on it is that one number converted for that one diameter.

You can prove it in four divisions, with no product involved. The standard rim speed for a reinforced disc on a hand-held machine is 80 metres a second. Convert that to revolutions a minute for each common diameter and you get 13,286 at 115 millimetres, 12,223 at 125, 8,488 at 180 and 6,643 at 230. The numbers actually printed on those discs are 13,300, 12,200, 8,500 and 6,650. Every one matches to within two tenths of one percent.

So the whole ladder of speed markings is 4,800 divided by pi times the diameter. It is not four engineering decisions. It is one constant, and the diameter is the only variable in it.

Why rim speed is the quantity, and not the rotation rate

A spinning disc is trying to tear itself apart. Every piece of it wants to travel in a straight line, and the material has to pull it round instead. The force needed on a small element at radius r turning at rate w is proportional to r times w squared, and when you integrate that across a disc the stress that matters comes out proportional to the square of the rim speed. The density of the material appears, the diameter and the rotation rate do not appear separately, only their product.

That is why the rating is a rim speed. Two discs of the same material tear at the same rim speed whatever their size, and a disc half the diameter may safely turn twice as fast. The rotation rate on the label is a convenience for the user, who can read an rpm off a tool nameplate and cannot read a metre per second off anything.

And the consequence is the one the question is really circling. Diameter and speed trade against each other at a fixed exchange rate, so a bigger disc on the same machine is not a bigger version of the same thing. It is the same machine asking the material for more than it was built to give, by a factor that goes as the square.

Our own grinder publishes both halves and never multiplies them

A DCK 9.0 amp angle grinder is the tool in our catalogue that makes this checkable, because its record publishes every input the arithmetic needs and never puts them together. It states a 4-1/2 inch disc size, 11,800 revolutions a minute, an 1100 watt motor, a 3.5 pound body, "a standard 7/8 inch arbor with a 5/8 inch 11 threaded spindle", and a six piece set of grinding, cutting and flap discs in the box.

Multiply the first two. A 114.3 millimetre disc at 11,800 revolutions a minute has a rim speed of 70.60 metres a second, which is 88.3 percent of the 80 metre ceiling. On the nominal 115 millimetre size it is 71.05. So the tool is designed to run its intended disc at close to the limit with about an eighth of the speed in reserve, which is a sensible place to be and tells you the 11,800 was chosen from the disc rating rather than the other way round.

Now fit a 180 millimetre disc, which is the next common size up. The rim speed becomes 111.21 metres a second, which is 139.0 percent of the ceiling, and because the stress goes as the square of the speed the material is carrying 1.932 times what it was designed for. A 230 millimetre disc reaches 142.11 metres a second and 3.155 times the design stress.

Here is the part the published arbor figure makes uncomfortable. A 7/8 inch bore is 22.2 millimetres, and 180 millimetre and 230 millimetre discs use the same 22.2 millimetre bore, because the bore is standardised across the sizes. The wrong disc does not jam, bind or feel odd. It slides on, the flange seats, the nut tightens and the guard closes. Nothing in the assembly objects, and the only thing that knows is the arithmetic.

Our guide to using an angle grinder safely states the rule exactly right in words, saying to "Use the correct disc for the material, rated at least for the grinder's speed", and it gives no number anywhere on the page. The product record says the same thing the same way, in its own drawbacks, with "never exceed a disc's rated speed". Both are correct. This page is those two sentences with the division under them, and our review of the grinder has the rest of its feature list.

Now the saw, which is the question as asked

The same algebra runs on a circular saw blade, with a different constant, and it answers the companion question in the same forum about whether to buy a 6-1/2 inch or a 7-1/4 inch saw.

Carbide-tipped blades for wood are speed-rated the same way, by a tooth speed rather than a rotation rate, and the rotation rate printed on the blade is again that speed divided by the circumference. Which means a 7-1/4 inch blade and a 6-1/2 inch blade cannot carry the same rpm marking and never do, and a saw built around one of them has its no-load speed chosen to suit.

Three other things follow from the diameter, and the second is the one people miss. The cut depth is the obvious one and the question already grants it. The second is the force available at each tooth: a motor delivers power, power is force times speed, and at a fixed power and a fixed rotation rate a larger diameter means a faster tooth and therefore a proportionally smaller force behind it. The third is the overhang, because a blade is a cantilevered disc and its stiffness against wandering off the line falls as the unsupported radius grows.

We carry no circular saw as a product record, so there is nothing of ours to run those numbers against, and inventing a blade speed to make the paragraph look quantitative would be the opposite of the point. Our circular saw roundup publishes blade sizes for the group, 6-1/2 inch and 7-1/4 inch among them, and not one speed for any of them, which is the same gap as everywhere else in this category.

One boxed diamond set spans a factor of 32.5

The clearest demonstration of the tie between diameter and speed is a set of bits that all share one recommended speed and cannot all be right.

A FOCSTOL 10 piece diamond core drill bit set running 6 millimetres to 65 publishes an unusually complete set of numbers. Seven core bits at 6, 8, 10, 25, 35, 50 and 65 millimetres. A 5/8 inch 11 thread angle grinder as the intended tool, at "a recommended 6000 RPM, up to 11000 RPM". And a hex adapter that "allows an electric drill rated over 2000 RPM".

Run those. At 6,000 revolutions a minute the rim speeds come out at 1.885, 2.513, 3.142, 7.854, 10.996, 15.708 and 20.420 metres a second. From the smallest bit to the largest, at the one speed the listing recommends, is a factor of 10.83.

Then take the second route the same listing offers. The 6 millimetre bit in a drill at 2,000 revolutions a minute runs at 0.628 metres a second. The 65 millimetre bit on the grinder at the recommended speed runs at 20.420. That is a spread of 32.5 times across two bits sold in the same bag, under one recommended speed, and no instruction anywhere that they want different ones.

None of that is a criticism of the bits, and the record is better than most on this: it states a recommended speed, a ceiling and a separate figure for the drill route, which three of its competitors in our catalogue do not. The point is that a single rpm recommendation cannot be correct for seven diameters, because the quantity the diamond cares about is how fast the grit is sliding across the stone and that is the rim speed. Our page on why one diamond bit needs water and another cuts granite dry works through what the grit is actually doing and already reports the gap it leaves, that the count of published figures which would let you set a dial correctly is zero. This page takes that finding and supplies the geometry it was missing.

Two of our own records disagree once you convert them

A Drilax Pro 4 inch diamond hole saw is the same kind of tool at nearly twice the diameter, and it declares the same mount: "Dual compatibility fits both an angle grinder, via a 5/8 inch by 11 thread, and a drill using an adapter." Its record describes the body as spinning "true at high RPM for stable, accurate cutting" and never states what high means.

So borrow the ceiling from the other record. If 65 millimetres is allowed 11,000 revolutions a minute, that is a rim speed of 37.44 metres a second. A 4 inch bit is 101.6 millimetres, which reaches 37.44 metres a second at 7,037 revolutions a minute. The only grinder we carry runs at 11,800 and has no speed control, which is 67.7 percent above that figure and would put the 4 inch bit at 62.77 metres a second.

Which of those two records is right is not something this page can settle, and that is the finding rather than a dodge. Two products in the same catalogue, specified for the same thread on the same class of tool, carry speed guidance that is inconsistent the moment you convert it to the quantity that matters, and the tool we sell alongside them runs faster than either implies. Nothing on any of the three listings would ever show you that, because none of them states a rim speed.

A FOCSTOL 5 piece 10 millimetre dry diamond hole saw kit sits at the other end of the same ladder and is the most instructive of the three, because it asks for the opposite. It is 10 millimetres only, with an 8 millimetre diamond section at grit 50 or 60, and its guidance is "at least 2000 RPM, with higher RPM extending life". Ten millimetres at 2,000 revolutions a minute is 1.047 metres a second, the slowest rim speed anywhere in this catalogue, and even on the grinder route with a chuck fitted it only reaches 5.76. A small bit asking to be spun faster and a large bit asking to be spun slower are the same instruction, written from opposite ends, and both are really asking for a rim speed.

The rating that is not a rim speed at all

It is worth putting one more rpm figure next to those, because it shows how little the unit tells you on its own.

A pair of EXPEDMAN 4V cordless electric scissors publishes a "300RPM motor" alongside a titanium-coated blade, a 2000mAh battery and a 0.83 pound body. Three hundred revolutions a minute next to the grinder's 11,800 looks like a tool forty times gentler, and the comparison is meaningless, because there is no rim. The mechanism is a scissor: the motor drives a crank and the blade reciprocates, so 300 rpm is 300 cuts a minute and the useful speed is the blade edge closing, which depends on the stroke rather than on any diameter. Nothing about it tears outward, so there is no centrifugal stress to limit and no 80 metre ceiling to approach. Its own record frames the limit correctly and in the right units, as a material limit rather than a speed one: it is "designed for smooth cuts on cardboard, fabric and light materials" and is "not a heavy-duty tool for thick, dense or hard materials".

That is the distinction worth carrying away from the whole family. On anything that spins, the rpm is a stand-in for a rim speed and the diameter is already inside it. On anything that reciprocates, shears or hammers, the rpm is a rate of events and the diameter has nothing to do with it. Our page on why drill bits go blunt in metal is the same argument in the cutting-speed direction, where the right rim speed is set by what the edge can survive thermally rather than by what the body can survive mechanically.

The honest limit, and the one number to read off a disc

What is exact on this page is the geometry and the stress law. Rim speed is pi times diameter times rotation rate, with no approximations. Centrifugal stress in a rotating disc is proportional to density times the square of the rim speed, which is why the ratios in the middle panel hold for any disc material without knowing what it is. And the four rpm markings reproducing one constant to two decimal places is not a model, it is a measurement of what the industry is actually rating.

What is not product data is the 80 metres a second itself. That is the standards figure for reinforced discs on hand-held machines, not something any listing we carry publishes, and some discs are rated to 100 metres a second instead, which moves the whole ladder up by a quarter. Run the middle panel against 100 and the intended disc sits at 70.6 percent of the ceiling instead of 88.3, and the 180 millimetre disc at 111.2 percent instead of 139.0, with a stress ratio of 1.237 rather than 1.932. The overspeed shrinks and does not disappear, because the ratio between two diameters on one spindle is fixed by geometry and no rating changes it.

What this page deliberately does not compute is anything about what happens when a disc fails, how much energy a fragment carries, or how any of it should affect what anybody does. That is a question about products we do not have the data for and about behaviour that is not ours to prescribe, and the arithmetic stops at the stress ratio.

Which leaves one genuinely useful habit, and it costs nothing. The maximum speed is printed on the disc itself, on the paper label, next to the diameter. Read it, and read the nameplate speed of the tool. If the tool's number is the larger of the two, the disc is the wrong disc, and you now know the reason in one line: both numbers are the same 80 metres a second, divided by two different circumferences.