Saw Blade Diameter, RPMs, and Rim Speed

      A technical discussion of the thinking required to calibrate tool speeds to blade sizes. September 26, 2009

I am curious about how saw arbors are produced. They have an arbor that is surrounded by a bearing. The bearing is somehow captured by some kind of casting. Is this a press fit or is there heat involved? How is the assembly installed so as to keep the arbor from drifting side to side along the length direction of the arbor?

Forum Responses
(Cabinetmaking Forum)
From contributor G:
Basically two bearings, one shoulder and one nut. The bearings are retained in two seats by virtue of being on opposite sides of the casting. Have never torn one down but I imagine, at least in theory, a semi press fit on both shaft and casting. I doubt that they use clearances that require heat shrink fits.

The lateral (axial) play (and radial play for that matter) of the arbor (and blade) is at the mercy of the fit of the ball bearings in their races. (If you want better, one goes to a higher class bearing, or to a system using bearings with greater thrust capacity and preloads them so that the pair of bearings are forced to ride at either their axial maximum or minimum separation. Which reduces both axial and radial play. (Compare to zero lash CNC axes drives.) Or was that what you wanted to know?

From the original questioner:
Thank you for your very comprehensive answer. How is rim speed measured for tooling? I see maximum rim speed listed for various tooling. Sometimes it will say something like maximum rim speed 6000 RPM. As I understand it, RPM from the motor is transmitted to arbor via a belt and pulley. The relative sizes of the pulley at each end determine whether the arbor turns faster or slower than the motor. If everything else was constant, would a larger diameter tool have a higher rim speed than a smaller diameter tool? And how do you measure the rim speed? Is this done with something like the timing light I used to use on my Volkswagen tune-ups?

From contributor G:
Maximum safe RPM speed is a conservative number (meaning one that has a safety factor built in) relating to how fast a tool may revolve before the combination of centrifugal force (the outward force vector of each little bit of the tool, force = mass x velocity squared) added up (integrated is the fancy word) over every spot on the tool, plus the sum of the outward forces being generated as each tooth (acting as a chisel) removes stock, plus that safety factor, as that in total compares to the ability (strength) of the disk and other components to resist being torn apart. Failing from the stress. (It may also refer to the ability of the shaft, like on 1/4 in shaft router bits, to stand the forces without failing from bending, or for a hand held tool the maximum speed before the thing has such force as is likely to get away from you. That should be given as max RPM, although it could be given as rim speed. Rim speed is not measured in RPM; rim speed is the speed the rim is traveling measured in feet per second. Or any linear measurement per a time unit, and not as a count of the number of revolutions per unit of time.) A bigger disk drags a lot more teeth (and length) by in each revolution.

Rim speed = How fast the rim is traveling... If the circumference, the distance around the disk, is 36 inches and the angular speed is 1000 rpm, then the rim speed is circumference times RPM, here 36 x 1000 or 36,000 inches per minute. That equals 3,000 feet per minute (divide by 12). It also equals 600 inches per second (divide by 60) or 50 feet per second (divide by 12 and then 60.) Think of it as how fast the wind or scenery is going past if you are riding on the edge of the disk.

To imagine the why of rim speed, just think of each tooth as a wood plane... How fast do you want that plane to be traveling? You are dealing with heat from friction, the ability of the tool to clear chips, the amount of horsepower (push) you got, whether the material behaves better by taking a deep slow cut or a shallow fast one, how fast the material is fed. If you feed maple too slow or run the tool too fast each little bit of maple sees too many passes with heat being generated by each cut, or the blade just skating over without cutting, and the heat burns the wood.

The circumference of a disk is its diameter (or twice its radius) times pi (3.14159). So rim speed is (diameter times 3.14159) times RPM.

The other way of thinking about it is to unwind the disk. Take the teeth off the cutter or saw and stick them on a long string. Bingo - you got a hand saw or a band saw.

From various book tables or the manufacturer, you can get feeds and speeds, which is how much the tool is able to cut per tooth per pass. The combination of rim speed and feed speed. Too deep and you lose temper from heat, load the gullet with cuttings or stall the saw. Too little and you lose production, may have heat problems, or the teeth may not engage but just skate over the work piece.

If you use that VW strobe and it is calibrated in RPMs, it can give you the RPMs. If you know the motor speed and work through the pulley changes, you can get arbor RPMs. Say 1850 RPM on motor, 2 inch pulley on motor and 5 inch on arbor, then every turn of the motor gives you 2/5 turns on the arbor. 2/5 times 1850 is 740 rpm on the arbor. If you have an 8 inch blade on the arbor it has a circumference (distance around) of 8 x 3.14159 or 24.9 inches so rev times distance is 740 times 24.9 or 18,426 inches per minute, or 307 inches per second or about 25.6 feet per second.

Also people get sloppy. Since they have worked out what the rim speed should be for a given feed rate they may just tell you, "For hand fed lumber just run that cutter at such and such RPM." They are giving you a figure that applies to that tool's diameter and is easier to say and set on the machine, which only knows RPMs, than referring to the rim speed, but the tool's performance is measured in its rim speed nonetheless.

And to your question, yes - if the diameter goes up, the rim speed goes up, assuming a fixed RPM. In fact if the tool is twice the diameter, the rim speed will be double. (And in theory you should either double the feed speed or half the RPM if you double the cutter diameter... all else being equal.)

From contributor S:
RPM and "rim speed" are quite different. RPM refers to the revolutions per minute of the shaft. Most common motors are 1700 or 3400 approximate RPM. A direct drive, ungeared 3400RPM motor will have a 3400 RPM shaft speed. A geared or belt drive will require a ration of the pulley size multiplied by the motor speed. A 3400 RPM motor with a 4 inch pulley connected to a saw shaft with a 2 inch pulley will have a shaft RPM of 6800 RPM. If you put the 2 inch pulley on the motor and the 4 inch on the saw shaft, the RPM drops to 1750. The power rating also changes by the same ratio.

To find the rim speed, which is usually shown as inches or feet per minute, multiply the diameter of the blade or cutter by PI (3.1416) and multiply that figure by the shaft RPM.

A 10 inch blade on a 5000RPM shaft would be:
10 x 3.1416 = 31.416 x 5000 = approximately 155, 680 inches per minute.

A 1" diameter router but in the same machine would have an edge speed of 15,560 inches per minute.

Cutter speed (rim speed) is a lot more critical in metal working that wood, but this is why it is difficult to use router bits in a shaper. The shaper has a slower shaft speed, mainly due to its being generally designed for larger diameter cutters. Likewise, the same reasoning applies to why you slow down a router as the bit diameter increases. It all relates to the force being applied to the cutting edge.

From contributor M:
The practical thing you need to know is saw blade speed is based on the blade size. If a saw can handle different size blades (most sliders do), they will have different pulleys to accommodate the needed speeds. Shapers are always variable speed because cutters can vary dramatically. I keep a speed for cutter size chart near the shaper.

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