A Little Shop Math, Bench Grinder Speed vs Hand Held Grinder Speed

I have noticed a fairly frequent error occurs when we compare "Dremel"type buffers to bench mounted buffers. The error is understandable because the speed of the hand held devices is considerably higher than that of the bench grinders. Here is a simple guide to accurately comparing the speed of various devices.

Hand Held Grinder vs 8” Bench Grinder

•Hand held (“Dremel” type) grinders have a typical range of 5000 Revolutions Per Minute (RPM) to 20,000 RPM.
•8” bench grinders range from 1700 RPM to 4000 RPM.
While at first glance this may sound like the hand held machine is much faster than the bench grinder, in fact the opposite is true. Our concern is not the speed of the motor but the amount of abrasive material (buffing wheel) passing against the work piece. Therefore, what really matters is the rate of rotation times the circumference of the wheel.
Circumference of the Wheel
Calculate the wheel’s circumference by using the following formula:
C=π·d
C=circumference of the wheel
π=3.14
D=diameter of the wheel
For the sake of this discussion we’ll assume the hand held machine has a one inch wheel and the bench grinder an eight inch wheel.
Hand Held Wheel Circumference:
C=1”x3.14
C=3.14”
Bench Grinder Wheel Circumference:
C=8”x3.14
C=25.12”
So, at the highest speed possible for your hand held grinder, a whopping 20,000 RPM, your work piece is subjected to 62,800 inches of buffing wheel in one minute of buffing. With the bench grinder at its highest speed of only 3,400 RPM, 85,408 inches of buffing wheel passes over your work piece in one minute. If you want to calculate the speed of the wheel in the more familiar Miles Per Hour (MPH), simply multiply your inches per minute by 60 to get inches per hour and then divide that number by 63,360 (the number of inches in a mile).
Hand Held Grinder: 62,800 x 60 = 3,768,000/63,360=59.470MPH
Bench Grinder: 85,408 x 60 = 5,124,480/63,360=80.879MPH

Thanks Brad.

Given the power of the bench grinder motor, 80MPH is the speed with which the blade will hit you if a mistake. This is the reason why I prefer the slower but much safer dremel, at a low RPM setting.
Bench buffer wheels are pure evil, and they will sneak up on you when you least suspect it.

:chop:

Joe Chandler sliced the top off his finger (like... when you are sharpening a pencil with a knife) when a cotton loop grabbed the blade he was buffing and swung it around.
WayneD could have started a new career as a eunuch if it hadn't been for the heavy leather apron he was wearing.
And I think it was Gary who said one of his employees or coworkers got a thumb or finger ripped out.

Always think about safety guys.

There is another aspect of the difference between a handheld buffer and the bench model. If we are concerned with friction causing drag and subsequent heat build up, we must look not only at the speed of the wheel against the workpiece but also the patch size. What is the "patch size"? That is the area of the portion of the rotating wheel in contact with the workpiece. We will assume for this discussion the contact patch with a fabric buffing wheel against a steel workpiece to be elliptical in shape.

The area of a circle is calculated: π·r²
As an ellipse is basically a stretched circle we have two different radii:

http://www.math.hmc.edu/funfacts/figures/10006.3.1.gif

So with this our formula is: π·A·B

For our 1” wheel let’s assume a width of .25” and a length of .5”
π x .25 x .5
3.14 x .25 x .5 = 0.4 square inches
For our 8” bench wheel let’s assume a patch width of 1” and a length of 1.5”
3.14 x 1 x 1.5= 4.7 square inches
Conclusion:
Even if the wheels were passing the steel at the same rate, the bench wheel contact patch is ten times the hand held contact patch. The 8” wheel clearly will generate much more heat and drag.

Brad

I think you are neglecting to think about the pressure being used. With the smaller contact area of the dremel, when using the same amount of pressure as the grinder, the PSI is through the roof. Let's say you use 1 pound of force using either the dremel or the buffer. Pressing the dremel into the blade with 1lb of force, or holding the blade to the grinder with 1lb of force. In this case of equal pressure, since the grinder contact area is 11.75x (4.7/0.4) GREATER than the dremel, the distributed pressure applied (PSI) is 11.75x LESS when using the grinder. This will generate much less heat using the grinder, assuming the same speed of the wheels and pressure.

My knowledge of the subject sort of ends here, but I think the equations to prove it are relatively linear such that your initial conclusions (not calculations) using 59.47mph and 80.879mph for the dremel and grinder respectively are misleading. If you include the pressure, the numbers would be off by a factor of 11.75 if it's linear. That is, with the dremel at 20,000rpm, with the same pressure as the grinder, even though the wheel speed is slower, you are generating local heat equivalent to running the grinder at (59.47mph * 11.75) = 698.7725mph, or, 29375 rpm.

This whole heat issue gets wayy more complicated when you try to compare the two directly like this, because it's not that simple. You start to get into how much of the blade are you heating and how much is heatsinked by the surrounding metal, etc, etc, none of which I can even begin to understand or explain, let alone prove with equations. So even what I'm saying isn't the end all. For all I know, you're still right because the localized heat generated with the dremel is in such a small area that it is easily heatsinked away by the surrounding metal.

Does this make sense? Please forgive me if I'm overlooking something or just being completely stupid.

Maybe someone else can step in and explain this better. I just think that your equations are technically correct, but your conclusions are misleading. Now if you are talking about using much less pressure with the dremel than with the grinder, 11.75x less that is, then this entire post is moot :p

Pjrage,

I'm not sure what you are saying but I appreciate your thoughts. Let me make a few comments and see if that makes me more righter or wronger.

My initial point is that people frequently say the Dremel type machine is more arduous and dangerous because the speed of revolution is so much higher than that of the bench grinder. I want to point out the comparison is not as simple as that and the size of the wheel is very important. I think I am correct in my calculations on this. You mentioned pressure.

Most problems arise with bench grinders because people have a tendency to apply much more pressure with both hands pressing a workpiece against a mounted wheel than they do with a blade in one hand and a Dremel in the other.

Brad

I agree that your calculations appear to be correct, and that the wheel speed is actually faster for the bench grinder than for the dremel, even given dramatic differences at motor rpm.

I'm just not so sure that this translates into less friction and therefore heat. And I believe the reason is due to the pressure per square inch, or, the amount of pressure spread out over what area.

If you take a certain amount of applied pressure and spread it over a small area, such as the contact area of the dremel tool, it will have a certain pressure per square inch. If you take that same pressure and spread it over a larger area, such as the greater area of the bench grinder's contact surface, it will translate to less pressure per square inch. This is dividing the given pressure by the area to which it is being applied. By decreasing the pressure per square inch as in the grinder example, this will reduce the amount of friction, which, given the same wheel speeds, will decrease the generated heat. All this meaning that if we set the bench grinder and dremel motor rpms accounting for wheel diameter such that the end wheel speeds are the same, and we use the same pressure with either tool, then it's down to the one with more friction will generate more heat. Given the same applied pressure, say even just the weight of the blade, the dremel will produce significantly more heat. Granted, the generated heat will be contained to the (relatively) small contact area of the dremel. Since this contact area is pretty small, the heat that is generated may not cause any problems, and certainly not as many problems as if the same heat were generated in the much larger contact area of the bench grinder. Either way, given these (reasonable) circumstances, the dremel is actually producing much more heat.

I think. Hehe.

I hope that was more clear of what I'm thinking anyway.

But we aren't only concerned with heat. Read Bruno's post. The big safety concern is drag and the possibility of a razor being torn from your grasp by a bench grinder and thrown at 80 MPH.

What is it around here? Do you guys win points for discrediting old Icedog?

Ah, I guess I misunderstood the point of your post, my fault :o:fim:

I'm not trying to discredit you at all. I love reading the technical posts.

But we don't need a list of equations to know that a dremel is safer than a bench grinder, do we :shrug: I thought you were trying to prove something else.

First off I want to thank Icedog for showing and making us remember what we're dealing with.

Those numbers are pretty impressive and I think by now we should all know the danger involved working with any of the Dremel or bench buffers. As experienced as one can be, danger always lurks around the corner.

You can wear all the protection and use all safety measures in the world but never let your guard down when using those tools.

Once in a while what does happen when using my buffer and makes my adrenaline pump through my body is the loosening of one of the cotton threads or even small pieces of sisal that come loose.

Those cannot only grab your razor or fingers but they are at times ejected at lightning speed. I had one eject itself against my safety glasses. I can tell you it's not a pleasant experience.

Compounds and tiny micron buffing fibers fly all over. Protect your face and eyes.

Besides the safety glasses and leather apron I always use finger cots or kevlar gloves.

With the dremel it's important to tighten the chuck/collet with the chuck wrench. I can bet you anything many people just tighten the chuck with their hands.

Most important, be safe and work safe!

Quote:

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Originally Posted by icedog

My initial point is that people frequently say the Dremel type machine is more arduous and dangerous because the speed of revolution is so much higher than that of the bench grinder. I want to point out the comparison is not as simple as that and the size of the wheel is very important. I think I am correct in my calculations on this. You mentioned pressure.

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Whoa Nelly:
Now you just did open a huge can-o-worms there if that was the presumtion...

You can march out all the math in the world, and never ever prove that a Dremel is near as safe as a bench mounted buffer....
There is one huge glaring difference... the Dremel is handheld!!!!! this one fact alone makes it way, way, way, more unpredictable when being used...

I thought you where just showing that heat generation was similar or less...

Sharp metal + fast spining wheels = Dangerous stuff, period...

Now you guys that are holding the razor in one hand and the Dremel in the other, you should be on TV on one of those extreme sports things.... at least hold the edge of the razor on a surface....