John in Oly, WA

Trying to figure belt speed

23 posts in this topic

I'm starting a belt grinder build and I'm trying to figure out the surface feet per minute I'll end up with. Not sure if my math is correct.

I'm using a treadmill motor and speed control (seems to be a pretty cheap and popular way to go). Due to the configuration of the motor shaft, I have to use the existing flywheel/pulley, which is a poly-v pulley 1.125" in diameter and transfer the energy to a second shaft for the drive wheel.

So the max RPM of the motor is 7099 (according to the spec. plate). The way I'm figuring it - 1.125" x 3.1416 to get circumference at 3.5343" x 7099rpm to get inches per minute at 25,090 or 2091 feet per minute. If I transfer that to an intermediate pulley that's 2" in diameter, or 6.2832" circumference, then divide 25,090 by 6.2832 I'll have the second shaft's RPM at 3993? Then if I have a 5" drive wheel spinning at 3993RPM - 15.7080"  circumference - 3993 x 15.7080 gives me 62,725 inches per minute, or 5227 feet per minute maximum belt speed? Does that sound correct? Is my math even close or am I multiplying where I should be dividing? And is that a fast enough top speed for a belt grinder?

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This is WAY less complicated than we were taught in school if we were lucky enough to go to a school that taught practical things. :huh: Just a word about the basic physics then onto the meat of the trick. A pully is a wheel and a wheel is a lever that goes all the way around. Same for gears, chain sprockets, etc. they're wheels for transmitting force at differing ratios.

Dump all the extra numbers and go straight to diameters, the speed change goes in the direction power is transmitted and torque goes the other way. Power starts at the drive wheel and goes to the driven. Calculate it like the fractions they are. The mechanically driven pully is always on top, the belt or gear driven one on the bottom. Motor pully 1" tumbler pully 24" = 1/24 A 1728 RPM motor drives the tumbler drum @ 1/24 or 72RPM. With 24X the torque.

A hard mechanical coupling between pullies is zero gain between them, each diameter turns the same RPM and has the same torque.

In your case you have 1.25" pully, belt driving a 2" one for 1.25/2 (rpm decrease) you don't say if the 2" pully is attached via shaft or belt to the 5" so can't prove your calcs. However if it's a shaft the RPM increases another 5/2. If on the other hand you have a double 2" pully so it's belt driving the 5" then the RPM is now 2/5

The only time you need to calculate surface speed is at the final drum, at the sanding belt. Skip desert till you're done with your homework. Then it's time for Pi. B)

Make sense?

Frosty The Lucky.

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Not quite getting my head around that, but is it then 7099rpm x 1.125" / 2" = 3993rpm? The 2" pulley and the 5" drive wheel are on the same shaft, so then the 5" wheel has a circumference of 15.71" x 3993rpm = 62730 inches per minute surface speed or /12" = roughly 5227 surface feet per minute? So I went the unnecessarily long way around to get to the same point. I do that some times (a lot actually).

Thanks Frosty

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Forgive my ignorance but is the exact speed of the belt really that important?

I only ask because I have a grinder build coming up soon as I can find/fabricate a few more parts and I too am using a treadmill motor with variable speed control. 

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IMHO knowing the exact speed of the belt is not particularly important.  However, it is desirable to have a good speed range and to have enough power so that you don't bog the machine down easily if you lean into it a little. I found that 1hp with a 4 step pulley system gave me a decent selection of speeds, but not enough power at the top end.  I'm much happier with the 2hp variable speed setup I have now. When/if I get around to it I have a treadmill with a 2.9 hp DC motor that I will probably build another belt grinder from, but I have not built one from a treadmill yet.

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I'm in complete agreement with the unimportance of knowing the exact belt FPM. 

My only purpose for "contributing" to this thread is to help streamline this particular calculation. In that spirit. First reduce the fractions to decimal. 1.25/2 = 0.625. "We know this is inches so there is no reason to note that every time we write a number." 5x.625=3.125.

The first reduction of 7099x .625 = 4436.875 Rounded to 4440

5" 3.1416= 15.71 rounded to 15.7" . 12 = 1.31' x 4440 = 5816.4'/min  or 96'/sec.

Call it a little over 60mph.

I have NO idea how fast my belt grinder ran and have never needed to know. However if I get around to building one with the yard sale tread mill that's been taking up space in the shop I WILL want a ball park figure so as not to over speed the belts. I don't make knives so I don't have any experience with the benefits of a different belt speeds. I'll reserve the right of an opinion at a later date.

Frosty The Lucky.

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FWIW Frosty, I really liked your explanation above and especially enjoyed the last bit about dessert.

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I understand it's not important to know exactly how fast the belt is going, but I do think it's important to have SOME idea of the speed range of the tool. I'd hate to build a belt grinder only to find it didn't spin fast enough to do the job, or worse spun too fast. And I thought it was a good bit of education to learn how to calculate the transfer of energy through the shafts and pulley diameters.

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One of the few things I remember from algebra class was to reduce calculations, you don't have to make the same conversion many times just do it to the beginning or end. I gave it a shot figuring belt speeds once and darned if it didn't work, then I noticed writing the ratios as a fraction poked me in the eye with the answer.

We all tend to complicate things and one of the most common is wanting to know more about our equipment than we really need. Unfortunately it's hard to know if you need it or not without knowing. It's better to know the fiddly bits you don't really need than get bit by one down the line.

I liked the pi for dessert thing too. Those things just come to me, it's like a super power.

Frosty The Lucky.

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The last lines in my Wednesday post was to do all the other calculations before worrying about a circumference and said , 'save PI for last' It was a dessert pun Buzzkill caught. Not important to the answer, literally true though it is.

Frosty The Lucky.

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Good Morning Frosty,

I understand what you are trying to do, make it simple 'Do it in your Head, Simple'

I always thought, Cake R Square, Pi R Round. lol

Neil

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On ‎10‎/‎1‎/‎2016 at 4:32 PM, Frosty said:

I liked the pi for dessert thing too. Those things just come to me, it's like a super power.

Look out, Fosty is gonna get recruited to the X-men...

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5 hours ago, aessinus said:

Look out, Fosty is gonna get recruited to the X-men...

So long as I get a cool mutant superhero name.

Oh Neil, that's "Pi are round, Cornbread are square."

Frosty The Lucky.

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hmmm Ice man is already taken, so how about BIrch man? Capt'n Cornbread?

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Well, I finished my belt grinder built from a treadmill a while ago. Now I wonder how I ever got along without one.

I thought I'd just post my cobbled together attempt to increase the life of the treadmill motor by keeping all the grinder swarf out of it. I wired in a 110v outlet to the motor circuit. Bought a computer fan and wall wart of appropriate output to power it. Built a pattern out of wood and heat shrunk a couple of plastic bottles over the pattern to form a duct. One large bottle couldn't accommodate the square size at the fan end and shrink enough to form the diameter of the motor at the other. So I had to use two of different sizes and trim them and goop them together. Bought a furnace filter to cut into squares to fit. It's pretty ugly, but it is trapping a lot of particulate.

I don't know if I really need the computer fan, but I put it in there to counter any decrease in the built-in motor fan's airflow caused by the added filter, and figured it wouldn't hurt anything.

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That looks many times better than what mine is looking so far. I might have to steal the fan and filter idea. Please forgive me if I overlooked where you mention the spring, is it one from one of those blue or orange stores? I almost talked to one of the maintenance guys at work about getting one of the extras they have (that's been collecting dust for several years) but decided I should buy one if I go with a spring so I know exactly what it is.

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John: Is that motor strong and fast enough for a belt grinder? You see old treadmills at yard, etc. sales for cheap all the time. Deb keeps buying them the latest was pretty nice, programmable and everything. It's folded up behind my recliner with my insulated Carharts and parka  draped on it. It's right in front of the wood stove and keeps the cold weather gear nice and toasty for forays into the coldness outside.

Anyway, I have an earlier acquisition in the shop I've been meaning to salvage but haven't had a good enough reason till maybe now.

I'm still waiting for a cool mutant superhero name guys. :blink:

Frosty The Lucky.

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Michael - what spring are you referring to? The belt tensioning spring? Yeah, it's a box store purchase. Fan and filter idea - steal away. I picked up the idea from other conversations on IFI.

Frosty - Yes, the motor is pretty strong at the high end. The label on it states 2 HP and max 7099 RPM. I have mostly run it full speed, which according to the calc's above for the pulley configuration is about 5227 SFPM. I thought it was kind of weak at first, but then I realized the belt was slipping. Installed a belt tensioner and solved that problem.

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John - Looks nice - I've been contemplating building one lately.  Where did you source the wheels?  And is there a tracking adjustment somewhere?  I couldn't spot it in the photos. Thanks - Dave

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The wheels I picked up on eBay from oregonblademaker. The tracking adjustment is just a door hinge I welded to the top angled square tube. If you look closely at the bottom two pictures - the top most wheel, you'll see a brass knob. That's the tracking adjustment. I drilled a hole in the door hinge for a 5/8" bolt, slid the bolt through and welded the bolt to the door hinge. The tracking wheel slides onto that bolt. Lined up the hinge on the upper square tube and welded the other leaf of the hinge to that. Welded a nut to the bottom side of that square tube and ran a bolt through it to contact the bottom edge of the hanging hinge leaf (actually welded a bit of an extension to that bottom edge of the hinge. Ran a spring onto the bolt before screwing it into the welded on nut just to keep some tension on it to hold it in place. Cast some brass knobs onto all the adjuster bolts just for fun.

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Nice, thanks for that explanation.  I can see the hinge now.  And I really like the cast brass knobs - I hadn't picked up on that detail before!  -- Dave

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1 hour ago, John in Oly, WA said:

Michael - what spring are you referring to? The belt tensioning spring? Yeah, it's a box store purchase. Fan and filter idea - steal away. I picked up the idea from other conversations on IFI.

I retyped that post a couple time before I actually submitted it. I did mean the tensioning spring, I just neglected to finish my thought. Thanks for clearing that up for me.

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