Calculating Total Number of Speeds on Drill Press

[bostonman]

I have an odd question, but it's in an area I get confused (somewhat of a probability area).

My drill press has three pullies with four belt placements on each comprised of different diameters (they are conic shaped). Pully one is the motor pully, pully two is the "idler" pully (conic shape is large on top with small on the bottom opposed to the other two), and pully three is the actual shaft for drilling.

It's a twelve-speed drill press meaning, I can put the belt on the first slot on the motor to the idler, and, since slot one is now used on the idler, I can put the belt from the idler to the shaft on two (or three to three, or four to four).

If this was a bicycle, I'd multiply the number of gears on the crank by the number of gears on the rear wheel (hence a twelve-speed bike would have two gears in front and six in the back, or some combination).

What is the correct method to calculate this twelve-speed drill press with three pullies?

[CatalinaWOW]

The key to your confusion is that each sprocket on the rear cassette of your bike can be paired with each gear on the crank.  Can't do that on your drill press.  The idler can only have the number of steps on the pulley different speeds.  And then since the idler can only drive the quil with one less ratio than the number of steps (the belt from the motor is occupying one of the choices) your speeds are the number of pulley steps times the number of pulley steps minus one (n*(n-1)).  Your twelve speed press has four step pulleys.

[bostonman]

Guess I don’t grasp the concept on how to derive to that equation.

The equation works obviously, but I couldn’t derive it with your help.

[antenna]

Guess I don’t grasp the concept on how to derive to that equation.

The equation works obviously, but I couldn’t derive it with your help.

Putting on the first belt, you have 4 choices.  Putting on the second belt, you only have three choices because the first belt is occupying a spot. N is the number of positions for belt 1, (n-1) is the number of positions for belt 2. The "1" in (N-1) represents the spot being taken by the first belt.

Replacing (N-1) with M, M being the number of positions for belt 2, would work too. But it doesn't make sense to write it like that because if the two pulleys had different number of positions, the belts wouldnt line up.  Since all pulleys have the same number of positions, writing it like N*(N-1) makes more sense.

[bostonman]

What if four pullys were used?

The first one would still be n, the second would still be (n-1), would the third be (n-1) too?

That would be 36 speeds.

[CatalinaWOW]

Yep

[jpanhalt]

Remember too, each conical pulley can be inverted.  I have an ancient, made in Japan JET drill press, and even went so far as to build a floating intermediate pulley on rails so I didn't have to mess with belt length so much.

Then, I solved the problem years ago with an inexpensive 3-phase and VFD and kept just the motor and spindle pulleys.  Of course that doesn't answer your questions, but if you use your drill press for drilling holes and a few other thing, there's no comparison.

[CatalinaWOW]

Remember too, each conical pulley can be inverted.  I have an ancient, made in Japan JET drill press, and even went so far as to build a floating intermediate pulley on rails so I didn't have to mess with belt length so much.

Then, I solved the problem years ago with an inexpensive 3-phase and VFD and kept just the motor and spindle pulleys.  Of course that doesn't answer your questions, but if you use your drill press for drilling holes and a few other thing, there's no comparison.

I'll have to check my drill press, but I think the pulleys are the same on many for cost reasons.  So inverting one from the way it was delivered would give you four identical 1:1 ratios.  I do agree that the VFD gives wonderful flexibility.   But also think that the hobby user of a drill press won't be going for maximum throughput with top drill life as intensely as a commercial shop, and would probably do fine with two or three speeds.  In fact, I suspect that most home shop drill presses only see wood and possibly a little aluminum and could be operated single speed with no serious issues.

[jpanhalt]

I basically have 2 speed settings with the pulleys and a pot installed on the side of the drill press head.  I have any speed I need between a very slow walk (suitable for winding something) to full speed.  Any speed with virtually full torque is easily adjusted between the two extremes.  Can't beat that with belts regardless of how many pulleys you have.

EDIT:
Here's a photo of the set up.  Of note: That is a link belt drive.  At first I was skeptical.  Used one once and converted.  Buy it by the foot and adjust as needed.  Runs smoother than regular V-belts.  Don't get an imitation.  Second, the JET drill press is 14" bench type and the column is a full 3".  Bought in 1974, made in Japan, and I have used it for everything from 1" holes in steel to tiny carbide drills for PCB.  With a hole saw, I have gone to 4" in steel. 

The VFD is K-B Drives, but more modern ones are smaller and cheaper.  The speed control is the pot knob on the side.  I only use the lower two positions for the belt.

On the left side, you may notice a small lever.  That is a quill lock I added to hold it in position.  It's very useful for precise positioning.  Of course, there is a brass button in the threaded hole to avoid scaring the quil.

[bostonman]

I haven't used my drill press much at all. A few years ago I kept checking CL for a used one and found someone selling the one I have. Slight rust, but talked him down to $60. A bit of cleaning, steel wool, etc... and the thing is practically new.

As for speeds, I think twelve-speeds is more than enough for me. If anything, I'd like the ability to go in reverse (I've seen videos of this, but don't have the desire to spin it by hand to start). Due to not using my drill press much, I think the belts developed hard spots due to not turning much and may cause some vibration when using (it's something I recently suspected and may need to remove tension on the belts when not in use).

One thing I need to check is whether the chuck wobbles. Upon buying it, I didn't consider this to be an issue, however, I have a Harbor Freight wood bit in there now and it wobbles. Most likely the culprit is the bit since HF doesn't offer quality tools.

One other feature I'd like to add would be a push button emergency stop button. Mine has a toggle switch encased in a thin metal rail to prevent accidental turn on; but it also eliminates quick emergency turn off. The few times I've looked for such switches (the rotary type that lock in the off position and require turning to unlock), I found them to be expensive.

[themadhippy]

The few times I've looked for such switches (the rotary type that lock in the off position and require turning to unlock)

Dont tell me something in the uk is cheaper? you can pick one up .in an enclosure, for around £5 over here

[jpanhalt]

If anything, I'd like the ability to go in reverse (I've seen videos of this, but don't have the desire to spin it by hand to start).

Great selling point for 3-phase and VFD.

[bostonman]

Mine isn't three-phase, it's only a standard 120V AC.

I'd also fear trying to build anything that could blow or damage the motor since I have quite the nice drill press that I didn't pay much for.

The only accessory I've wanted is a mobile base. I've seen some DIY online, and some ones being sold, but not sure how well they are. The DIY ones I don't really have time to build. I'd like one that lifts, allows me to move the drill press, and then sits flat on the floor rather than a wobbly base (my basement floor lumpy).

[jpanhalt]

Of course, you have to buy a 3-phase motor.  They are cheap.  Mine runs on ordinary 110V.  It works better than any other solution and gives you adjustable slow start, infinitely adjustable speed, and reverse with those same advantages with never having to change a belt.  Of course, some people like messing with belts and always have a speed that is just a little too slow or two fast.

[bostonman]

Tonight I measured the circumference of each pulley by wrapping a piece of string around each slot and measuring (in inches) the length.

The attached is all the measurements, a picture of the label that shows the speeds for all the belt settings, and their locations.

I'm confused because, picking out the first one (A-4), I should calculate 350RPMs, however, I'm calculating 161RPMs.

Am I doing something wrong? All the slots on all the pulleys were measured the same with the same tightness and steps.

Update: I forgot to mention the motor measures 1777 RPMs (the sticker is worn off so I measured it). We can call it 1800 RPMs for the most part

[jpanhalt]

You need to estimate the PITCH diameter.  Then use those ratios.

[bostonman]

I'll dig further into how to figure this out. A quick read stated I need to use the number of teeth, however, these belts (A22 and A23) don't have any teeth. Due to them being the same 'A' belt, I assume the pitch is the same for both belts.

My initial assumption was: with all measurements being equal, then the ratios should the same regardless. After not getting the correct speed, I assumed maybe this wasn't the case, so I arbitrarily added 0.3" to all the measurements and was still far off the final speed.

I'll dig deeper into figuring out the pitch and maybe that will get my speed calculation correct. I've already measured one of the settings and the speed was correct, so the plate seems to be correct.

[MarkF]

My Delta drill press has three pulleys like yours.
The speed table from mine may help you.

[bostonman]

You have a wider range.

Mine is missing speeds in the 1000 - 1200 range.

The reason I'm trying to manually calculate the speeds is so I can maybe buy a second pulley to have those additional speeds and/or flip one of the pulleys. Obviously I can do this by measuring the speeds, but wanted to plug all the pulley diameters into Excel and tinker with flipping pulleys.

[bostonman]

Long story short, I created an Excel sheet to perform some ratio calculations and had issues, so I posted the question on the computer/programming section which deviated a bit towards this thread.

So I'm somewhat ceasing that thread as the Excel question got answered and now I remain baffled at why my drill press is so far off when I measure the speeds with a meter.

The attached are the measurements I got, the belt setting, and the speed it should be from the plate on the drill press.

My initial desire was to buy a secondary pulley and/or figure out if I can drive directly from the motor to the chuck and get the middle speeds (1000/1100/1200), however, now I'm finding that maybe someone replaced a pulley since my numbers are far off.

Also, I know some replace the motor with a three-phase and use a knob, but my goal is more or less understanding how to calculate the ratios correctly, correctly measure the pulleys, and find out just what someone may have done to get these numbers so far off.

If I didn't mention it already, my motor speed (according to my meter) is 1777RPMs.

One other thing is that I used an elastic band to drive the motor and idler to eliminate the pitch diameter of the belt. These numbers I have written somewhere, but believe the lower speeds were close to my idler calculated, but the higher speeds were grossly off (much higher).

[Ian.M]

You *cant* use an elastic band as a proxy for a reinforced V belt  for measurement purposes - it stretches and slips under even slight load far far more than the V belt.

With that said, its quite possible that any chart that came with the drill press could be entirely bogus.  The chart may well be correct for a different model with different diameter pulleys (and a different HP motor), but got slapped on your drill press because some beancounter at the factory didn't know any better so only stocks *one* chart for *all* 12 speed drill presses!  Most users don't care and  if they bother moving the belt at all select between the highest and lowest speed and if they are particularly sophisticated. one somewhere in the middle, based on gut feelings rather than material appropriate cutting speed considerations. 

[themadhippy]

my motor speed (according to my meter) is 1777RPMs.

guess its a 4 pole motor as they like to spin at 18000 rpm on 60hz

[MarkF]

my motor speed (according to my meter) is 1777RPMs.

guess its a 4 pole motor as they like to spin at 18000 rpm on 60hz

I believe a lot of those small motors are 1725RPM.  How does that work out with your numbers?

[CatalinaWOW]

I think the bogus chart answer may be the winner here.

According to my ancient Mark's Mechanical Engineers Handbook the pitch diameter for this class of belts is 0.375 inches less than the actual pulley diameter.  However on my drill press the belt actually rides up outside the pulley and a pretty strong argument can be made that the pitch diameter in this lightly loaded condition will equal the pulley diameter.

I measured all of the pulley diameters on my chinesium drill press and found the best match to the speed table came with using the pulley diameter.  But this match was not terrific, with a couple of really outlying values.  Maybe these are errors that occurred in the path from the original designer through the manufacturing department and the printing vendor.  And the bean counters said it wasn't worth fixing when someone noticed the error.

The attached spreadsheet shows what I came up with.  I haven't set up to actually measure the speeds.  Maybe I will do that sometime.  I am definitely one who rarely sets optimum speed.  I am only making a few holes here and there and don't really care about optimum drilling rate or maximum tool life.  If the drill is generating appropriate chips/curls the speed is close enough for me.  I do at least pick my speed very roughly based on material and drill size and the accuracy of the chart doesn't really hurt my usage.  For that matter, on mine, if the real speeds are anywhere close to either my calculations or the chart it would be good enough for "optimum" speed setting which usually has a range of more than +/- 50% from the nominal.

[jpanhalt]

@CatalinaWOW
Exactly.  The TS needs to estimate the Pitch Diameter for his A-section (presumably) belts that ride slightly above, not below, the physical outside diameter of the pulleys.  That fudge factor is easily found and estimated.  The TS has mentioned counting gear teeth.  It's true that with geared drives, one can simply count teeth to get the exact ratios, but that number of teeth (there are no fractional teeth), is directly related to the PD.