Calculating Total Number of Speeds on Drill Press

[bostonman]

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

Is a standard 60Hz 120V AC outlet a "4 pole" motor? If so, then yes, it's 4-pole. I will not give the impression I understand AC motors, so I'd rather provide the information on the power supplied to it.

Well, let's start with how to properly calculate three pulleys as I believe this hasn't been answered. I do understand gears for the most part (or a pulley in this case) where a small drive pulley connected to a larger pulley slows down the speed whereas a large drive pulley turning a smaller one will move faster.

I've always dealt with two pulley systems like the gears on a bike. It was answered early on in this thread how to find the total number of speeds, but believe my thought on how to calculate the chuck speed on a three pulley system is still confusing me.

As mentioned, my thought process was: I need the speed of the idler to know the speed of the chuck. Therefore, if the motor is spinning at (rounding up) 1800RPMs, the idler is 3" in circumference, and the motor is 1" in circumference, it's simply 1800*(1/3) = 600RPMs.

Now if the chuck pulley is 4" in circumference, I divide the idler pulley size (now this belt would be on a different location since it can't share the same pulley) by the chuck pulley size. Let's say the idler is 2" in circumference, and the chuck pulley is 5" in circumference, then it's: 600*(2/5) = 240RPMs

Am I doing the math correctly or am I miscalculating (let's ignore belt pitch diameter for now until I grasp the concept of properly calculating speeds)?

If I'm doing the math correctly or not, does an easier method exist to run these calculations because each time I want to figure out one speed, I need to work through all the math again.

As for why I used an elastic band, this wasn't my initial method of measuring the speed. I used the normal setup, however, when I began questioning pitch diameter and stuff, I thought the best way to catch the surface of the pulleys without the thickness of the belt messing up things was to use elastics.

For the most part it seems the pulley was turning correctly and not slipping as the drill press is lubricated and spins quite freely, but I will not disagree, it's a crazy and not accurate way of performing a speed measurement.

The theory of the speed chart on the side of the drill press being wrong is a very good possibility. What I"d like to do is first learn the correct (and simplified) method of calculating the speeds, fix my Excel spreadsheet, and then be able to tinker with the "fudge" number factor along with maybe figuring out whether I can buy another off-the-shelf pulley that will give me middle speeds.

[CatalinaWOW]

Bostonman the spreadsheet I attached a couple of posts prior shows the speed calculations.  You could just plugin your pulley diameters.  My motors nominal speed is effectively the same as yours.  There are slight variations from vendor to vendor depending on the slip baked into their design (OTO 25 Hz.)

If you have solver installed as one of the tools in Excel the spreadsheet is set up to find the minimum square error estimate of the pitch diameter, assuming a simple model. 

[bostonman]

I downloaded it, but it was a bit hard to follow. I'll dig deeper into reading it

[CatalinaWOW]

I downloaded it, but it was a bit hard to follow. I'll dig deeper into reading it

Shouldn't be too hard to follow.  Use the formula trace function to aid.

1.  Top left part of spreadsheet.  Measured diameters of the pulleys in inches (all units in this spreadsheet are inches).  P1 is the motor drive pulley, P2 is the idler, P3 is the one on the quill

2.  Below that are the computed pitch diameters.  Actual diameter minus a fudge factor.  There are several theories as to what the fudge factor should be, but I just put in a constant.  The Excel solver function was used to find the best fit between computed values and the printed table on the drill press.  More explanation later.  To the right of that are the "gear ratios" that result from these. 

3.  Below that are four columns of computed quill speeds.  The one on the left is for the motor belt in the top position (-1).  In the next three columns move this belt down one row.   The equations in these columns are the ones you are looking for to calculate speeds.  They are exactly what you described in words.   There are many ways to actually implement the equations.  I hard coded the motor speed in each cell, used the "gear ratios" mentioned in step 2 to get the speed of the idler pulley and then instead of using the "gear ratios" for the idler to quill step directly computed it using the appropriate pitch diameters.

4.  Below that are the values in the table printed on a label on my drill press.

5.  Below that are the percent errors between the computed speeds and the table values.

6.  To the right of the columns of computed quill speeds are four columns contained the squared difference between the computed speeds and the nominal speeds from the table.  There are many definitions for how to best fit data to a model, but minimizing the square of the differences is the most common and has the most theoretical work supporting it.  It also provides results that are intuitively satisfying.  Just above those error columns is a cell containing the sum of these errors.  The solver function is used to minimize this value by varying the value of the pitch diameter fudge factor, with the constraint that the value be greater than zero (in other words the pitch diameter cannot be greater than the diameter of the pulley).  It turned out that this value was driven up against the constraint, effectively zero. 

[CatalinaWOW]

I did some spot speed measurements on my drill press.

1.  Motor speed wasn't exactly the speed on the motor plate.  1795 vs 1750.

2.  Plugged that motor speed into my spreadsheet and measured idler pulley speed for top two belt positions.  Predicted speeds were 637 and 971.  Measured speeds were 621 and 970.

3.  Tried three belt combos for quill speed.

Nominal            Predicted           Measured
from label
     
200                     225                  212
640                     711                  685
720                     786                  754


I suspect most of the issue is variations in belt tension affecting pitch diameter.  The predictions are within 6% of the measured values.  And the measured values are within 7% of the label values.  More than good enough for picking a good drilling speed.

[jpanhalt]

If I were an investigator for 3-letter Federal agency, my conclusion for bostonman 's problem is "pilot error."  I am also somewhat amazed that he calculated circumference rather than simply use diameter.

[bostonman]

If I were an investigator for 3-letter Federal agency, my conclusion for bostonman 's problem is "pilot error."  I am also somewhat amazed that he calculated circumference rather than simply use diameter.

I'm uncertain where the issue is, but one thing is certain: the measured speeds differ greatly from the label (and it's been suggested the label is wrong).

As for why I didn't measure diameter, does it matter? Initially I used calipers, however, I couldn't get a good angle to use them and/or see the measurements. I thought using a string and getting the circumference was just as good.

So the way I'm calculating the chuck speed (quill ?) is correct? I'm multiplying the motor speed by the ratio of the motor pulley and idler pulley (motor pulley position 1 / idler pulley position 1). Then I take the idler pulley speed from that calculation and multiply that by the ratio of the quill speed and the idler speed (idler pulley position 2 / quill pulley position 2)?

Maybe I'll take the indirect suggestion and get the diameters directly using calipers if I can fit them in and read the numbers. This way I can get a much more accurate set of calculations.

[IanB]

In the other thread, I described how to get the gear ratios by making marks on the belts. Did that suggestion get lost in the noise? No need for calipers, string, or guesswork.

1.  Motor speed wasn't exactly the speed on the motor plate.  1795 vs 1750.

Doesn't the speed of an induction motor depend on the load? The nameplate speed is probably the full load speed rather than the idle speed. I think the idle speed will be pretty close to 1800 rpm.

[CatalinaWOW]

In the other thread, I described how to get the gear ratios by making marks on the belts. Did that suggestion get lost in the noise? No need for calipers, string, or guesswork.

1.  Motor speed wasn't exactly the speed on the motor plate.  1795 vs 1750.

Doesn't the speed of an induction motor depend on the load? The nameplate speed is probably the full load speed rather than the idle speed. I think the idle speed will be pretty close to 1800 rpm.

I think that is the way most are rated.  There is also possibility of measurement error.  I haven't recently calibrated my strobe light and we are only talking a couple of percent here.

[CatalinaWOW]

If I were an investigator for 3-letter Federal agency, my conclusion for bostonman 's problem is "pilot error."  I am also somewhat amazed that he calculated circumference rather than simply use diameter.

I'm uncertain where the issue is, but one thing is certain: the measured speeds differ greatly from the label (and it's been suggested the label is wrong).

As for why I didn't measure diameter, does it matter? Initially I used calipers, however, I couldn't get a good angle to use them and/or see the measurements. I thought using a string and getting the circumference was just as good.

So the way I'm calculating the chuck speed (quill ?) is correct? I'm multiplying the motor speed by the ratio of the motor pulley and idler pulley (motor pulley position 1 / idler pulley position 1). Then I take the idler pulley speed from that calculation and multiply that by the ratio of the quill speed and the idler speed (idler pulley position 2 / quill pulley position 2)?

Maybe I'll take the indirect suggestion and get the diameters directly using calipers if I can fit them in and read the numbers. This way I can get a much more accurate set of calculations.

That is correct for the theory. 

On my pulleys it would be difficult to get an accurate circumference because of the small ledge to the next pulley and because there is no wall on the bottom pulley.  You are measuring the outside diameter aren't you, not the diameter of the valley under the belt?  Also, on my drill press the pitch diameter was about equal to the pulley diameter.  Depending on who made your pulleys and belt, wear of the belt and how much tension you put on the belts it may be different in your case.

IanB's suggestion of just marking the pulleys and counting the ratio gets around most of the measurement issues.  It does require using a protractor or other method to measure fractional turns, or turning the first pulley enough revolutions so you reach an even number of revolutions of the driven pulley.  Just watch the book keeping, it is easy to drop a turn here or there.

[IanB]

IanB's suggestion of just marking the pulleys and counting the ratio gets around most of the measurement issues.  It does require using a protractor or other method to measure fractional turns, or turning the first pulley enough revolutions so you reach an even number of revolutions of the driven pulley.  Just watch the book keeping, it is easy to drop a turn here or there.

No, I didn't suggest protractors, or fractional turns, or anything like that. You simply make a mark on the belt that lines up with a mark on the pulley. Then you make one complete turn of the pulley until the mark returns, and make a second mark on the belt. The distance between the two marks on the belt is the circumference of the pulley. Measuring between the two marks on the belt is a simple matter of straight line distance.

[CatalinaWOW]

IanB's suggestion of just marking the pulleys and counting the ratio gets around most of the measurement issues.  It does require using a protractor or other method to measure fractional turns, or turning the first pulley enough revolutions so you reach an even number of revolutions of the driven pulley.  Just watch the book keeping, it is easy to drop a turn here or there.

No, I didn't suggest protractors, or fractional turns, or anything like that. You simply make a mark on the belt that lines up with a mark on the pulley. Then you make one complete turn of the pulley until the mark returns, and make a second mark on the belt. The distance between the two marks on the belt is the circumference of the pulley. Measuring between the two marks on the belt is a simple matter of straight line distance.

Ah!  Sorry about the misunderstanding.  Better suggestion.  And I believe it also corrects for any pitch diameter issues implicitly if used consistently on both pulleys.

[CatalinaWOW]

Back to OPs question:  Why are the speeds far off.

I see only a few possibilities for errors greater than 10-15 percent.  Measurements of speed are wrong, label is wrong or pulleys have been changed..

If measurements of speed and calculations of speed agree to within 10-15 percent then label is wrong.  If speeds other than found are needed a pulley change is required. It doesn't really matter if the label is wrong because of a manufacturing error or an aftermarket change to a pulley, though if the labeled speeds meet the users requirement they could be used to back calculate a proper pulley dimension and there is some likelihood that the pulley is available on the market somewhere.

If measurements of speed and calculations of speed don't agree to that tolerance there is an error in either the speed measurement, the pulley measurement or the calculation.  The latter error can be eliminated by inspection and pulley measurements can be cross checked with other measurement techniques.  Speed measurement is probably the hardest for most people to cross check.

[bostonman]

In the other thread, I described how to get the gear ratios by making marks on the belts. Did that suggestion get lost in the noise? No need for calipers, string, or guesswork.

It didn't get lost, but now that you elaborated on the method, it seems to be a much more accurate way of measuring the circumference. Initially I didn't quite grasp how I could figure out fractional turns of the second pulley after a full revolution of the first.

You are measuring the outside diameter aren't you, not the diameter of the valley under the belt?

No, I am measuring the "valley" under the belt. To make sure we are talking about the same thing, I wrapped the string between the two walls of each position capturing the deepest part of each pulley. This is why I attempted to use elastic bands to measure the speeds at one point (initially my speeds were measured using the normal belt setup). They are able to sit on the floor ("valley" ?) of each pulley position much like the tight string I used to get the circumference.

This is why I added a "fudge" number to my (incorrectly formulated) spreadsheet. I was figuring that I could add some additional circumference number to offset any belt pitch diameter I wasn't able to calculate correctly. If I could measure each pulley exact using the string, and both belts are the same (one is an A22 and the other A23), then that would mean the "fudge" number would tweak all the pulley sizes equally and the  calculations would (hopefully) equal the speeds stamped on the drill press; or I could figure out which pulley was swapped by a previous owner and how to find the correct size pulley to get the drill press speeds stamped on it (we've somewhat agreed the speeds stamped on the drill press are probably wrong, but I'm just stating my initial goals).

Basically, I need to start my process over. First is getting a more accurate circumference of the pulley using the marking method. For laughs, I'd like to use calipers to measure the pulley directly so I can get an exact (?) pitch diameter number too. But I do like the belt marking idea.

[bostonman]

I see only a few possibilities for errors greater than 10-15 percent.  Measurements of speed are wrong, label is wrong or pulleys have been changed..

Let me get accurate circumference sizes by using the belt marking idea. This way I'll have (hopefully) exact circumferences to rule out the first part.

To rule out my measuring device as possibly being incorrect, the attached datasheet is the meter I'm using (DT2234A). It seems to be quite consistent because I've held it for a few minutes, close up, far away, resting on something, holding freehand (i.e. not steady), etc... It takes all of about 2-3 seconds before locking onto a velocity.

The speed that really blows my mind is 2800RPMs posted on the sticker, but I measured 3815RPMs. This is when I said to myself, even if I'm not taking into account the correct pitch diameter, my circumference measurements are slightly off, etc... there is no way it can be one thousand RPMs faster.

Also, keep in mind, this whole thing began because my drill press goes from 860RPMs to 1380RPMs (as posted on the sticker, my measurements were different though) and I was looking on what size pulley I can buy (or possibly drive the motor directly to the chuck) to get some of the middle speeds because I've seen speed charts that suggest 1000 and 1100 for drill certain metals.

Update: I attached the measured idler and chuck speeds I measured for reference

[bostonman]

Attached is the most recent (and most accurate) pulley sizes.

I began trying the belt marking technique, but I noticed the belt would bend slightly throwing off my measurements. Pulling the belt extra tight helped, but I used a pair of outside (?) calipers (similar to the ones in the attached photo), marked the distance on paper, and used regular calipers (with the dial) to measure the distance.

The measurements were very close to my initial string measuring technique and the few I measured by marking the belt. I took the measurements several times to confirm my measurements.

I entered all the formulas to calculate the ratios. Keep in mind that when the speed is on A-4 (as an example), it's A on the motor pulley to A on the idler pulley, but 4 on the idler pulley to 4 on the chuck.

From what I can tell, I need an average pitch diameter of approximately 0.633. The calculated speeds are close to my measured speeds, but I would like to see them much closer. The 3815 is 98RPMs off, but when I tweak the belt pitch number to help that ratio, I throw off the others by a greater margin.

Now I've at least pieced together a spreadsheet with the correct sizes and calculations. From here I can figure out if I can buy a different pulley to get some mid range speeds or whatever.

Does anyone see an error in my calculations or do they seem correct?

[mendip_discovery]

Just skimmed read the thread.

If you measured the rpm of the motor shaft to see what it spins at with all belts moving. Then change each of the belts around to use the different gears could you calculate the diameter of the pulleys and then use that to fit in the blanks.

Are the pulleys a v shape? If you know the angle you can use either some pins and a very near to measure the diameter. But you would have to work out where the belt is touching the v. If it sits higher or lower it can change the ratios.

[CatalinaWOW]

Your worst difference between calculated and measured speed is under 3%.  I think you're there.   

Rather than calculating a perfect pulley, I would recommend finding what you can buy and seeing if they will work for you. 

[bostonman]

Your worst difference between calculated and measured speed is under 3%.  I think you're there. 

I agree. Ideally I'd like to tweak it a bit closer, but each time I tweak one pulley size or alter the speed slightly (assuming the speed changes slightly depending on belt tension and less torque needed depending on pulley location), the other numbers go south.

Rather than calculating a perfect pulley, I would recommend finding what you can buy and seeing if they will work for you. 

I agree with this. At least now I have a better idea of pitch diameter along with my other measurements being correct. Now I can remove the idler from the equation to see what my speeds will be when driving the chuck directly along with adding pulley dimensions that I find online.

Ironically, I zeroed the pitch diameters and looked at my speed measurements when I put an elastic from the motor to the idler. The A setting is exact, the B setting is 37 less than calculated, the C setting is 89 less than calculated, and the D setting is 341 less than calculated.

Most likely the elastic was slipping more and more as I changed the pulley to the higher speed settings. From visual observation, and letting it run for several seconds, I thought the pulley picked up enough speed and friction was reduced enough to assume I was getting the correct speed, but I guess it didn't.

One problem I had with these calculations: which pulley is the one getting divided. In my head I know a small drive pulley driving a large pulley will have more torque on the drive pulley but slower speed on the secondary pulley. A large drive pulley has less torque, but will spin the secondary much faster.

When I tried doing the math, I kept getting confused which one needs to be divided. Without the visual, I wouldn't know how to write the ratios or which one gets divided by which; so I'm still a bit confused on the math portion (plugging and chucking was kind of the cheating way to do this).

[CatalinaWOW]

I think you are doing something I often do - overthinking it.  Don't worry about the ratios when you are setting up the calculations.

Driven pulley speed = Driving pulley speed times driving pulley diameter divided by driven pulley diameter.   

This is true regardless of the relative diameters of the pulleys so enter the equations into your spreadsheet based on positions and then enter diameters, again based on positions.  Same equation going from idler to the quill remembering that in this case the idler is the driving pulley, with speed determined by the first stage equation.

There are many factors which can affect the pitch diameter correction.   Here are just a few I can think of.   Belt stiffness.  Differential wear of the pulley or belt through the depth of the belt.  Radius of the pulley.  Belt tension.  Load.  Pulley geometry.  Belt geometry.  These later two are have specified nominal values and tolerances, but can vary from step to step of the pulley and belt section to belt section.  On my drill press I found that I couldn't stick a tape marker on the quill pulley because lubricant from the quill had spread all over the top of the pulley.  I would guess that some has also migrated to the v-surfaces.  Unless you are trying to set up a multispeed v-belt system to drive an audio turntable I wouldn't obsess about getting exact matches or numbers.

[bostonman]

Overthinking is absolutely correct. Most often what I work on doesn't require precision, however, I think what if high precision is needed and how pros would proceed. This is why I tend to ask questions based on "perfection".

As for pitch diameter and other factors affecting speed, this spreadsheet certainly shed some light on slight variations causing drastic changes (assuming precision is necessary).

It still amazes me the sticker on the unit (picking the worst case) is 2800 but I'm measuring and calculating 3800 and 3900. The thing spins so fast that it wobbles the entire unit, but now I know it's over 1000RPMs too high.

[bostonman]

I've somewhat readdressed my drill press.

After finishing a recent project that required the drill press, it's safe to tinker with it since I shouldn't need it for a bit. The bearings seem a bit worn because the chuck has some very slight wobble when I try bending the chuck with my hand, however, after removing the top bearings (it has two back to back on top and maybe the bottom too) and spinning the shaft, I can feel some grinding. I don't see a serious need to replace them, however, now that I have it partially disassembled, it's worth replacing. Thankfully the bearings have a name and number on them (NTN 6203Z), so I was able to find them online.

As previously discussed, it's possible the sticker showing the speeds is just wrong (as I've accepted this as the only reason the speeds and sticker don't match). After tinkering with my spreadsheet, none of the diameter sizes I enter satisfies matching the sticker speeds indicating I couldn't replace one that will give me a good range of speeds (and that one of the pulleys isn't original).

Ignoring this conflict between actual speed and sticker speeds, my question is: what is a typical maximum speed a drill press spins?

The sticker states on the maximum setting it should be 2800, but I'm measuring 3815 (and calculating 3878 based on adding an average 0.6" belt pitch diameter).

It seems so strange a drill press would be made to spin this fast because most charts for various materials I find online only require a maximum speed of 3000. When I set it to the highest speed, the drill press shakes/wobbles/vibrates and can't imagine any material needing this speed.

The motor, pulleys, etc... all have the same color paint and appear to be original. So it doesn't appear anything was changed by a previous owner, but still baffling a company would make it spin that fast and/or slap the wrong sticker on it. For the most part, as the attached shows, I don't have any mid speeds to drill materials needing speeds around the 800-1800 range).

Just to be clear, I also accept that the speed doesn't need to exactly match the material speed chart. I'm not seeking to find a pulley that will match the speed chart label exactly, but it baffles me that the label is so far off AND the fast setting is so fast that it's practically useless due to how much it vibrates/shakes/wobbles (not to mentioned I haven't see any material needing this speed).

[jpanhalt]

Thankfully the bearings have a name and number on them (NTN 6203Z), so I was able to find them online.

What class of bearings did you buy?  For a drill press, I would move up a step or two above the "standard" class.  Also note that the classification for ANSI and ISO/DIN are quite different (https://ntnamericas.com/wp-content/uploads/2020/04/NTN-Bearing-Tolerance-Tables.pdf )

If  you buy in the future, look around.  I found a bearing distributor in Cleveland  that is quite cheap for the same bearing compared to "online" retail.  I got full SS bearings for the aerator motor in my septic system quite cheaply compared to online prices.  I used to have to rebuild it every 2 years.  Now it's been going since Spring 2017 without a problem.   You don't need stainless.  I mention that example to illustrate the difference between retail and specialty commercial/manufacturer prices.

[bostonman]

I haven't purchased them yet. Upon removing them, the bearing had Taiwan with NTN marking, and 6203Z.

Last night I searched and quickly found NTN the company who sells these (I'm assuming) part number, but they appear American based, so I'm wondering if these bearings were replaced with counterfeit ones by a previous owner, or, since the drill press isn't made in America, that these bearings were purchased in their Taiwan facility.

For clarification, I sent an email to NTN, however, from experience, nowadays receiving a reply is rare, so I'm not holding my breath.

Update: my mind went off track when I was typing the reply. I meant that because the bearings are marked NTN and includes a part number, my train of thought was: only one replacement type exists. So maybe I can order the same size, from a different company (or maybe the same company), that are higher grade. I wasn't thinking this at first as my assumption was order them from the same company, but if I can get better quality, then obviously I should. Also, if you want to laugh, on the NTN website it allows you to "add to cart", states the item has been added, but then doesn't display a cart anywhere. Their "find a distributor" page seems to loop me back to their website along with asking to create an account.

In any case, if I'm going through the trouble of replacing the bearings (I may also replace the bottom ones but that appears to involve removing the spring that retracts the chuck - and I'm not sure if that's easy to reinstall), they might as well be high quality; although I don't use this drill press often at all.

The other concern: I have a drill press with speeds extremely on the high and low side of useful speeds. While I'm not looking to match the speeds on the sticker, replacing a pulley to get a good mid range would be nice, however, I'm assuming finding a pulley that will have the diameters needed for this will be difficult. Also, the pulley for the chuck appears to be tapered which makes me assume it's not a common shaft size.

[jpanhalt]

Absolutely, you can substitute different brands with the same specifications.  They have been standardized for years.  SKF (SKF.com) is another common brand.  Timken is made in Akron/North Canton, OH.  Just watch which specification is used.