# Pulley ratios vs. the Real World



## jschmidling (Jun 4, 2019)

I acquired a Power King drill press from a friend who upgraded and I am having a strange problem with speed control.

The first thing I did was to replace the 3000 RPM motor with a 1700 to get rational speeds but the slowest speed is still too high at around 800 RPM.

The sheaves on the motor and the quill seem to be the same although the quill sheave seems to be the original and the motor one is newer.

At the lowest speed, the motor is 1" and the quill is a bit under 4".  Roughly speaking, a ratio of 4:1.

The measured motor speed is 1700 and the quill is about 800 or a ratio of about 2:1.  This can be confirmed by manually turning the motor shaft and comparing revs on the shafts and I come up with about the same ratio.

Even considering the problems of measuring the pitch diameter of the sheaves, I don't see how I could be off by that much.

What can be going on here?

The only thing that occurs to me is the belt width and cross section but this would seem to have the same effect on both sheaves and cancel out.

Not knowing where to find the answer, I ordered a 3/8" to test this hypothesis.  The belt on the machine now is 1/2".

Hopefully, someone in this group has been here before.

Thanks.

Jack Schmidling
Marengo, Il


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## matthewsx (Jun 4, 2019)

In the real world a good solution will be a 3-phase motor with a VFD. The Chinese ones are so cheap now that any tool that needs variable speed should get one. JMHO

John


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## francist (Jun 4, 2019)

One inch (motor pulley) is an awfully small diameter for a 1/2" belt, any chance you might have made a mistake measuring it? 

-frank


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## ELHEAD (Jun 4, 2019)

Outside diameter or inside of pulleys?


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## pstemari (Jun 4, 2019)

What ELHEAD said. I'm guess the 1" diameter is the bottom of the groove? I think you need to measure diameter at the midpoint of the belt—if you measure at the surface of the belt and then subtract the belt's thickness you should be pretty close. On a small pulley that will make a larger difference than on a larger one.

Sent from my Pixel XL using Tapatalk


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## JimDawson (Jun 4, 2019)

The pitch diameter is measured at about 1/3ish of the way to the bottom of the groove from the outside depending on the profile.  Easier is to just measure the OD which will get you real close for calculating the ratio as long as the pulleys have the same profile.


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## rwm (Jun 4, 2019)

Interesting thread. When you say OD I assume you mean the belt surface with the belt seated?
Robert


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## JimDawson (Jun 4, 2019)

rwm said:


> Interesting thread. When you say OD I assume you mean the belt surface with the belt seated?
> Robert



No, just measure the outer rim of the pulley, but I guess either way would work for calculating the ratio.


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## westerner (Jun 4, 2019)

I believe the relevant measurement is "circumference".  Diameter x 3.1415. Can't find the Pi symbol on this keyboard....


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## T Bredehoft (Jun 4, 2019)

ALT KEY + 227 π


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## NortonDommi (Jun 4, 2019)

http://www.homemetalshopclub.org/library/applets/two_pulley2.html


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## westerner (Jun 4, 2019)

π    Well, looky there! Thanks!  And how do I find the symbol for "cake"?  Cobbler?  Sorry, I will stop now.


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## MrWhoopee (Jun 5, 2019)

westerner said:


> I believe the relevant measurement is "circumference".  Diameter x 3.1415. Can't find the Pi symbol on this keyboard....


 
Because both diameters are multiplied by Pi, the Pi's cancel out. The ratio of the diameters equals the ratio of the circumferences. (D1*Pi)/(D2*Pi)=D1/D2 (Alt key codes only seem to work with a 10-key pad, at least for me).


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## hman (Jun 5, 2019)

π is option-p on the Mac.  But I don't know if I'm going to like my Mac as much after they kill iTunes in the next OS!  Might have to move all my songs to one o' them thar dreaded PCs


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## westerner (Jun 5, 2019)

MrWhoopee said:


> Because both diameters are multiplied by Pi, the Pi's cancel out.


See how simple that is? See why I have a calculator within easy reach at all times? See why my wife balances the checkbook?
Thank You, Mr. Whoopee


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## jschmidling (Jun 7, 2019)

First of all,I am glad I found this forum and I want to thank all who responded.  Too many to name but you know who you are.

1.  I am so old that I thought VFD's still cost in the thou$ands.  Seems like I could have bought one for less than the cost of the new motor and solved all the problems at once.

2.  I think I was working with ID and OD on the ratio problem but even with the corrections, it still runs too fast.  The manual posted was a real help.  I was able to take the vertical slop out of the spindle by following the directions I never would have guessed at.

The lowest speed is supposed to be around 700 but the best I could do was about 850.

By changing to a 3/8" belt I do get about 700.

3.  That is still too fast for what I have in mind for this thing which is to make a crude milling/boring machine out of it.

The first step was to buy a cross slide vise which is a story in itself  but it does what it does and is useful in a limited way.

I then attacked the speed problem like my old mill/drill did it, i.e. another speed control pulley in the loop.  Don't what this is called but the pic included here is what I came up with.  I am now down to about 300 RPM.

The next problem was an up-stop, not to be confused with the down stop.

I added the gray plastic knob that runs up and down on a 1/4-20 threaded rod.  The bottom of the knob pushes on an extension the drives the spindle down at 1/20 inch per turn.  That and the locking knob gives the vertical finesse needed.

I should point out that I have more fun building or redesigning things than just throwing money at problems.

As a point of interest, my shop and barn were totally destroyed in a fire last year and I was hard pressed to find a screwdriver the next day.  We rebuilt the shop and barn but replacing all the toys and treasures is a hopeless task but I'm slowly getting things together again in a much smaller way.

Thanks for the help,

Jack Schmidling
Marengo, Il


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## CluelessNewB (Jun 7, 2019)

Jack,  are you the same Jack Schmidling of "Maltmill" fame?


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## jpackard56 (Jun 7, 2019)

Thanks guys for all the input on this. Cleared up a couple things for me as well.
Jack, I feel your pain on trying to get set up again, some things can just not be replaced...course some things do get replaced and the "way I always wished they had been" in the first go around,
Good luck with the rebuilding and remember Churchill "Never Give Up"


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## jschmidling (Jun 7, 2019)

CluelessNewB said:


> Jack,  are you the same Jack Schmidling of "Maltmill" fame?


Yes indeed.  The MALTMILL (R) was forced into retirement.    All that is left is a few souvenirs.
On top of all else, our roller vendor had a very large lot of knurled rollers ready to ship.  We had to pay for these and tell him to give them to his scrap dealer.

Then there was the insurance policy that I never bothered to read.  Structures not covered if any business was carried on within.  Couldn't get a penny for the shop and had to rebuild it at my own expense.

God works in mysterious ways. 

Jack Schmidling


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## CluelessNewB (Jun 7, 2019)

Jack, The MALTMILL ® served me well back when I was still brewing.   Unfortunately having beer always available on tap did nothing good for my waistline.


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## jschmidling (Jun 7, 2019)

CluelessNewB said:


> Jack, The MALTMILL ® served me well back when I was still brewing.   Unfortunately having beer always available on tap did nothing good for my waistline.


I know the problem.  Lost about 30 lbs since I quit  brewing.  Beer Time is now 2  bottles  between me and my wife.  She takes about half and I get the rest.

js


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## Ulma Doctor (Jun 8, 2019)

sorry to be late to the party, but an 1140 rpm motor would also be a viable swap out.

i have a South Bend drill press that ran way too fast with a 1740 rpm motor,
i installed a 1140 rpm motor and now the drill press is useful for larger diameter bits


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## Bi11Hudson (Jun 8, 2019)

Been following all week without comment. Seems the thread digressed a couple of times without any real answer. Beats me too, unless there is a third pulley involved. 

The outer diameter of each sheave is close enough for a ball park speed figure. Adjusting belt size will make a small difference but not the sort you would call a radical change. Generating the symbol for "pi" on a laptop is a pita, I just spell it out. Fewer keystrokes, that I can't remember anyway.

One thing that bothers me is the motor specs. An AC motor runs based on frequency. A 2 pole motor synchronous field is at 3600 RPM. A 4 pole motor field is at 1800. This for the States at 60 Hz. 50 Hz motors are a fuzz slower. But if run on 60 Hz, will run at 3600/1800  RPM. There is a formula for figuring that but throws in more complication. [F=PS/120] F of course is frequency, 60 here, 50 overseas. P is poles, and S is speed. The 120 is a constant. This is the rotating field, and works for both single phase and three phase motors. Basic algebra shifting things around yields the desired variable. 

Slip, a technical term, is the actual speed of the shaft. It will show _unloaded_ as ~3450/~1740, and is where the motor gets its' power. The ~3000 speed you described doesn't fit unless the motor is a 50 Hz at the name plate. But even then, if the motor runs at 60 Hz, which will be 3450/1740 RPM at the shaft.

I have a "recent" Craftsman DP.(within the last 20 odd years) There is a third sheave that allows for relatively low running speed. Call it two belts, in series. That's the only answer I can see that fits the wide difference between the calculated speed VS the measured speed you described. 

That, or a gear reduction, which I don't see on a drill press, unless home brew. I had one I fitted a few years ago, gone now. Look at my site, http://www.hudsontelcom.com/9X20Gear.html for a description of the mechanism. The gizmo is roughly 3:1. Running backward would yield what you describe. But unlikely. There is no other answer unless you *mis*-measured the pulleys. That can happen, but you would have to be dumb as a box of rocks. And I don't see that happening, not to a machinist. Sorry for the "negative" comment, it's the only thing that fit here.

You have my sympathies dealing with the insurance company. I imagine with all you had to deal with, they took a solid punch in the solar plexus and look for the slightest excuse not to pay off. Nothing to do but start over. Losing all the old stuff hurts bad. I have books dating back to the 19th century. First editions... I worry about the same thing, constantly. Many cannot be replaced, at *any* cost.

Best of luck, Sir. and sorry I don't have a better answer. 
Bill Hudson​


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## jschmidling (Jun 9, 2019)

"One thing that bothers me is the motor specs. An AC motor runs based on frequency. A 2 pole motor synchronous field is at 3600 RPM. A 4 pole motor field is at 1800. This for the States at 60 Hz. 50 Hz motors are a fuzz slower. But if run on 60 Hz, will run at 3600/1800  RPM. "



Thanks for your thoughts.

Don't understand the 3600/1800.  Not the numbers but the slash.  One of my old drill presses had a motor with a switch to select either of  two speeds.  Don't know exactly what they were but combined with the step pulleys gave a good range of speeds.  Never understood how this worked.

Another question I have is about the Chinese VFD's.  Even the ones that have single phase input spec the output as 3 phase.
Does this mean they only work on 3 phase motors?

Jack Schmidling


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## Bi11Hudson (Jun 9, 2019)

The 3600/1800 is referencing a 2 pole motor *and* a 4 pole motor. The actual shaft speed will be more like 3450/1745 RPM. The difference is called "slip" and varies somewhat from motor to motor and with or without load. 3600 for a 2 pole and 1800 for a 4 pole. There is no such thing as a 3 pole. They are in pairs. There are slower motors, but 3600(2 pole) and 1800(4 pole) is the norm for home shops. The slower motors are available but are horrendously expensive, to put it simply. I worked on one(a long time ago) that ran at 275 RPM. Field at 300 RPM. But at 900 HP, probably a bit large for home use.

Multi-speed motors I have worked with in the past. They usually are wired differently from motor to motor and I didn't run across them that often so failed to memorize the connections. Sorry... ... Basically, they would be wound both 2 pole and 4 pole, switching for fast or slow.

A variable frequency(variable speed) drive synthesizes the output wave form electronicly. Single phase AC input is converted to pure DC, which is then converted to three phase output. There are some adjustments for the magnetics of the motor to run at variable speed. When I "retired" from the industrial electrical field, VFDs had *just* become available, at several thousand bux. I have not followed the advancements as I don't trust the electronics package. To my knowledge, currently, there is no single phase device. Sorry, I just don't like them and being retired, I can turn my back on them, even the knowledge of them.

Bill Hudson​


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## Flyinfool (Jun 9, 2019)

From some limited research that I once did the 1ph output VFDs are not for equipment but more for things like fans and other low load devices with fractional HP motors. The problem comes from the capacitors and the internal start switches. When the motors is slowed down it thinks it is starting and then stats switching things and that will mess with the VFD.


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## jschmidling (Jun 10, 2019)

Bi11Hudson said:


> The 3600/1800 is referencing a 2 pole motor *and* a 4 pole motor. The actual shaft speed will be more like 3450/1745 RPM. The difference is called "slip" and varies somewhat from motor to motor and with or without load. 3600 for a 2 pole and 1800 for a 4 pole. There is no such thing as a 3 pole. They are in pairs. There are slower motors, but 3600(2 pole) and 1800(4 pole) is the norm for home shops. The slower motors are available but are horrendously expensive, to put it simply. I worked on one(a long time ago) that ran at 275 RPM. Field at 300 RPM. But at 900 HP, probably a bit large for home use.
> 
> Multi-speed motors I have worked with in the past. They usually are wired differently from motor to motor and I didn't run across them that often so failed to memorize the connections. Sorry... ... Basically, they would be wound both 2 pole and 4 pole, switching for fast or slow.
> 
> ...


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## jschmidling (Jun 10, 2019)

I am so old that my first experience with a VFD had vacuum tubes as the series pass component.

Just a super high powered VFO.

js


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## jschmidling (Sep 3, 2019)

Here is an update on my Power King conversion to a milling machine.

I made a lot of changes since starting this thread but the most serious is mounting the cross-slide vice directly onto the base casting instead of on the adjustable drill table.

This not only improves the rigidity to near absolute but also buys me several more inches of vertical space which it was really hurting for.

The key to getting this to work was realizing that the head was designed to move up and down in addition to rotating horizontally.  The problem then became figuring how to move it up and down as it probably had not been moved for 50 years or more.

This was solved by a video 



in which a small bottle jack was used.  I immediately ordered one and it works perfectly.








I have been tempted to ditch the cross slide vise in favor of an X - Y table but have come to realize a serious advantage of the vice, especially if most of one's work is done in a vice.  The vice never has to be squared with the table as this is built into it.

Also, I have not found a vice and table combo that uses as little vertical space as the CS vise.

I also made some changes to the CS vise but I will save them for later.

Jack 

Astronomy, Beer, Cheese, Fiber, Gems,
Nature, Radio, Sheep, Sausage, Silver




__





						Jack Schmidling Productions, Inc. - Home Page
					

Home Page for Jack Schmidling Productions, Inc.



					schmidling.com


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## DiscoDan (Sep 3, 2019)

Jack, I assume if you found the video of that guy using a DP as a mill you also found the dozens of others that say why it is also a bad idea. I am curious how he hold his tool holder attached to the DP.


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## hman (Sep 3, 2019)

DiscoDan - Looks like Jack is using a Weldon type adapter to hold the tools inside the spindle.  So he's avoiding the main problem with using a DP for milling (the poor side load capability of Morse and Jacobs tapers).

Jack - I get this crazy vision of your substituting an air-over-oil jack for your manual one, thus having a Z power feed  
(Told you it was crazy!)

Substituting the XY vise for the table does make sense, especially if that's what you know what you'll be using most of the time.  Plus, you can always go back and forth as needed - might have to re-level, but the same shim set would probably work for both.  And of course, you're now a member of the "round column mill club" (as I am), and get to experience the joys and wonders of having to re-establish 0,0 every time you raise or lower the head.  Every machine tool has its quirks and trade-offs.  Looks like you're doing pretty well at very low cost.


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## jschmidling (Sep 3, 2019)

DiscoDan said:


> Jack, I assume if you found the video of that guy using a DP as a mill you also found the dozens of others that say why it is also a bad idea.



Sure.  Don't remember who said it but this seems to fit:  "The people who say it can't be done, need to get out of the way of the people who can do it.

Lot's of compromises but like I say about my mini-lathe, it's  infinitely better than no lathe.

> I am curious how he hold his tool holder attached to the DP.

Yo no comprendo.

Jack


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## jschmidling (Sep 3, 2019)

hman said:


> DiscoDan - Looks like Jack is using a Weldon type adapter to hold the tools inside the spindle.  So he's avoiding the main problem with using a DP for milling (the poor side load capability of Morse and Jacobs tapers).



You guys are over my head.  Weldon adapter is not part of my vocabulary and I got tired of looking for a definition.

Does it have anything to do with the flat I see on some end mills?

I am just chucking the tools into the chuck you see which I assume is the one it came with.

No problems with chuck falling out so far and I just assume it's been there so long that it wants to stay there.

I am concerned with the side loading of the bearings but don't know any simple way of dealing with that.  Is this possibly one I missed?

I assume the chatter that starts when I push it too hard is caused by bearing play and this is really the limiting factor in the setup.

Jack


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## hman (Sep 3, 2019)

Yes.  The flats on end mils are called "Weldun flats" and are used to secure the end mills within end mill holders.





						MT3-3/4" End Mill Holder,"A" Style - with Tang End: Abrasive Accessories: Amazon.com: Industrial & Scientific
					

MT3-3/4" End Mill Holder,"A" Style - with Tang End: Abrasive Accessories: Amazon.com: Industrial & Scientific



					www.amazon.com
				








						HHIP 3900-0107 R8 End Mill Holder, 1": Amazon.com: Industrial & Scientific
					

HHIP 3900-0107 R8 End Mill Holder, 1": Amazon.com: Industrial & Scientific



					www.amazon.com
				











						R-8 End Mill Holder, 5 pc. Set at Grizzly.com
					

Hold various sized end mills in your R-8 spindle with this End Mill Holder Set. Includes holders for 3/16", 3/8", 1/2", 5/8", and 3/4" end mills. Takes 7/16"-20 drawbar.




					www.grizzly.com
				




I assumed you were doing something like this when I watched your video and saw the screw head sticking out of your spindle.  Then I saw you re-installing the chuck later on.  Apologies if I've misinterpreted what (I thought) I saw


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## jschmidling (Sep 3, 2019)

hman said:


> I assumed you were doing something like this when I watched your video and saw the screw head sticking out of your spindle.  Then I saw you re-installing the chuck later on.  Apologies if I've misinterpreted what (I thought) I saw



I believe I caused the confusion by inserting that video link in the text.  That is not my video.  I just inserted it to give credit to the person who came  with the bottle jack idea.

My setup is in the still pic that followed it.  My previous setup was pictured up thread.

Sorry but now I know what a Weldon flat is.;

Thanks,

Jack


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## rock_breaker (Sep 4, 2019)

In your photos, it looks like the shafts sre realatively close to each other  which might cause slippage of the smaller pulley do to less belt contact area. If this is happening the smaller pulley will get hot.  Another thought is whether or not the bottom of the belt is riding on the inner diameter of either pulleyagain slippage.
Have a good day
Ray


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## jschmidling (Sep 4, 2019)

rock_breaker said:


> In your photos, it looks like the shafts sre realatively close to each other  which might cause slippage of the smaller pulley do to less belt contact area. If this is happening the smaller pulley will get hot.  Another thought is whether or not the bottom of the belt is riding on the inner diameter of either pulley again slippage.



Never thought of that last point but I forgot to mention (you can see in the latest pic) that I ditched the two belt mod and went back to the original config.  It complicated moving the head up and down and there doesn't seem to be any pressing need for speeds less than 700 RPM.

It was fun working out the problem and if I go back to it, I will put the 3rd pulley much farther off the center line.

Thanks for your thoughts,

js


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## jschmidling (Sep 15, 2019)

Does anyone know how to remove the drive pulley from this drill press?  Photos up thread.

Seems like most of the chatter I hear sounds a lot like the same sound as I get when just moving the pulley up and down and might just need some sort of fiber washer/spaces but I can't figure out how to move the pulley beyond the up/down limits.

The manual explains how to adjust longitudinal slop but no clue in the drawings.

js


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## jschmidling (Nov 6, 2019)

Here is another update on my drill to mill conversion and a couple of questions.

The run out of a drill rod in my mill/drill is about 12 mils and seems to be the cause of lots of problems milling with it.

Finally got the chuck off and find near zero runout on the spindle.

Two questions:

1.  There is no clue on the taper of the chuck in the manual or the machine so, how do I determine what the taper is so that I can get a new chuck?

2.  Is there any alternative to a Jacob's chuck for holding end mills in a drill press?

Here is a pic with the new X Y table.  I changed my mind of the cross slide vice and really like this table and for $100, it's a real steal.





Jack


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## MrWhoopee (Nov 6, 2019)

I'm impressed that your runout is only .012. Even more impressed that the chuck hasn't fallen out of the spindle. It must be seated in the taper quite firmly. If you succeed in removing it to try a different method of holding the cutter I suspect you will discover why everyone says that a morse taper is not suitable for this purpose.


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## nnam (Nov 7, 2019)

The taper you removed can be measured and compare with a Morse taper chart for ID.

Does your have a place to use Drill Chuck Drift? Mine is big and I made an adapter for screwing up the mt#4 tang from inside to hold it.  Mt#4 is large though.


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## CluelessNewB (Nov 7, 2019)

The taper on my Power King is JT33.   I replaced the original with a keyless chuck from Shars with significantly less runout.  I still think it is very questionable for milling.


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## jschmidling (Nov 7, 2019)

CluelessNewB said:


> The taper on my Power King is JT33.   I replaced the original with a keyless chuck from Shars with significantly less runout.  I still think it is very questionable for milling.



It's called making a silk purse from a sow's ear but sometimes we are forced to do this by forces beyond our control like a catastrophic fire that destroyed my whole shop and everything in it.

I found a chart that  I compared to my spindle and it is indeed a JT33.  

This has been another learning experience.  I always assumed that the taper was defined by the angle and the length was sort of optional.

Examining the taper and the chuck, it appears that a previous owner solved the holding problem with some sort of epoxy.  It was conpicuous on one side of the arbor and hoping this could be the cause of runout I cleaned off and "replaced" the chuck.

Without getting violent all attempts left me with a chuck that falls out just by swearing at it.

However, my first try left me with about half the run out it originally had.  This may just be a fluke, but if I can determine that the runout is well defined, I might try grinding one of the jaws with a Dremel before buying a new one.  I solved the loose chuck problem once with a drop of super glue and it worked great.  I suspect that was not invented at the time the expoxy was used.

I notice that LMS offers two similar chucks but with different runout specs and prices.  If all else fails, this is what I will try next.

Thanks,

Jack


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## jschmidling (Nov 7, 2019)

CluelessNewB said:


> The taper on my Power King is JT33.   I replaced the original with a keyless chuck from Shars with significantly less runout.  I still think it is very questionable for milling.



We might want to move this to a different topic, but I just realized you own a Power King and might be interested in something I learned about this drill press.

First of all, there are a several re-branded (almost) look-a-likes and close comparison of the available manuals show conspicuous differences.

The one of interest is the quill construction.  One has a bearing or bushing at each end of the quill and the other has one continuous bronze bushing running the entire length (5") of the quill.  Mine is the latter type and I think I am happy about this. Seems like a 5" long bushing should last about for ever and be the better option for the side loading during milling.

The bad news would be trying to replace this.  As I have found no runout without the chuck, I don't have to worry about this.

Wonder what your or anyone else's thoughts are on this issue.

Jack


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## nnam (Nov 7, 2019)

This is an adapter I made to be inserted into the drift hole.  The bolt goes inside of the tool (mine is mt#4 to er32 holder).  The tool would have its small hole made.  Mine is a 16mm thread.  So I cut a bolt, drilled and thread lock it.  I use a bolt since it's cheap and also I don't have a metric threading gear.

This is like a poor man draw bar goes from bottom

For a solid steel arbor, drilling a small long hole in the middle using a lathe is probably very doable


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## nnam (Nov 7, 2019)

For the run out, did you check with various size cylinders?  If it is consistent, then maybe cutting the jaw would do, else, it can be the other parts

The arbor likely has two different tapers.  One for each end.

Maybe try the er20 adapter on yours (maybe mt#2 or 3)


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## nnam (Nov 7, 2019)

Mt2 to er25, has draw bar thread


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## jschmidling (Nov 7, 2019)

CluelessNewB said:


> The taper on my Power King is JT33.   I replaced the original with a keyless chuck from Shars with significantly less runout.  I still think it is very questionable for milling.



One more question on the Power King.

Immediately above the chuck is a round threaded piece with what looks like a hole for a spanner.  The manual simply calls it a nut.  It seems to serve no obvious purpose other than possibly forcing off the chuck with a spanner but that is not the way the manual says to do it.

Any ideas what this is for?




The manual mentions an attachment for a shaper but no other info.  Above the nut is the collar that gets pushed down by the vertical feed and above that is a thrust bearing.


js


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## CluelessNewB (Nov 7, 2019)

You are correct, it is for forcing off the chuck.    Walker Turner DPs of similar vintage came with a pair of spanner wrenches for removing the chuck.

This is a link to the instructions for the WT, see the section under "Chucks and Adapters"

http://vintagemachinery.org/pubs/808/386.pdf

I'm not sure why Power King recommended using wedges.   Maybe they were concerned that the JT33 taper is longer and the nut doesn't reach far enough?  It worked for me.


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