Project Question: Spur Gear to ride on a leadscrew

1. Aluminum
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## Project Question: Spur Gear to ride on a leadscrew

I have a lathe that has a 4mm pitch lead screw 20mm in diameter. If I turn the lead screw one full turn the table moves exactly 4mm.

I want to make a spur gear to ride on the lead screw similar to those used in threading dials. I would like the gear to be about 20mm in diameter if possible. How do I calculate how many teeth it needs to have on it to be approximately 20mm in diameter? It doesn't need to be exactly 20mm in diameter. In fact, I would imagine that I would need to settle for whatever diameter is close to 20mm in order to work out correctly.

But I'm not sure how to even start this problem?

NOTE: I understand that technically this isn't a "spur" gear, it's a worm gear. But it's my understanding that for my application a spur gear will work just fine. All it needs to do is drive a dial similar to a threading dial. It doesn't need to be a super precise fit.

All I'm asking for is how to calculate the precise diameter and number of teeth it needs to have to be close to 20mm in size and mesh with a 4mm lead screw.

Thanks.

2. Titanium
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So 4mm axial pitch has a lead of .1575". A 20 DP spur gear has a circular pitch of Pi/20= .1517" or 3.85mm The addendum of a 20 dp gear is 1/20=.050"=1.27mm.

You want a gear OD of 20mm, so the pitch diameter of your gear will be near 20-(2 x 1.27)= 17.46 mm. A pitch diameter of 17.46mm has a circumference of Pi x 17.46= 54.85mm. 54.85/3.85= 14.26 teeth- you can round down or up- say 14 teeth. A 14 tooth 20 DP gear has an OD of 0.800" or 20.32 mm.

This are very hand grenade ball park numbers and there are other issues to be considered such as the normal pitch of your screw that is dependent on the pitch diameter etc. A 1.25 module gear has a circular pitch of .1545" or 3.92mm which is a little closer to your screw lead but the math is pretty much the same. If you mesh things very loosely you might get it to work. Laying the gear over to the lead angle of your screw will help also as the normal lead of the screw will always be less than the axial lead and both the 20 DP and the 1.25 mod spur gears are a little short on circular pitch you require. Depending on your application this might or might not be possible.

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Some years ago I scrapped a very large ,old ,lathe ,that used this principle ....the leadscrew? ran along the back of the bed ,and a slightly skewed spur gear meshed with it,and drove a shaft across the saddle to the front apron ......this shaft was then geared clutchably?(is that a word?)to a screw across the saddle for cross feed......The long feed was similarly arranged by clutching a gear train driving a rack pinion ..............The lathe weighed somewhere around 20 tons,and had a 6ft dia faceplate (with an internal drive gear round the rim)mounted on a solid spindle.

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@ Dan,

Thanks for the quick reply and detailed information. This will be very helpful. Now that I know how to get into the ball park I can try to hit a home run.

5. Cast Iron
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4 mm pitch, you want a 25-tooth to give a nice neat 100mm per turn, surely?
A 25-tooth 20DP will be a touch bigger than 20mm diameter though, closer to 35mm

Dave H. (the other one)

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Originally Posted by Hopefuldave
4 mm pitch, you want a 25-tooth to give a nice neat 100mm per turn, surely?
A 25-tooth 20DP will be a touch bigger than 20mm diameter though, closer to 35mm

Dave H. (the other one)
I confess to being somewhat confused about the whole shebang.

First let me explain that my lathe came with threading instructions that tell me to never disengage the half-nut lever during threading. They say to cut to the end of the thread, then without disengaging, back the tool out and reverse the direction of the lathe to get back to the beginning for the next cut.

Using this method I can indeed cut all the threads the lathe is capable of cutting. The problem is that it's a real pain to have to do it this way. There is no brake on the machine so it coasts a long way after being shut off. Because of that you need a lot of room between the end of the thread and when the lathe will finally come to a stop. And secondly it takes time to reverse it and wait for it to return to the beginning, especially if you are cutting a long thread.

I can't understand why they didn't include a thread dial so you can disengage the half-nut lever. That would have been such a minor option to add for something like a lathe. In any case, it is what it is. So making a thread dial sounds like a good project for this lathe.

My lathe came with gears to cut the following Metric threads:

The Roman numeral I and II at the top of the chart indicate two lead screw speeds the lathe has.

On the right is a diagram of the threading gears. Gear A is driven from the spindle, gear B is an idler, and D drives the lead screw. B is set to 120 teeth for all metric threads.

Gear D comes in sizes from 24 teeth to 60 teeth, and gear A comes in sizes from 24 to 75 teeth.

As I say, I can cut all these metric threads as long as I don't disengage the half-nut lever and just reverse the lathe.

However after some research I discovered that there are 6 Metric thread pitches that I can cut by disengaging the half-nut because in the case of these threads it doesn't matter where the half-nut is reengaged. Therefore no threading dial is required for the following threads highlighted in orange, red, and green.

This is certainly nice to know. At least I have six threads I can cut normally without the need for a threading dial.

Unfortunately I need to cut a 1.5 mm pitch thread, and clearly I'll need a threading dial for that if I want to disengage the half-nut between cuts.

My lathe will also cut the following Imperial threads:

Unfortunately I don't think I can cut any of those without a threading dial. Unless I settle for just reversing the lathe, etc. But like I say, that can be a real pain.

~~~~

As a somewhat crazy caveat:

I did watch a video where a fellow explained how to cut any thread without a thread dial and still be able to disengage the half-nut lever between cuts. It's a slightly more complicated process, but it basically requires three step.

1. Mark the lathe chuck or spindle with a scribe line and pointer.
2. Do the same for the lead screw.
3. Finally place a table stop or indicator on the ways to mark the precise starting point of the table.

Supposedly when you reach the end of the cut and disengage the half-nut you can bring the table back to the stop (or indicated zero position), and turn the lathe over until both the chuck and lead screw are lined up with their respective marks. Engage the half-nut and make the next cut.

That might sound like a lot of stuff, but it's actually not too bad and allows disengaging the half-nut rather than depending on the lathe to coast to a stop and have to run it in reverse back to the beginning.

Obviously having a threading dial would be the easiest way to go.

I think different gears may be required on the threading dial for cutting metric and imperial threads?

Currently I'd just like to cut a 1.5 mm pitch thread and be able to do it by releasing the half-but between cuts.

I've been thinking about using either a 1 mm or 2 mm pitch thread instead. The problem is that I would then need to make matching nuts as it would probably be difficult to find commercial nuts the right diameter with those thread pitches.

For example the thread that's called for is M10 X 1.5. I could make my own M10 x 1 or M10 x 2, which I could do without a thread dial, but then where would I get nuts to fit? I'd have to make those too.

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Originally Posted by Hopefuldave
4 mm pitch, you want a 25-tooth to give a nice neat 100mm per turn, surely?
A 25-tooth 20DP will be a touch bigger than 20mm diameter though, closer to 35mm

Dave H. (the other one)
Getting back to the size of the gear,...

I could make a larger gear on the thread dial, but 35 mm would be pretty bulky on this lathe. This is a fairly small lathe. It's a 17.5" swing by 24" centers. Not too small, but the table apron is pretty cramped.

I would also like to put the thread dial on the left side of the apron instead of the traditional right-hand side. This is because I often use the tailstock for support and the table comes right up to the tailstock when I do that. No room left on that side of the table for a thread dial indicator.

Finally, I actually bought a small thread dial indicator. Unfortunately it doesn't fit my lead screw. It was designed for a lathe with a very fine thread lead screw. The gear that's currently on it is 18.8 mm, (outside diameter including the current gear teeth. It's about 17.4 mm diameter at the bottom of the teeth.

If I could use a 17.4 diameter gear as suggested by Dan, I might actually be be able to use this original gear as the blank. Just turn the current teeth off it and carve in the new 4mm teeth.

This would certainly make everything quite easy. That would give me a thread dial gear of 14 teeth. Not sure if that would do me any good?

What's the min number of teeth I would need on a thread dial to cut a 1.5 mm pitch thread?

That's a size I use quite often so I wouldn't mind having a thread dial dedicated to that pitch.

Keeping the gear small would be nice if possible. I already have a thread dial indicator and holder that could fit on this apron if the gear is small enough. A larger 35 mm gear would be too large and run into other things.

I'm actually thinking of making some nice indicators on the spindle and lead screw, and using a table stop or indicator instead of a thread dial as I had explained in the caveat of my last post. That might be a doable solution. I just want to be able to disengage the half-nut when I come to the end of the thread. My lathe doesn't have a brake and it coasts too far to be useful the way the instructions say to do threading. My slowest RPM is also 150. I can't go any slower than that.

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If youd said you wanted a thread dial gear,most here would have said simple ,it doesnt need to do anymore than mesh ,so you can cut one freehand with an angle grinder.Problem solved.

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Originally Posted by john.k
If youd said you wanted a thread dial gear,most here would have said simple ,it doesnt need to do anymore than mesh ,so you can cut one freehand with an angle grinder.Problem solved.
The number of teeth don't matter?

I'm pretty sure they do.

The dial indicator I got came with two gears. A 28 tooth gear for cutting 0.4, 0.7, 0.8, 1.75 mm threads and a 30 tooth gear for cutting 0.3, 0.5, 0.6, 0.75, 1, 1.25, 1.5, 2, 2.5, 3 mm threads.

The problem is that these gears don't mesh with my 4 mm lead screw. Not sure what thread pitch they are meant to ride on, but it's clearly a lot finer threaded lead screw.

I want to cut a 1.5 mm thread. So what's the smallest tooth count I can get by with on a thread dial riding on a 4 mm lead screw? What's the formula for figuring that out?

As far as cutting the actual teeth I was planning on doing that with a fly cutter shaped to a 4 mm gear profile. But I need to know what diameter to make the blank and how many teeth to cut. Like I say, I want the smallest diameter possible, or at least something around 20 mm or smaller if possible.

Where do I find the formulas to calculate gear sizes for a thread dial based on lead screw pitch and the pitch of the thread I want to cut?

I have a 4 mm lead screw. I want to cut a 1.5 mm pitch thread. What's the smallest number of teeth I can use on a thread dial for this. Or better yet, what are all the options? I need the formula before I can start cutting gears.

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Thank you to everyone who posted.

I found what I needed:

This is a really nice calculator as you can choose however many teeth you want. Of course only certain numbers of teeth will work for certain pitches, but you can discover what all the options are.

It looks like I can get by with as little as 12 teeth for what I want to do. Although if I use 15 teeth I can use it for a lot more Metric threads. So it looks like 15 teeth wins the day.

Now that I know what gear to make I can move forward to actually making the gear.

I just tried 21 teeth which accommodates even more pitches. But I think I'll settle for the 15 teeth to keep the gear as small as possible. That still covers a pretty nice range of metric threads. Or maybe I'll make one of each size just for kicks.

I just realized that I would need both of these thread dial gears to cover every possible metric thread my lathe can cut with it's current gear-cutting gear set.

The 15 tooth thread dial can cut all but the thread pitches shown in orange below:

The 21 tooth thread dial can cut all but the thread pitches shown in orange in the table below:

So in order to have thread dial capability for every metric thread my lathe can cut, I'll need to make both gears. In fact, now that I think about it, that's how this thread dial indicator came originally. It came with two size gears. In the case of that lathe they were 28 teeth and 30 teeth. In the case of my lathe it's going to be 15 and 21.

So I guess that's just the way it is for all metric thread dials.

So now I know.

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You might consider figuring out the helix angle of your leadscrew then cutting a helical to match. That would be slightly better than a spur gear.

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Originally Posted by EmanuelGoldstein
You might consider figuring out the helix angle of your leadscrew then cutting a helical to match. That would be slightly better than a spur gear.
Yes, I plan on taking that into consideration. That's just a matter of tilting the dividing head slightly relative to the cutter.and the helical angle will be taken care of. Also, if I use a fly cutter that's the same diameter as my lead screw I'll also have a curvature on the teeth that matches the lead screw. My lead screw is 20 mm in diameter so if I use a fly cutter that's also 20 mm in diameter that feature will be taken care of as well. So I should be able to cut a gear that meshes with the lead screw very closely. That's probably over kill for all this gear needs to do, but it will be a good learning project to see what's possible.

To shape the cutter I'll use some modeling clay. Just impress the clay into the lead screw to get the lead screw profile, and then grind the HHS fly cutter tool to match that profile. It should work out pretty well. If I have the diameter correct on the blank and the depth of cut correct, all the rest of the dimensions should automatically fall into place via the dividing head. 15 teeth on the correct diameter blank cut to the correct depth, should produce a perfectly matched gear. At least in theory.

I have yet to calculate the correct pitch diameter for a 15 tooth gear. The thread dial calculator doesn't include that information. But I can probably work this out using the information Dan posted earlier.

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You need to cut a gear with circular pitch of 4 mm. 15 Teeth*4mm= pitch circumference. 15*4/pi= pitch diameter.

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Disengage, let it coast to a stop. Reverse, and re-engage when the dial lines up where you started.

Retract the tool in between those 2, of course.

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A lot of hobby machinists dont realize that while a imperial (inch) leadscrew needs just one thread dial gear,a metric leadscrew needs three different gears for the range of pitches..........As I mentioned ,the gear need do no more than mesh ,a washer with approximate equal notches that meshes with the screw ,no matter how loosely,will indicate the thread quite successfully....... ,obviously the number of notches must correspond with the dial markings.

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Originally Posted by wesg
Disengage, let it coast to a stop. Reverse, and re-engage when the dial lines up where you started.

Retract the tool in between those 2, of course.
As soon as I get some dial lines I'll do that.

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Originally Posted by Sweet Dreamer
To shape the cutter I'll use some modeling clay. Just impress the clay into the lead screw to get the lead screw profile, and then grind the HHS fly cutter tool to match that profile. It should work out pretty well.
Actually, it won't work at all. Not if the screw turns, anyhow

Think about this a second - as the screw turns, the thread traverses laterally, yes ? And the gear is engaged with the thread. What happens to the shape of the tooth as it rotates and passes through the thread space ?

18. Just a thought. And I may be very wrong. But you can
cut a 1mm and a 2mm while disengaging the half nuts.
The change gears are 1:2 and 2:1

The gears for 1.5mm are 3:2.

Could you change gear -B- to maybe an 80 tooth and bring
the gears for 1.5mm to 1:2 or 2:1.

I don't know if that would work, just a top of the head thought.

It actually seems like a fun problem to figure, but I've got

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Originally Posted by EmanuelGoldstein
Actually, it won't work at all. Not if the screw turns, anyhow

Think about this a second - as the screw turns, the thread traverses laterally, yes ? And the gear is engaged with the thread. What happens to the shape of the tooth as it rotates and passes through the thread space ?

Is there an online calculator to go with the graphic you posted?

It does get quite complicated doesn't it? We also need to take into consideration that the tool used to cut the gear teeth needs to be shaped to match the groove between the teeth, not shaped to match the profile of the tooth itself.

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Originally Posted by Bobw
Just a thought. And I may be very wrong. But you can
cut a 1mm and a 2mm while disengaging the half nuts.
The change gears are 1:2 and 2:1

The gears for 1.5mm are 3:2.

Could you change gear -B- to maybe an 80 tooth and bring
the gears for 1.5mm to 1:2 or 2:1.

I don't know if that would work, just a top of the head thought.

It actually seems like a fun problem to figure, but I've got
That's a very interesting thought! I never even thought of doing something like that. Unfortunately I don't have an 80 tooth gear in the gear set that came with this lathe. If I had one I'd run out and try it right now.

That would be pretty cool if it worked.