# Thread: WORM GEARS - Challenging but confusing!

1. ## WORM GEARS - Challenging but confusing!

I would like to design a nice little 4th axis indexing fixture that has a worm and worm-gear connected to a nema23 motor; unfortunately, my knowledge of gears and gear terminology is limited! I know the indexing is done in degrees, but should I design it for 1, 10, and 100th of a degree or make it deg, minutes, seconds of a degree? Each of these designs will require a different gear set, at least I think so? Which one do they use in Europe?

What pitch would I need for each design?

McMaster Carr has their worm gears listed in 6,8,10,12 pitch, all with 14.5° pressure angles.
Also, each pitch has a list with the number of teeth. I suppose the number of teeth would control the divisions of degrees.
Am I going in the right direction?

Challenging but confusing!
Eric

2. The angle of the tooth (deg.) is 360 divided by the number of teeth.
The 6,8,10,12 pitch relate to the size of the tooth.
Once you have decided what tooth size you require and the number of teeth this will determine the diameter of your gear.
When cutting with a dividing head you do not need to worry about the angle, just calculate the number of turns and holes on the appropiate plate.

3. I think what is confusing me is the ratio of worm to worm wheel "20:1 ratio" and the NEMA23 motor with 200 steps/revolution

So a 10 pitch, 20 tooth, and 2.3" dia worm wheel is 18° per tooth

This is from McMaster Carr:
Note: Speed-reduction ratio is determined by number of teeth. For example, a 20-tooth worm gear and its mating worm will give you a 20:1 ratio, and will reduce 200 rpm to 10 rpm.

4. If the stepper motor is 200 steps/rev and 1.8°/step

The worm/wormwheel ratio is 20:1, the motor steps 10, the wheel turns ?°

5. .9 degrees. 200 steps * 20:1 = 4000 steps per rotation. 4000/360 = .09000 degrees per step, * 10 steps = .9000 degrees

if its wrong i blame it on the hour

right then 360* in a circle, 365 days in a year. close

6. 1.8/20 = .09 degrees per step
.09 * 10 steps = .9 degrees for every 10 steps

I think

BTW, thanks a lot Eric, I had been working on shaft movement to pulses per rev for my projects so now my mind is all screwed up.

7. The worms from McMaster Carr are probably just short sections of acme thread. You have it correct in your ratio example. The worm advances one pitch per revolution ( I suppose to get really picky it advances one lead but for single start pitch and lead are the same.) There is a play-off between the worm gear diameter and the screw pitch. For instance a coarse pitch such as 6 will not work with very small gear so you would use a smaller pitch. So you can get the same reduction ratios for different pitches and different worm gear sizes. Or different reduction ratios for a single pitch meshing with different size gears.

If you are starting from scratch to design a worm and worm-gear combination for a particular ratio to fit with a particular diameter you have to start getting involved in pitch diameter. I did do this years ago for a worm gear assembly and can tell you that 6 pitch worm will run at 60 : 1 ratio on a 60 tooth worm gear that has a diameter of a smidgeon less than 4". Once you have figured out one pair you can scale upwards but not necessarily downwards; 6 pitch would give 90 : 1 on a 6" dia. worm gear with 90 teeth and 120 : 1 on 8" with 120 teeth. It is not likely that you could make a 30 tooth worm gear to mesh adequately with 6 pitch.

You will need to decide what type of resolution you want in terms of number of steps per degree rotation on the worm gear. I think it is very likely you will find you have to have a reduction ratio between the motor and the worm gear because to get fine enough resolution by direct driving the worm you would need a worm gear too large to be practical.

It is fairly simple to cut the worm gears just using an acme tap as a hob. I have a setup shown below on and old bench lathe that has made hundreds of worm gears.

8. Originally Posted by Ken_Shea
1.8/20 = .09 degrees per step
.09 * 10 steps = .9 degrees for every 10 steps

I think

BTW, thanks a lot Eric, I had been working on shaft movement to pulses per rev for my projects so now my mind is all screwed up.
I'm so glad I'm not the only one with a "Brain Cloud"

My ears are still ringing from all the blockbusters going of in my neighnorhood!
I'll probably fall asleep tonight, and wake up to one last KaBoom!

9. Geof,

Is the 'pitch' you are referring to in your examples a regular thread tap pitch, not a diametral pitch that would be more commonly referred to in a gear catalogue? 6 diametral pitch would have 1 inch of diameter for every 6 teeth on the gear, hence a 4" pitch diameter gear would have 24 teeth.

10. Originally Posted by HuFlungDung
Geof,

Is the 'pitch' you are referring to in your examples a regular thread tap pitch, not a diametral pitch that would be more commonly referred to in a gear catalogue? 6 diametral pitch would have 1 inch of diameter for every 6 teeth on the gear, hence a 4" pitch diameter gear would have 24 teeth.
Tap pitch. My machine generated a 60 tooth wormgear and I think the pitch diameter of the gear was somewhere close to 3.86". I can no longer recall the details but I needed a worm gear for a tilting mechanism on a desk I designed. I intended to make the gear from leaded steel and the largest diameter I could part-off in my big turret lathe was 4". So a played around with different worm pitches and gear tooth counts until I happened onto this combination. Diametral pitch confused me then and it confuses me now so I ignore it.

11. Originally Posted by Ken_Shea
1.8/20 = .09 degrees per step
.09 * 10 steps = .9 degrees for every 10 steps

So by using an 18 tooth gear, I get this:

1.8°/18=.1 * 10 steps = 1° per 10 steps of the motor!

Now thats what I want!

I hope it's right!

Eric

12. I was wondering what you were going to do with .9 degrees

The math looks right Eric.

Ken

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