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

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.

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.

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 ?°

.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

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

I think :D

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. :D

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.

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

I think :D

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. :D

I'm so glad I'm not the only one with a "Brain Cloud" (chair)

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! :rolleyes:

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.

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.

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

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

The math looks right Eric.

Ken

The 18 tooth worm wheel is small

Pitch Dia = 1.5"
OD = 1.75"
Bore = .5"

The worm is:
Pitch Dia = 1"
OD = 1.17"
Length = 1.125"
Bore = .5"

Worm

I plan on making a really small rotary table with a base that mounts vert/horiz.

Looks like another neet project to add to my list!


NOW, what kind of torque can I expect when a
200 oz/in motor is connected at 20:1 ratio?
Is it 200 x 20 = 4000 oz/in at the rotary table?



Eric

You might want to consider an anti-backlash worm design for CNC use. Additionally, some rotary tables have a slip clutch between the worm and motor to limit mechanical overload. The clutch essentially only works one way, from the motor to the table, not vice versa. I've seen this feature save thousands of dollars and weeks of downtime when a machinist crashes the rotary.

1.8°/18=.1 * 10 steps = 1° per 10 steps of the motor!
Now thats what I want!


i was thinking about this earlier in the thread - what exactly is the objective. most rotary tables and dividing heads (manual) are 40:1 but I'd say that while, based on my experience, its common to need to accurately divide, its rare that you need to really accurately do angular division.

Yet with this device, you don't have the benefit of dividing plates. I'm thinking that rather than determining the ratio based on a convenient number for degrees, that it should be determined by taking a circle as large as you are likely to divide, and then picking a tolerance that you'd be happy with, and then work backwards.

For example, if the largest dia you could ever conceive dividing was 6", and you used and 18:1 worm, that's a resolution of 18*200=3600 per rev. on the the circumference of a 6" circle that's .005" - are you willing to live with only 5 thou accuracy on dividing work? If you need 1 thou accuracy, working backwards that's worm ration of 90:1.

not sure what the best solution for you is, just wanted to point out that were it me, I'd be more interested in the tolerance it could hold on dividing (non angular) than accurately doing angular division

I'd follow the commercial 40:1 practice myself, unless there was a hugely compelling reason not to. My logic would be twofold. First, a lot of others have been successful with it. Second, the handwheels are calibrated to 100 graduations, the step motors have 200, everything will work out to an even equivalent and you can be sure it'll do anything a manual rotab will at least as well.

As I am sure you are probably already aware, John Stevenson does this kind of thing over in the UK. As I understand it, the fruits of his labor are sold here:

http://www.arceurotrade.co.uk/

I believe he does a 4" table with a 200 oz in motor. You can track down a lot more details on the HSM board. His partner Tony Jeffree has a controller you can use with the table so manual machinists also benefit (dividing plates on a chip you might say!):

http://www.jeffree.co.uk/DivisionMaster.html

Perhaps you could hook up with them to get a controller. I don't think they are selling their products on this side of the pond as yet.

Best,

BW

I think the challenge is: are you striving to make a rotary table which is backlash free, so it can be used for 4-axis milling, or a table which should be unlocked, moved and locked? The worm and gear parts require high concentricity to maintain constant backlash, so it can be adjusted to minimal. I second the 1/40 division. With half-step you get 400*40 = 16000 divisions for 360 degrees. If the controller software is non accumulative, this means calculation for division is for example:
Position1 = 1/43 * 16000
Position2 = 2/43 * 16000
PositionX = Oops over 360, subtract 360, subtract division
This will lead to an error, I think up and about equal to the stack of prime number disks I have, backlash of the table calculated in.

Carel

Bob the compelling reason I thought was that a 40:1 dividing head relies on accurate plates to make the divisions - that's absent here. the 40:1 works imo not because it creates a neat angular division, but because with half steps, the 16k div gets you to a about a thou on a 6" circle, then again, it depends on the use. backlash is a good point and can't be adjusted for (me thinks) if its not concentric - then again if you weren't reversing direction or climbing, backlash wouldn't an issue, ie hobbing, cutting flutes, hex head, whatever, its all unidirectional on the head. hmmm. what are the commercial 4th axis units like?

I made an extra set of division discs for my rotary table, so I have all the prime number below 60. These were made on another rotary table. With this copying you get (for free) the eccentricity of the first rotary table, the division error and backlash of the first rotary table and the mounting play on the second rotary table. The last holds also true for the plates that come with the table. In detail there is a grey area on a rotary table. I see it as a mechanical calculator. If you are dividing consequently in the same direction it's accurate.

Carel

I would like to design a nice little 4th axis indexing fixture that has a worm and worm-gear connected to a nema23 motor.
Eric

I suppose I should have better qualified my intentions by saying that I want to design and build a CNC 4th Axis Indexer!

I think with the small diameter of the WormWheel with 18 teeth, the whole unit may have a 3-4" diameter round cast iron t-slot plate!
With a little insight, I should be able to get the concentricity of the gears really true, and add an adjustment for backlash!

I'm not trying to re-invent the wheel, just make a simple but efficient gizmo thats affordable to the average DIY'er. I have never made one before, and it looks like and item of interest to many DIY Router Builders!

As I investigated the gears and such, I realized the motor steps and the controller will be doing all the finite positioning. That is why I wanted to find a gear set that would give me 1° for every 10-steps of the motor. This should be an adequate resolution for the software and the user!

To make the unit sit vertically and horizontally, it will be very usefull on the mini mills as well!

Thanks everyone for your input!
Eric

I would suggest you make the worm wheel as large as possible with the smallest teeth acceptable. With this combination you will have a better chance of reducing the backlash.
I also think your ratio is too high <1° for every 10-steps> . The figures look nice but very rarely do the angles workout. If you divide say 1 to 360 into 3600, I doubt very many come to a even number. You will need your software to select the nearest step. The more steps gives you a better chance to be nearer the correct angle.
My 2 cents worth...Just trying to be helpfull.

The more I think on this, the more I think Mcgyver has the right analysis. Choose a diameter, check the resolution against that diameter, and ask whether that is a close enough tolerance for the work you want to do. I look at it from several aspects. First, you might be trying to make a gear or some such, which wants to be accurate. Second, you may be positioning your work to access it on 3 or 4 sides, or potentially even indexing more than one part into position. You want that to be accurate. If you can't do that to 0.001" (or at least the accuracy of your other axes), the 4th axis is going to be the weak link in the chain.

Given that its to be a small 4th axis, 4" or 6" is probably adequate. If we take the 200 step resolution of the average stepper, that means for 0.001" resolution you want a reduction of at least 50:1 for the 4" case and 70:1 for the 6" case.

Something else to think about is what will be the effective rapids speed if you spin the stepper at 1000 rpm (it's torque peak). Using 4" and 6" diameters, and the 50:1 and 70:1 ratios, respectively, we would get rapids of 1" per minute. Surprise! 1000 rpm times the 0.001" resolution we aimed for.

It seems like a rotab cries out for a servo's higher rpm capabilities when looked at this way.

Best,

BW

I think the challenge is: are you striving to make a rotary table which is backlash free, so it can be used for 4-axis milling, or a table which should be unlocked, moved and locked?

Carel

Anyone's thoughts on Carel's input earlier?

Andy

I had a dividing head with backlash. Kept getting a tight spot. My solution was to ream the bush at one end until a little loose, adjusted the gears until free at tightest spot, then added a spring to pull the worm into mesh.
Crude but effective.

Something else to think about is what will be the effective rapids speed if you spin the stepper at 1000 rpm (it's torque peak). Using 4" and 6" diameters, and the 50:1 and 70:1 ratios, respectively, we would get rapids of 1" per minute. Surprise! 1000 rpm times the 0.001" resolution we aimed for.

I doubt your numbers.
Just for the 4":
1000 / 50 = 20 rev/min
4" * Pi(3.14) = 12.56"
20 * 12.56" = 251.2"/min

Resolution:
50 * 200 = 10000 steps per table revolution
12.56" / 10000 = 0.001256"

The virtual pitch at 4":
12.56" / 50 = 0.2512"

Carel

Hi widgets, I made a small Dividing head years ago, by using a hardened steel gearwheel of 60 teeth and meshing it with an acme threaded worm, cut for the pupose, and slewed over to the helix angle of the worm. The worm was close meshed to give almost zero back lash and as it ran slowly and lubed with grease, wear was not a problem.
Dividing heads are normally 40:1 ratio and rotary tables are 60:1. The rotary table is usually used in the horizontal plane where angular positioning is required whereas the dividing head is used for circular divisions, e.g. gearcutting etc. but both will do the same.
There is another design wherin a train of gears, like in a pocket watch, lying in the same plane as the table, and compounded to give the ratio reqd, is calculated, and the end gear is driven by the stepper motor. The imput being 200 steps per rev is just a factor in the output requirement.
If you are using this for angular work in the horizontal plane then it comes down to 360 deg of table movement divided by 200 steps of the motor and gearing to get the resolution down to whatever you want. 1/10 of a degree per step is easily obtained, but this will take some revs of the motor if you want to do some machining on the move as opposed to just positioning and drilling. The gears would all have to run in ball or needle bearings for rigidity and be hardened and close meshed. Lubricant would be as per car gearboxes where hardened gears are use throughout. To give a low aspect ratio the stepper motor would have to be mounted so as to hang over the edge of the machine table, or a pancake design used.
Ian.

:cheers: I find it very interesting to cut worms with an acme thread. Is this thoretical or have you accomplished this? I have a very difficult time cuting a size as large as 1/2" 13 threads. I realize home shope tools don't have the umphh to do much. Perhaps these are cut in aluminum.
I've made a few wood lathes and one parallel arm duplicator and am interested in developing my knowledge base to make a small duplicator using linear bearings,stepper motors and ball screws. pw

Hi dtoggs, cutting acme threads is is no more difficult than cutting square threads and vee threads. The only problem is where you are coming from. If you are using one of those micro lathes then you are going to struggle like a drowning man in a beer barrel.
When it comes down to working with metal then you must have the tools with enough guts to do the job. My lathe was made in 1920 - 1930 era and cuts true because I'm a fitter and turner and so there lies the answer.
You just gotta know what you're doing otherwise it's a long and painfull learning curve.
Most engineering apprentices learn to handle a lathe with good skill by the time they've been on it for six months. I would avoid those mini lathes if you don't have the skill to exploit their limitations and get some skill levels on a bigger and older more featured lathe.
There's one going on EBAY at the moment, 6" centre height, for A$500 and no bidders so far, one hour to go. Might bid for it.

Yelp,I have run out lathe(atlas 12") and expertise. Guess I will stick to buying my gears. I did manage to make a two spindle worm turning appartus for my home shop duplicarver. I have to confess however,with an anti reverse,I think a chain drive would be as good and a whole lot easier and less expensive to make-just have to take up the slack and keep turning same direction. JMHO.dt:cheers: