# Best worm gear for dividing head



## Holt (Apr 8, 2011)

I would like to build a combined rotary table/dividing head, for the RT a 36:1 worm gear would be perfect (10 deg at each revolution) but most dividing heads use 40:1 worm gears. What would be the best compromise? I can't remember how to calculate divisions, i haven't used it since technical school, so i cant figure out if the 40:1 gear is just for convenience, or there is any other reason for it ???

Holt


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## arnoldb (Apr 8, 2011)

Hi Holt

A 36 tooth gear for the worm on a rotary table might be a bit coarse - or have to be made too small... A 72 tooth works well, giving 5 degrees per turn which is very convenient. A lot of commercial rotary tables use a 90 tooth gear. The more teeth you have on the gear, the finer you can easily adjust the angle.

Like you said, most dividing heads have 40 tooth gears. Mine actually have a 60 tooth gear, and it allows for some more variations without having to change dividing plates.

If you want to make a combination, and you're going to make your own division hole plates, the 72 tooth might be the best way to go.

Marv (mklotz) wrote a great little utility to calculate spacings on division plates for different worm ratios, and it is easy to add your own setups to it.
If you see a post from Marv, just follow the link in his signature line to get to the software; there's a lot of other useful utilities he wrote as well.

Regards, Arnold


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## Mainer (Apr 8, 2011)

"It all depends." Basically, you want a gear ratio with a lot of factors. 36:1 has factors of 2, 3, 4, 6, 9, 12, and 18. 40:1 gives you 2, 4, 5, 8, 10, and 20. 60:1 gives 2, 3, 4, 5, 6, 10, 12, 15, 20, 30. And so forth.

To figure out what you need to get a particular number of divisions, divide the wormgear ratio by the number of divisions you want to get. For example, if you want 16 divisions:

If the gear ratio is 36:1, 16 divisions would be 36/16 = 2 full turns + 1/4 of a turn

If the gear ratio is 40:1, 16 divisions would be 40/16 = 2 full turns + 1/2 of a turn

If the gear ratio is 60:1, 26 divisions would be 60/16 = 3 full turns + 3/4 of a turn

The more factors there are in the wormgear ratio, the more often the number of divisions you're trying to get can be achieved with a smaller set of index plates. To see this more clearly, imagine using a gear ratio that is a prime number, say, 37:1. You would quickly discover that you would need a huge number of index plate hole circles because there would never be a common factor:

37/16 = 2 full turns + 5/16 of a turn   but 36/16 = 2 full turns + 1/4 turn
37/24 = 2 full turns + 13/24 of a turn  but 36/24 = 1 full turn + 1/2 turn

With the 37:1 ratio, you would need hole circles with factors of 16 and 24. With the 36:1 ratio a single hole circle with a factor of 4 would serve in both cases.

A higher ratio gives you, at least in theory, more accuracy. On the other hand, the tradeoff is more cranking. Most commercial dividing heads use 40:1. Rotary table ratios seem to be a bit more variable. I've seen 72:1 and 90:1 and heard of others.

When I built my dividing head I used a 60:1 ratio, giving more built-in factors and hopefully more accuracy in the divisions. In the end it's how you want to balance the advantages and disadvantages.


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## mklotz (Apr 8, 2011)

If you download my DIVHEAD archive you get, in addition to the main program, a program called DPLATES, which will allow you to calculate the hole plates you will need to do any number of divisions up to a user-input maximum. The fewer the hole plates needed, the more "useful" is the designated worm gear ratio.

Below I've included part of the writeup included with the archive. It describes in more detail the use of DPLATES.

------------------------------------------------------------------------------


	The problem of just which hole plates one NEEDS piqued my curiosity
and so I wrote a short program (DPLATES) to calculate what is needed as a
function of the gear ratio and the largest number of divisions one might
anticipate needing (no rapid indexing plate assumed). It's offered here as a
'bonus' for those of you who might consider building a dividing head. Let me
know if I got something wrong.

	Below are some sample outputs with my annotations.

-----------------------------------------------------------------------------
REQUIRED DIVIDING HEAD HOLE PLATES

DH worm gear ratio [40] ?
Maximum number of divisions needed [50] ?

Hole plates required for all divisions up to 50
4,5,6,17,19,21,23,27,29,31,33,37,39,41,43,47,49,

	It would appear that the 15 and 16 hole circles normally supplied with
commonly available devices aren't really needed to get the advertised "all
possible divisions up to 50". Maybe it's done to make the low number plate
look better. (You need the 20 hole plate for 4 and 5 and the 18 hole plate
supplies the 6.)

REQUIRED DIVIDING HEAD HOLE PLATES

DH worm gear ratio [40] ? 90
Maximum number of divisions needed [50] ?

Hole plates required for all divisions up to 50
3,5,13,14,16,17,19,22,23,29,31,37,41,43,47,49,

	One less plate with a 90:1 ratio to get everything up to 50.

REQUIRED DIVIDING HEAD HOLE PLATES

DH worm gear ratio [40] ? 100
Maximum number of divisions needed [50] ?

Hole plates required for all divisions up to 50
8,12,17,19,21,23,27,29,31,33,37,39,41,43,47,49,

	A 100:1 ratio doesn't save a lot of drilling effort.

REQUIRED DIVIDING HEAD HOLE PLATES

DH worm gear ratio [40] ? 60
Maximum number of divisions needed [50] ?

Hole plates required for all divisions up to 50
5,8,9,11,13,17,19,23,29,31,37,41,43,47,49,

	A 60:1 ratio is good because 60 is evenly divisible by a lot of
integers.

-----------------------------------------------------------------------------


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## Holt (Apr 8, 2011)

Thanks every one. I have downloaded mklotz's program, and it seems i could do with a 72:1 worm gear. if i can't find one, i guess i have to make one eventually, lets see, i am not in a hurry. 

Holt


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## Mainer (Apr 8, 2011)

A worm and wormgear set from Boston Gear is not horribly expensive.

Hey Marv ---- in your copious free time ;D could you perhaps find a moment to upgrade your programs so they run on 64-bit W7? I can get them to run, with some pain, by running them in an XP virtual machine under W7, but it would be a lot easier if they would just run.

Thanks!


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## Holt (Apr 9, 2011)

Mainer  said:
			
		

> A worm and wormgear set from Boston Gear is not horribly expensive



I am sure once the postage and customs to Denmark is payed, it would be cheaper (and more fun) to make your own set


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## arnoldb (Apr 9, 2011)

Hi Holt

Making a worm gear is a lot of fun ;D

Dean built a very nice rotary table - you can look on his web site - which inspired me to make my own rotary table. I have the build log here on HMEM including making the worm and wheel. Maybe there's some useful information for you.

I did have the advantage of having a dividing head already, which made some things easier, but it's not really needed. If you have change gears for your lathe, you can easily cobble together indexing setups from those.

Mainer, Marv's utilities run just fine in DOSBox - and DOSBox can run on Win 7 / 64 bit.

Regards, Arnold


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## mklotz (Apr 9, 2011)

Mainer  said:
			
		

> A worm and wormgear set from Boston Gear is not horribly expensive.
> 
> Hey Marv ---- in your copious free time ;D could you perhaps find a moment to upgrade your programs so they run on 64-bit W7? I can get them to run, with some pain, by running them in an XP virtual machine under W7, but it would be a lot easier if they would just run.
> 
> Thanks!



One of the reasons I include the source code with my programs is so users can experience for themselves the exquisite joy of porting programs to another OS. I wouldn't want to deny that feeling to anyone.

Sorry, porting programs just isn't on my bucket list.


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