Calculate worm gear tpi for a cog

Ongoing. I'm still hunting down info but I'm sure I'm not the only one

The cog is a bullgear on a drummond.

Say 60 teethies, 5 inches in diameter

I want to make a basic worm gear to fit it so the bullgear can be used as a dividing head

I am after the TPI of the "worm of best fit" kind or thing, for this cog, with a diameter of up to an inch (although bigger is acceptable)

All not-too-complicated suggestions and answers gratefully received

Edited By Ady1 on 08/10/2015 11:16:07

Ady,

Geo. H Thomas describes the process, in his typically thorough manner, in 'Dividing and Graduating' [and presumably, therefore, also in a Model Engineer article].

Sorry, I'm on the 'bus at the moment; but will dig out the details tonight ... unless someone beats me to it.

The gist of it is that you convert the DP of your gear into Circular Pitch, and screwcut the Worm accordingly. ... The Worm is then set to lie at its helix angle [which will vary according to its diameter].

Hope that makes sufficient sense for now.

MichaelG.

Ady You may find the article on my website of help as it deals with the three methods that can crop up in the home workshop.

1. A conventional gear driven by a conventional worm where the two axis are at right angles to each other. Due to the engagement of the two gears not being ideal it is unlikely to appear in commercial equipment.

2.Generally as 1 but with the worm gear set at an angle to the worm wheel axis to improve the engagement of the two gears.

3. The worm wheel having its teeth cut at an angle so that satisfactory engagement can be achieved with the two gears axis at right angles to each other. Even better, the worm wheel can be cut in a concave form so that the wheel wraps partially around the worm gear.

Method 3 is not of course applicable to your situation as the worm wheel already exists.

The web pages also deal with calculating and setting up the required change wheels, See the following Web page

Harold

Assuming the gear is the reference angle

The diameter of the worm will sets the angle it needs to be to mesh with the gear correctly. There will be point contact where they mesh what ever the diameter is but larger diameters reduce the angle. Many rotary tables and dividing heads have been made that use simple gashed worm wheels - they are just normal gears really with the teeth at an angle. The worm is then cut to suite and are usually in the range of 5/8 to 3/4" diameter. There are commercial suppliers of these parts. The worms are then simply swung down to engage with the wheel as the angles will match. In your case it would probably pay to design in the ability to alter the angle of the worm as well otherwise you will need to set a very precise angle to get a backlash free arrangement with as many teeth in contact as possible.

It's important that the worm and wheel only mesh on the flanks. I would cut the worm too deep on purpose to help with that and also make it between centres so that the od could be trimmed up after a trial fit if needed. Some might do a lot of sums but who knows what running clearance etc was designed into the bull wheel.

The flank angle of the worm needs to match the pressure angle of the gear.

John

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Thanks for everything so far chaps.

working tonite but I can feel a c++ project stirring within to try and simplify the process

Ady - assuming that you're looking at the bull gear on an M type lathe - and it's the same as the one on mine, then the dp of the bull wheel is 14dp - common to the change wheels as well. Now 14dp has 14 teeth to every 1 inch of pcd or every 3.142 (pi) inches of pitch circle circumference. So the circular pitch is pi/14 = 0.2244 inches which makes the tpi (reciprocal of pitch) you need for the worm to be 4.4563 (tpi). The diameter of the worm doesn't affect the pitch or tpi you need, but will change the helix angle, so you can choose the diameter which gives you the best helix angle for you application.

Ady,

I'm home now, so here's a quick update:

GHT's book was first published in 1983, so any ME articles will pre-date that.

Chapter 18 [pages 147-154] is 'Worms and Worm Gears'.

Much of this is adequately covered elsewhere; but it's concise, and a useful reference.

One very useful point: For this purpose 22/7 is a reasonable approximation for Pi.

... and ... This translates to 55/35 x 2/1 [which should not be difficult ratios to find]

Have a Happy Evening, Programming

MichaelG.

Edited By Michael Gilligan on 08/10/2015 20:59:19

Ady,

This is probably the original ME article:

MichaelG.

Sorry about the messy formatting 'Copy & Paste' looked good until I posted it !!

Edited By Michael Gilligan on 09/10/2015 00:12:32

Edited By Michael Gilligan on 09/10/2015 00:14:25

There are a couple of programs on lathes co uk where the available gears tooth counts are entered along with the pitch required and it will find the closest approximation. One for lathes with a gearbox and one for those without.

I find this chart useful at times

John

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Are you going to cut it on the Drummond using only the standard gear set? 6 gear train permitted as I believe 2 studs are standard.

I will be looking to do it on the lathe. Seem to be so busy nowadays, so much to do, so little time to do it

Thanks to all of you for the references.

I've saved Johns chart to my pooter, a nice timesaver

It's important that the worm and wheel only mesh on the flanks etc. :noted

Keith your post is a gold nugget I needed, breaking the process down into simplified chunks and going back to the original cog which is all many amateurs have with which to start a wormgear job

To get the DP, just add 2 to the tooth count and divide by the outside diameter
of the gear. So, 42 divided by 3.49inches is 12.

Ady - assuming that you're looking at the bull gear on an M type lathe - and it's the same as the one on mine, then the dp of the bull wheel is 14dp - common to the change wheels as well. Now 14dp has 14 teeth to every 1 inch of pcd or every 3.142 (pi) inches of pitch circle circumference. So the circular pitch is pi/14 = 0.2244 inches which makes the tpi (reciprocal of pitch) you need for the worm to be 4.4563 (tpi). The diameter of the worm doesn't affect the pitch or tpi you need, but will change the helix angle, so you can choose the diameter which gives you the best helix angle for your application.

(The helix angle in particular was an unknown in my head)

Now I can make a start

Edited By Ady1 on 09/10/2015 11:10:11

The flank angle of the worm needs to match the pressure angle of the gear.

The cutting tool angle? not the helix angle.

Gotit here

Edited By Ady1 on 09/10/2015 11:27:55

Yes the cutting tool angles. The form on the worm will be the same as a rack meant to mesh with the gear.

The helix angle needs to be in a pretty precise relationship to the angle the worm is at when meshed with the gear. That's why I suggested making the worm angle adjustable. It could be locked once the mesh is set correctly.

John

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