Mechanical Engineering Question

[Cursitor Doom]

Hi all,

I have a gear wheel missing from my lathe and need to cut a new one from scratch as they don't appear to be available any more. Question is, given that I can measure for myself everything concerning the leadscrew this gear needs to mesh with, can I from those measurements, calculate the outside diameter (OD) for a blank to make another gear wheel from? I'm guessing there must be a fairly simple formula for this but I'm damned if I can find it. To keep things simple and for the sake of argument, let's say the leadscrew's OD is 1", its helix angle is 10 degrees and it has 10 TPI.

cheers, cd.

[The Natural Philosopher]

Not enough information., What is the desired reduction ratio, or the distance to the shaft its goes on?

[gareth]

I fear that you are providing irrelevant information because the reason that they are known as changewheels is that they get changed in order to give different feedrates to the leadscrew, either for cutting screw threads of different sizes, or for giving a smooth feed for cutting.

So, to try to answer your question in the sense that you have put it, for a start, we need to know the arrangement of the other gears from the main shaft, and what TPI of the screw thread it is that you wish to cut.

Also, for one of the existing gears, we will need to know the outside diameter and the number of teeth in the gear, from which we could estimate either the DP or the module of the gears that you already have.

It would also help tp know what make and model of lathe that you have, as that gives us a firmer base for knowledge.

[Cursitor Doom]

Apologies NP and Gareth; I think we're at cross purposes here (my fault!). I'm talking about the indexing indicator. This is the dial that tells you when you can drop the half-nuts so you always re-cut in sync with previous passes. So if you can visualise it, I've got the indicator dial at the top, the missing gear wheel at the bottom (meshing with the leadscrew when screwcutting) and a plain shaft with a keyway coupling one to t'other.

[Scott M]

Check out Ivan Law's book "Gears and Gear Cutting" in the Workshop Practice series.

OOI, what gear is it to mesh with a leadscrew? Thread Dial Indicator?

[Cursitor Doom]

Harrison M300. I've come across a couple of equations from Ivan Law's book on gear cutting which *might* be of use here:

OD=N+2/DP

or:

CP(N+2)/pi

Does that help at all?

[Cursitor Doom]

Oddly enough, I just have!

[gareth]

Although 5 years ago I had read up on the theory of helical gearing (to produce the "HobNail" spreadsheet, which is used by a few machinists on such machines as a Barber-Coleman, I've no experience of the production of wormwheels.

Also, on my lathe,I've never had a TDI so cannot visualise what you describe.

Ivan Law's book has some suitable information but greater analysis is covered in The Machinery's Handbook.

[<no_spam]

A better place to ask might be uk.rec.models.engineering or on the

forums ... someone may even have one or offer to make one ...

[Cursitor Doom]

This is eight mins well spent on the subject:

[The Natural Philosopher]

Still tells me nothing iuseful.

To can have any sioze pof gear meshing with the leadscrew. Its diameter and threadpitch are not by themselves defining factors. You need to know the axis offset of the shaft you are mounting it on from the leadscrew.

[F Murtz]

He does not seem to be talking about the screw cutting gears.he is talking about the indicator on the lead screw. I would be looking at second hand machinery places or the maker of the lathe maybe ebay or maybe too rare

[Cursitor Doom]

Then we must still be at cross purposes here as I can't see what relevance the axis offset is to the original question.

Anyway, some kind soul has emailed me the solution. I'm going to mock up a cog from these calcs using some cheap, machinable plastic and if it works I'll remake it in brass for permanent attachment. Here's what he sent me:

************************************** [begins] I made one out of acetal using a fly cutter but I had the original gears to work from. I did not worry about helix as the gear is only say 4 mm thick.

Anyway this is the working - sub my leadscrew TPI for yours:

Leadscrew is 4 TPI = 6.35 mm per tooth

mm per tooth / Pi = MOD = 6.35/3.1418 = 2.021268 MOD

DP = 2.54/MOD = 2.54/2.021268 = 12.56637 DP

OD of gear = N+2/DP = 16 (desired tooth count)+2 /12.56637 = 1.432" [ends]