Machining Helical Gears

[Oldmechthings]

A little over a year ago I built a scale model Gatling gun. For this project I needed a pair of helical gears. They could have been purchased from a bearing supply house, but there is not much satisfaction in buying something that someone else has made when you can do it yourself.
If you think about it, a helical gear is a short section of a vary course pitch screw with multiple leads; as many leads, as teeth in the gear. Theoretically you could machine a helical gear in a lathe, but actual practice and theory do not always coincide. However if you set up a work holding spindle on the mill table, that represents the lathe spindle, and gear it to the table traversing screw, that represents the lathe lead screw, the theory works great. By the way I did not invent this idea, I just adapted what others had already done to my own mill.

A bracket was built and several gears machined that will remain a permanent part of the fixture. Note that I even installed reversing gears, just like on a lathe, so it will machine both right and left hand helix. Then change gears are needed in order to get the proper ratios, and I just used the gears from an old antique lathe in my collection. It took an extra pair of reduction gears more than used on a lathe, but that was worked in too. When it was all put together the counterbalance knob on the regular mill handle hit the gears so I had to make a new different shaped handle.

To figure the ratio, you need to determine how far the mill table would have to travel for the work piece to rotate one revolution. Then divide the the table screw pitch (mine is .200") into that, and that is your ratio. Simple as that, well almost. The gear I was machining was specified as 1" pitch diameter, therefore the long travel at 45 degrees would be equal to one times pi. Now pi is not a very nice number to try and factor into a nice ratio. I had several choices. I could machine a couple more change gears of the desired ratio for a one time use. I could change the helix angle slightly so the long travel would come out to a nice even number, or I could change the pitch diameter to make the long travel come out even. I chose the latter, as it only required changing the pitch diameter by a few thousandths of an inch. (I cannot remember for sure, but it was about .015") The housing holding the gears had not been made and so when I got to that part it was only a matter of spacing the center distance of the gears a few thousandths different than what the drawing specified.

The mill head was tilted to get the cutter in the same plane as the helix. I used a hand ground one tooth cutter for this job. The big work holding spindle drive gear had a multiple number of teeth of the blank I was working on. One grove was cut, Then the gear train carefully loosened and the big gear turned the proper number of teeth and re-engaged, and the next grove cut, and so on.

The last picture shows the gears after I finished cutting all the teeth. The gears were installed in the gun and it functions beautifully.

Now I have the means to pursue one of those little side shaft engines that I have wished for, for so many years.
Give it a try, you might surprise the heck out of yourself what you can do.
Birk

 

[Powder keg]

Birk, If I learn as much as you've forgot, I think I'll be doing good:O) Thanks so much for sharing with us.

Wes

 

[mklotz]

Birk wrote, "Now pi is not a very nice number to try and factor into a nice ratio."

pi~=355/113 with an error of only 0.002% (22/7 is in error by 0.9%)

If you have to use a calculator that has no pi key, the ratio above will get you close enough for any practical application.

My mnemonic for remembering the ratio is to write each of the odd integers down twice, e.g. 113355, then split that down the middle into two three digit numbers, 113 and 355. Now, if you can't decide which of those numbers to divide into the other to approximate pi, you have no business doing math.

 

[Mcgyver]

nice work Birk

 

[BobWarfield]

Birk wrote, "Now pi is not a very nice number to try and factor into a nice ratio."

pi~=355/113 with an error of only 0.002% (22/7 is in error by 0.9%)

If you have to use a calculator that has no pi key, the ratio above will get you close enough for any practical application.

My mnemonic for remembering the ratio is to write each of the odd integers down twice, e.g. 113355, then split that down the middle into two three digit numbers, 113 and 355. Now, if you can't decide which of those numbers to divide into the other to approximate pi, you have no business doing math.

3.1415927

There, now that wasn't so bad, was it? One more digit than a phone number, but one less than a social security number. It has only 17% of the error of 355/113, and if you can remember to write down odd integers twice and split them in the middle, you can certainly memorize an 8 digit number. I'll bet you already new almost half those digits, so an extra 4 or 5 isn't going to kill you, right?

I'll give a hint: the optimal way to memorize anything is through repetition. That we all knew. But, it turns out the timing of the repetitions also matters. Oddly, it helps if repetition matches our units of time. That shouldn't be surprising, we run on rhythms. Even my schnauzer knows what day of the week it is (I'll explain if you insist).

So how do we apply time to repetition and memory?

Simply:

- Repeat once a minute for an hour.
- Repeat once an hour for a day (waking hours only!).
- Repeat once a day for a week.
- Repeat once a week for a month.
- Repeat once a month for a year.

This works for memorizing pi, and for more complex things, like rehearsing a song for your garage band. You probably can't quite play it every minute of the hour, but play it as many times as you can in the first hour, then once an hour. You'll be amazed at how well this works.

Amazing thing, the human mind. Use it or lose it!

Cheers,

BW

 

[mklotz]

Or you can do a lot of orbital mechanics math programming. I wish sometimes that I could forget

pi = 3.1415926535898

and

e=2.718281828045049

(both done from memory)

Remember, Bob, that Birk was looking for a ratio that would approximate pi. Remembering the number is a good thing to do but finding a ratio that approximates it with some known precision is a subject for extended division.

 

[cfellows]

Birk,

I love your helical gear cutting attachment. I've spent many, many hours thinking about different attachments that would work on the milling machine. I've never built one, however, since I've never really had a need for any helical gears.

I would like to be able to make 30 / 60 degree helical gears for a sideshaft engine some day. I think, using the 30 / 60 degree angles on the teeth would give me a 2:1 ratio with the two gears being the same pitch diameter. Isn't that correct?

Chuck

 

[Oldmechthings]

Chuck
That sounds right to me. My gears have a 2 to 1 ratio. However one is twice the size of the other. The machinery hand book has a whole section on helical gears. There are all sorts of things that you can do with them. Enough to boggle one's mind.
Birk
Oh, I plan to post a picture showing the machining of some cams using the same helical fixture tomorrow.

 

[compound driver 2]

Hi Birk
I was at Ali Pali in London for the model engineering show a few weeks back. THEre was a chap with a Gatteling gun built in Stainles steel and brass Looked to be about 9 inch to the foot or there abouts. Superb model and I would imagine built from the same drawings you used. Do you have any pictures? Would love to see your model.

Cheers Kevin

 

[bhjones]

I can wrap my head around how this rotates the gear. What I'm unclear on is if the mill spindle is rotating the cutter or if the cutter is fix in it's position.

Which is it?

Does anyone know of an online video of this type of cut being made?

Thanks.

 

[Oldmechthings]

bhjones
The one tooth cutter is spinning around just like you were cutting a straight spur gear, only at an angle, (the helix angle) and then the gear blank rotates slowly as it passes the cutter, producing the helical teeth.
Take a drill bit and hold it lightly between your thumb and finger, then with your other hand, push the drill long ways through your fingers, and as you do the drill will rotate. That is the same kind of action that is happening when doing helical milling.
Hope that clears it up for you.
Birk

 

[bhjones]

Thanks Birk.

The angle of the head/cutter was confusing me. In your other post regarding helical cutting it all made sense with the cutter 90 degrees to the mill table, but while I was trying to envision the operation with the cutter at that angle it seemed like the cutter would cut more material that what it in fact does.

 

[cfellows]

I found a video of cutting a helical gear using a single point overhead cutter to cut a helical gear in brass. Does anyone have any experience using this method? Any sense of how well that would work? The cutter just looks like a d-bit with a gear tooth profile.

[ame=http://www.youtube.com/watch?v=fps0OR1eF_s]http://www.youtube.com/watch?v=fps0OR1eF_s[/ame]

Chuck

 

[bhjones]

Thanks Chuck.

Is this your setup?

That rocking table/work bench makes me nervous.

 

[gilessim]

Here's a pic of a tuning peg for a double bass I made some years ago,we made some spares!, I did the turning and my friend cut the gears with a setup similar to Birk's but made from the "gearbox" from an old lathe, I never completely understood how he got it to work! but it did!, unfortunately he's now gone CNC, for me ,he might just as well have moved to China! (JJ!)

Giles

 

[cfellows]

Thanks Chuck.

Is this your setup?

That rocking table/work bench makes me nervous.

Nope, not mine. I think the rocking motion is in the camera mount, not the machine...

Chuck