Gear cutting with forms

[dp]

I have Ivan Law's book on gears and have also seen John Stevenson's first article on using forms to make gear cutters. I haven't seen the math to create forms for other pressure angles. Anyone know? Here's a link to Sir Sudspumpwater's page: http://www.metalwebnews.com/howto/gear/gear1.html

[LES A W HARRIS]

Forms for gearcutters.

I have Ivan Law's book on gears and have also seen John Stevenson's first article on using forms to make gear cutters. I haven't seen the math to create forms for other pressure angles. Anyone know? Here's a link to Sir Sudspumpwater's page: http://www.metalwebnews.com/howto/gear/gear1.html

DP,
In the Brown & Sharp Tretise, the layout is shown, which is an approxamation, and of course is, as of that time period 1890's, revised 1905? 14.50° PA. The radius was struck from the base dia, passing through the pitch dia being (1/4, 3/7ths) or some such.

As an old cog maker ground a lot of gears with a radius approximation dresser, which used 3 points calculated for the actual tooth thickness, form comes out as an elongated 'S' on the involute, real close on 30 plus teeth, as number of teeth decrease error may get up to a thousandth.

Single tooth Flycutter type can also be made like this; use a radius attachment to get a good radius:








Will dig out B&S Treatise, see if I can get you what you are asking.
Cheers,

[loose nut]

Don't forget that the arbor must be off set from the center of the cutter so there is relief, see Ivan laws book for the correct amount.

[oldtiffie]

Forms

I have Ivan Law's book on gears and have also seen John Stevenson's first article on using forms to make gear cutters. I haven't seen the math to create forms for other pressure angles. Anyone know? Here's a link to Sir Sudspumpwater's page: http://www.metalwebnews.com/howto/gear/gear1.html

Dennis.

The answer may well be in using Ivan Law's explantion of the involute form and pressure angle (pages 24>28 inclusive) and constructing it in CAD and then over-lay a range of "forms" that meet your required "best fit" and then make those "forms".

[John Stevenson]

Dennis,
I have the tables for 14.5 degrees I'll email them if you want them.
The lower numbers of teeth have to be cut with a slitting saw to overcome interference at 14.5 degrees.



In this pic a 14.5 PA gear is drawn in black, note the bulge below the pitch line making it impossible to cut with a rotating cutter, shown in red.
If the bottom is trimmed out using a slitting saw, shown in blue either before of after the red cutter this will get the best fit without using a generating method such as hobbing.

the lower the number of teeth the worse this becomes. I believe the figure is under 30 teeth for 14.5 PA and 18 for 20 degrees PA which is why 20 has superseded 14.5 PA.

.

[lazlo]

Dennis,
I have the tables for 14.5 degrees I'll email them if you want them.

John, the 14.5° tables are in Ivan's book.

Dennis, if I may be so presumptuous, Les has a fabulous Excel spreadsheet that IIRC calculates the correct pin size and spacing for any pitch angle.

[dp]

Dennis.

The answer may well be in using Ivan Law's explantion of the involute form and pressure angle (pages 24>28 inclusive) and constructing it in CAD and then over-lay a range of "forms" that meet your required "best fit" and then make those "forms".

That's what I decided, too, Tiffie - I'm going to try it in Rhino and see how it goes. I have (fragile) metric change gears so want to build a limited set of cutters and see how they work out. The replacement gears I've been buying from Grizzly don't last any longer than the originals.

[dp]

John, the 14.5° tables are in Ivan's book.

Dennis, if I may be so presumptuous, Les has a fabulous Excel spreadsheet that IIRC calculates the correct pin size and spacing for any pitch angle.

Thanks, John and Lazlo - the good news is my lowest tooth count is 30T. My interest was to see if I could devise a cutter set that better fit my specific change gear set with fewer cutters than that defined in the B&S set. When I looked at the math to calculate a whole lot of involutes I figured there might be another way that someone has found and assists define the button cutters and spacing. The spreadsheet would be a good thing to look at.

[dp]

Will dig out B&S Treatise, see if I can get you what you are asking.
Cheers,

Thanks much, Les.

[oldtiffie]

Its in the book!!

Once again, I've heard about how something is "in the/a book" with only "they" having access to them which to me is a real PITA. I get a bit pi$$ed off about that. On this occasion I've compounded it and compromised my bloody self for doing it as well, so I thought I'd better remedy that situation and at least try and get myself out of a mess of my own making.

So here we go.

First of all, just to revise a little. Here is a rolling pair of meshing involute gears. The involute is "unwound" (see later) from the base line. The Pressure Angle is the line of contact along which the involutes pass.


Here are the pages from the book referred to. They are a great read and put it all in practical terms without the "assistance" of "academia's" "heavy hand". They should be "just right" for anyone to draw any involute at any pressure angle, with any addendum, dedendum, whole-full depth etc. etc. they like on pretty well any simple (or "better") CAD system.

That way they can explore involute gear profiles and the making of "forms" for them-selves.

Note that these are large files as I scanned them at 200 dpi for clarity. I have posted them as images instead of links so as to maintain continuity - my aplogies to those with "dial-up" access as I try to avoid this happening

[dp]

Once again, I've heard about how something is "in the/a book" with only "they" having access to them which to me is a real PITA. I get a bit pi$$ed off about that. On this occasion I've compounded it and compromised my bloody self for doing it as well, so I thought I'd better remedy that situation and at least try and get myself out of a mess of my own making.

Thanks, Tiffie - great animation. I have to admit when I first got the Ivan Law book I was amazed at the amount of information provided in that little tome. After examining the section on cutting cutters with buttons it occurred to me there may be adequate tabular data compiled somewhere for the button cutters that a person could use it to create nomograms to reveal interpolated data points for uncommon applications. That's so much easier than iterative calculations or cobbing up some transforms that, while getting you there, in many cases would not be useful

[oldtiffie]

Mes(s/h)ed-up

A lot of "gear-cutting" and "gear-cutters" is some-where between a "kludge" and a practical compromise.

Even accepting that, the one thing that does stand out is that which is seemingly assumed or presumed to be correct in that it is rarely mentioned or considered is that the form of the cutter and that the tooth is both centred and symmetrical. It may not be.

Even with "store-bought" gear-cutters there is scant attention paid to having the centre/axis of the cutter accurately intersecting the axis of the work.

In "shop-made" cutters, even if set correctly on the tool shank, there appears to be little consideration of assuring that the cutter profile axis/centre is both square to and intersects the axis of the job.

In these situations, even assuming squareness and symmetry, I find it difficult to see what practical use a gear caliper would be with "shop-made" gear-cutters ("forms") as "Machinery's Handbook" does not seem to address it.

The "touch the OD and wind the cutter in to the full depth" method (not necessarily with or without gear calipers), as used traditionally, works very well too.

The ultimate test is to "see how it runs" (in mesh with a matching gear at correct centre distances).

It is surprising how gears made this way "perform" so well.

[LES A W HARRIS]

Practical Treatise On Gearing.

DP,

For one who wishes to know how:

"Practcal Treatise on Gearing" by Brown & Sharp, can be obtained from Google Books Downloads, it explains how the numbers & half numbers came to be, you will have to do some work to arrive at 20° PA. sizes.

Enjoy! 3.3meg dowload in PDF.


http://books.google.com/books?id=jfd...27LYX6kgTYvKlL



Cheers,

[LES A W HARRIS]

Single tooth cutters.

Don't forget that the arbor must be off set from the center of the cutter so there is relief, see Ivan laws book for the correct amount.

Loose Nut,

the single tooth cutter shown, is set into the boring head, align cutter face with the offset, say 0.06" and lock the slide, it spins eccentric, thus providing clearance, it is sharpened radially maintaining form.














If you make it like this before hardening, you can climb or coventional cut, from the front or back as you prefer. Algining the required face in line to provide clearance.





Cheers,

[dp]

John, the 14.5° tables are in Ivan's book.

Dennis, if I may be so presumptuous, Les has a fabulous Excel spreadsheet that IIRC calculates the correct pin size and spacing for any pitch angle.

My copy of Ivan's book has only 20° and 30° tables. The 14.5° would be a nice addition to explore building some nomograms. The links that Les provided are some serious treatments of gear concepts. Great reading.