PDA

View Full Version : Involute gear tooth template



SMurray
12-21-2006, 12:10 AM
Is there such a thing as an involute gear tooth template (guage?). I just purchased a shaper and want to be able to grind a single point cutter to be able to cut gears for different projects I have in mind. I don't have gears to match up the cutter to so am looking to find a template-guage to use. Anybody know of a company or supplier for such a beast? TIA for your response.

Forrest Addy
12-21-2006, 12:40 AM
No, not really. The involute is a generated form that varies with tooth count, pressure angle, and pitch. The trick is to see your tool's profile and tune it to suit the closest approximation to the actual infolute form. OPtical enlargement of the tool is a good starting point. An overlay of the desired form accurately drawn 10 to 20 times the size of the tool is the next step. An older drawing text will give you directions for drawing a true involute from starting data.

If an optical comparator is unavailble, you can extemporize one from a 35MM slide projector and a screen on which you've attached a scaled up involute. Or you can use a pawn shop enlarger or anything with a suitable lens. There's ways if you really want to mess with it.

A formed involute has to be very accurately made if it's to run quietly at any speed. Generated involutes from hobs, reciprocating rack sections, Fellowes Cutters, and the like are far more accurate but tha's a long way from your question. There are also several geometric approximations like Grant's Odontograph where radii are swung from construction circles. There are others which may be found in older handbooks dealing with foundry practice.

Many shaper hands use formed gear tooth space milling cutters postioned to present a single tooth to the work in a shaper clapper box. When one tooth dulls it's indexed to the next.

It's possible to cut pretty good gears in a shaper but you have to jump through some hoops if they are to run smoothly.

Tinkerer
12-21-2006, 03:18 AM
This may work for what you need Gear Tooth Pitch Gauges (http://www.mcmaster.com/ctlg/DisplCtlgPage.asp?ReqTyp=CATALOG&CtlgPgNbr=2106&term=Gear+Tooth+Gauges&sesnextrep=636211299025957&ScreenWidth=800&McMMainWidth=593). Look near the bottom of the page.

So what kind of shaper do you have?

JCHannum
12-21-2006, 06:36 AM
Forrest's answer, no, is correct. The stick type gear templates can only be used to duplicate a cutter for rack gears only. For proper tooth form, a series of cutters is needed to accomodate various tooth counts. Eight different cutters are typically needed.

The cutter profile can be generated by using the two disc method described in Ivan Law's book, Gears and Gear Cutting. It is also described in this article by John Stevenson;

http://www.metalwebnews.com/howto/gear/gear1.html

The procedures involve making cutters for use with a milling machine, but are easily adapted to making single point cutters for use in a shaper.

Evan
12-21-2006, 06:42 AM
You can generate templates programmatically.

See here: http://hobbing.com/

You can also download the free version of Allycad. It will generate spur gears.

http://www.allycad.com/

Example:

http://vts.bc.ca/pics/20t145.gif

Weston Bye
12-21-2006, 07:23 AM
...use a pawn shop enlarger or anything with a suitable lens.

The germ of an idea. Been wondering about what to do with that unused enlarger I have been hanging on to. Thanks, Forrest.

SGW
12-21-2006, 08:02 AM
It is possible to generate the involute tooth form on a shaper, using a rack-shaped cutter (straight sides). The approach is more or less as described here http://homepage.ntlworld.com/peter_harrison/workshop/gearcutting/index.htm

It would take quite a while, but it would be do-able.

Al Messer
12-21-2006, 10:23 AM
At one time, Boston Gear Co. published the profiles of several different tooth forms for identification purposes. You laid the gear in question on the profiles and were able to identify the pitch. If you can find an old catalogue with these shapes illustrated, perhaps this can form your template.

Dick Plasencia
12-21-2006, 10:33 AM
I do exactly what Al Messer suggests. I have a Boston Gear catalog showing gear tooth profiles. I copy the desired gear with my scanner and compare the outline to the tool as I grind it to shape. I can also enlarge the tool image to better see the contour. I neither have the finances or room for every involute gear cutter so this method works best for me.

Evan
12-21-2006, 10:36 AM
If you register at Boston Gear (free) you can download cad 2D and 3D drawings of thier products.

http://www.bostongear.com/

SMurray
12-23-2006, 03:26 PM
Thanks for all the great responses. I was away from the computer for a bit while I went down to Montana to pick up my new-to-me Ammco shaper. Didn't expect it to arrive this soon but was pleasantly surprised when it did. Now all I need to do is get it cleaned up and serviced to start making chips. Getting this shaper was one of the reasons I asked about a template/guage for gears. I am going to need to make some cutting bits to make gears for some projects I have in mind. Thanks again for all your help.

Tin Falcon
12-23-2006, 04:27 PM
Marv has a program on his site that may help
http://www.myvirtualnetwork.com/mklotz/
it is called cutters it is designed to design gear cutters.
Tin

lazlo
12-23-2006, 05:28 PM
Marv has a program on his site that may help it is called cutters it is designed to design gear cutters.

The program on Marv's site (by Joe Smit of South Africa) has a lot of potential, but it makes a vague reference to an article published in Model Engineering Workshop Nuber 41, April 1997.

I typed in a 14.5, 16 DP gear, and it gave me the correct gear blank diameter, tooth depth, et al, but it gives "pin diameter" and "pin centre" -- which apparently is reference to a table in the MEW article.

I'm guessing the pins centers and radii are the radius of the involute form.

Anyone have this article?

Paul Alciatore
12-23-2006, 09:46 PM
I believe I have read the Model Engineering article and I have it on my home computer. Unfortunately, I am out of town and can not access it now. But, if it's what I am thinking of, the idea goes something like this:

An involute can be approximated by a circular segment of the appropriate diameter. So a tool for cutting a gear tooth cutter can be made by placing two disks of tool steel an appropriate distance apart on a support with a notch cut between the disks. This tool is used to form the milling cutter.

I know that a close approximation can be had in this manner, but it will not be 100% accurate and small errors in the gear shape can cause noise, etc.

I suspect that Marv's program calculates the diameters and spacing of these disks on the tool.

Frankly, I do not trust any of the approximate methods, including grinding the tool to a template. Can you see tenths? I sure can't.

franco
12-24-2006, 12:05 AM
Lazlo,

I still have a copy of the MEW article - 4 pages. If you want a copy PM me with an e-mail address and I will scan it for you.

franco

J Tiers
12-24-2006, 01:08 AM
Frankly, I do not trust any of the approximate methods, including grinding the tool to a template. Can you see tenths? I sure can't.


Yep..... put a light behind....... you can see 'fit" or "not fit", but not "how much of not fit" you have. No calibration, just go-no-go.

JCHannum
12-24-2006, 07:53 AM
The program on Marv's site (by Joe Smit of South Africa) has a lot of potential, but it makes a vague reference to an article published in Model Engineering Workshop Nuber 41, April 1997.

I typed in a 14.5, 16 DP gear, and it gave me the correct gear blank diameter, tooth depth, et al, but it gives "pin diameter" and "pin centre" -- which apparently is reference to a table in the MEW article.

I'm guessing the pins centers and radii are the radius of the involute form.

Anyone have this article?

The method is also described in the write up by John Stevenson, I mentioned previously; http://www.metalwebnews.com/howto/gear/gear1.html

It does not have a table for 14-12*, and neither does Ivan Law's book for some reason, but the procedure is spelled out in both. Using the dimensions from Marv's program will give the necessary information.

It is also possible to make a non standard cutter by this method that will serve to make a pair of gears that might not be accomodated by the standard range of involute cutters. They might not have perfect form, but will suffice in many cases.

Nick Carter
12-24-2006, 04:02 PM
I should have an article in the next issue of "Digital Machinist" that shows how to draw gears in CAD (and the technique can be used with pencil and paper as well) from first principles.
No idea when it's coming out though.
The principle can be easily used to make toolbit templates for a shaper.

It's fun to be able to make gears without special tooling, but a set of proper gear cutters is still pretty quick and easy.

On a shaper you can make a toolbit that looks like a rack and use the same approximate hobbing method that some use on their mills.

Evan
12-24-2006, 04:17 PM
Here is a web page that shows in detail how to draw an involute tooth shape correctly using a method called Unwin's Construction. It produces a very close approximation to the correct shape.

http://www.ul.ie/~nolk/gears.htm#To%20construct%20a%20gear%20profile%20us ing%20Unwins

lazlo
12-24-2006, 04:25 PM
I'm guessing the pins centers and radii are the radius of the involute form.

I suspect that Marv's program calculates the diameters and spacing of these disks on the tool.

Yep, that's what I meant.


Frankly, I do not trust any of the approximate methods, including grinding the tool to a template. Can you see tenths? I sure can't.

Good point.

Considering the trouble of making a form cutter and the cost of a complete involute cutter set for each DP diameter, it seems a lot more cost effective to build a hobber like Steve's stepper-controlled gearbox (very slick!).

John Stevenson
12-29-2006, 11:43 AM
Quote: Originally Posted by Paul Alciatore
Frankly, I do not trust any of the approximate methods, including grinding the tool to a template. Can you see tenths? I sure can't.




Good point.

Considering the trouble of making a form cutter and the cost of a complete involute cutter set for each DP diameter, it seems a lot more cost effective to build a hobber like Steve's stepper-controlled gearbox (very slick!).



Working to tenths doesn't apply when using form cutters. Take say a Number 5 cutter which is for 21 to 25 teeth, a span of only 5 teeth but the geometry is only accurate for the 21 tooth gear.
If you cut the 25 tooth gear with this cutter as you are expected to do then the true differences will be a lot more than a few tenths out.

This is the problem with form cutters, by rights you need one per tooth count but manufacturing costs prohibit this and that is why there are 1/2 steps available in the range of cutters making 16 to the set instead of the standard 8.

.

lazlo
12-30-2006, 11:05 AM
John,

This brings up two gear questions that have been bugging me -- did the non-premium lathe manufacturers (South Bend, Clausing, Myford, Rockford, Logan, ...) use involute gear cutters to manufacture the change gears, or were they hobbed?

In other words, if you replace a change gear on your lathe with one made from an involute cutter (where, like you say, the tooth form is only accurate for the lowest tooth pitch in the range), are you making a gear "worse" than the one the lathe manufacturer made?

Also, the various gear cutter manufacturers (Brown and Sharpe, UTD, Niagara,...) use different addendum and dedendum on their cutters. Does this make a lot of difference when piecing together an involute cutter set of a certain diametral pitch?

In other words, if you're replacing gears on your lathe, are you better off just buying the gear from Boston Gear, SPI, SDP, or is a gear cut with an involute cutter just as good as the standard part from South Bend, Clausing et al?

Thanks,

Robert

lazlo
12-30-2006, 11:09 AM
By the way, to explain my "premium lathes" comment -- Hardinge advertizes that their change gears are "precision hobbed" and hardened and finish-ground from tool steel.

lazlo
12-30-2006, 11:19 AM
The method is also described in the write up by John Stevenson, I mentioned previously

It does not have a table for 14-12*, and neither does Ivan Law's book for some reason, but the procedure is spelled out in both.

Ivan Law's book doesn't have the 14 1/2 table, and the 20 table is incomplete -- it only goes up to the number 6 cutter (??)


Using the dimensions from Marv's program will give the necessary information.

The pin diameters and centers in Ivan's book don't match the data in Joe Smit's program (the one on Marv's page), which is just spitting-out the table from Don Unwin's MEW article. Joe's program is a DOS Visual Basic Script. I just made an Excel spreadsheet with the data from Don's article, which is a lot more convenient.

John Stevenson's article has the same pin centers from Don Unwin's article.

I'm actually curious if anyone has successfully made an involute cutter from Ivan's table -- I'm wondering if those numbers are off...

John Stevenson
01-01-2007, 07:49 AM
Lazo,
Answers to a few questions in no order.
Change wheels even on the cheaper machines would have been hobbed or shaped on a hobber or something like a Sunderland or fellows shaper due to speed.
Using form cutters is very time consuming and is usually only a tool room operation or very short run.

Technically different cutters should cut the same profile but the inaccuracies are very small and as gears have to run with backlash then the backlash is probably greater then the errors.

Ivan's tables and the others all work but in different ways that's not immediately obvious [ it had me going at first ].
First off the my calculations were made using information from an old book containing various formulae by a guy called Grant who do a lot of work on the involute curve as did Buckingham. I presume that given the closeness of the figures Joe and Unwin did the same.
I do have a 14-1/2 degree chart that I have previously posted, I'll sort the link out.

Not sure where Ivan got his calculations from but the main difference is in how the pins are setup to the blank.
Never seen Joe's work so can't comment but in mine and Dave Unwins the tool is centered with the buttons touching a blank of known thickness, THEN the infeed is applied.

In Ivan's book the buttons are touched on the OD of the cutter blank THEN moved over to be central and then the infeed is applied.

This difference in where the cutter starts makes the difference in the tables.
Mine and Dave's start cutting immediately as they are touching the blank, Ivan's cuts air until it reaches the side of the blank.

Not really a big deal once you spot the difference.

I have never cut a gear using Ivan's method but when I was working this out I did draw his setup out for a given gear, then superimposed mine over the top then superimposed a geometrically correct gear on top of this, The differences were very very tiny and it's hard to say who's was better given that they change from number to number.

So really the answer is stick to just one set of tables, no matter who's, and all will be OK.

.

Spin Doctor
01-01-2007, 08:26 AM
In other words, if you replace a change gear on your lathe with one made from an involute cutter (where, like you say, the tooth form is only accurate for the lowest tooth pitch in the range), are you making a gear "worse" than the one the lathe manufacturer made?Robert

The Addendum and Deddendum should be set as a ratio of a 1DP gear tooth. The Addendum is 1/DP and the Deddendum is 1.25/DP IIRC (idon't have the handbook right in front of me). Any addition depth is that built in by the manufacture for tooth clearance and fillets at the bottom of the tooth form. Any hob has the information on it as type, DP, Pressure Angle and Depth to Finish (DtF). I've used hobs made by various manufacturers and never had a problem with gears not meshing properly because of that. Just don't get me started on the problems of dealing with Bastard Gears (gears with non-standard pitch diameters used in special situations), Stub Tooth Gears in all of their various forms (we used Fellows Stub Tooths a lot), Helical Gears and trying to figure out the index and feed gears that would work given the gears on hand (the Pitch Diameter of a Helical is Number of Teeth/Diametral Pitch x Cosine of the Lead Angle of the helix).

The Tooth form is a mathematical model of the rack tooth form wrapped around an axis. The involute tooth form by a hob is not perfect. But it comes a lot closer than trying to use an involute cutter and a dividing head. And the finer the feed rate on the hob cutter head the smaller the flat spots will be to the teeth. A gear shaper poduces a nicer gear but for one or two gears they are a lot more trouble to set up (the trouble is in the work piece not the machine). Plus with a shaper if time is not a major constraint then you can always let the machine make two or three revolutions of the work piece to shave off the high spots. Most of the gears we made were for the repair of gear trains in multiple spindle gear heads. Sometimes they would be made up in advance for jobs slated for a major repair or they would be done as a hurry up job to get the unit back into production.

lazlo
01-01-2007, 11:55 AM
John,

First, many thanks for the extremely detailed reply!! You're the gear master! :D


Change wheels even on the cheaper machines would have been hobbed

OK, that's an important tidbit. As you can probably tell, my questions aren't arbitrary -- I have a 32T (16 DP) changewheel on my Clausing that a little chewed up. The replacements through McMaster or Martin are inexpensive, but I'd love to make my own...

My concern is that 32T falls on the tail-end of a number 4 cutter, so the resulting tooth error would be pretty large.


Not sure where Ivan got his calculations from but the main difference is in how the pins are setup to the blank.
...
but in mine and Dave Unwins the tool is centered with the buttons touching a blank of known thickness, THEN the infeed is applied.

In Ivan's book the buttons are touched on the OD of the cutter blank THEN moved over to be central and then the infeed is applied.

Ah! That explains a lot!

If I get a copy of Grant's book, would I be able to derive the pin diameters for a specific tooth count? The pin center technique would be a lot more useful to me if I could generate the correct pin centers for a 32T gear.

I'm also wondering if my time would be better spent building the divider circuit on your electronic hobber...

lazlo
01-01-2007, 12:04 PM
The Addendum is 1/DP and the Deddendum is 1.25/DP IIRC (idon't have the handbook right in front of me). Any addition depth is that built in by the manufacture for tooth clearance and fillets at the bottom of the tooth form.

Right, but the problem is that the involute cutters from Brown and Sharpe, Morse, UTD,... all have different Addendum and Deddendums for a particular pitch range. In other words, the manufacturers chose difference clearances. So if you're piecing together involute cutters from Ebay (like manyof us do), you've got addendums and deddendums all over the place. John's response is that the clearances are small compared to the inherent backlash anyway, but it makes you wonder as you get to to the ends of the involute cutter range, where your errors are piling up already...


The involute tooth form by a hob is not perfect. But it comes a lot closer than trying to use an involute cutter and a dividing head. And the finer the feed rate on the hob cutter head the smaller the flat spots will be to the teeth.

Huh, I didn't know that -- I thought a hob produced a perfect involute (limited by the machinery, of course).

J Tiers
01-01-2007, 04:52 PM
It should be close...... limited by the size of the "facets" produced by a finite number of teeth..... A problem true of shapers, or any other method, but the hob has some problems due to the lockup between blank and tool.

The hob "generates" the shape, having itself the shape of a rack. But by spinning in lock-step with the blank, it may fail to clean up everything.

Essentially it produces a perfect shape, but only through a set of points on the various facets.

A hob that is not helical, where spinning and feed movement are not connected might do better. You could spin it fast and feed it slow.... it would be like a reciprocating gear shaper.

There is NO PROCESS that generates perfect teeth....... ALL fall short of perfect.

John Stevenson
01-01-2007, 07:29 PM
John,

I have a 32T (16 DP) changewheel on my Clausing that a little chewed up. The replacements through McMaster or Martin are inexpensive, but I'd love to make my own...

My concern is that 32T falls on the tail-end of a number 4 cutter, so the resulting tooth error would be pretty large.

If I get a copy of Grant's book, would I be able to derive the pin diameters for a specific tooth count? The pin center technique would be a lot more useful to me if I could generate the correct pin centers for a 32T gear.



So for a Clausing these are 14-1/2 PA and not 20, not played with the program on Marv's page but I'll look tomorrow, 1:30 am here.
If that doesn't do the correct buttons and pin centres then I'll work a set out for you but to be honest you are worrying too much and off the shelf cutters will work fine.

.

lazlo
01-01-2007, 08:26 PM
So for a Clausing these are 14-1/2 PA and not 20

Right -- 16DP, 14 1/2 PA. 32 teeth, in this case, but I'd also like to cutting a 127-tooth gear ;)


not played with the program on Marv's page but I'll look tomorrow

The program on Marv's page just prints out the table from Don Unwin's MEW article. So if you enter any number of teeth between 35 and 54, for example, you get the same Pin Diameter (13.77 inches). By the way John, you might be amused that Joe Smit (the guy who wrote the DOS program) references your Metalweb article in his readme file :)


If that doesn't do the correct buttons and pin centres then I'll work a set out for you

No, no -- please don't. I was just interested in writing a program that calculated the actual pin diameter for a given number of teeth, hoping to reduce the compounding of errors from the involute cutter range plus the pin diameter approximation (plus my limited skills as a hobby machinist :) ).

I mentioned earlier that I made an Excel spreadsheet with the data from the MEW article. The changes in pin diameter are (not surprisingly) nonlinear, but it looks like I can do a b-spline interpolation for a cutter with an exact number of teeth without understanding all the involute curve trigonometry.


to be honest you are worrying too much and off the shelf cutters will work fine.

Guilty as charged -- I have a tendency to do that :o I haven't been able to find a number 4, 16 DP cutter yet, and I figure I can build the Ivan Law/Don Unwin/John Stevenson button tool in an afternoon...

John Stevenson
01-02-2007, 03:19 AM
The program on Marv's page just prints out the table from Don Unwin's MEW article. So if you enter any number of teeth between 35 and 54, for example, you get the same Pin Diameter (13.77 inches). By the way John, you might be amused that Joe Smit (the guy who wrote the DOS program) references your Metalweb article in his readme file :)



Had a look at the program and fed in the required numbers but I got 13.9065mm out and not 13.77 in.
If this does use Don Unwin's tables where does he get the 14.5 angles from ?

The tables I did ages ago for 14.5 are posted here http://homepage.ntlworld.com/stevenson.engineers/lsteve/hidden/14.5degree.jpg

Using these figures for 35 teeth at 16DP I get
Button Centres Feed Width
15.05 16.98 5.03 6.35 his table gets
13.91 15.12 5.05 6.35

Be interesting to draw these out and compare to a geometrically correct tooth shape.

.

lazlo
01-02-2007, 12:49 PM
Had a look at the program and fed in the required numbers but I got 13.9065mm out and not 13.77 in.Right, Don Unwin's tables in MEW are in inches, and Joe converted the figures to millimeters in his program.

The 13.77 inch number is Don's table for 1 DP. For any tooth range between 55 and 134, Joe's program will give you the same value: 348.758 mm, or 13.77 in.

For 16 DP, Joe's program will give you 13.9065mm for any number of teeth between 35 and 54.


If this does use Don Unwin's tables where does he get the 14.5 angles from ? Don Unwin's article does have the complete (cutter 1 - 9) 14.5 pitch angle tables, as well as the 20 and 30 tables.


Be interesting to draw these out and compare to a geometrically correct tooth shape.

I'm curious too. I'll print out the chart of my Excel spreadsheet of Don's pin diameters for 14.5, 20, and 30 across the various tooth ranges -- it's pretty interesting.

lazlo
01-02-2007, 12:57 PM
The tables I did ages ago for 14.5 are posted here http://homepage.ntlworld.com/stevenson.engineers/lsteve/hidden/14.5degree.jpg

Using these figures for 35 teeth at 16DP I get
Button Centres Feed Width
15.05 16.98 5.03 6.35 his table gets
13.91 15.12 5.05 6.35


Oh, that's very interesting John -- I thought you had the same tables/derivation as Don Unwin!
Do you have a table for the 20 PA? Does it match either Ivan Law's pin diameters or Don Unwins, or do you have a third derivation?

J Tiers
01-02-2007, 04:11 PM
As far as the original question......

it seems that one SHOULD be able to generate an involute form as a drawing, for any given tooth count (or tooth count range). Then a form cutter or a fit gage could be made from that with a pantograph setup.

But, I'll bet that an actual gear tooth is really a bit different from the involute form.....

For one thing, the area below the pitch line is basically a clearance, with no contacting surfaces.

Then also, since the cutter (non-generating machine) covers a range, the involute form can't be right for all tooth counts, so some "fiddle factor" is probably in there to adjust for "best overall operation".

I know that mating a "form cutter gear" to "generated" gears (hobbed, most likely) isn't necessarily going to give quiet gears..... even when the depth is carefully adhered to.... They seem to turn out noisier than hobbed gears, which would be noisier than shaped gears, which would be noisier than shaved gears...... which are noisier than "perfect" gears..... I have not tried the round button for making a formed cutter.

The question is what is the 'fiddle factor" applied to the basic generated involute to get a "range type" form cutter?

And, what is done for the low tooth counts because the "clearance" can't have an undercut.... do they just clear out the area "over" the "undercut"?

With a few pieces of info one could make any formed cutter wanted..... almost on demand.

Naturally with a set of large DP gear cutters, and a suitable pantograph, a drawing/gage for any other DP could be made.....

Of course having a relieving attachment would help in either case!

John Stevenson
01-02-2007, 05:43 PM
The tables I did ages ago for 14.5 are posted here http://homepage.ntlworld.com/stevenson.engineers/lsteve/hidden/14.5degree.jpg

Using these figures for 35 teeth at 16DP I get
Button Centres Feed Width
15.05 16.98 5.03 6.35 his table gets
13.91 15.12 5.05 6.35

Be interesting to draw these out and compare to a geometrically correct tooth shape.

.
Well something weird here.
Drew the three profiles out, GCG in black [ centre ] my table setting for above on the left in red and the Don / Joe table settings on the right in green.

http://homepage.ntlworld.com/stevenson.engineers/lsteve/files/35T_16DP.BMP

The green one from Don's tables are way out and a quick check on the others figures shows the same. Even by altering the infeed you can't get the green cutter to match up with the black tooth space.

Most errors show up on gears when the tooth count is small so I'm just doing one now for 12 teeth in 16DP and 14.5 PA.
This should show up better.

.

John Stevenson
01-02-2007, 07:07 PM
Lazlo,
I think you should disregard the 14.5 degree files from the Unwin article or at least Joe's program [ need to check the two out together ]

Something seriously wrong.
Here's the pic of a 12 tooth gear, again in 16DP and 14.5 pressure angle, bit cluttered but can't get it better. Note the undercutting like a mangle wheel.

http://homepage.ntlworld.com/stevenson.engineers/lsteve/files/12T_16DP.BMP

Again black is the GC gear, Green is the Joe's gear, note how the infeed with small buttons gives the nearly correct clearance slot at the expense of a wrong radius.

The red cutter is from my tables and although the radius is correct the dedendium is too thin and won't clear hence the extra chart for a slitting cutter, shown in blue to give a better approximation of the shape.
Bear in mind that this pic is about 40 times bigger than the actual tooth so these errors seen will be very small.

.

LES A W HARRIS
01-02-2007, 11:16 PM
APPROXIMATE INVOLUTE CURVE:

There is yet another way; you need to be able to turn accurate radii.
Take three precise calculated points on the Involute curve.
The OD, The PD, and The Root Dia, or in cases where the root dia is
Smaller than the Base Dia, Use the Base dia as the 3rd point.
An arc passing through these points are correct at those points.

This radius between the base or root dia & the PD is too large resulting
In the form being too flat or minus flank, in your case by about .0003?.
This radius between the PD & the OD is too small, resulting in a slight hump
From correct position, or plus upper flank a tad over .0005? in your case, on an involute tester, which no HSMer will be fortunate enough to possess, a correct involute would be a Straight line, this method would (does, ran many gears this way) produce An elongated ?S?, reversed on the other side. The deviations are in most cases within the Tolerance Band for Class 8 gears, which would encompass lathe change gears.

Using the Vogel equations, the tooth space is oriented to the 12:00 O-Clock,
Or 90 deg position, normal for Form Gear grinders, a set of 10 points from the Base Dia or Root Dia to the OD is calculated by putting the equations in a spread sheet, Zap, Done. Anyone with n/c could spline them for a really good job. Next Cadd the Gear & Single tooth cutter, extracting required dimensions.

Make cutter with required relief, Harden, carefully radialy grind the face of the cutter, mount at .05?-.075? offset in boring head, tighten gib, cut teeth.

Here is your 35T16DP14p5PA gear and cutter data.
Spreadsheet input & output of points, gear & cutter, cutter with dimensions.
http://i37.photobucket.com/albums/e97/CURVIC9/07%20SHOPSTUFF/collage3.jpg

Gear.
http://i37.photobucket.com/albums/e97/CURVIC9/07%20SHOPSTUFF/32t16dp14p5pa07.jpg

The single toothed cutter. (Hardened Drill rod,)
http://i37.photobucket.com/albums/e97/CURVIC9/07%20SHOPSTUFF/32t16dp14paLandRcutter01.jpg