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Acurrate manually drawn involute gear tooth form

Acurrate manually drawn involute gear tooth form

Acurrate manually drawn involute gear tooth form

I'm actually a chemist by trade, but an inventor by night, I need to custom build my own equipment for a particular home project. What i need to know is how to acurrately draw and fabricate from standard stock 3/4 acrylic plate, a large annular involute gearset with a 6:1 reduction.The outer annular ring can be no larger than 17 in diameter. The problem I dont know how to solve is accurately drawing and cutting the invloute tooth profile. I am aquainted with most of the relevent principles and formulae for gear design, but it seems that no one does anyhting by hand any more-and I dont have access to Autocad to draw it for me.

RE: Acurrate manually drawn involute gear tooth form

where can I e-mail you? I might be able to help you with the first problem, how to draw it; but to machine the gear you do not need an accurate drawing - you need some cutting parameters...

RE: Acurrate manually drawn involute gear tooth form


the gear specs i have so far are as follows;

central gear
8 teeth, pitch diameter 2.5",diametral pitch 3.2",addendum .3125", dedendum .3906", tooth thickness .4908",25 deg pressure angle,outside diameter 3.125"

then there are 2 oposite gears to transfer the motion to the outside ring with the teeth on the inside, These gears are also not a problem.

So far, designing and drawing the outside ring has given me the most trouble.For the 48 teeth on the inside of the outer annular gear(pitch diametrer ~15") how do you calculate and draw a corresponding involute profile for a 25 deg pressure angle.

Fabrication tips would also be much appreciated, since i have no real gear fab. experience. However i am fairly familiar with milling mmachines, metal lathes, etc. What would be the best way to generate a gear from the 3/4 inch acrylic plate?

RE: Acurrate manually drawn involute gear tooth form

Just to be sure:
We are talking about a planetary gear set, where
sun (central gear) has 8 teeth (!!! Undercut !!!)
    3.2 Dia Pitch, 25 deg. Press. angle etc...
2 pinions, 20 teeth (as I calculated)
Annulus (or ring gear, external gear) with 48 teeth

RE: Acurrate manually drawn involute gear tooth form

you got it perfect man, but what to do with thosae pesky annulus teeth? How to draw annulus tooth profile, how to machine?

RE: Acurrate manually drawn involute gear tooth form

I did draw them for you, man.
I have a *.dxf file, (any CAD opens it)
*.dwg file, ACAD, (ACAD LT file)
and also a picture file (*.jpg) for you.
But I do not have your e-mail address, man!

The annulus is usually machined with a tool of the same shape as the tooth space, or with a "Fellows cutter" - cutting tool in the shape of the gear. In you case it can be problem, the teeth you designed are not very "standard". I'll try to find more info for you.

I also realized, that you calculated the tooth thickness without any backlash; you need some backlash (clearance between teeth - thinner teeth than theoretical 1/2 of the circular pitch).

RE: Acurrate manually drawn involute gear tooth form


Thank you very much for all your help,I really appreciate it.
you can email me at Tombel74@uwosh.edu
the gear calculations were really just a quick of the cuff guide to what i needed, so i didn't bother to mess with backlash or fillet shapes or undercut. Thanks again.   

RE: Acurrate manually drawn involute gear tooth form

If you have a better suggestion for tooth shapes or numbers, I would be glad to hear them.

As I said, I am an inventor who is capable of some mechanical engineering, and only because of all the math I took for chemistry in college, and of course Perry's handbook. The only firm requirements are that the ratio be 6:1 and the annulus od be no larger than 17".

Thanks for all your help.

RE: Acurrate manually drawn involute gear tooth form

Nobody yet seems to have addressed your problem of how to actually make the gears. If I were doing it, I would NC machine them using a small diameter milling cutter - say 5/16" diameter, provided your fillet radius is not too small. (I am lucky enough to have a Bridgeport E-Z track in my basement, although it would require at least two set ups because I only have 12" of cross travel). To actually generate the teeth using a Fellows rack-type shaper cutter or a hobbing cutter is well nigh impossible without gear cutting equipment - (and big equipment at that) - I suppose you could design and build something special, but that would be quite a project. Since this does not appear to be an application that requires great precision, generating them is probably not necessary. If you could make, or have someone make, a single tooth master template for each gear, you might be able to make the gears on a router table by hand, using one of those router cutters with a guide bearing on the end - you could locate the master in successive positions on the plastic sheet by using two pins and pre-drilling some mating holes. But whether an appropriate router cutter with a bearing is available in a 3/4" length I don't know.

RE: Acurrate manually drawn involute gear tooth form

I can not help you machine your gears for you however, reading the above information from the other sources, there are three important points not memtioned. First, the diametral pitch and pressure angle of meshing gears must match and their pitch circles must be tangent to each other. The base circles of all gears must be calculated in order to develop the involute files properly.              
If you can get your hands on Kent Mechanical Engineering" Design and Production" you will have all the formulae to figure out the base diameters,outside diameters, addendum, deddendum, root diameters, chordal thicknesses, etc...  

RE: Acurrate manually drawn involute gear tooth form

What is the most efficient method to reverse engineer a spur gear? It appears to be a custom gear as I can't match any numbers to existing standard gears.
  It's 48 teeth with 6.92 OD. I wrote some simple programs to calculate the data, but it doesn't make sense. There is no other known information. Using those two numbers I can only make things jive (somewhat) when the DP is 7.2254, tooth thk .2174 using a pressure angle of 20 deg. Over .250 dia pins the dimension is 6.972. So far I'm a bit at a loss as to how to go about this because of so many unknowns.

  I have access to a CMM to take points, but no software for purposes of reverse engineer it although I've seen one called Features from here  http://sofengsvc.com/
The information I provide must be fairly accurate, so hopefully someone can steer me in the right direction. Thanks.

RE: Acurrate manually drawn involute gear tooth form

Using the few details you have given this works out to a stock gear  of 3.5 module.
OD of a mod gear is number of teeth +2 x mod so 48 + 2 = 50 x 3.5 = 175mm = 6.89"
Tooth thickness is Pi x mod / 2 sp 3.1412 x 3.5 / 2 = 5.49mm = 0.216"

This looks as close as you can get commercial gears.

John S.

RE: Acurrate manually drawn involute gear tooth form

If you have a program to draw external gears,
use the dededum ratio for the addendum and
the addendum ratio for the dedendum and enter
the tooth space for the tooth thickness.
Remember to fillet the od which is actually
the root diameter of the internal gear.
I would use a 20 percent long and short
addendum system to increase the actual
line of action ratio and minimize the undercutting
of the pinions.  Gearguru knows gearing very
well and probably come up with the profiles
for you.  If you offset the profile and radius
by your cutter radius as well as the id, this
would be the tool path centerline of the cutter
that would make the final profile.  I assume you
will use a circular router type tool to make
the internal gear.

RE: Acurrate manually drawn involute gear tooth form

As the original post stated using 3/4" acrylic plate as the material the best way to achieve these gears with good precision is to pass the DXF files over to a laser cutting company.
This material cuts very well and leaves a mirrow surface finish.

John S.

RE: Acurrate manually drawn involute gear tooth form


Positional accuracy and surface finish when NC laser cutting acrylic are undoubtedly excellent, but edge squareness may not be, especially on 3/4" thick acrylic - it's one of the things they don't talk about much in the brochures (always a bad sign). It is affected by the degree of beam conicity, and if the beam is not circularly polarised the squareness will also vary around the part. I am skeptical that you could do better than about .005" in .75". But if it was absolutely consistent and matched on both gears, you could flip one over and get perfect contact. I would be interested to know if there is anyone who can positively refute my .005" guess from practical experience.

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