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Interference equation valid for internal gear?

Interference equation valid for internal gear?

Interference equation valid for internal gear?

I'm designing and helical gear set made of and internal gear and a small pinion gear.  I have an equation to know if there is interference between gears but this was developped for regular spur gear.

To use it for helical gear I just have to use the transversal parameters but I don't know if it still works for internal gears.

N1=number of pinion teeth
N2=number of large gear teeth
p=pressure angle

to avoid interference, equation must be greater or equal to 0:


Robin B

Mech eng
Montréal, Canada

RE: Interference equation valid for internal gear?

I do not know your formula (where it came from?) but if it works for spur gears it also has to be good for helical gears if you use the transverse pressure angle in it. Here is why:
You can think of a helical gear as if it were created from very thin spur gears (with the pressure angle = transverse pressure angle of the helical gear), slightly twisted against each other (by the helical angle) and "glued" together.
If none of these thin spur gears interferes (checked by your formula, I assume that it is correct), then none of them does - therefore no interference...

Could you post some more data?  

RE: Interference equation valid for internal gear?

My question is not related to if I can or not use the equation for helical gear but for internal gear.  You explained it well!  I've found the theory behind this equation and they do some example with external gears and rack but not with internal gear.  The rack is simulated in the equation by dividing all term by N2 and push the limits of N2 to infini.

The development for the equation is in a french book but I could scan it.

Do you Know any gear cutter in North America that can cut small internal helical gear? (64dp 325 teeth).  I've just got one.

RE: Interference equation valid for internal gear?

I apologize. The internal gear/pinion should be checked for interference, especially if the numbers of teeth differ just a little; the external gears are checked (sometimes, if the pinion has small no. of teeth - it depends also on the pressure angle) for undercut.
There are three equations for checking the internal gear/pinion for the interference.

For the info about the gear manufacturers look at


RE: Interference equation valid for internal gear?

You will want to enter pinion
and gear data to calculate
parameters.  You might want to
use a 25 percent long addendum
on the pinion and a 25 percent
short addendum on the gear.  Just
good internal gear practice.
Or use 50 percent long on pinion and
none on the internal gear.  
This works well in most cases as well.
Mike Bull has a spread sheet free if
you check out his website.  It is an
excell spread sheet, but you do have
to know general gear design parameters.
I have the fairfield gear design program
and find in invaluable especially to
calculate helical gears.  It would have to
be a specialty house to cut such a fine
diametral pitch gear.  Would be glad to fax
you an output of the fairfield gear program.
e-mail J.GEISEY@juno.com  I would think you
would have someone up there who could cut
a module system on the same center distance.
Does it have to be a 64dp system?

RE: Interference equation valid for internal gear?

Here is the post I sent to something like 30 gear cuttersin america:

We want to find a gear cutter that can make a gear for us.  Right now we have a gear set (64 D.P., 14.5 degrees, agma 10) composed of a small pinion in SS 303 (18 teeth) and an internal gear (325 teeth) made of plastic (Ertalyte).  Sound and backlash are a BIG issue (there is no load beside a 6in Kaydon bearing) so we plan to try helical gear to drop the sound at a minimum level.
Backlash was proven enough small with the spur gear set but sound is still too high even with tight tolerances.  Next step is then helical gear and if you are interested in that small project we can exchange a little bit more and I can send 3D/2D file.  Need is immediate and a quotation for a prototype and a prototype would follow.

I've searched for a while to find a gear cutter that can do it but it seems hard to find.  If you cannot cut it, can you redirect me to another that could do it?


Robin Boudreault
Mech ing.

Complement information: Pressure angle was defined to 14.5 degrees (instead of 20) to minimise backlash related to center-to-center distance error but could go to 20 degree (sacrifying backlash for smoothness of operation).  Quick research has shown that helix angle decreases sound as the helix angle reach 30 degrees, which seems to be the best angle (over that it does not decrease the sound).

Direction doesn't matter since there is almost no load.  My only concern is having a ratio of 18 to 14 (right now the internal gear has 325 teeth and the pinion has 18 teeth, giving a ratio of 18.06).  Gear could be metric or english, could have and helical angle between 15 and 30 degree and a pitch angle of 14.5 to 20 degree.  Center to center distance is not imposed by the design.  All those parameter must be
validated since the system is placed inside a really compact case filled with a lot of stuff.

RE: Interference equation valid for internal gear?

Is the bearing a slimline syle bearing?
Is the Ertalyte bonded to the inner
race id?  Reinforced plastic with canvas
mesh? Was this plastic cut or molded?

You implied that you had an external spur
gear set and it was too noisy.
What kind of speeds are you talking about?
Just from preliminary calculation, the contact
ratios are 1.8 and larger which means that
you are having at least 2 teeth in contact
80 percent of the mesh cycle.  How is this
lubed?  The greater the helix angle, the greater
thrust load is imposed on the bearings and I assume
greater turning torque.

The modified pinion had a tooth thickness at the tip of .006, i.e. almost pointed.  Will run some other
calcs to improve the tip condition.

Feel free to call me tomorrow.  330-562-4000 x238
Cleveland Ohio area.

RE: Interference equation valid for internal gear?

The bearing is a self made slim bearing (we removed the Kaydon to build one).  The Ertalyte gear is screwed on the bearing inner race and rotational speed is 60 rpm, then one turn per second.  We have to run the system dry.  thrust load should be almost equal to zero since it is just rotating a pointing device, it does not transmit any power beside the friction of the bearing.

I downloaded the Fairfield software and played with it but I often get a message saying that the sap diameter is less the base diameter.  Is that the signal for undercutting problem?  I'm just exploring the software.  I'll continue the design and if you know any people that could cut it I would send them a quotation request.

The hardest part of the problem is to have a small pinion to keep the transmission ratio around 18 while maintaining the internal gear pitch diameter around 5.

Thanks for your time, I'mm following this thread with interest and like to design gears.



RE: Interference equation valid for internal gear?

Glad you have the fairfield program.
When you get that the sap is smaller than the
base diameter, you should enlarge the pinion
say starting at 30 and -30 on the internal
gear.  What makes me nervous is the 64 dp
gear only has a working depth of .031 meshing.
A 1 module would be about .079 inches in mesh
but you would have fewer teeth in each member.
I have a hard time visualizing these small
gears.  I do not enter the tooth thicknesses
and only enter the percent addendum modification
and the min and max backlash for the system.
Then check the results.  You can also stub
the addendum on the internal gear if you had
more whole depth.  I like to see the sap angle
about 8 degrees to reduce the sliding velocity
at this critical area.  When you start out with
only .031 working depth, you cannot do much other
than change the long and short addendum ratios
and watch that pinion teeth do not become too
thin at the o.d.  I am a strong believer in
the recess action that long and short addendum
offer.  They run more efficiently and probably
quieter.  We manufacture the big stuff and only
get down to around 10 inch inside diameters.
We do not cut helicals in house and send these
out.  We have not designed anything this small.
Only know principals after doing much of the
calcs by hand until fairfield offered their program
when we were working together on a joint effort.
I see in catalogues .5  .75  and .8 module pinions
on the shelf and was quite surprised to find them
in the catalogues.  I know nothing about these and
the only helical that they offere was 45 degree helical.
Sounds like an exciting project and wish I could
be of some help other than offering some design
guidance.  Please keep us posted on your success.
You will also note that the higher helical angles
reduce your contact ratios.

RE: Interference equation valid for internal gear?

What does SAP stand for??  Yes, I started by extending the addendum and shortening the dedendum.  I enterned the datas like you; adendum/dedendum modification and backlash.  Did you say that extended addendum will run qiter?  Why?

I'm not limited to 64 pitch (me too found it really small) but I'll give you my design guidelines:

1-Internal gear should have 5 inches pitch diameter

2-System has no load and must be as quiet as possible (this is why I use plastic internal gear.

3-Backlash should not be to high but sound is a bigger issue than backlash

4-Pinion pitch diameter should be as low as possible, around 0.280" (here is why it was a small pitch of 64) to get a pinion/gear ratio of around 18.

5-Gear width is around 0.125"

6-Reading shows that an helix angle greater than 30 degrees does not yield in a quieter system so  30 degrees is a maximum.

I will play with the parameters and come back.

RE: Interference equation valid for internal gear?

I forgot to mention that the 5" pitch diameter is transverse, not normal.

RE: Interference equation valid for internal gear?

I did a couple of run and 48 of pitch could be used.

Pinion and internal gear: pressure angle 20, helix angle 30, diametral normal pitch of 48, no addendum or dedendum modification.

pinion: 12 teeth

internal gear of 210 teeth

From the run, I do not have any sap problem and slip ratio are between 0 and 1.  contact ratio of 1.4.  How do I know that I don't have undercutting and that my design will work?


P.s.  The program keeps crashing if I do not select the expand sig fig but it works great.

p.p.s.  I got the same addendum height for two different pitch, isn't the addendum supposed to be 1/P so different for different pitches?

RE: Interference equation valid for internal gear?

The addendums should be different
if you are holding the helical angle
and only changing the diametral pitch.
I do not know why you do not use an
addendum modification for the pinion.
SAP is just another term for the lowest
point of single tooth contact and means
start of active profile, i.e. from this
point to the o.d. is the working portion
of the tooth.  To have such a low contact
ratio, you must be using a high helical
angle.  Just for you own discovery, change
the helix by 5 degree increments and check
out the differences in contact ratios as
well as center distances.
As you mentioned 1/p is the normal addendum
formula for spur gear.  Helical gears are
reduced by a function of the helical angle.
If you are getting the same addendums for
diffent diametral pitch gears, I would exit
the program and come back into it and reenter
the data.

RE: Interference equation valid for internal gear?

Why not use a Synchronous Belt ???


RE: Interference equation valid for internal gear?


I do not have space outside the turning internal gear so the driving device must be inside.


RE: Interference equation valid for internal gear?

Hi Robin , on a early post you wrote

"and if you are interested in that small project we can exchange a little bit more and I can send 3D/2D file."

Could you send it to


Other alternaltive is to use a 2 step reducer by timing belts.
I will be pleasured if I can help you.



RE: Interference equation valid for internal gear?

There is no space to put any reducer (and no space outside the internal gear).  The design is going to be a single helical internal gear with a small pinion driving it (then from the inside).  The only unwnowns are the paramaters of the gears to meet the requirement I wrote in a previous post.  Up to now it will be a 48 diametral pitch with an helix angle of 30 degree and a pressure angle of 20 degree.  An adendum modification of 25% will be used to minimize undercutting and avoid interference.  Internal gear will be in plastic (ertalyte) and the pinion in ss.

RE: Interference equation valid for internal gear?


Hope I can help other time.



RE: Interference equation valid for internal gear?

Hi Robin, please apologize me for be so insistent , could you send me your sketch at least?
I think that it could be a cheaper solution.


RE: Interference equation valid for internal gear?

Ok, after a while of playing with the software and good advice from diamondjm I went to that final design:

This is a pair composed of a small pinion and an internal gear:  (Fairfield run is available on request)

DP: 48
pressure angle: 20
Helix angle: 30 (right angle)

Pinion: 12 teeth, addendum offset 50%
internal gear: 213 teeth, no offset.

there is no load on the gear and the only concert is noise and vibration.

Any suggestion?

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