# Help regarding internal gear



## Don Pittman (Nov 23, 2019)

Hi I've done some research and forum searching but having difficulty finding needed info.

I'm wanting to attempt to cut an internal gear on a small lathe using a slotting device attached on the carriage.  I want to use a single point cutter bit.  I can't seem to find Info regarding how to get the right profile for this task.  I know Info regarding an external gear tooth profile is easy to come by, but for the matching internal tooth profile I am lost.  I want to cut a Module 0.5 72 tooth internal gear.  
I have the book by Ivan Law "Cutting Gears" but it doesn't address my problem.
Can someone direct me?  Probably any advice will be helpful.

thanks


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## ninefinger (Nov 25, 2019)

Using software you can determine the shape of the cutter.  I used a free add-in for Fusion 360 from FM Gears that lets you draw very easily an internal (or external) gear.  You could then model your cutter from the resulting gear. If you don't have Fusion 360 the same author of the add in offers a stand alone version for making DXF drawings  https://www.forestmoon.com/Software/GearDXF/  I didn't try it.  


Hope that helps.
Mike


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## Don Pittman (Nov 25, 2019)

Thank you for the info and link, I will study and check it out.
Much appreciated


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## Jasonb (Nov 26, 2019)

You may also be able to find one on something like Grabcad, even if teh MOD is different that can be scaled provided the tooth count is similar. It's then just a case of grinding a tool to fit the print out and cutting away. I would suggest drilling most of teh waste away to help reduce what the tool has to remove. How I did one in this post and carries on down and over the page


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## tornitore45 (Nov 26, 2019)

Just for kicks, I wondered if an internal gear could be cut by generating the tooth shape like is done with a pseudo hob in spur gears.
Take a spur pinion made in any way you know how and hollow grind it a bit so it can cut mowing axially.
Gash the internal gear, an chuck it on the lathe.
Mount the pinion like a boring bar, then push the pinion to shave 3 or 4 teeth a few thousands.
Rotate and shave the 5 tooth and a bit more of the teeth N0 4, 3, 2 wile the No 1 recede out of engagement.
Go all around
Move the cross slide to shave the teeth a bit deeper all around.

After thinking of this method for my Forest Edwards Radial I spent $113 for the gear from SDP.   It was a cope out but would have been interesting to try.


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## Don Pittman (Nov 30, 2019)

So I've managed (with help from friends) to get a print out of the gear I want to make and now see that grinding a single point cutter accurately that small would be dang near impossible!  It's a 0.5 module gear.  
I'm wanting to broach on my lathe, a brass internal 72 tooth gear.  Do you suppose if I cut a few teeth with an involute cutter in a steel partial blank I could use that as a broaching tool?


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## Don Pittman (Nov 30, 2019)

Maybe I should cut just one tooth in the cutter blank and use that as my single point cutter broach???


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## Jasonb (Dec 1, 2019)

Unfortunately that won't work

As the small gear rotates it needs gaps in the outer ring that are wider than it's teeth so if cut to the same profile as the internal gear it will just lock up. You can see it here for the gear I cut in the thread I linked to but that may not have shown up as it was an attachment.

What is the gear set going to be used for? if just a slow running lightly loaded application then it would not matter if the exact shape was a bit off and if you do it as I showed the gears can be tested for mesh before being removed so easy to take a bit more off if needed.


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## Richard Carlstedt (Dec 1, 2019)

Don, Doing your gear is not impossible
There is so much good information available to help you in your endeavor
I think the best is work  articles by the late "great" John Stevenson
Go to post 6 on this thread where I list the resources

https://bbs.homeshopmachinist.net/forum/general/76512-john-stevenson-s-gear-cutting-writeup
You do not have to "grind a cutter
You can form it as John does, or
Go to Mikes workshop where mike developed another forming method

http://mikesworkshop.weebly.com/making-gear-cutters.html

http://mikesworkshop.weebly.com/update-on-gear-cutters.html

Happy Chips !
Rich

PS By the way , when you cut an internal gear , because the cutter is on the inside of the gear circle, it automatically makes the ring gear tooth narrower to give clearace to your pinion gear.


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## Don Pittman (Dec 1, 2019)

Thanks for the helpful info and links.  Although I'm thinking it will be near impossible to get good enough accuracy, I am still leaning to attempting to grind a single point cutter I can use for broaching.  

The gear is for an "Elmers #5 geared engine". It's a big project for my skill level and tools and I am starting with the gears!   I may eventually have to "bail ship" on this but I thought it would be fun trying, I've already learned a lot.


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## TSutrina (Dec 1, 2019)

I looked at the GearDXF program and it is really a spur gear pattern used to cut an internal gear.  The reason for saying this is that the root radius is not in the correct location but where it would be on a spur gear.

  I use FreeCAD and it has the exact same approach but can export step, igus and many others.  On the new 18 version their is a work bench for gears that designs a profile without specifying the root radius.  The spur gear choice lets you add other features like clearance and shift in the profile which may be needed for a gear be it a spur helix or internal.  The GearDXF exact same approach on the part design work bench by looking at the table for picking the list on top for that bench.  

Want to see the product I have entered a design in the GrabCAD  contest Grundfos Challenge.   50 and 51 mod 1mm internal gear and the mating 46 and 47 spur gear are in step files and in the mating locations.


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## Jasonb (Dec 1, 2019)

If you are finding 0.5MOD to hard to see when grinding the tool you could probably get away with 1MOD and 36/18T, just check that there is enough clearance around the screw holes.


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## petertha (Dec 2, 2019)

TSutrina said:


> I looked at the GearDXF program and it is really a spur gear pattern used to cut an internal gear.  The reason for saying this is that the root radius is not in the correct location but where it would be on a spur gear



Just to be clear, are you saying the resultant internal gear shape that the software yields is not quite a correct tooth form with the various clearance factors designed to run with a conventional spur gear inside it? Are we talking the same software that Mike mentions in post #2? Like maybe the external/spur gears are correct & the internal/ring gears are kind of a graphical transpose as opposed to going through the calculation gyrations to yield the tooth shape? I read the documentation but it didn't really reference anything, but that in itself doesn't mean much.
https://www.forestmoon.com/Software/GearDXF/Help/Gear DXF Help v3_1_1.pdf

_Mike post #2> Using software you can determine the shape of the cutter. I used a free add-in for Fusion 360 from FM Gears that lets you draw very easily an internal (or external) gear. You could then model your cutter from the resulting gear. If you don't have Fusion 360 the same author of the add in offers a stand alone version for making DXF drawings https://www.forestmoon.com/Software/GearDXF/ I didn't try it._


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## TSutrina (Dec 2, 2019)

petertha: Gears with rolling contact, involute, doesn't care if  the gear is external or internal.   However, to mate two gears the tip of one should not hit the root of the other.  When the internal gear model has a root radius on the tip clearly the software does take into account the additional depth needed.  What else is not included in the model?   And what features are provided to correctly form of a gear to conform to the standard parameters we find in gear design books that are standard in the industry?    I didn't see the program Gear DXF offering some of these standard parameters to adjust gears.   I pointed out that FreeCAD 18 work bench for gear and specifically the spur gear/ internal gear (basically the same as Gear DXF) has added some.   I looked at the other two gears the work bench offers, and I do not understand what they make.   

petertha and Mike: I am throwing up the "user be where sign".  The models I have pointed to in my GrabCAD are examples of what you get from FreeCAD18.  I have a MathCAD7 calculation sheet for those standard gear parameters that I applied to the work bench model.  Also in some comments which include me saying that I have no idea the accuracy of the model.  The zoom capacity of my laptop and the FreeCAD18 software does not let me zoom in sufficiently, stops increasing the screen flats use to represent the curves of the mating gears.  I can not verify the contact angle or the clearance.   If you have a better program to load the step files maybe you can tell me.

Some math can be used to make good gears from the Gear DXF or any program that creates involute gears, there are many.   I could use the parameters from MathCAD7  for example and change the contact angle to the programs calculated value ~ 34.2 deg. and adjust the module off 1 mm to get the base circle diameter.   And by hand cut the root radius into the internal gear.   So good gears can be produced.   I have done this to make bevel gears from two sketches using the gear option in FreeCAD  part design work bench, see the GrabCAD model of the Atlas Lathe.


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## petertha (Dec 2, 2019)

Thanks for your reply TSutrina, that's exactly what I was wondering myself. I think 'user beware' is appropriate. No disrespect to the software/app because it looks useful, but the absence of some standard parameter inputs that influence gear shape should probably be verified before trusting the outlines 100%.

I want to better understand your methodologies. I have never used Mathcad but now you have me interested. Are you saying you use a Mathcad app to modify an existing involute shape? Or you have a more start-to-finish app where one can specify gear design input parameters & it calculates resultant tooth form? Then what - does it output x,y coordinates from which you load into CAD program and spline curve intercept or something? Or maybe it exports in DXF? 

I did a Google search on internal gear + Mathcad. Not sure it was a direct hit re internal but for sure some useful gear related worksheets.
https://community.ptc.com/t5/PTC-Ma...rning-spur-gear-calculation/m-p/117478#M45971


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## TSutrina (Dec 2, 2019)

MathCAD is a program to do math.  I basically typed in the equations found at this web site or the handbook from Stock Drive Products  metric gear book.   https://khkgears.net/new/gear_knowledge/gear_technical_reference/calculation_gear_dimensions.html

Looks nice but it just doing math.  A few functions in the program let you fit data with a curve and find a value that solves an equation or group of them.   Lucky I have the last version that does not require a code to use.  It is not open source.  It is a decade old.   There are a few other programs that are nice but hard to read: Scilab, Octave, and Sage. 

I used MathCAD do calculate the calculation given in the gear hand book.  By using software I can change the values until I like the results.  I do not change the involute equation.  I change the base circle diameter in the involute equation.   The rest is using that curve.   Pick the average pressure angle, 14.5 and 20 are standard.  The diameter associated is the pitch diameter.  The mode is determined by where the distance to the same involute curve that forms the other side of the tooth.   The root and tip are just  different diameters.   The handbook defines standards for determining them.  And means of changing the pressure angle choice, thus change the base circle.  and the width of the gear is also changeable.  Thus clearance is created by moving the curve closer to the opposite side curve.   

When I was at Electrolux vacuum cleaner company an engineer in sketcher input the involute curve as a table of points and copied and mirrored it until he had a gear.   He forgot about clearance and I ended up adjusting his model by moving the mirrored curve.   Thank god there is a repeat after moving the angle between teeth.


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## TSutrina (Dec 2, 2019)

MathCAD is version like 20 so I can not use anything published in version 7.   However it is a very popular program for people to use.  A lot of masters papers are done using mathCAD for the same reason I like it.  Great place to find the equations and method of solving them.  You could use them to write programs in an open source program.


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## Cogsy (Dec 2, 2019)

I've never used MathCAD but have used Matlab quite a bit. It's also an expensive program but Octave is a completely free 'clone' which is very close to the real thing (code written on Octave will mostly run on Matlab and vise versa). On first glance they look like 'just' math solvers but in reality will handle many complex tasks including things like image analysis and complex simulations of many variables.


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## petertha (Dec 2, 2019)

Does Fusion allow for parametric design / global variables / equations / functions etc. to design gears right inside the CAD file similar to this Solidworks example?
https://blogs.solidworks.com/tech/2014/07/how-to-create-spur-and-helical-gears-in-solidworks.html

I didn't look too hard at the SDP link that TSutrina provided, but if its basically a step-wise sequence of operations based on some defined input values, then possibly a true gear of any design with all the appropriate compensations could be entirely modeled entirely within the CAD app itself. That would cut out middle men, the in-between calculation program. And from from what I can see of discussion thus far, still requires some manipulation to turn into actual tooth curves. Even DXF import can be fiddly, there are resolution parameters & things to fart with or else you get weird things like facets or disconnected geometry.

Developing a gear inside CAD would not be button click automatic, it would likely require intermediary drawing steps so one would likely have a procedure sheet to follow. I assume there is no iteration or convergence type math involved - that would be the only show stopper. Fusion is free for hobbyists I believe?


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## TSutrina (Dec 3, 2019)

I believe that all the gear programs do a good job creating the involute curves.  What they seem to not do is to make the small changes that experts gear designers do.  And that is expected because the coders are not gear designers.  So let us say your making a planetary gear set, design three gears.  The centers can not be moved to create clearance, but ideal involute curves for the three gears have no clearance and will not work.  This is what the earlier mentioned person did.   So who can clearance be added if the gear generating program doesn't do it?   One approach is to copy the gear and rotated at the pitch diameter the clearance wanted.  The gear wanted is the combine volume they have together.   Roots of the gears is also a cutting or added or the tips of the mate lowered.    

For the gear set of an internal gear and a spur gear where the teeth count are close or small pinion gear with undercut.  The solution is to change the pitch angle which the programs do well.  But you will have to determine that angle with the gear hand book.   And also to make a bevel gear from the generated sketch for gears.   Scale the standard gear inputs. to the two ends of the gear.


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## propclock (Dec 3, 2019)

I used Gearotic to cnc machine My Elmers gear engine internal gear. I made it 2x bigger than the plans
because I felt it was too small and the endmill required was also too small.  I made it out of Delrin.
I know you are looking for a single tooth profile, Gearotic does this and the earlier version of Gearotic
generated code for producing the cutter. I am not sure if the free version will output
the dxf profile but you can try. The software does provide single tooth data.
 At the time, many years ago the Gearotic licence was less than the Boston gear price for this gear  ,
 I purchased the licence and have used it many times,
 including elliptical and helical gears. And the free version of Gearotic
is just fun to play with. Just my 1.414 cents worth.


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## TSutrina (Dec 3, 2019)

I when through Gearotic tutorials.  Clearly this is a professional program and can take care of every issue.  I was not clear if the two spur gear model that were made with the minimum input actually inserted clearance.  Note typically the center distance is increased by some fraction of the needed clearance.  The clearances of the bearing may result in a gear tooth clearance.   The image shown on the screen did not show any clearance.   Tooth thickness I think is the way clearance is added which is a box that is automatically filled but can be adjusted.   The imaginary gear capacity actually makes it possible to make gears that can not be back driven or only driven in one direction.


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## petertha (Dec 5, 2019)

Interesting. I looked up Gearotic & perused their forum a bit. This post is applicable to discussion.
http://gearotic.com/ESW/FavIcons/index.php?topic=1197.0

I'm actually kind of surprised there aren't more homebrew gear apps out there written by hobbyists. But like TSutrina says, it may well not be a button click solution depending on the actual application. Some engineering adjustments may still be required.


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## Jasonb (Dec 5, 2019)

I tried the Gear DXF and all it does is produce a cut out of a spur gear. You can see this where the blue spur gear fits exactly into the grey external gear.

Also pictured is the 24T internal gear I use for the post I linked to with a 24T spur gear placed into it, you can see the difference in profiles. This was so that a 12T could rotate within


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## awake (Dec 5, 2019)

I don't know if it would be of interest or help in this situation, but ... I have experimented with modeling the results of semi-hobbing a gear using a couple of open-source programs - BRLCad and OpenSCAD. Both are programmed using a scripting mechanism, but of course they use completely different scripting languages.

By semi-hobbing, I mean cutting the gear in a series of discrete passes, maybe 4 or 5 per tooth, rather than the "infinite" number of passes that occurs in the continuous action of true hobbing.

BRLCad is difficult to use, but can produce a very high-resolution result (*not* a triangulated mesh), though if tooth count is high or number of passes is greater than 3 or 4, it will not be quick. OpenSCAD is much easier to use, but you have to choose between very low-resolution results that are slow, or very high resolution results that are utterly, painfully, maybe even impossibly slow. Any resolution of results on OpenSCAD will be in a triangulated mesh format.

Important caveat: My experiments have only been with generating external spur gears, not internal gears. With BRLCad, you would have to have the program first generate the external gear, and then in the same script use that gear to generate the internal gear. With OpenSCAD, it should be possible to import a gear in .stl format (e.g., generated by FreeCAD), extrude it, and use it to "hob" the internal gear.

Note that with either program, you can save an enormous amount of time by generating only a few teeth, just enough to be sure that you have at least one or two fully-formed teeth / spaces.

If anyone is interested, I'll try to dig up either or both of my experiments; just let me know which one(s) you'd like to see.


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## awake (Dec 5, 2019)

awake said:


> BRLCad is difficult to use, but can produce a very high-resolution result (*not* a triangulated mesh), though if tooth count is high or number of passes is greater than 3 or 4, it will not be quick. OpenSCAD is much easier to use, but you have to choose between very low-resolution results that are slow, or very high resolution results that are utterly, painfully, maybe even impossibly slow. Any resolution of results on OpenSCAD will be in a triangulated mesh format.



Okay, let me adjust that paragraph. I just went back and tried the OpenSCAD version again. It actually is pretty quick to generate a gear, even with a high number of passes (I tried as many as 25) ... as long as you are only generating the "preview" version. When you generate the "render" version is where it slows down drastically, and may be too slow to be practical - again depending on number of teeth, number of passes, etc.

As a test, I've been generating a module 1, 20°, 20-tooth gear while I've been typing this follow up message, using 8 passes. (I.e., the "hob" cuts 8 times per tooth profile, rotating the gear 1/8 of a tooth and moving the hob as if in mesh for each cut. Not sure if that makes sense.) For those who know OpenSCAD, I've had $fn = 256, so the triangles in the mesh should be very tiny.

After several minutes, as I have typed this and done some other things, it is still not complete, and the cooling fan has kicked up to high, meaning the CPU is running flat-out on my i5 laptop. I'll wait until it is done to post this message, and I'll include the .stl of the results.

Okay, it is done at last - took 30 minutes and 25 seconds on my i5 laptop with 16 GB of RAM. Attached are two screen shots from OpenSCAD, one from the top and one from an angle; each of these will let you see the tiny "jaggies" in the corners and the tiny faceting on the tooth faces that is the result of the "semi-hobbing." I've also attached the .stl file. Definitely not a perfectly formed gear, but it would be more than good enough to use as a template for grinding a cutter. Again, this is just the external gear ...


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## awake (Dec 5, 2019)

One more post on this topic: I've attached the OpenSCAD program that generated the above to this post. (I had to zip it since the forum software didn't want to upload a file with the .scad suffix.)

For anyone who wants to play with the OpenSCAD program: I didn't put a proper license into it, but just a quick note that I retain the copyright but make it available to be freely copied or modified so long as credit is given to the original. You will see that there is a module, hobbed_gear, which is intended to be the one called by the user. (Other modules help generate the "hob" and carry out the "hobbing.") There are comments to indicate what each of the parameters of this module do. To generate the .stl file and screen shots attached, I used the following:

$fn = 256;
hobbed_gear(m=1, pa=20, n=20, passes=8);

The way the program works: It determines whether the user has entered a diametral pitch or a module gear, and calculates the size of the blank accordingly for the number of teeth specified. It generates a "hob" consisting of a straight rack with teeth of the appropriate size and shape for the specified dp/module and pressure angle. It then positions the blank and the rack at the appropriate distance and "cuts" the blank using the rack. Then it rotates the blank, adjusts the position of the rack (for incremental passes / cuts), and takes another cut. And so on until it finishes.

I'll play with creating a similar program that will take a previously generated gear in .stl format, using it to "hob" an internal gear. May take me a few days ... and if anyone else wants to give it a whirl, have at it with my blessings!


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## lohring (Dec 5, 2019)

Fusion 360 has alot of gear generation programs available.  My free version came with a spur gear generator, but lots of others are available in the app store.

Lohring Miller


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## awake (Dec 5, 2019)

I should have offered a disclaimer up front: the programs I am talking about are NOT the best / easiest way to get a good model of an external gear - much easier to use the gear generation built into various CAD programs. But as noted above, those programs may not generate a correct internal gear. And some may generate a less-than-ideal model even of an external gear. FreeCAD, for example, has a module to generate both internal and external gears, but the external gear is not quite involute, and the internal gear is like the one that jasonb showed above - just a cutout of an internal gear, with none of the clearance needed for actual use.

The point of the BRLCad and OpenSCAD programs I reference above is less about modeling a gear, and more about modeling the process of approximating a gear through "semi-hobbing." But it does have the advantage that, with a high number of passes, the result really does approach very closely to the theoretical ideal.


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## TSutrina (Dec 5, 2019)

You may try drawing and calculating software offered by gear manufacture.  Manufactures get expert gear designers involved so the likelihood of getting usable gears is higher then the coders that make the gear design listed above except for  Gearotic. You need to signup with them.  I didn't do that since I am not designing gears right now.   https://khkgears.net/new/gear_calculator.html    Go to the bottom.


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## petertha (Dec 5, 2019)

For the price of 'logging in', the KHK calculator utility seems like a very good solution IMO.


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## ninefinger (Dec 15, 2019)

I created a log in for the KHK and it does generate dxf outputs for taking into your cad program.  As can be seen the internal gear tooth profile gets modified at the root and the ID is smaller as well,  the left side was the original gear as drawn by the add-in to Fusion 360, and the right side is the gear as modified by the output from the KHK program, using all the default values (0.5M 72 tooth, 36T mating small gear).  The line drawing is from the KHK program and shows the meshing of the 36T with the 72T internal gear.


What I'd like to know is how expert gear designers decide what parameters need to be modified for a given set of gears?  I realize this is beyond what Don was looking for but if a pointer can be given to a resource that helps explain why a person would vary certain parameters it would be appreciated.  I'm in the middle of re-drawing a set of 48DP gears to use 0.5M and beyond adjusting the center distances am wondering what else to consider.
Mike


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## Don Pittman (Dec 15, 2019)

So I soon realized that I bit off much more than I could handle with this internal gear thing, the level of expertise and understanding concepts are still a bit beyond me.  
However I still wanted to try so I did what I do best...I flew by the seat of my pants and tried "poking" out an internal gear with a broaching/slotting device on my lathe.
I had to do the tool point grinding and fitting mostly under a microscope because module 0.5 teeth are pretty small.  To my untrained eye it appears the fit might be passable.  The external gear was cut with an involute cutter and I believe it should be pretty close to correct.  Anyhow it was a learning experience!


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## Ken I (Dec 16, 2019)

I typically generate my own profiles - starting from a rack of whatever module or DP required - this also allows me to play with pressure angles and clearance radii etc.
vis:-







You draw the rack - array one flank linearly in pitches corresponding to 1, 2 or 3 degrees of rotation (depending on how fine you wish to resolve it) and then rotate each flank into position - then draw a best fit radius or series of rads. Mirror profile for the opposite flank. (This emulates the way a Fellows gear shaper generates gear profiles.)
In the case of the epicyclic, you have to generate the pinion tooth profile from a rack and then use that developed profile - arrayed about its centre and rotated back on the internal gear centre. (This emulates the way a Maag gear shaper generates gear profiles.)
Add clearance (if required - generally I don't) - use data *.dwg or *.dxf for EDM wire erode or waterjet (minimum 2 Module because of waterjet kerf)
Sometimes force the rad to the nearest standard cutter if you plan on making a cutter - then regenerate the matching gear to suit. This is very useful for avoiding interference and undercutting.
A PITB to be sure but I find it gratifying to develop my own profiles.
You can also use this method to develop non-standard profiles or non standard centreline distances - such as ninefinger is asking about.




Example - waterjet cut M2 synchronising gears on my radius gauge.
Regards,  Ken


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## TSutrina (Dec 16, 2019)

I had the opportunity to have experts design the gears for the few times I needed them.  As an aerospace company we pushed gear and bearing hard.  Purchase many of them so the manufactures were happy to present seminars which I did attend.   Basic understanding is that a gears do not move if they are made exactly to the volute path and at the calculated centers.  (Sand blasted the gears to create clearance.)   So the approach to get clearance is to offset the profile, thin the gear.  That is one parameter on a gear design chart.  If the centers can be move then this to will create clearance but increase the contact angle.  Thinning is the only method possible for planetary gears since the centers are fixed.  The other problems of undercutting and interference is determined by math.  Those equations are available or compute models will show the problem.  Then the discussion that the experts have put into articles will instruct the solution direction.  I have named one such expert above.  General solution is to change the angle of contact or change the height or depth of a gear off the circle at the contact angle.    Under cut gears require increasing the contact angle.    DIY builders have the advantage of being able to make new tools where manufactures adjust their machine because they need to use existing tooling.


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