Internal Gear Contact Ratio Chart? 2

[NuclearNerd]

I am considering the design of a lightweight gearbox. I was hoping that by using an internal-external gear pair, I could get away with a much thinner gearset than I would with an external-external gear pair for the same torque. However I have not been able to find a good online reference for the amount of load sharing between internal and external gear teeth of a given ratio. The AGMA J factor charts give a good indication of tooth-load sharing for external gears. Does anyone know of a similar chart for internal gears?

 

[dinjin]

You can get an approximation by using a gear and a rack contact ratio.
If you have a gear program, simply use 10000 teeth to simulate a rack.
The contact ratio will be lower than the internal external gear combo
and certainly higher than the external external como. If you need exact
numbers, someone offered excel spread sheets awhile back but I do not
know if they re still available. They were metric spread sheets, but
if you use the same combinations, the contact ratios would be the same.
If you provide, the numbers, I can send you the contact ratio of the
set. Will you be using modified addendums on the internal gear? It is
customary to truncate the internal gear addendum to avoid interference
in the root of the external gear.

 

[NuclearNerd]

Thanks Dinjin. I looked at using the rack figures, but for the concept to work, it needs to show 2 or 3 x less bending strength than an equal thickness external spur gear.

If you have a spreadsheet available, can you plug in the following ratios and let me know what you get for contact ratio? That way I can check to see if my assumption is valid:

case 1) 96 t internal, 30 tooth external
case 2) 72 t internal, 50 tooth external

compare against:
base case) 72 t external, 50 tooth external.

 

[dinjin]

case 1) 96 t internal, 30 tooth external 1.853 contact ratio internal gear must be shortened .05xModule to avoid involute interference.

case 2) 72 t internal, 50 tooth external 1.909 contact ratio internal gear must be shortened .075xModule to avoid involute interference.

compare against:
base case) 72 t external, 50 tooth external 1.783 contact ratio

Lewis Y factors at tips
30 t ext .358
50 t ext .408
72 t ext .430
72 t int .584
96 t int .441

So you are not going to get that great of an increase in bending strength.
This is a simple analysis based on tip loading. Even using a stub tooth
form, you will not gain much. You may have to look at different materials
to see the increases that you are looking for or increase the face widths.

 

[NuclearNerd]

So much for that brilliant idea. Thanks Dinjin!

 

[tbuelna]

NuclearNerd- Besides the excellent comments by dinjin, I would add that if your goal is minimizing total gearbox weight rather than just the weight of the gear teeth and rims, then you must also take into account the differences in bearings, housings, shafts, etc. between the two configurations. You need to consider more than simple root stress due to tooth bending with regards to face width. For example, the stiffness of the gear structures and bearings/housings can greatly affect load distribution along the tooth face. Displacement at the mesh line usually requires some degree of face crown to compensate, which in turn necessitates an increase in face width.

Also, if efficiency or scoring/scuffing are a concern, an external gear pair would have a slight advantage over the pinion/internal ring combination. Even using lots of profile shift to produce recess action, the pinion/internal ring combination will still have greater sliding losses than the external gears will.

Lastly, in case you had not considered the issue, the relative direction of rotation from input to output is not the same with a pair of external gears and a pinion/internal ring gear pair.

Hope that helps.
Terry

 

[NuclearNerd]

Thanks tbuelna. I was hoping that the internal gear pair would have so much more load-sharing (at least 2-3x that of an external gear pair) that it would compensate for the extra support requirements for the internal gear. (I was imagining something like a belt drive, but with a fixed center-to-center distance). I've never seen a gearbox made this way, so I shouldn't be surprised that the concept isn't advantageous.

 

[tbuelna]

NuclearNerd- Glad my comments were helpful. While your proposal may not provide much weight advantage when the entire gearbox system is taken into account, that does not mean your logic (using a pinion & internal ring to increase contact ratio and thus decrease face width) was flawed. In fact, the basic concept of distributing mesh loads among a greater number of contacts is a common approach to reducing gearbox weight. The torque split concept has recently been used to reduce weight and increase torque capacity in high-performance helicopter transmissions such as the AH-64 block III and CH-53K.

 

[gearcutter]

While the increase in bending strength is negligible when going from an external to internal design; there will however be a substantial increase in surface durability.
The root cause of the majority of the gear failures that I've seen have been associated with surface durability issues not bending strength.

Ron Volmershausen
Brunkerville Engineering
Newcastle Australia

http://www.aussieweb.com.au/email.aspx?id=1194181