What is the input
HP, Torque, and RPM
Material, and hardness

aebt,

AGMA 6123-B06 sec 7.7 provides an answer to your second question. "7.7 Pressure angle - Best strength to weight ratio is achieved with high operating pressure angles at the sun to planet mesh and low operating pressure angles at the planet to ring mesh."

Just curious why you chose to use small tooth numbers for your sun (15T) and planet (15T) gears? Using smaller tooth size and higher tooth numbers (say 21T or 24T for the sun and planets) would make your job much easier.

Try reversing the sign of profile shift for the ring gear, i.e. use +0.5
The center distance sun/planet must be the same as ring gear/planet.
Does it look better now?

@mfgengear, those are irrelevant to the problem. I am trying to get the code to work out basic dimensions of an arbitrary gearset working. The power and speeds etc are further down the line.

@tbuelna, they're just arbitrary values to highlight the problems I'm experiencing. While they might not be used in practice they're simple values to test the code. Thank you for the AGMA reference, I will look into that further

@spigor, Changing the sign to positive will result in the sun gear requiring a -1.5 to fit. I'm comparing my code with some known software, so I know there is an error in my calculations/theory.

Here's the data:
α = 25 degrees
z1 = 15
z2 = -45
x1 = -0.5
x2 = -0.5

No playing with the signs yet.
Using the formula 5 in Table 5-1 under the link you provided I get:
inv αw = 2 tan α (x2-x1)/(z2-z1)+ inv α
inv αw = 0.029975345
This is correct.
So what was wrong?

Might be helpful: https://keisan.casio.com/exec/system/1374045743819...

The formula requires that the internal gear teeth value is expressed as a positive value.
I verified this using their numbers and results - unless both their formulas and answers are wrong, I have found errors in their literature before...

The example I gave had "x1" as +0.5, not -0.5.

2*tan(25) = 0.9326
x2 - x1 = -1
z2 - z1 = 30
inv (25deg) = 0.03

Solving = -0.061

If I was to use the ring teeth as a negative number, their example in table 5-1 would output a working pressure angle of 19.6 degrees, rather than 31.09 degrees. Both seem feasible...

I take the example in question:
α = 20 deg.
z1 = 16
z2 = 24
x1 = 0
x2 = 0.5

inv αw = 2 tan α (x2-x1)/(z2-z1)+ inv α
inv αw = 0.060400663
αw = 31.09362066 deg.
That is correct.
Just as I suspected, you need to change the sign of the profile shift for the internal gear.

Here's your example again with corrections:
α = 25 deg.
z1 = 15
z2 = 45
x1 = 0.5
x2 = 0.5

inv αw = 0.029975345

Of course changing the value to positive 0.5 makes it work because you are taking a negative number out of the equation. I only care about the values that don't work.

As I keep saying those values are purely arbitrary, and I want to know why the equation doesn't work for a profile shift in the ring gear in a certain range.

Ignore the fact I am trying to create an epicyclic, even for a simple gear/ringgear combo I can't get the equation to work.


EDIT: Checking with some additional software, the reason is because the "Frontal contact pressure angle became less than zero."

So my sums and assumptions were correct, it's just pushed the ring gear beyond a natural limit.

I ran this through the Fairfield program and it was freezing.
Theoretically it should be possible.
It is common to use a negative x factor
To compensate for the planets. But I don't calculate enough manually to fiquire itout.
And I to busy to do it now.
May try a different combo of gears as
Suggested by tbuelna. Spigor is very good
To.
Generally if a gear can not be calculated, bombs out it's for a reason.
Error in the design.

ae-bt
I know what I'm talking about, but find it hard to explain it to you. I'll try once more.

General: 3.0M 25PA, standard tooth proportions

Sun gear:
z0=15
x0=-0.5
OD=48 mm (if x=0 OD=51 mm, so it is a diminished gear, other names are here: https://www.geartechnology.com/blog/the-long-and-s... )

Planet gear:
z1=15
x1=0.5
OD=54 mm (if x=0 OD=51 mm, so it is an enlarged gear, other names as before)

The sun and planet(s) mesh at center distance A=45 mm

Ring gear:
z2=-45
x2=-0.5
ID=132 mm (if x=0 OD=129 mm, so it is an enlarged gear, other names as before )

The planet(s) and the ring mesh at center distance A=-45 mm

The negative value of z2 and negative profile shift of enlarged internal gear are a convention. As you wanted to use a positive number of teeth yourself, it should be:
Ring gear:
z2=45
x2=-0.5
ID=132 mm
Here inv αw = 0.029975345

Now let's start diminishing the ring gear. First let's change it to:
Ring gear:
z2=45
x2=0
ID=129 mm

We don't touch the planet gear, so the absolute center distance must get smaller and becomes:
A=43.34 mm
Here inv αw = 0.014431757

Let's continue diminishing the ring gear aiming for x2=0.5, what you seemed to think I was doing simply to avoid the problem, but I hope it is clear now I was not. The last stop is at:
x2=0.464:
ID=126.22 mm
A=40.8 mm
inv αw = 0.000007306325654932170
Here serious problems with the meshing emerge.

If the ring gear gets diminished more, no involute meshing will be possible.

Fairfield did crash on that? Wow!

In that bicycle planetary gearbox I showed in other post all the planetaries were profile shifted and the diameters were modified, so there were interferences in meshing of the gears and also in meshing of the gears with their respective tools, making it a surprisingly complex system. It occurred to me, how important it is to have a convention strictly defined and t stick to it in order not to get lost when things get more complicated.

I hope it helps.

I forgot: you might find lots of information on profile shifting in DIN 3992 and DIN 3993

@spigor well done

"I know what I'm talking about, but find it hard to explain it to you. I'll try once more."

If you had read what I was saying correctly, you would understand that I was talking about a gear and ring gear in isolation.

And like I said, the problem was as I had assumed - I had reached the natural limit of the gear.

Quote (ae-bt)

If you had read what I was saying correctly, you would understand that I was talking about a gear and ring gear in isolation.

I probably got misled as the original question was about the working pressure angle αw, which does not exist in isolated gears.

@Ae-BT
Please advise if this is trying to proof your calculations and/or you trying to design a gear train ?

Properly designing a gear train is with experience, what works or doesn't.
Have you proofed this out with an other program?