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Planetary Gear System Identification?

Planetary Gear System Identification?

Planetary Gear System Identification?


Very new to gear design here so please bear with me.

I am attempting to reverse engineer a 2-stage stainless steel planetary gear set at work and am looking to verify the diametral pitch and pressure angle I have calculated.
I suspect that due to the slightly worn condition of the gears and possible inaccuracy in measurement that my calculated pitch and pressure angle could be wrong.

We are 99% sure these are English system gears and will identify them as such. However, I have found excellent metric resources and have done calculations in both English and metric.

Knowns for the gears in the planetary system:
# sun teeth = 10
# planet teeth = 13
# ring teeth = 38
# of planet gears = 3

Measured values (I have used an optical comparator to measure but the gears are slightly worn with soft edges so values may not be 100% correct):
planet outside diameter = 0.1315" (3.340mm)
sun outside diameter = 0.1535" (3.899mm)
center distance from sun to planet = 0.1290" (3.277mmm)

Condition #1 for a planetary system: Determines number of teeth in ring gear

Zc = Za + 2Zb --> Zc = (10) + 2(13) --> Zc(theoretical) = 36
Zc(actual) = 38 --> Therefore profile shift must be present

Condition #2 for a planetary system: Verifies if equal center distance of planets is valid

(Za + Zc)/N = Integer --> (10)+(38)/(3) = 16 --> Equal center distance verified

Condition #3 for a planetary system: Verifies if planets can operate without interference

I know this is true as I am reverse engineering this system --> Non-interference verified


Solving for Diametric Pitch:

D0 = (N+2)/P --> Therefore P = (N+2)/D0 --> P = [(13)+2)/(.1535")] --> P = 97.7
Closest "standard" P = 96 --> Diametric pitch of 96 is assumed (teeth/in)

Solving for Base Pitch:

Multiple measurements were taken using high precision digital calipers of the span between 2,3, and 4 teeth respectively.

Span of 2 Avg. = 0.0465"
Span of 3 Avg. = 0.0775"
Span of 4 Avg. = 0.1060"

Span4 - Span3 = 0.0285"
Span3 - Span2 = 0.0310"

Avg. Span Difference (Base Pitch) = 0.02975"

Solving for Pressure Angle:

BP = Π*cos(θ)/DP --> (0.2975") = Π*cos(θ)/96 --> 0.9091 = cos(θ) --> θ (pressure angle) = 24.619deg
"Standard" pressure angles are 14.5deg, 20deg, and 25deg --> Pressure angle of 25deg assumed

Undercutting Condition:

Assuming P=96 and θ = 25deg, there should be no undercut on the planet gear with 13 teeth.


1) Assuming:
Pplanet = Psun --> 96
θplanet = θsun --> 25deg

I found that... (formulas not shown as it was done in metric and there were quite a few of them)(Ref. KHK Gear Technical Reference Guide)

- Minimum coefficient of profile shiftsun to avoid undercut is xmin = 0.106969
- Coefficient of center distance modification (using x = 0.106969) is ymin = 0.1048149
- Center Distancemin = 3.071mm

2) Assuming:
Center distance measured = 3.277mm

I found that...

- Coefficient of center distance modification (using measured center distance)is y = 0.8847317
- Actual coefficient of profile shiftsun is x = 1.017309


My main concern with these calculations is that:

1) If my measured diameters, center distances, or tooth spans are off just a tiny bit, my assumed pressure angle and diametral pitch go out the window

2) Center Distancemin = 3.071mm (0.1209"), giving x = 0.106969

Center Distancemeasured = 3.277mm (0.1290"), giving x = 1.017309

Center Distancemeasured - Center Distancemin = 0.206mm (0.008")

This small change in center distance drastically changes my profile shift coefficient and makes me wonder if I even need to call it out on the drawing at all.
Can't I simply make a judgement call and say x=0.5 and create my specified center distance for the gears using this?

Are these numbers close enough to determine an acceptable specification for these gears?

Sorry for the long post y'all. I have tried to make it as easy to follow my train of thought as possible.
Also to you gear professionals out there, please let me know if you catch errors in assumptions I made during calculations.
Thanks for any advice or help you can offer!

RE: Planetary Gear System Identification?

Hi NinerEng

D0 = (N+2)/P --> Therefore P = (N+2)/D0 --> P = [(13)+2)/(.1535")] --> P = 97.7
Closest "standard" P = 96 --> Diametric pitch of 96 is assumed (teeth/in)

The above is for standard gears.

Inspect the Circular Pitch in the optical comparator DP=Pi/Cp
verify the planet and the sun gear.
Measure centerline of tooth to tooth

measure the root diameter to obtain whole depth. (OD -root )/2=whole depth

edit: also : never assume gears are standard Diametral Pitch & Pressure angle.
designers will use bastard numbers to to prevent reverse engineering.

Ninereng do you have access to a cnc gear checker. this the best way to reverse engineer gears.

RE: Planetary Gear System Identification?

once DP is solved , take a gear an angle measurement at the pitch diameter. and record.
base pitch measurements is correct in theory but is some times difficult to obtain a tangent
measurement. so double verify with a visual.
here is attached is base pitch tables and the correct method for measurement.

RE: Planetary Gear System Identification?

once the diametral pitch and pressure angle are obtain a measurement over wires can be calculated.
with 3 different wire size Diameter to locate near the tip, near the pitch diameter and near the tif (True Involute form)
this will verify the involute profile. but is not as precise as an involute verification with a gear checker.
if the involute is straight then the DP & PA are correct. this is a must.

RE: Planetary Gear System Identification?

don't worry for the about the X profile shift , because the outside diameter and whole depth is measured.
until the correct DP and PA are obtained. once you have the data we will continue.
again if you can hire a gear shop to run lead and profile verification, it will nail the above dead solid.

RE: Planetary Gear System Identification?

Hello Mfgenggear,

You are the man!

Thank you for breaking it down for me I will rework the numbers and follow up on Monday.

But to measure the circular pitch correctly I need to know the pitch circle diameter to measure it from don't I?

I notice that the table doesn't quite go up to 96 DP so I can't tell what BP the proper pressure angle corresponds to.

Also, I am a little unclear on what you mean by getting a straight involute with the wire measurements. Should the involute not be a curve and how do those measurements give me a involute profile?

Sorry if these are silly questions I am still learning.

Either way, I will be sending the gears off to a gear shop to see what numbers they get as a backup. However, I'd like to get to a point where we can identify these ourselves but that may require justification for a cnc gear checker purchase.

Again, thanks for the awesome insight.

RE: Planetary Gear System Identification?

Looking at your numbers, I'd say 96DP 20PA would be my first assumption.

Quote (mfgenggear)

don't worry [...] about the X profile shift [...] until the correct DP and PA are obtained.
I fully agree.

You need a verification of the DP and PA, no doubt about that.
Checking the DP and PA with a CNC gear checker will be challenging with such small teeth - there are other ways to do it, it may be hard to find the right people.

Good luck!

RE: Planetary Gear System Identification?


may want to purchase this specification AGMA 2000 AGMA 2015 , some prints require the old AGMA 2000

When a spur or helical gear profile is inspected and recorded on a involute chart, it is interpolated to a straight line. see attached chart from agma
when a spur or helical gear is charted for lead,(parallel) it is also charted in a straight line.
unless it is a modified or crowned profile and lead
In current CNC software charts are recorded and printed for archiving.
see attached screen shots

RE: Planetary Gear System Identification?

Understood. Thanks for the AGMA reference as well. Will update with what the gear people say as well once I send them off. Judging from what you guys said I definitely need another set of eyes on these

RE: Planetary Gear System Identification?

those are tiny fine pitch gears , and will be a challenge

RE: Planetary Gear System Identification?

for a ref only. I cranked out the data on MIT calc.
edit: I nput the exact measure data that was on the previous post.
the MIT calc I would have to make a user material for stainless
look at the Tip diameter sizes, chordal thickness at the tip
use a gear calculator like zakgear on line, to calculate measurement over wires, for GP, I like playing with gears.
find attached.

RE: Planetary Gear System Identification?

any luck

RE: Planetary Gear System Identification?

Hey Mfgenggear,

Sent the gears off for material testing.
Following that I will send off to gear vendor for identifying.

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