Could someone please explain to me how to calculate the gear mesh frequencies and speeds of a 3 stage rex planetary gearbox. The formulas I have do not seem to work. The input speed is 1793 CPM the first gear has 23 teeth the 3 planets have 43 teeth the input into the 2nd reduction has 35 teeth the 3 planets have 37 the input into the third reduction has 47 teeth and the 3 planets have 31 the ring gear at all three stages has 109 teeth and the output speed is measured at 22 cpm. Thanks in advance.

Each stage will have its own tooth mesh frequency. The speed of any of the moving gears in a stage x the number of teeth will give the tooth mesh for that stage. You need to be specific as to what is fixed and what is moving (input and output) for each of the three stages.

Walt

The ring gear is fixed in all 3 stages.

With the ring gear fixed, and the planet carrier being the output, the formula you are looking for is
Output = (Input) (1/(1+(N3/N1))
With N3 being the ring gear teeth, and N1 being sun gear.
The carrier output will have a sun on the end of it, and the output of first red. will be input to second, etc.
I get 22.87 something with a 1793 input using the numbers you gave.

Been a while since I figured something like that (20 yrs?). I'm in the habit of plugging it into Odyssey now. Probably bad habit to be in for the brain

Dave

This message has been edited. Last edited by: RRS_Dave,

See attached for various related speeds and frequencies.

John from PA

3_stage_planetary.pdf (3 Kb, 76 downloads)

John, The only formula that I have for these Planet frequincies are from the CSI training manuals and Art Crawfords "Simplified Handbook of Vibration Analysis".
The ratio is coming out fine, the GMF and Planet gear speed is what I am having trouble with.
What are the formula's that you use for the GMF and planet speed?
I have attached a spread sheet using the CSI formula's. Maybe someone can see what I am missing.
Thanks Scott

Planet_gear.xls (885 Kb, 49 downloads)

That is the same problem I was having that is why I started this post and any input would be greatly appreciated.

wsegrav
Try one of these sites
http://www.roymech.co.uk/Useful_Tables/Drive/Epi_cyclic_gears.html
http://www.dliengineering.com/vibman/planetarygears.htm

The Roymech reference link is better than the DLI reference, since if identifies different formulas depending upon what is moving or fixed. Some folks over simplify epicyclic gear formulas.

Walt

Here's how I would calculate them.

Planetary_Gear_Freqs.xls (16 Kb, 26 downloads)

Thanks everyone this has been alot of help.