Gear Calculations

I could not be bothered tying to work this out, someone has done it before, I just have to find it.

On my search journey I found the gear system we are using are call Epicyclic gears.

Anyway I did find a website that published the equation for this specific gear system (http://www.efunda.com/DesignStandards/gears/gears_epicyclic_train.cfm).

If the gear train is Na/Nb/Nc and Nd/Ne (i.e. Sun1/Planet1/Ring1 and Planet2/Ring2) where Ring1 (Nc) is fixed ,and the planets (Nb and Nd) are locked the the reduction ratio is:

R=(1+Nc/Na)/(1-Nc*Nd/Nb/Ne)

Here is the worked example from the website:

Gear Train – Worked Example
NA	21	Sun 1	Driven
NB	61	Planet 1	Locked to Planet 2
NC	141	Ring 1	Fixed
ND	41	Planet 2	Locked to Planet 1
NE	121	Ring 2	Output
	Gearing 1	7.7143	Check
	Gearing 2	0.2168	Check
	Gearing	0.0281	Check
	Reduction	35.5870

Here is Daren's design:

Gear Train – Daren
NA	18	Sun 1	Driven
NB	21	Planet 1	Locked to Planet 2
NC	60	Ring 1	Fixed
ND	21	Planet 2	Locked to Planet 1
NE	57	Ring 2	Output
	Gearing 1	4.3333
	Gearing 2	-0.0526
	Gearing	-0.0121
	Reduction	-82.3333

Note the sign change in the reduction ratio, this appear to be correct.

And here is my five planet version:

Gear Train – Alan v2
NA	25	Sun 1	Driven
NB	20	Planet 1	Locked to Planet 2
NC	65	Ring 1	Fixed
ND	20	Planet 2	Locked to Planet 1
NE	60	Ring 2	Output
	Gearing 1	3.6000
	Gearing 2	-0.0833
	Gearing	-0.0231
	Reduction	-43.2000

Realisation

The gear design has migrated such that the requirement for the two planetary gears to have the same number of teeth is no longer valid.

AlanX

Discussions

MasterOfNull wrote 04/19/2019 at 14:28

First stage is 3.3~:1 for mine, not 4.3:1.

Yes, the negative sign is correct. It switches directions depending on if the output has more teeth than the input or vice versa.

33:1 is a more workable ratio than the original. Good job.

Also, at this point you have contributed more to the project than 90% of all contributors I have had for projects. @Morning.Star is still winning in that regard, but the two of you may just change my mind about contributors... :)

Are you sure? yes | no

Gear Calculations