Definition:
A planetary gear train is a system containing a total of three or more gears where a ring gear
encircles the entire system. There are three main parts to planetary gear systems, often called
sun, planet, and ring gears.
Variables:
Let us give variables to the three main parts of the system.
o Sun Gear Teeth = S
o Planet Gear Teeth = P
o Ring Gear Teeth = R
o Turns of Sun Gear = Ts
o Turns of Planetary Gear = Tp
o Turns of Ring Gear = Tr
Finding the number of teeth:
In order for the gear system to work properly, the teeth of all three gears must be able to fit
according to how many teeth each one has. To find the number of teeth the third gear must have,
you can use the equation R=2*P+S. The number of teeth the third gear must have equals twice
the number of planetary teeth, plus the number of sun teeth.
Gear turn ratios:
The formula for the turn ration is (R+S)*Tp=R*Tr+Ts*S. You can use this formula to find the
gear ratio, no matter which gear you choose to be stationary.
EXAMPLE:
If we hold the sun gear in place, Ts will always equal zero because it is not moving. This allows
us to edit the formula to (R+S)*Tp=R*Tr. If we choose to make the ring gear driven, we would
rearrange the formula like so:
Tp=Tr*(R/(R+S))
Meaning the gear ratio is (R/(R+S)).
Advantages & Disadvantages:
Advantages of planetary gears include:
o High power density
o Small volume
o Many combinations
Disadvantages include:
o High bearing loads
o Inaccessibility
o Design complexity
Aaron Maynard
STEM Engineering Math