Represent set of carrier, inner planet, and outer planet gear wheels with specified planet-planet gear ratio
The Planet-Planet gear block represents a set of carrier, inner planet, and outer planet gear wheels. The outer planet is connected to and rotates with respect to the carrier. The inner planet rotates independently. The planets corotate with a fixed gear ratio that you specify and in opposite directions with respect to the carrier. A planet-planet gear is, along with a ring-planet gear, a basic element of a planetary gear set.
The Planet-Planet block imposes one kinematic and one geometric constraint on the three connected axes:
rCωC = rPoωPo+ rPiωPi , rC = rPo + rPi
In terms of the outer planet-to-inner planet gear ratio goi = rPo/rPi, the effective kinematic constraint is
(1 + goi)ωC = ωPi + goi·ωPo ,
reducing the three axes to two independent degrees of freedom.
The gear ratio is also the ratio of the number of teeth on each gear and the ratio of the torques in each axis, goi = NPo/NPi = τPo/τPi.
Warning All gear ratios must be strictly positive. If any gear ratio equals 0 or becomes negative at any time, a SimDriveline™ simulation stops with an error.
In general, as shown in the first instance, the inner planet shaft does not have to be aligned with the carrier shaft.
Planet-Planet Gear Set