Planetary gear set of carrier, inner planet, and outer planet wheels with adjustable gear ratio and friction losses
The Planet-Planet gear block represents a set of carrier, inner planet, and outer planet gear wheels. Both planetary gears are connected to and rotate with respect to the carrier. The planets corotate with a fixed gear ratio that you specify. For model details, see Planet-Planet Gear Model.
Planet-Planet Gear Set
C, Po, and Pi are rotational conserving ports representing, respectively, the carrier, outer planet, and inner planet gear wheels.
The dialog box has one active area, Parameters, with three tabs.
Ratio goi of the outer planet gear radius wheel to the inner planet gear wheel radius. This gear ratio must be strictly positive. The default is 2.
Select how to implement friction losses from nonideal meshing of gear teeth. The default is No meshing losses.
No meshing losses — Suitable for HIL simulation — Gear meshing is ideal.
Constant efficiency — Transfer of torque between gear wheel pairs is reduced by a constant efficiency η satisfying 0 < η ≤ 1. If you select this option, the panel changes from its default.
Planet-Planet imposes one kinematic and one geometric constraint on the three connected axes:
rCωC = rPoωPo+ rPiωPi , rC = rPo + rPi .
The outer planet-to-inner planet gear ratio goi = rPo/rPi = NPo/NPi. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:
(1 + goi)ωC = ωPi + goiωPo .
The three degrees of freedom reduce to two independent degrees of freedom. The gear pair is (1,2) = (Pi,Po).
The torque transfer is:
goiτPi + τPo – τloss = 0 ,
with τloss = 0 in the ideal case.
In the nonideal case, τloss ≠ 0. See Model Gears with Losses.
Gear ratios must be positive. Gear inertia and compliance are ignored. Coulomb friction reduces simulation performance. See Adjust Model Fidelity.