Planetary gear set of carrier, sun, planet, and ring wheels with adjustable gear ratio and friction losses
The Planetary Gear block represents a set of carrier, ring, planet, and sun gear wheels. A planetary gear set can be constructed from sun-planet and ring-planet gears. The ring and sun corotate with a fixed gear ratio. For model details, see Planetary Gear Model.
Planetary Gear Set
C, R, and S are rotational conserving ports representing, respectively, the carrier, ring, and sun gear wheels.
The dialog box has one active area, Parameters, with three tabs.
Ratio gRS of the ring gear wheel radius to the sun gear wheel radius. This gear ratio must be strictly greater than 1. 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.
Planetary Gear imposes two kinematic and two geometric constraints on the three connected axes and the fourth, internal gear (planet):
rCωC = rSωS+ rPωP , rC = rS + rP ,
rRωR = rCωC+ rPωP , rR = rC + rP .
The ring-sun gear ratio gRS = rS/rS = NR/NS. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:
(1 + gRS)ωC = ωS + gRSωR .
The four degrees of freedom reduce to two independent degrees of freedom. The gear pairs are (1,2) = (S,P) and (P,R).
The torque transfer is:
gRSτS + τR – 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.