Compound planetary gear set of carrier, ring, planet, and sun wheels with adjustable gear ratios and friction losses
The Compound Planetary Gear block represents a set of carrier, sun, planet, and ring gear wheels. The planetary shaft has two gear wheels with different radii meshing with the ring and the sun, respectively. The ring and planet corotate with one fixed gear ratio. The planet and sun corotate with another fixed gear ratio. For this reason, a compound planetary gear is also called a dual-ratio planetary gear. For model details, see Compound Planetary Gear Model.
Compound 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.
Fixed ratio gRP of the ring gear to the planet gear. The gear ratio must be strictly greater than 1. The default is 2.
Fixed ratio gPS of the planet gear to the sun gear. The gear ratio must be strictly positive. The default is 1.
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.
Compound Planetary Gear imposes two kinematic and two geometric constraints on the three connected axes and the fourth, internal wheel (planet):
rCωC = rSωS+ rP1ωP , rC = rS + rP1 ,
rRωR = rCωC+ rP2ωP , rR = rC + rP2 .
The ring-planet gear ratio gRP = rR/rP2 = NR/NP2 and the planet-sun gear ratio gPS = rP1/rS = NP1/NS. N is the number of teeth on each gear. In terms of these ratios, the key kinematic constraint is:
(1 + gRP·gPS)ωC = ωS + gRP·gPSωR .
The four degrees of freedom reduce to two independent degrees of freedom. The gear pairs are (1,2) = (P2,R) and (S,P1).
The torque transfers are:
gRPτP2 + τR – τloss(P2,R) = 0 , gPSτS + τP1 – τloss(S,P1) = 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.