Planetary gear set of carrier, planet, and sun wheels with adjustable gear ratio and friction losses
The Sun-Planet gear block represents a set of carrier, planet, and sun gear wheels. The planet is connected to and rotates with respect to the carrier. The planet and sun corotate with a fixed gear ratio that you specify and in the same direction with respect to the carrier. A sun-planet and a ring-planet gear are basic elements of a planetary gear set. For model details, see Sun-Planet Gear Model.
C, P, and S are rotational conserving ports representing, respectively, the carrier, planet, 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 value 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.
Sun-Planet imposes one kinematic and one geometric constraint on the three connected axes:
rCωC = rSωS + rPωP , rC = rP + rS .
The planet-sun gear ratio gPS = rP/rS = NP/NS. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:
ωS = –gPSωP + (1 + gPS)ωC .
The three degrees of freedom reduce to two independent degrees of freedom. The gear pair is (1,2) = (S,P).
The torque transfer is:
gPSτS + τP – 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.