Planetary gear set of carrier, beveled planet, and sun wheels with adjustable gear ratio, assembly orientation, and friction losses
The Sun-Planet Bevel 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 and in a direction that you specify. You control the direction by setting the assembly orientation, left or right. A sun-planet and a ring-planet gear are basic elements of a planetary gear set. For model details, see Sun-Planet Bevel 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 gPS of the planet gear wheel radius to the sun gear wheel radius. This gear ratio must be strictly greater than 1. The default value is 2.
Relative orientation of sun and planet gears, controlling their corotation direction. Left or right orientation imply, respectively, that the gears corotate in the same or opposite direction.
The default is Left — Sun and planet gears rotate in same direction.
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 Bevel imposes one kinematic and one geometric constraint on the three connected axes:
rCωC = rSωS ± rPωP , rC = rS ± rP .
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 upper or lower sign applies, respectively, to left-oriented or right-oriented bevel assembly. 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.
These SimDriveline™ example models use the Sun-Planet Bevel gear to create custom gear sets: