Planetary gear set of carrier, planet, and ring wheels with adjustable gear ratio and friction losses


Gears/Planetary Subcomponents


The Ring-Planet gear block represents a set of carrier, planet, and ring gear wheels. The planet is connected to and rotates with respect to the carrier. The planet and ring corotate with a fixed gear ratio that you specify. A ring-planet and a sun-planet gear are basic elements of a planetary gear set. For model details, see Ring-Planet Gear Model.


C, P, and R are rotational conserving ports representing, respectively, the carrier, planet, and ring gear wheels.

Dialog Box and Parameters


Ring (R) to planet (P) teeth ratio (NR/NP)

Ratio gRP of the ring gear wheel radius to the planet gear wheel radius. This gear ratio must be strictly greater than 1. The default value is 2.

Meshing Losses

Friction model

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.

     Constant Efficiency

Viscous Losses

Planet-carrier viscous friction coefficient

Viscous friction coefficient μP for the planet-carrier gear motion. The default is 0.

From the drop-down list, choose units. The default is newton-meters/(radians/second) (N*m/(rad/s)).

Ring-Planet Gear Model

Ideal Gear Constraints and Gear Ratios

Ring-Planet imposes one kinematic and one geometric constraint on the three connected axes:

rRωR = rCωC + rPωP , rR = rC + rP .

The ring-planet gear ratio gRP = rR/rP = NR/NP. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:

gRPωR = ωP + (gRP – 1)ωC .

The three degrees of freedom reduce to two independent degrees of freedom. The gear pair is (1,2) = (P,R).

    Warning   The ring-planet gear ratio gRP must be strictly greater than one.

The torque transfer is:

gRPτP + τRτloss = 0 ,

with τloss = 0 in the ideal case.

Nonideal Gear Constraints and Losses

In the nonideal case, τloss ≠ 0. See Model Gears with Losses.


  • Gear inertia is negligible. It does not impact gear dynamics.

  • Gears are rigid. They do not deform.

  • Coulomb friction slows down simulation. See Adjust Model Fidelity.


The sdl_epicyclic_gearboxsdl_epicyclic_gearbox example model uses two Ring-Planet gears to model a nonideal epicyclic gear set.

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