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


Gears/Planetary Subcomponents


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.

Dialog Box and Parameters


Ring (R) to sun (S) teeth ratio (NP/NS)

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.

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

Sun-carrier viscous friction coefficient

Viscous friction coefficient μS for the sun-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)).

Sun-Planet Gear Model

Ideal Gear Constraints and Gear Ratios

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).

    Warning   The planet-sun gear ratio gPS must be strictly greater than one.

The torque transfer is:

gPSτS + τPτloss = 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.

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