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


Gears/Planetary Subcomponents


The Planet-Planet gear block represents a set of carrier, inner planet, and outer planet gear wheels. Both planetary gears are connected to and rotate with respect to the carrier. The planets corotate with a fixed gear ratio that you specify. For model details, see Planet-Planet Gear Model.


C, Po, and Pi are rotational conserving ports representing, respectively, the carrier, outer planet, and inner planet gear wheels.

Dialog Box and Parameters


Outer planet (Po) to inner planet (Pi) teeth ratio (NPo/NPi)

Ratio goi of the outer planet gear radius wheel to the inner planet gear wheel radius. This gear ratio must be strictly positive. The default 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

Inner planet-carrier viscous friction coefficient

Viscous friction coefficient μPi for the inner 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)).

Planet-Planet Gear Model

Ideal Gear Constraints and Gear Ratios

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

rCωC = rPoωPo+ rPiωPi , rC = rPo + rPi .

The outer planet-to-inner planet gear ratio goi = rPo/rPi = NPo/NPi. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:

(1 + goi)ωC = ωPi + goiωPo .

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

The torque transfer is:

goiτPi + τPoτloss = 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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