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


Simscape / Driveline / 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.

Thermal Modeling

You can model the effects of heat flow and temperature change through an optional thermal conserving port. By default, the thermal port is hidden. To expose the thermal port, right-click the block in your model and, from the context menu, select Simscape > Block choices. Select a variant that includes a thermal port. Specify the associated thermal parameters for the component.

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, τloss0. See Model Gears with Losses.


  • Gear inertia is assumed negligible.

  • Gears are treated as rigid components.

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


CRotational conserving port representing the planet carrier
PoRotational conserving port representing the outer planet gear
PiRotational conserving port representing the inner planet gear
HThermal conserving port for thermal modeling



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

Parameters for meshing losses vary with the block variant chosen—one with a thermal port for thermal modeling and one without it.

 Without Thermal Port

 With Thermal Port

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)).

Thermal Port

Thermal mass

Thermal energy required to change the component temperature by a single degree. The greater the thermal mass, the more resistant the component is to temperature change. The default value is 50 J/K.

Initial temperature

Component temperature at the start of simulation. The initial temperature alters the component efficiency according to an efficiency vector that you specify, affecting the starting meshing or friction losses. The default value is 300 K.

Real-Time Simulation

Hardware-in-the-Loop Simulation

For optimal simulation performance, use the Meshing Losses > Friction model parameter default setting, No meshing losses - Suitable for HIL simulation.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Introduced in R2011a