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.

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

*r*_{C}ω_{C} =
*r*_{Po}*ω*_{Po}+
*r*_{Pi}*ω*_{Pi}
, *r*_{C} =
*r*_{Po} +
*r*_{Pi} .

The outer planet-to-inner planet gear ratio *g*_{oi} =
*r*_{Po}/*r*_{Pi}
=
*N*_{Po}/*N*_{Pi}. *N* is the number of teeth on each gear. In
terms of this ratio, the key kinematic constraint is:

(1 +
*g*_{oi})*ω*_{C}
= *ω*_{Pi} +
*g*_{oi}*ω*_{Po}
.

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

The torque transfer is:

*g*_{oi}*τ*_{Pi}
+ *τ*_{Po} –
*τ*_{loss} = 0 ,

with *τ*_{loss} = 0 in the ideal case.

In the nonideal case, $${\tau}_{loss}\ne 0$$. 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.

Port | Description |
---|---|

C | Rotational conserving port representing the planet carrier |

Po | Rotational conserving port representing the outer planet gear |

Pi | Rotational conserving port representing the inner planet gear |

H | Thermal conserving port for thermal modeling |

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

*g*_{oi}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`

.

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

**Inner planet-carrier viscous friction coefficient**Viscous friction coefficient

*μ*_{Pi}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 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.

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

.