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.

The block models the effects of heat flow and temperature change
through an optional thermal port. To expose the thermal port, right-click
the block and select **Simscape** > **Block choices** > **Show thermal
port**. Exposing the thermal port causes
new parameters specific to thermal modeling to appear in the block
dialog box.

**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 influences the starting meshing or friction losses by altering the component efficiency according to an efficiency vector that you specify. The default value is

`300`

K.

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, *τ*_{loss} ≠
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 |

Planetary Gear | Ravigneaux Gear | Ring-Planet | Sun-Planet | Sun-Planet Bevel

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