Planetary gear with two sun gears and two planet gear sets

Simscape / Driveline / Gears

This block represents a planetary gear train with dual sun and planet gear sets. The two sun gears are centrally located and separated longitudinally along a common rotation axis. The smaller of these gears engages an inner planet gear set, which in turn engages an outer planet gear set. The outer planet gear set, whose length spans the distance between the two sun gears, engages both the larger sun gear and the ring gear.

A carrier holds the planet gear sets in place at different radii. The carrier, which rigidly connects to a drive shaft, can spin as a unit with respect to the sun and ring gears. Revolute joints, each located between a planet gear and the carrier, enable the gears to spin about their individual longitudinal axes.

The relative angular velocities of the sun, planet, and ring gears follow from the kinematic constraints between them. For more information, see Ravigneaux Gear Model.

The block models the Ravigneaux gear as a structural component based on Sun-Planet, Planet-Planet, and Ring-Planet Simscape™ Driveline™ blocks. The figure shows the block diagram of this structural component.

To increase the fidelity of the gear model, you can specify properties such as gear inertia, meshing losses, and viscous losses. By default, gear inertia and viscous losses are assumed negligible. The block enables you to specify the inertias of the internal planet gears only. To model the inertias of the carrier, large sun, small sun, and ring gears, connect Simscape Inertia blocks to ports C, SL, SS, and R.

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.

Ravigneaux imposes four kinematic and four geometric constraints on the four connected axes and the two internal wheels (inner and outer planets):

*r*_{Ci}*ω*_{C} = *r*_{SS}*ω*_{SS} + *r*_{Pi}*ω*_{Pi} , *r*_{Ci} = *r*_{SS} + *r*_{Pi} ,

*r*_{Co}*ω*_{C} = *r*_{SL}*ω*_{SL} + *r*_{Po}*ω*_{Po} , *r*_{Co} = *r*_{SL} + *r*_{Po} ,

(*r*_{Co} – *r*_{Ci})*ω*_{C} = *r*_{Pi}*ω*_{Pi} + *r*_{Po}ω_{Po} , *r*_{Co} – *r*_{Ci}= *r*_{Po} + *r*_{Pi} ,

*r*_{R}*ω*_{R} = *r*_{Co}*ω*_{C} + *r*_{Po}*ω*_{Po} , *r*_{R} = *r*_{Co} + *r*_{Po} .

The ring-small sun ratio *g*_{RSS} = *r*_{R}/*r*_{SS} = *N*_{R}/*N*_{SS} and
ring-large sun gear ratio *g*_{RSL} = *r*_{R}/*r*_{SL} = *N*_{R}/*N*_{SL}. *N* is
the number of teeth on each gear. In terms of these ratios, the key
kinematic constraints are:

(*g*_{RSS} –
1)*ω*_{C} = *g*_{RSS}*ω*_{R} – *ω*_{SS} ,

(*g*_{RSL} + 1)*ω*_{C} = *g*_{RSL}*ω*_{R} + *ω*_{SL} .

The six degrees of freedom reduce to two independent degrees of freedom. The gear pairs are (1,2) = (LS,P), (SS,P), (P,R), and (P,P).

The gear ratio *g*_{RSS} must
be strictly greater than the gear ratio *g*_{RSL}.
The gear ratio *g*_{RSL} must
be strictly greater than one.

The torque transfers are:

*g*_{RSS}*τ*_{SS} + *τ*_{R} – *τ*_{loss}(SS,R)
= 0 , *g*_{RSL}*τ*_{SL} + *τ*_{R} – *τ*_{loss}(SL,R)
= 0 ,

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

In the nonideal case, $${\tau}_{loss}\ne 0$$. See Model Gears with Losses.

Gears are assumed rigid.

Coulomb friction slows down simulation. See Adjust Model Fidelity.

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

C | Rotational conserving port representing the planet gear carrier |

R | Rotational conserving port representing the ring gear |

SL | Rotational conserving port representing the large sun gear |

SS | Rotational conserving port representing the small sun gear |

H | Thermal conserving port for thermal modeling |

**Ring (R) to large sun (SL) teeth ratio (NR/NSL)**Ratio

*g*_{RSL}of the ring gear wheel radius to the large sun gear wheel radius. This gear ratio must be strictly greater than 1. The default is`2`

.**Ring (R) to small sun (SS) teeth ratio (NR/NSS)**Ratio

*g*_{RSS}of the ring gear wheel radius to the small sun gear wheel radius. This gear ratio must be strictly greater than the ring-large sun gear ratio. The default is`3`

.

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

**Large sun-carrier, small sun-carrier, large sun planet-carrier, and small sun planet-carrier viscous friction coefficients**Vector of viscous friction coefficients [

*μ*_{LS}*μ*_{SS}*μ*_{LSP}*μ*_{SSP}] for the large sun-carrier, small sun-carrier, large sun planet-carrier, and small sun planet-carrier gear motions, respectively. The default is`[0 0 0 0]`

.From the drop-down list, choose units. The default is newton-meters/(radians/second) (

`N*m/(rad/s)`

).

**Inner planet gear inertia**Moment of inertia of the planet gear carrier. This value must be positive or zero. Enter

`0`

to ignore carrier inertia. The default value is`0`

kg*m^2.**Outer planet gear inertia**Moment of inertia of the combined planet gears. This value must be positive or zero. Enter

`0`

to ignore gear inertia. The default value is`0`

kg*m^2.

**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
```

.