Planetary gear train with stepped planet gear set

**Library:**Simscape / Driveline / Gears

The Compound Planetary Gear block represents a planetary gear train with composite planet gears. Each composite planet gear is a pair of rigidly connected and longitudinally arranged gears of different radii. One of the two gears engages the centrally located sun gear while the other engages the outer ring gear.

**Compound Planetary Gear**

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

To increase the fidelity of the gear model, specify properties such as gear inertia,
meshing losses, and viscous losses. By default, gear inertia and viscous losses are
assumed to be negligible. The block enables you to specify the inertias of the internal
planet gears only. To model the inertias of the carrier, sun, and ring gears, connect
Simscape
Inertia blocks to ports
**C**, **S**, 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 model variant that includes a thermal port. Specify the
associated thermal parameters for the component.

The Compound Planetary Gear block imposes two kinematic and two geometric constraints on the three connected axes and the fourth, internal wheel (planet):

r_{C}ω_{C}
=
r_{S}ω_{S}+
r_{P1}ω_{P}
, r_{C} =
r_{S} +
r_{P1} , | (1) |

r_{R}ω_{R}
=
r_{C}ω_{C}+
r_{P2}ω_{P}
, r_{R} =
r_{C} +
r_{P2} . | (2) |

The ring-planet gear ratio is *g*_{RP} =
*r*_{R}/*r*_{P2}
=
*N*_{R}/*N*_{P2} and the planet-sun gear ratio is *g*_{PS} =
*r*_{P1}/*r*_{S}
=
*N*_{P1}/*N*_{S}. *N* is the number of teeth on each gear. In
terms of these ratios, the key kinematic constraint is:

(1 +
g_{RP}·g_{PS})ω_{C}
= ω_{S} +
g_{RP}·g_{PS}ω_{R}
. | (3) |

The four degrees of freedom reduce to two independent degrees of freedom. The gear pairs are (1,2) = (P2,R) and (S,P1).

The gear ratio *g*_{RP} must be
strictly greater than one.

The torque transfers are:

g_{RP}τ_{P2}
+ τ_{R} –
τ_{loss}(P2,R) = 0 ,
g_{PS}τ_{S}
+ τ_{P1} –
τ_{loss}(S,P1) = 0 , | (4) |

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.