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

**Library:**Simscape / Driveline / Gears / Planetary Subcomponents

The Planet-Planet gear block represents a carrier and two inner-outer planet gear couples. Both planet gears are connected to and rotate with respect to the carrier. The planet gears corotate with a fixed gear ratio that you specify. For model details, see Equations.

You can model
the effects of heat flow and temperature change by enabling the optional thermal port. To enable
the port, set **Friction model** to ```
Temperature-dependent
efficiency
```

.

The Planet-Planet block imposes one kinematic and one geometric constraint on the three connected axes:

$${r}_{\text{C}}{\omega}_{\text{C}}={r}_{\text{Po}}{\omega}_{\text{Po}}+{r}_{\text{Pi}}{\omega}_{\text{Pi}}$$

$${r}_{\text{C}}={r}_{\text{Po}}+{r}_{\text{Pi}}$$

The outer planet-to-inner planet gear ratio is

$${g}_{\text{oi}}={r}_{\text{Po}}/{r}_{\text{Pi}}={N}_{\text{Po}}/{N}_{\text{Pi}},$$

where *N* is the number of teeth on each gear. In terms of
this ratio, the key kinematic constraint is

$$\left(\text{1}+{g}_{\text{oi}}\right){\omega}_{\text{C}}={\omega}_{\text{Pi}}+{g}_{\text{oi}}{\omega}_{\text{Po}}.$$

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

The torque transfer is

$${g}_{\text{oi}}{\tau}_{\text{Pi}}+{\tau}_{\text{Po}}\u2013{\tau}_{\text{loss}}=\text{}0.$$

In the ideal
case where there is no torque loss, *τ _{loss}* = 0.

In the nonideal case, *τ _{loss}* ≠ 0. For more information, see Model Gears with Losses.

Use the **Variables** settings to set the priority and initial target
values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables.

Gear inertia is assumed to be negligible.

Gears are treated as rigid components.

Coulomb friction slows down simulation. For more information, see Adjust Model Fidelity.