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

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

The Sun-Planet gear block represents a set of carrier, planet, and sun gear wheels. The planet is connected to and rotates with respect to the carrier. The planet and sun corotate with a fixed gear ratio that you specify and in the same direction with respect to the carrier. A sun-planet and a ring-planet gear are basic elements of a planetary gear set. 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
```

.

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

$${r}_{\text{C}}{\omega}_{\text{C}}={r}_{\text{S}}{\omega}_{\text{S}}+{r}_{\text{P}}{\omega}_{\text{P}}$$

The planet-sun gear ratio is

$${g}_{\text{PS}}={r}_{\text{P}}/{r}_{\text{S}}={N}_{\text{P}}/{N}_{\text{S}}$$

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

$${\omega}_{\text{S}}=\text{}\u2013{g}_{\text{PS}}{\omega}_{\text{P}}+\text{}(\text{1}+{g}_{\text{PS}}){\omega}_{\text{C}}$$

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

**Warning**

The planet-sun gear ratio *g _{PS}*
must be strictly greater than one.

The torque transfer is:

$${g}_{\text{PS}}{\tau}_{\text{S}}+{\tau}_{\text{P}}\u2013{\tau}_{\text{loss}}=\text{}0$$

In the ideal case, there is no torque loss,
that is *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.