# Planet-Planet

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

**Libraries:**

Simscape /
Driveline /
Gears /
Planetary Subcomponents

## Description

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.

### Thermal Model

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
```

.

### Equations

**Ideal Gear Constraints and Gear Ratios**

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.

**Nonideal Gear Constraints and Losses**

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

### Variables

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.

### Assumptions and Limitations

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.

## Ports

### Conserving

## Parameters

## More About

## Extended Capabilities

## Version History

**Introduced in R2011a**