# Ring-Planet

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

**Libraries:**

Simscape /
Driveline /
Gears /
Planetary Subcomponents

## Description

The Ring-Planet block represents a carrier, a ring gear, and a set of planet gears. The planet gears are connected to and rotate with respect to the carrier. The planet and ring gears corotate with a fixed gear ratio that you specify. A ring-planet and a sun-planet gear are basic elements of a planetary gear set. 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 Ring-Planet block imposes one kinematic and one geometric constraint on the three connected axes:

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

$${r}_{\text{R}}={r}_{\text{C}}+{r}_{\text{P}}$$

The ring-planet gear ratio is

$${g}_{\text{RP}}={r}_{\text{R}}/{r}_{\text{P}}={N}_{\text{R}}/{N}_{\text{P}},$$

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

$${g}_{\text{RP}}{\omega}_{\text{R}}={\omega}_{\text{P}}+\text{}({g}_{\text{RP}}\u2013\text{1}){\omega}_{\text{C}}.$$

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

**Warning**

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

The torque transfer is:

$${g}_{\text{RP}}{\tau}_{\text{P}}+{\tau}_{\text{R}}\u2013{\tau}_{\text{loss}}=\text{}0.$$

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**