# Sun-Planet

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

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

## Description

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.

### 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**

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.

**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.

## Limitations and Assumptions

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**