# Planetary Gear

Gear train with sun, planet, and ring gears

## Library

Simscape / Driveline / Gears

## Description

This block models a gear train with sun, planet, and ring gears. Planetary gears are common in transmission systems, where they provide high gear ratios in compact geometries. A carrier connected to a drive shaft holds the planet gears. Ports C, R, and S represent the shafts connected to the planet gear carrier, ring gear, and sun gear.

The block models the planetary gear as a structural component based on Sun-Planet and Ring-Planet Simscape™ Driveline™ blocks. The figure shows the block diagram of this structural component.

To increase the fidelity of the gear model, you can specify properties such as gear inertia, meshing losses, and viscous losses. By default, gear inertia and viscous losses are assumed negligible. The block enables you to specify the inertias of the internal planet gears only. To model the inertias of the carrier, sun, and ring gears, connect Simscape Inertia blocks to ports C, S, and R.

### Thermal Modeling

You can model the effects of heat flow and temperature change through an optional thermal conserving port. By default, the thermal port is hidden. To expose the thermal port, right-click the block in your model and, from the context menu, select Simscape > Block choices. Select a variant that includes a thermal port. Specify the associated thermal parameters for the component.

## Planetary Gear Model

### Ideal Gear Constraints and Gear Ratios

Planetary Gear imposes two kinematic and two geometric constraints on the three connected axes and the fourth, internal gear (planet):

rCωC = rSωS+ rPωP , rC = rS + rP ,

rRωR = rCωC+ rPωP , rR = rC + rP .

The ring-sun gear ratio gRS = rR/rS = NR/NS. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:

(1 + gRSC = ωS + gRSωR .

The four degrees of freedom reduce to two independent degrees of freedom. The gear pairs are (1,2) = (S,P) and (P,R).

### Warning

The gear ratio gRS must be strictly greater than one.

The torque transfer is:

gRSτS + τRτloss = 0 ,

with τloss = 0 in the ideal case.

### Nonideal Gear Constraints and Losses

In the nonideal case, τloss ≠ 0. See Model Gears with Losses.

## Ports

PortDescription
CRotational conserving port that represents the planet gear carrier
RRotational conserving port that represents the ring gear
SRotational conserving port that represents the sun gear
HThermal conserving port for thermal modeling

## Parameters

### Main

Ring (R) to sun (S) teeth ratio (NR/NS)

Ratio gRS of the ring gear wheel radius to the sun gear wheel radius. This gear ratio must be strictly greater than 1. The default is 2.

### Meshing Losses

Parameters for meshing losses vary with the block variant chosen—one with a thermal port for thermal modeling and one without it.

### Viscous Losses

Sun-carrier and planet-carrier viscous friction coefficients

Vector of viscous friction coefficients [μS μP] for the sun-carrier and planet-carrier gear motions, respectively. The default is [0 0].

From the drop-down list, choose units. The default is newton-meters/(radians/second) (N*m/(rad/s)).

### Inertia

Planet gear inertia

Moment of inertia of the combined planet gears. This value must be positive or zero. Enter 0 to ignore gear inertia. The default value is 0 kg*m^2.

### Thermal Port

Thermal mass

Thermal energy required to change the component temperature by a single degree. The greater the thermal mass, the more resistant the component is to temperature change. The default value is 50 J/K.

Initial temperature

Component temperature at the start of simulation. The initial temperature alters the component efficiency according to an efficiency vector that you specify, affecting the starting meshing or friction losses. The default value is 300 K.

## Extended Capabilities

### Real-Time and Hardware-in-the-Loop Simulation

For optimal simulation performance, use the Meshing Losses > Friction model parameter default setting, No meshing losses - Suitable for HIL simulation.