# Double-Pinion Planetary Gear

Planetary gear train with two meshed planet gear sets

## Library

Simscape / Driveline / Gears

## Description

This block represents a planetary gear train with two meshed planet gear sets between the sun gear and the ring gear. A single carrier holds the two planet gear sets at different radii from the sun gear centerline, while allowing the individual gears to rotate with respect to each other. The gear model includes power losses due to friction between meshing gear teeth and viscous damping of the spinning gear shafts.

Structurally, the double-pinion planetary gear resembles a Ravigneaux gear without its second, large, sun gear. The inner planet gears mesh with the sun gear and the outer planet gears mesh with the ring gear. Because it contains two planet gear sets, the double-pinion planetary gear reverses the relative rotation directions of the ring and sun gears.

The teeth ratio of a meshed gear pair fixes the relative angular velocities of the two gears in that pair. The dialog box provides two parameters to set the ring-sun and outer planet-inner planet gear teeth ratios. A geometric constraint fixes the remaining teeth ratios—ring-outer planet and inner planet-sun. This geometric constraint requires that the ring gear radius equal the sum of the sun gear radius with the inner and outer planet gear diameters:

`${r}_{r}={r}_{s}+2\cdot {r}_{pi}+2\cdot {r}_{po},$`
where:

• rr is the ring gear radius

• rs is the sun gear radius

• rpi is the inner planet gear radius

• rpo is the outer planet gear radius

In terms of the ring-sun and outer planet-inner planet teeth ratios, the ring-outer planet teeth ratio is

`$\frac{{r}_{r}}{{r}_{po}}=2\cdot \frac{\frac{{r}_{r}}{{r}_{s}}}{\left(\frac{{r}_{r}}{{r}_{s}}-1\right)}\cdot \frac{\left(\frac{{r}_{po}}{{r}_{pi}}+1\right)}{\frac{{r}_{po}}{{r}_{pi}}},$`
The inner planet-sun teeth ratio is
`$\frac{{r}_{pi}}{{r}_{s}}=\frac{\left(\frac{{r}_{r}}{{r}_{s}}-1\right)}{2\left(\frac{{r}_{po}}{{r}_{pi}}+1\right)},$`

The Differential block is a composite component. It contains three underlying blocks—Ring-Planet, Planet-Planet, and Sun-Planet—connected as shown in the figure. Each block connects to a separate drive shaft through a rotational conserving port.

### 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.

## Ports

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

## Parameters

### Main

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

Teeth ratio between the ring and sun gears. This ratio is the number of teeth in the ring gear divided by the number of teeth in the sun gear. The default value is `2`.

Outer planet (Po) to inner planet (Pi) teeth ratio (NPo/NPi)

Teeth ratio between the outer-planet and inner-planet gears. This ratio is the number of teeth in the outer planet divided by the number of gear teeth in the inner planet. The default value is `1`.

### 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

Specify the power losses due to viscous damping of the gear carriers.

Sun-carrier, ring-carrier, and planet-carrier viscous friction coefficients

Enter a vector with the viscous friction coefficients that dampen sun-carrier, ring-carrier, and planet-carrier motion, in that order. From the drop-down list, select a physical unit. The default vector is `[0 0 0]` `N*m/(rad/s)`.

### 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```.