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# Planet-Planet

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

## Library

Gears/Planetary Subcomponents

## Description

The Planet-Planet gear block represents a set of carrier, inner planet, and outer planet gear wheels. Both planetary gears are connected to and rotate with respect to the carrier. The planets corotate with a fixed gear ratio that you specify. For model details, see Planet-Planet Gear Model.

Planet-Planet Gear Set

### Ports

C, Po, and Pi are rotational conserving ports representing, respectively, the carrier, outer planet, and inner planet gear wheels.

## Dialog Box and Parameters

The dialog box has one active area, Parameters, with three tabs.

### Main

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

Ratio goi of the outer planet gear radius wheel to the inner planet gear wheel radius. This gear ratio must be strictly positive. The default is 2.

### Meshing Losses

Friction model

Select how to implement friction losses from nonideal meshing of gear teeth. The default is No meshing losses.

• No meshing losses — Suitable for HIL simulation — Gear meshing is ideal.

• Constant efficiency — Transfer of torque between gear wheel pairs is reduced by a constant efficiency η satisfying 0 < η ≤ 1. If you select this option, the panel changes from its default.

### Viscous Losses

Inner planet-carrier viscous friction coefficient

Viscous friction coefficient μPi for the inner planet-carrier gear motion. The default is 0.

## Planet-Planet Gear Model

### Ideal Gear Constraints and Gear Ratios

Planet-Planet imposes one kinematic and one geometric constraint on the three connected axes:

rCωC = rPoωPo+ rPiωPi , rC = rPo + rPi .

The outer planet-to-inner planet gear ratio goi = rPo/rPi = NPo/NPi. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:

(1 + goi)ωC = ωPi + goiωPo .

The three degrees of freedom reduce to two independent degrees of freedom. The gear pair is (1,2) = (Pi,Po).

The torque transfer is:

goiτPi + τPoτloss = 0 ,

with τloss = 0 in the ideal case.

### Nonideal Gear Constraints and Losses

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

## Limitations

Gear ratios must be positive. Gear inertia and compliance are ignored. Coulomb friction reduces simulation performance. See Adjust Model Fidelity.