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# PlanetaryGear

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# PlanetaryGear

## Library

Iconic Diagrams\Mechanical\Rotation\Gears

## Use

Domains: Continuous. Size: 1-D. Kind: Iconic Diagrams (Rotation).

## Description

A planetary gear is well known for its use in automotive mechanics. It transfers power from a sun wheel to the planet wheels and the ring. In standard planetary gears, the planet wheels are connected by a carriage. I.e the gear has three rotation ports: the sun, the carriage and the ring.

The model that is used here is ideal. I.e. there is only power flow between the three axes. No internal dynamics or friction are incorporated. If the inertia cannot be neglected, you can easily add inertia models to the ports of the planetary gear model.

The number of teeth of the planet wheels are uniquely defined by the number of teeth of the sun wheel and the ring by:

zp = (zr - zs)/2;

Therefore the ratio between the sun teeth and the ring teeth:

z = zr / zs;

determine the transmission ratio of the gearbox and therefore the dynamic equations of the gearbox:

carriage.omega = sun.omega * (1/(1 + z)) + ring.omega * (z/(1 + z));

ring.T = carriage.T * (z/(1 + z));

sun.T = carriage.T * (1/(1 + z));

## Interface

 Ports Description sun carriage ring shaft attached to the sun wheel (Rotation) shaft attached to the carriage (Rotation) shaft attached to the ring (Rotation) Parameters z number of ring teeth divided by the number of sun teeth []