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# Ring-Planet

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

## Library

Gears/Planetary Subcomponents

## Description

The Ring-Planet gear block represents a set of carrier, planet, and ring gear wheels. The planet is connected to and rotates with respect to the carrier. The planet and ring corotate with a fixed gear ratio that you specify. A ring-planet and a sun-planet gear are basic elements of a planetary gear set. For model details, see Ring-Planet Gear Model.

### Ports

C, P, and R are rotational conserving ports representing, respectively, the carrier, planet, and ring gear wheels.

## Dialog Box and Parameters

### Main

Ring (R) to planet (P) teeth ratio (NR/NP)

Ratio gRP of the ring gear wheel radius to the planet gear wheel radius. This gear ratio must be strictly greater than 1. The default value 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

Planet-carrier viscous friction coefficient

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

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

## Ring-Planet Gear Model

### Ideal Gear Constraints and Gear Ratios

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

rRωR = rCωC + rPωP , rR = rC + rP .

The ring-planet gear ratio gRP = rR/rP = NR/NP. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:

gRPωR = ωP + (gRP – 1)ωC .

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

 Warning   The ring-planet gear ratio gRP must be strictly greater than one.

The torque transfer is:

gRPτP + 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.

## Limitations

• Gear inertia is negligible. It does not impact gear dynamics.

• Gears are rigid. They do not deform.

• Coulomb friction slows down simulation. See Adjust Model Fidelity.

## Example

The sdl_epicyclic_gearboxsdl_epicyclic_gearbox example model uses two Ring-Planet gears to model a nonideal epicyclic gear set.