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# Planetary Gear

High-ratio gear reduction mechanism with sun, planet, and ring gears

Gears

## Description

This block represents a high-ratio gear reduction mechanism with four key components:

• Sun gear

• Planet Gear Set

• Planet Gear Carrier

• Ring Gear

The centrally located sun gear engages the planet gear set, which in turn engages the ring gear. A carrier holds the planet gear set. Each of these components, with the exception of the planet gear set, connects to a drive shaft.

Depending on which shaft is driving, driven, or fixed, the planetary gear train can achieve a variety of speed reduction ratios. These ratios are a function of the sun and ring radii, and therefore of their tooth numbers. You specify the tooth numbers directly in the block dialog box.

This block is a composite component with two underlying blocks:

The figure shows the connections between the two blocks.

## Dialog Box and 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

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

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].

## 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.

## 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.

## Ports

PortDescription
CConserving rotational port that represents the planet gear carrier
RConserving rotational port that represents the ring gear
SConserving rotational port that represents the sun gear