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Planetary Gear

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

Gears

Description

The Planetary Gear block represents a set of carrier, ring, planet, and sun gear wheels. A planetary gear set can be constructed from sun-planet and ring-planet gears. The ring and sun corotate with a fixed gear ratio. For model details, see Planetary Gear Model.

Planetary Gear Set

Ports

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

Dialog Box and Parameters

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

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