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

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.

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

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

*g*_{oi}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`.

**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.

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

*r*_{C}ω_{C} = *r*_{Po}*ω*_{Po}+ *r*_{Pi}*ω*_{Pi} , *r*_{C} = *r*_{Po} + *r*_{Pi} .

The outer planet-to-inner planet gear ratio *g*_{oi} = *r*_{Po}/*r*_{Pi} = *N*_{Po}/*N*_{Pi}. *N* is
the number of teeth on each gear. In terms of this ratio, the key
kinematic constraint is:

(1 + *g*_{oi})*ω*_{C} = *ω*_{Pi} + *g*_{oi}*ω*_{Po} .

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

The torque transfer is:

*g*_{oi}*τ*_{Pi} + *τ*_{Po} – *τ*_{loss} =
0 ,

with *τ*_{loss} =
0 in the ideal case.

In the nonideal case, *τ*_{loss} ≠
0. See Model Gears with Losses.

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.

Planetary Gear | Ravigneaux Gear | Ring-Planet | Sun-Planet | Sun-Planet Bevel

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