Planetary Gear

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




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.

The block models the effects of heat flow and temperature change through an optional thermal port. To expose the thermal port, right-click the block and select Simscape > Block choices > Show thermal port. Exposing the thermal port causes new parameters specific to thermal modeling to appear in the block dialog box.

Dialog Box and Parameters


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

Parameters for meshing losses vary with the block variant chosen—one with a thermal port for thermal modeling and one without it.

 Without Thermal Port

 With Thermal Port

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].

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

Thermal Port

Thermal mass

Thermal energy required to change the component temperature by a single degree. The greater the thermal mass, the more resistant the component is to temperature change. The default value is 50 J/K.

Initial temperature

Component temperature at the start of simulation. The initial temperature influences the starting meshing or friction losses by altering the component efficiency according to an efficiency vector that you specify. The default value is 300 K.

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.


  • Gear inertia is assumed negligible.

  • Gears are treated as rigid components.

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


CRotational conserving port that represents the planet gear carrier
RRotational conserving port that represents the ring gear
SRotational conserving port that represents the sun gear
HThermal conserving port for thermal modeling

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