Compound Planetary Gear

Planetary gear train with stepped planet gear set




This block represents a planetary gear train with a set of stepped planet gears. Each stepped planet gear consists of two rigidly connected gears possessing different radii. The larger gear engages a centrally located sun gear, while the smaller gear engages an outer ring gear.

The stepped planet gear set enables a larger speed-reduction ratio in a more compact geometry than an ordinary planetary gear can provide. The compound reduction ratio depends on two elementary reduction ratios, those of the sun-large planet and ring-little planet gear pairs. Because of this dependence, compound planetary gears are also known as dual-ratio planetary gears. For more information, see Compound Planetary Gear Model.

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 planet (P) teeth ratio (NR/NP)

Fixed ratio gRP of the ring gear to the planet gear. The gear ratio must be strictly greater than 1. The default is 2.

Planet (P) to sun (S) teeth ratio (NP/NS)

Fixed ratio gPS of the planet gear to the sun gear. The gear ratio must be strictly positive. The default is 1.

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.

Compound Planetary Gear Model

Ideal Gear Constraints and Gear Ratios

Compound Planetary Gear imposes two kinematic and two geometric constraints on the three connected axes and the fourth, internal wheel (planet):

rCωC = rSωS+ rP1ωP , rC = rS + rP1 ,

rRωR = rCωC+ rP2ωP , rR = rC + rP2 .

The ring-planet gear ratio gRP = rR/rP2 = NR/NP2 and the planet-sun gear ratio gPS = rP1/rS = NP1/NS. N is the number of teeth on each gear. In terms of these ratios, the key kinematic constraint is:

(1 + gRP·gPS)ωC = ωS + gRP·gPSωR .

The four degrees of freedom reduce to two independent degrees of freedom. The gear pairs are (1,2) = (P2,R) and (S,P1).

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

The torque transfers are:

gRPτP2 + τRτloss(P2,R) = 0 , gPSτS + τP1τloss(S,P1) = 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 representing the planet gear carrier
RRotational conserving port representing the ring gear
SRotational conserving port representing the sun gear
HThermal conserving port for thermal modeling

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