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.

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

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.

     Constant Efficiency

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)).

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 negligible. It does not impact gear dynamics.

  • Gears are rigid. They do not deform.

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


  • C — Rotational conserving port representing the planet gear carrier.

  • R — Rotational conserving port representing the ring gear.

  • S — Rotational conserving port representing the sun gear.

Was this topic helpful?