Sun-Planet Bevel

Planetary gear set of carrier, beveled planet, and sun wheels with adjustable gear ratio, assembly orientation, and friction losses


Gears/Planetary Subcomponents


The Sun-Planet Bevel gear block represents a set of carrier, planet, and sun gear wheels. The planet is connected to and rotates with respect to the carrier. The planet and sun corotate with a fixed gear ratio and in a direction that you specify. You control the direction by setting the assembly orientation, left or right. A sun-planet and a ring-planet gear are basic elements of a planetary gear set. For model details, see Sun-Planet Bevel Gear Model.


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

Dialog Box and Parameters


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

Ratio gPS of the planet gear wheel radius to the sun gear wheel radius. This gear ratio must be strictly greater than 1. The default value is 2.

Assembly orientation

Relative orientation of sun and planet gears, controlling their corotation direction. Left or right orientation imply, respectively, that the gears corotate in the same or opposite direction.

The default is Left — Sun and planet gears rotate in same direction.

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 viscous friction coefficient

Viscous friction coefficient μS for the sun-carrier gear motion. The default is 0.

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

Sun-Planet Bevel Gear Model

Ideal Gear Constraints and Gear Ratios

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

rCωC = rSωS ± rPωP , rC = rS ± rP .

The planet-sun gear ratio gPS = rP/rS = NP/NS. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:

ωS = ∓gPSωP + (1 ± gPS)ωC .

The three degrees of freedom reduce to two independent degrees of freedom. The upper or lower sign applies, respectively, to left-oriented or right-oriented bevel assembly. The gear pair is (1,2) = (S,P).

    Warning   The planet-sun gear ratio gPS must be strictly greater than one.

The torque transfer is:

gPSτS + τPτloss = 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.


These SimDriveline™ example models use the Sun-Planet Bevel gear to create custom gear sets:

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