Sun-Planet Bevel

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


Simscape / Driveline / 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. You control the direction of rotation 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.

Thermal Modeling

You can model the effects of heat flow and temperature change through an optional thermal conserving port. By default, the thermal port is hidden. To expose the thermal port, right-click the block in your model and, from the context menu, select Simscape > Block choices. Select a variant that includes a thermal port. Specify the associated thermal parameters for the component.

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.




  • rC is the radius of the carrier gear.

  • ωC is the angular velocity of the carrier gear.

  • rS is the radius of the sun gear.

  • ωS is the angular velocity of the sun gear.

  • rP is the radius of the planet gear.

  • ωP is the angular velocity of the planet gear.

The planet-sun gear ratio is defined as



  • gPS is the planet-sun gear ratio. As rP>rS, gPS>1.

  • NP is the number of teeth in the planet gear.

  • NS is the angular velocity of the sun gear.

In terms of this ratio, the key kinematic constraint is:

  • ωS=gPSωPωC for a left-oriented bevel assembly

  • ωS=gPSωP+ωC for a right-oriented bevel assembly

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


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

The torque transfer is defined as



  • τloss is the torque loss.

  • τs is the torque for the sun gear.

  • τp is the torque for the planet gear.

For the ideal case, there is no torque loss, that is τloss=0. Then the torque transfer equation is τP=gPSτS.

Nonideal Gear Constraints and Losses

In the nonideal case, τloss0. 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 gear carrier
PRotational conserving port representing the planet gear
SRotational conserving port representing the sun gear
HThermal conserving port for thermal modeling



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

Parameters for meshing and friction 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 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)).

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 alters the component efficiency according to an efficiency vector that you specify, affecting the starting meshing or friction losses. The default value is 300 K.

Real-Time Simulation

Hardware-in-the-Loop Simulation

For optimal simulation performance, use the Meshing Losses > Friction model parameter default setting, No meshing losses - Suitable for HIL simulation.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Introduced in R2011a