Planetary gear set of carrier, planet, and sun wheels with adjustable gear ratio and friction losses
The Sun-Planet 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 that you specify and in the same direction with respect to the carrier. A sun-planet and a ring-planet gear are basic elements of a planetary gear set. For model details, see Sun-Planet Gear Model.
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. Specify the associated thermal parameters for the component.
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 value is
Parameters for meshing losses vary with the block variant chosen—one with a thermal port for thermal modeling and one without it.
Viscous friction coefficient μS for
the sun-carrier gear motion. The default is
From the drop-down list, choose units. The default is newton-meters/(radians/second)
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
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
Sun-Planet imposes one kinematic and one geometric constraint on the three connected axes:
rCωC = rSωS + rPωP , rC = rP + rS .
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 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 + τP – τloss = 0 ,
with τloss = 0 in the ideal case.
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.
|C||Rotational conserving port representing the planet carrier|
|P||Rotational conserving port representing the planet gear|
|S||Rotational conserving port representing the sun gear|
|H||Thermal conserving port for thermal modeling|