Planetary gear set of carrier, beveled planet, and sun wheels with adjustable gear ratio, assembly orientation, and friction losses
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.
You can model the effects of heat flow and temperature change through an optional thermal conserving 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.
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
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.
Parameters for meshing and friction 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 influences the starting meshing or friction losses by
altering the component efficiency according to an efficiency vector
that you specify. The default value is
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 + 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 gear carrier|
|P||Rotational conserving port representing the planet gear|
|S||Rotational conserving port representing the sun gear|
|H||Thermal conserving port for thermal modeling|
These Simscape™ Driveline™ example models use the Sun-Planet Bevel gear to create custom gear sets: