Planetary gear set of carrier, planet, and ring wheels with adjustable gear ratio and friction losses
The Ring-Planet gear block represents a set of carrier, planet, and ring gear wheels. The planet is connected to and rotates with respect to the carrier. The planet and ring corotate with a fixed gear ratio that you specify. A ring-planet and a sun-planet gear are basic elements of a planetary gear set. For model details, see Ring-Planet 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 gRP of the ring
gear wheel radius to the planet 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 μP for
the planet-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
Ring-Planet imposes one kinematic and one geometric constraint on the three connected axes:
rRωR = rCωC + rPωP , rR = rC + rP .
The ring-planet gear ratio gRP = rR/rP = NR/NP. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:
gRPωR = ωP + (gRP – 1)ωC .
The three degrees of freedom reduce to two independent degrees of freedom. The gear pair is (1,2) = (P,R).
Warning The ring-planet gear ratio gRP must be strictly greater than one.
The torque transfer is:
gRPτP + τR – 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|
|R||Rotational conserving port representing the ring gear|
|H||Thermal conserving port for thermal modeling|
The sdl_epicyclic_gearbox example model uses two Ring-Planet gears to model a nonideal epicyclic gear set.