Planetary gear set of carrier, inner planet, and outer planet wheels with adjustable gear ratio and friction losses
The Planet-Planet gear block represents a set of carrier, inner planet, and outer planet gear wheels. Both planetary gears are connected to and rotate with respect to the carrier. The planets corotate with a fixed gear ratio that you specify. For model details, see Planet-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 goi of the outer
planet gear radius wheel to the inner planet gear wheel radius. This
gear ratio must be strictly positive. The default 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 μPi for
the inner 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
Planet-Planet imposes one kinematic and one geometric constraint on the three connected axes:
rCωC = rPoωPo+ rPiωPi , rC = rPo + rPi .
The outer planet-to-inner planet gear ratio goi = rPo/rPi = NPo/NPi. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:
(1 + goi)ωC = ωPi + goiωPo .
The three degrees of freedom reduce to two independent degrees of freedom. The gear pair is (1,2) = (Pi,Po).
The torque transfer is:
goiτPi + τPo – 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|
|Po||Rotational conserving port representing the outer planet gear|
|Pi||Rotational conserving port representing the inner planet gear|
|H||Thermal conserving port for thermal modeling|