Planetary gear set of carrier, planet, and sun wheels with adjustable gear ratio and friction losses
Gears/Planetary Subcomponents
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.
The block models the effects of heat flow and temperature change through an optional thermal 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 g_{RS} 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 2
.
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 μ_{S} 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 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.
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 300
K.
Sun-Planet imposes one kinematic and one geometric constraint on the three connected axes:
r_{C}ω_{C} = r_{S}ω_{S} + r_{P}ω_{P} , r_{C} = r_{P} + r_{S} .
The planet-sun gear ratio g_{PS} = r_{P}/r_{S} = N_{P}/N_{S}. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:
ω_{S} = –g_{PS}ω_{P} + (1 + g_{PS})ω_{C} .
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 g_{PS} must be strictly greater than one. |
The torque transfer is:
g_{PS}τ_{S} + τ_{P} – τ_{loss} = 0 ,
with τ_{loss} = 0 in the ideal case.
In the nonideal case, τ_{loss} ≠ 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.
Port | Description |
---|---|
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 |
Compound Planetary Gear | Planet-Planet | Planetary Gear | Ring-Planet | Sun-Planet Bevel