Planetary gear train with dual sun and planet gear sets
Gears
This block represents a planetary gear train with dual sun and planet gear sets. The two sun gears are centrally located and separated longitudinally along a common rotation axis. The smaller of these gears engages an inner planet gear set, which in turn engages an outer planet gear set. The outer planet gear set, whose length spans the distance between the two sun gears, engages both the larger sun gear and the ring gear.
A carrier holds the planet gear sets in place at different radii. The carrier, which rigidly connects to a drive shaft, can spin as a unit with respect to the sun and ring gears. Revolute joints, each located between a planet gear and the carrier, enable the gears to spin about their individual longitudinal axes.
The relative angular velocities of the sun, planet, and ring gears follow from the kinematic constraints between them. For more information, see Ravigneaux Gear Model.
This block is a composite component with four underlying blocks:
The figure shows the connections between the blocks.
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_{RSL} of the
ring gear wheel radius to the large sun gear wheel radius. This gear
ratio must be strictly greater than 1. The default is 2
.
Ratio g_{RSS} of the
ring gear wheel radius to the small sun gear wheel radius. This gear
ratio must be strictly greater than the ring-large sun gear ratio.
The default is 3
.
Parameters for meshing losses vary with the block variant chosen—one with a thermal port for thermal modeling and one without it.
Vector of viscous friction coefficients [μ_{LS} μ_{SS} μ_{LSP} μ_{SSP}]
for the large sun-carrier, small sun-carrier, large sun planet-carrier,
and small sun planet-carrier gear motions, respectively. The default
is [0 0 0 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.
Ravigneaux imposes four kinematic and four geometric constraints on the four connected axes and the two internal wheels (inner and outer planets):
r_{Ci}ω_{C} = r_{SS}ω_{SS} + r_{Pi}ω_{Pi} , r_{Ci} = r_{SS} + r_{Pi} ,
r_{Co}ω_{C} = r_{SL}ω_{SL} + r_{Po}ω_{Po} , r_{Co} = r_{SL} + r_{Po} ,
(r_{Co} – r_{Ci})ω_{C} = r_{Pi}ω_{Pi} + r_{Po}ω_{Po} , r_{Co} – r_{Ci}= r_{Po} + r_{Pi} ,
r_{R}ω_{R} = r_{Co}ω_{C} + r_{Po}ω_{Po} , r_{R} = r_{Co} + r_{Po} .
The ring-small sun ratio g_{RSS} = r_{R}/r_{SS} = N_{R}/N_{SS} and ring-large sun gear ratio g_{RSL} = r_{R}/r_{SL} = N_{R}/N_{SL}. N is the number of teeth on each gear. In terms of these ratios, the key kinematic constraints are:
(g_{RSS} – 1)ω_{C} = g_{RSS}ω_{R} – ω_{SS} ,
(g_{RSL} + 1)ω_{C} = g_{RSL}ω_{R} + ω_{SL} .
The six degrees of freedom reduce to two independent degrees of freedom. The gear pairs are (1,2) = (LS,P), (SS,P), (P,R), and (P,P).
Warning The gear ratio g_{RSS} must be strictly greater than the gear ratio g_{RSL}. The gear ratio g_{RSL} must be strictly greater than one. |
The torque transfers are:
g_{RSS}τ_{SS} + τ_{R} – τ_{loss}(SS,R) = 0 , g_{RSL}τ_{SL} + τ_{R} – τ_{loss}(SL,R) = 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.
The sdl_Ravigneaux_4_speedsdl_Ravigneaux_4_speed example model uses a Ravigneaux gear as the core of its transmission.
Port | Description |
---|---|
C | Rotational conserving port representing the planet gear carrier |
R | Rotational conserving port representing the ring gear |
SL | Rotational conserving port representing the large sun gear |
SS | Rotational conserving port representing the small sun gear |
H | Thermal conserving port for thermal modeling |
Compound Planetary Gear | Planet-Planet | Planetary Gear | Ring-Planet | Sun-Planet