Planetary gear train with stepped planet gear set
Gears
This block represents a planetary gear train with a set of stepped planet gears. Each stepped planet gear consists of two rigidly connected gears possessing different radii. The larger gear engages a centrally located sun gear, while the smaller gear engages an outer ring gear.
The stepped planet gear set enables a larger speed-reduction ratio in a more compact geometry than an ordinary planetary gear can provide. The compound reduction ratio depends on two elementary reduction ratios, those of the sun-large planet and ring-little planet gear pairs. Because of this dependence, compound planetary gears are also known as dual-ratio planetary gears. For more information, see Compound Planetary Gear Model.
This block is a composite component with two underlying blocks:
The figure shows the connections between the two 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.
Fixed ratio g_{RP} of
the ring gear to the planet gear. The gear ratio must be strictly
greater than 1. The default is 2
.
Fixed ratio g_{PS} of
the planet gear to the sun gear. The gear ratio must be strictly positive.
The default is 1
.
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_{S} μ_{P}]
for the sun-carrier and planet-carrier gear motions, respectively.
The default is [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.
Compound Planetary Gear imposes two kinematic and two geometric constraints on the three connected axes and the fourth, internal wheel (planet):
r_{C}ω_{C} = r_{S}ω_{S}+ r_{P1}ω_{P} , r_{C} = r_{S} + r_{P1} ,
r_{R}ω_{R} = r_{C}ω_{C}+ r_{P2}ω_{P} , r_{R} = r_{C} + r_{P2} .
The ring-planet gear ratio g_{RP} = r_{R}/r_{P2} = N_{R}/N_{P2} and the planet-sun gear ratio g_{PS} = r_{P1}/r_{S} = N_{P1}/N_{S}. N is the number of teeth on each gear. In terms of these ratios, the key kinematic constraint is:
(1 + g_{RP}·g_{PS})ω_{C} = ω_{S} + g_{RP}·g_{PS}ω_{R} .
The four degrees of freedom reduce to two independent degrees of freedom. The gear pairs are (1,2) = (P2,R) and (S,P1).
Warning The gear ratio g_{RP} must be strictly greater than one. |
The torque transfers are:
g_{RP}τ_{P2} + τ_{R} – τ_{loss}(P2,R) = 0 , g_{PS}τ_{S} + τ_{P1} – τ_{loss}(S,P1) = 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 gear carrier |
R | Rotational conserving port representing the ring gear |
S | Rotational conserving port representing the sun gear |
H | Thermal conserving port for thermal modeling |