High-ratio gear reduction mechanism with sun, planet, and ring gears
Gears
This block represents a high-ratio gear reduction mechanism with four key components:
Sun gear
Planet Gear Set
Planet Gear Carrier
Ring Gear
The centrally located sun gear engages the planet gear set, which in turn engages the ring gear. A carrier holds the planet gear set. Each of these components, with the exception of the planet gear set, connects to a drive shaft.
Depending on which shaft is driving, driven, or fixed, the planetary gear train can achieve a variety of speed reduction ratios. These ratios are a function of the sun and ring radii, and therefore of their tooth numbers. You specify the tooth numbers directly in the block dialog box.
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.
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 is 2
.
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.
Planetary Gear imposes two kinematic and two geometric constraints on the three connected axes and the fourth, internal gear (planet):
r_{C}ω_{C} = r_{S}ω_{S}+ r_{P}ω_{P} , r_{C} = r_{S} + r_{P} ,
r_{R}ω_{R} = r_{C}ω_{C}+ r_{P}ω_{P} , r_{R} = r_{C} + r_{P} .
The ring-sun gear ratio g_{RS} = r_{R}/r_{S} = N_{R}/N_{S}. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:
(1 + g_{RS})ω_{C} = ω_{S} + g_{RS}ω_{R} .
The four degrees of freedom reduce to two independent degrees of freedom. The gear pairs are (1,2) = (S,P) and (P,R).
Warning The gear ratio g_{RS} must be strictly greater than one. |
The torque transfer is:
g_{RS}τ_{S} + τ_{R} – 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 that represents the planet gear carrier |
R | Rotational conserving port that represents the ring gear |
S | Rotational conserving port that represents the sun gear |
H | Thermal conserving port for thermal modeling |