Documentation |
High-ratio gear reduction mechanism with sun, planet, and ring 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.
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.
Select how to implement friction losses from nonideal meshing of gear teeth. The default is No meshing losses.
No meshing losses — Suitable for HIL simulation — Gear meshing is ideal.
Constant efficiency — Transfer of torque between gear wheel pairs is reduced by a constant efficiency η satisfying 0 < η ≤ 1. If you select this option, the panel changes from its default.
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)).
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).
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 negligible. It does not impact gear dynamics.
Gears are rigid. They do not deform.
Coulomb friction slows down simulation. See Adjust Model Fidelity.
Port | Description |
---|---|
C | Conserving rotational port that represents the planet gear carrier |
R | Conserving rotational port that represents the ring gear |
S | Conserving rotational port that represents the sun gear |