Gear train with sun, planet, and ring gears
Gears
This block models a gear train with sun, planet, and ring gears. Planetary gears are common in transmission systems, where they provide high gear ratios in compact geometries. A carrier connected to a drive shaft holds the planet gears. Ports C, R, and S represent the shafts connected to the planet gear carrier, ring gear, and sun gear.
The block models the planetary gear as a structural component based on Sun-Planet and Ring-Planet Simscape™ Driveline™ blocks. The figure shows the block diagram of this structural component.
To increase the fidelity of the gear model, you can specify properties such as gear inertia, meshing losses, and viscous losses. By default, gear inertia and viscous losses are assumed negligible. The block enables you to specify the inertias of the internal planet gears only. To model the inertias of the carrier, sun, and ring gears, connect Simscape Inertia blocks to ports C, S, and R.
You can model the effects of heat flow and temperature change through an optional thermal conserving 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)
).
Moment of inertia of the combined planet gears. This value must
be positive or zero. Enter 0
to ignore gear inertia.
The default value is 0
kg*m^2.
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.
Gears are assumed rigid.
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 |