Ravigneaux planetary gear set of carrier, sun, planet, and ring wheels with adjustable gear ratios and friction losses
The Ravigneaux block represents a double planetary gear set commonly used in automatic transmissions. This planetary gear set is constructed from three gear pairs, ring-planet, planet-planet, and sun-planet. The Ravigneaux set has two sun gear wheels, a large sun and a small sun, and a single carrier gear with two independent planetary gear wheels connected to it, an inner planet and an outer planet.
The carrier is one wheel but has two radii to couple with the inner and outer planets, respectively.
The two planet gears rotate independently of the carrier but corotate in a fixed gear ratio with respect to each other.
The inner planet couples to the small sun gear and corotates at a fixed gear ratio.
The outer planet couples to the large sun gear and corotates with a fixed gear ratio.
The ring gear also couples to the outer planet gear and corotates with a fixed gear ratio.
For model details, see Ravigneaux Gear Model.
Ravigneaux Gear Set
C, R, SL, and SS are rotational conserving ports representing, respectively, the carrier, ring, and large and small sun gear wheels.
The dialog box has one active area, Parameters, with three tabs.
Ratio gRSL 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 gRSS 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.
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 [μLS μSS μLSP μSSP] 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)).
Ravigneaux imposes four kinematic and four geometric constraints on the four connected axes and the two internal wheels (inner and outer planets):
rCiωC = rSSωSS + rPiωPi , rCi = rSS + rPi ,
rCoωC = rSLωSL + rPoωPo , rCo = rSL + rPo ,
(rCo – rCi)ωC = rPiωPi + rPoωPo , rCo – rCi= rPo + rPi ,
rRωR = rCoωC + rPoωPo , rR = rCo + rPo .
The ring-small sun ratio gRSS = rR/rSS = NR/NSS and ring-large sun gear ratio gRSL = rR/rSL = NR/NSL. N is the number of teeth on each gear. In terms of these ratios, the key kinematic constraints are:
(gRSS – 1)ωC = gRSSωR – ωSS ,
(gRSL + 1)ωC = gRSLωR + ωSL .
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 gRSS must be strictly greater than the gear ratio gRSL. The gear ratio gRSL must be strictly greater than one.
The torque transfers are:
gRSSτSS + τR – τloss(SS,R) = 0 , gRSLτSL + τR – τloss(SL,R) = 0 ,
with τloss = 0 in the ideal case.
In the nonideal case, τloss ≠ 0. See Model Gears with Losses.
Gear ratios must be positive. Gear inertia and compliance are ignored. Coulomb friction reduces simulation performance. See Adjust Model Fidelity.