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Represent Ravigneaux planetary set of carrier, sun, planet, and ring gear wheels with specified ring-sun gear ratios




The Ravigneaux block represents a double planetary gear set commonly used in automatic transmissions. This planetary gear set is constructed from two gear pairs, ring-planet and planet-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 with a fixed gear ratio with respect to each other. The inner planet couples with the small sun gear and corotates at a fixed gear ratio with respect to it. The outer planet couples with the large sun gear and corotates with a fixed gear ratio with respect to it. Finally, the ring gear also couples and corotates with the outer planet in a fixed gear ratio with respect to it.

To model the planets' rotational inertia, connect an Inertia block to the optional planet connector port.

Axis Motions and Constraints

The Ravigneaux block 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 - rCiC = rPiωPi + rPoωPo , rCo - rCi= rPo + rPi

rRωR = rCoωC + rPoωPo , rR = rCo + rPo

In terms of the ring-to-small sun gear ratio gRSs = rR/rSs and the ring-to-large sun gear ratio gRSl = rR/rSl, the key kinematic constraints are

(gRSs – 1)ωC = gRSs·ωR - ωSs

(gRSl + 1)ωC = gRSl·ωR + ωSl

The six degrees of freedom are reduced to two independent degrees of freedom.

The gear ratios are also the ratios of the number of teeth on each gear and the ratios of torques in each axis, gRSl = NR/NSl = τRSl and gRSs = NR/NSs = τRSs.

    Warning:   All gear ratios must be strictly positive. If any gear ratio equals 0 or becomes negative at any time, a Simscape™ Driveline™ simulation stops with an error.

    The gear ratio gRSs must be strictly greater than the gear ratio gRSl.

Ravigneaux Gear Set

Dialog Box and Parameters

Ring (R)/Large Sun (S1) gear ratio

Ratio gRSl of the ring gear wheel radius to the large sun gear wheel radius. This gear ratio must be strictly smaller than the ring-small sun gear ratio. The default is 2.

Ring (R)/Small Sun (S2) gear ratio

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.

Show planet connector port (P)

Selecting this check box makes the connector port for the planet gears visible and available for connection to other driveline blocks.

Use this connector port to connect an Inertia block if you want to model the planet gears' inertia as a single body. The default is unselected, with the planet gears' inertia neglected in the dynamics.


The drive_ravigneaux_pic example illustrates the Ravigneaux gear with an animation.

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