Ravigneaux planetary gearset
Encyclopedia
The Ravigneaux gearset is a double planetary gear set commonly used in automatic transmission
s. 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 gear
s rotate independently of the carrier but co-rotate with a fixed gear ratio
with respect to each other. The inner planet couples with the small sun gear and co-rotates at a fixed gear ratio with respect to it. The outer planet couples with the large sun gear and co-rotates with a fixed gear ratio with respect to it. Finally, the ring gear also couples and co-rotates with the outer planet in a fixed gear ratio with respect to it.
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
In terms of the ring-to-small sun good 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 = τR/τSl and gRSs = NR/NSs = τR/τSs.
Automatic transmission
An automatic transmission is one type of motor vehicle transmission that can automatically change gear ratios as the vehicle moves, freeing the driver from having to shift gears manually...
s. 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
Wheel
A wheel is a device that allows heavy objects to be moved easily through rotating on an axle through its center, facilitating movement or transportation while supporting a load, or performing labor in machines. Common examples found in transport applications. A wheel, together with an axle,...
but has two radii
Radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...
to couple with the inner and outer planets, respectively. The two planet gear
Gear
A gear is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque. Two or more gears working in tandem are called a transmission and can produce a mechanical advantage through a gear ratio and thus may be considered a simple machine....
s rotate independently of the carrier but co-rotate with a fixed gear ratio
Ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...
with respect to each other. The inner planet couples with the small sun gear and co-rotates at a fixed gear ratio with respect to it. The outer planet couples with the large sun gear and co-rotates with a fixed gear ratio with respect to it. Finally, the ring gear also couples and co-rotates with the outer planet in a fixed gear ratio with respect to it.
Axis Motions and Constraints
The Ravigneaux block imposes four kinematic and four geometricGeometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
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
In terms of the ring-to-small sun good 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 = τR/τSl and gRSs = NR/NSs = τR/τSs.
External links
- Meccano model of a Ravigneaux Planetary Transmission in the H1 HummerHummer H1The Hummer H1 is a civilian off-road vehicle based on the M998 Humvee, which was created by AM General. The vehicle was produced from 1992 through 2006, and was the first of what became the Hummer line...
by Alan Wenbourne