Epicyclic gearing

Epicyclic gear are gear or friction wheel, which are not only fixed to the frame and axles shafts that rotate in circular orbits in the frame. In many embodiments, the rotating axes are parallel to the frame-mounted shafts, which is the reason clearly why the epicyclic gear often called planetary gear train (short: planetary gear ), respectively. The rotating to the rotating axes wheels revolve around a central wheel like the planets, the sun.

Epicyclic gear are compactly built with the special feature that the drive and output shaft are aligned.

• 6.1 Compact design
• 6.2 Two - and / or three -wave mode

• 7.1 hub gear 7.1.1 gear hub in the bicycle
• 7.1.2 planetary axle
• 7.1.3 Electric hub motor with gearbox

Basic Structure

A simple stationary gear ( no rotating axes) has a minimum of two waves and is single (only one gear pair ). A planetary gear system has a minimum of two shafts, and a rotating axis and has two stages. Two -fixed waves are needed in technical applications, you need a driving and a driven shaft. The rotation of the wheel ( bull 2 pictures below ) must be coaxial with which it is paired to two circled wheels ( 3 and 1), and, done. Consequently, these two fixed to the frame rotating wheels so-called central wheels. And both and the web ( 4) which supports the axis of the rotating wheel, are coaxial.

Different designs result from the shape of the second central wheel ( 1 or 3) and in that a simple planet wheel (2) or Umlaufradpaare occur (2 and 2 '). The second central wheel, a ring gear, as the transmission is particularly narrow (single planet wheel, 2).

Narrow Umlaufradgetriebe with ring gear ( internal gear teeth ), second planet gear requires no

Umlaufradpaare (2 and 2 ') Second central wheel (1) and sun gear ( 3) are outside serrated.

Bevel differential gear The large gear is not part of this particular planetary gear system.

When the rotating shaft is fixed to the frame parallel to the shafts and gears are all helical gears, the gears appear in the axis - perpendicular sectional view of the circular body. The revolving wheel encircles the central wheel with external teeth like a planet, which has led to a general, but not always of describing the planetary gear of a planetary gear. One speaks of the sun orbiting planet.

The bevel gear differential gear, the planetary gear system generally used, the center line of the rotary axis intersects the central axis fixed to the frame at right angles. Its designation as a planetary gear is not apt in the above sense. The two central wheels are mirror images of the same bevel gears. The planet gear is a bevel gear, the web is in the form of a cage.

Modes

In general, a planetary gear has three shafts, one of which, however, often is held (two- wave operation ), such as the web ( see above: second illustration or below: animation). The sun gear driving, so that the ring gear is driven and vice versa. What shaft / wheel is fixed and which / s is used as a drive or as an output, depends on the design task to be solved.

In certain applications, turn all three waves ( three-wave mode). Then there are two driving and driven one (addition gearbox) or vice versa ( transfer gearbox ).

Two -wave mode

In the two -wave mode, the transmission is positively (running degrees F = 1). The drive shaft of a rotation of the second is unique.

A distinction is made between stationary ratio and current translation:

• In the state of translation, the carrier shaft is stationary, and the two Zentralradwellen (ie sun and ring ) move. The stationary shaft may be fixedly connected to the housing and held in place by a brake or an overrunning clutch.
• In the recycle translation one of the two Zentralradwellen stands still. Input and output via the rotating center wheel and the planet carrier shaft.

Three -wave mode

In the three -wave mode, the transmission has to first run degrees F = 2 It works as a summing or transfer gearbox:

• When summing gear drive to 2 shafts, and 1 shaft is driven. Example is the summation gears in the rear hub of an electric bicycle. The driving speeds are freely chosen, the output speed is thus unique. By setting the two drive movements is finally Zwangläufigkeit (F = 1 ) guarantees.
• The transfer gearbox drives a shaft and the two shafts are driven. The speed ratio of the two output shafts must be set. The best known example of a Verteilgetriebes is the differential gear on the motor vehicle. Here, the speed ratio is determined by the wheelbase and turning radius. Due to the frictional contact of the wheels with the ground is finally Zwangläufigkeit (F = 1 ) guarantees.

Multiple or linkage

Often it is not only the simple Umlaufradsatz described here referred to as epicyclic gear, but also based on this basic design combinations of several in - and series-connected gears. Example are the hubs on the bike, in the using a multiple- gear more than achievable with simple Umlaufradsatz three courses were possible.

Other examples of multiple transmissions are the Ravigneaux set or Lepelletier gear.

Kinematics

The translations of the planetary gear can be graphically represented using the Kutzbachplanes and determined graphically.

For the analytical representation satisfies a single equation, the so-called Willis equation: [Note 1]

This is the speed ratio between the two central shafts 1 and 2 article held web S:

We call this ratio the stationary ratio of the epicyclic gearbox. In this case, each of the two central wheels are chosen as the driving wheel 1 or as a driven wheel 2. It is important that the stationary ratio has a negative value (so-called negative gear, contrary Plus gear ) when the two coaxial central wheels have opposite directions of rotation. The Willis equation applies regardless of how the epicyclic gear is built up inside. The revolving wheels are not covered by it.

With the determination of the stationary gear all speed ratios between the three frame-fixed waves are given. In the two -wave mode, there are six combinations for driving a driven and a pinned shaft. In the following table, the Willis equation for each of the six cases is changed, the central gear, for example, a ring gear and the stationary gear is shown with a driving sun gear.

.

With the numbers of teeth of the two wheels.

The directions of rotation of sun and ring are opposite to each other: is negative.

In non-stepped planet, the relative speed of the planet gear is calculated over the web ( Minusradsatz ) from:

This formula can also be used for calculating the relative rotational speed of the meshing with the ring gear the planetary gear of a Plusradsatzes.

The number of teeth of the planetary gear and the number of planetary gears is not significant for the state of translation, but has an influence on the speed of the planet gears and the maximum transmittable torque.

Distribution of the planets

The usually several planet gears can only be distributed uniformly over the circumference when the following relationship is an integer:

The illustrated example shows a transmission which requires unequal angular pitch. The right illustration shows the inability to engagement of the teeth at the same pitch angle.

Benefits

Compact design

• Low volume ( particularly when using a ring gear )
• Coaxial shafts
• Transmission of high torques ( multiplication by several parallel tooth pairings with several planet gears )

Two and / or three -wave mode

• Two -wave mode: the choice of two of three waves and the inversion between the driving and driven shaft results in six possible transmission.
• Intermittent three-wave mode: If the third wave fixed by a friction clutch in operation, the two-wave operation can be interrupted by uncoupling and coupling under load and restored.
• Three -wave mode: Addition of two rotational motions ( summing transmission ) to a third or distribution ( distribution gear ) rotary motion to two others.

Applications

Hub gear

A common application of Umlaufradgetriebes done in wheel hubs, which is very old in bicycles ( since about 1900).

Gear hub in the bicycle

In bicycle hub gears, the compact design of the Umlaufradgetriebes is exploited. It is both important to a gear to accommodate the ( rear ) hub to as it can also operate coaxial. Primary feature is its ability to switch, not its basic ratio between the chain sprocket and wheel speed increasing or underdrive. In the middle gear the transmission is bypassed and the translation is i = 1 Otherwise switching means a change between two different two-wave farms. The sun gear is fixed in the rule so that the other four options of the two- wave operation eliminated. A slow transition (i > 1) occurs when the ring gear is made impulsive, a faster ( i < 1) with driving web.

More than three ratios are achieved with more parts than a simple Umlaufradsatz has.

The rare Tretlagerschaltung the bicycle usually includes a planetary gear system.

Planetary axle

In the hub of the driven wheels of trucks, buses, construction and agricultural machinery can be incorporated into a Slow Umlaufradgetriebe for translation. In such a construction the driving parts are designed for relatively low torques, since the rotational speed is greater than that of the wheels. Used the strong Gearing down from the sun to the web, the ring gear is fixed. The conversion at the end of the drive train in the relatively small hub is possible due to the compact design of a Umlaufradgetriebes.

This technique of so-called planetary axis was introduced in 1953 by Magirus -Deutz and subsequently taken over time by numerous other manufacturers of commercial vehicles.

Electric hub motor with gearbox

The first used in automobiles, electric wheel hub motor is used in electric bicycles. So that the electric motor can be operated at its optimum speed, it is advantageously combined with a speed reducing translated Umlaufradgetriebe. This has the same two- wave mode as the planetary axle: driving sun gear and driven gear.

Distribution gear

Classic application of a transfer gearbox, the power distribution to two wheels of the drive axle of an automobile. This so-called differential gear unit is provided with front-wheel drive today majority stake in some cases no longer with bevel gears but with spur gears and fulfilled in this form, the vivid planetary gear concept. In four wheel drive vehicles comes to the so-called two axle differentials still a center differential added.

For hybrid electric motor vehicles, there is a combination variant, in which the power of the engine is distributed to the wheels and an electric generator.

For aircraft with coaxial propellers, the power distribution from the drive to the two counter-rotating propeller with a planet - transfer gearbox done.

Summation gear

In a summation gear two services are combined into one. In hybrid electric vehicles, which is designated as a parallel hybrid variant combination. Runs the motor backward at first, then can be realized even a clutch- free starting.

In the illustrated example ( Prius ) (1) is the output of the Vebrennungsmotors and (2) of the electric motor. Both engines drive the rear wheels on wheels on the shaft ( 3). Summing the engine in rotating the planet carrier ( 4) and the electric motor, the sun gear (5).

An example is the drive of a propeller by two motors through summation ..

Other applications have an engine that delivers great performance at a constant speed. With a smaller motor can easily be controlled in speed, and a summing transmission can in this way a change in speed can be achieved at the output, for example in a rolling mill so as to vary the speed of forming.

In aircraft applications are known in which driving for safety reasons two electric motors one fuel pump through summation. If one of the engines of ( stops ), the other can still drive the pump at half speed.

Clutch and shift

The two- wave operation is interrupted when the third wave of Umlaufradgetriebes is temporarily not being held. This possibility is used as a general clutch or shifting gears in a gear change.

Mainly in agricultural technology there under load shiftable clutches that work that way. For example, the PTO shaft is switched off. The ring gear is braked or left rotation.

Classic automatic transmission in motor vehicles have several successively arranged Umlaufradgetriebe. To change gears, another translation is switched by opening and closing of friction clutches and brakes. This happens as the load circuit, there is no interruption of traction.

Infinitely variable speed change

With a principle not suitable for high performance variable transmission, the speed provided with a high-power transmission of rotation can be varied as follows (though at reduced speed range ): First, the rotation transmission is divided with a Umlaufradgetriebe. A side branch at a lower power is taken via a variable transmission to a second Umlaufradgetriebe where it is then summed with the output from the main branch of the first Umlaufradgetriebes again.

An infinitely variable gear hub

For bicycles, there are infinitely variable NuVinci gear hub. In this brand name is the name of Leonardo da Vinci is included, who had already described the basic principle.

This is the well-known hub with a Umlaufradgetriebe whose gears ( form closure ) but by friction wheels ( force or friction ) are replaced. The epicyclic have become circulating balls (ball wheels). By swinging their axes relative to the hub axis, the radii on which they have rolling contact with the driving and the driven pulley (instead of sun and ring ) change. The infinitely possible pivoting means a continuous change of the transmission gear. Kinematic, the NuVinci hub gears a planetary gear system with variable negative level translation dar.

In the running hub gears, the gear ratio is (ratio of largest to smallest translation ) 360 %.

As in any frictional connection is also in the NuVinci hub gears slip with consequent wear possible.