Planetary gear sets include a central sun gear, surrounded by several planet gears, held by a planet carrier, and enclosed within a ring gear
The sun gear, ring gear, and planetary carrier form three possible insight/outputs from a planetary gear set
Typically, one part of a planetary set is held stationary, yielding an individual input and an individual output, with the overall gear ratio based on which part is held stationary, which is the input, and which the output
Rather than holding any kind of part stationary, two parts can be used mainly because inputs, with the single output being a function of both inputs
This is often accomplished in a two-stage gearbox, with the first stage generating two portions of the second stage. A very high gear ratio can be realized in a compact package. This sort of arrangement is sometimes called a ‘differential planetary’ set
I don’t think there is a mechanical engineer away there who doesn’t have a soft place for gears. There’s just something about spinning bits of steel (or some other materials) meshing together that is mesmerizing to watch, while checking so many opportunities functionally. Especially mesmerizing are planetary gears, where the gears not only spin, but orbit around a central axis as well. In this post we’re going to look at the particulars of planetary gears with an eyes towards investigating a particular family of planetary equipment setups sometimes referred to as a ‘differential planetary’ set.

The different parts of planetary gears
Fig.1 The different parts of a planetary gear

Planetary Gears
Planetary gears normally contain three parts; An individual sun gear at the center, an internal (ring) gear around the outside, and some number of planets that go in between. Usually the planets will be the same size, at a common middle range from the center of the planetary gear, and held by a planetary carrier.

In your basic set up, your ring gear could have teeth add up to the amount of one’s teeth in sunlight gear, plus two planets (though there could be advantages to modifying this slightly), due to the fact a line directly across the center in one end of the ring gear to the other will span the sun gear at the center, and area for a planet on either end. The planets will typically end up being spaced at regular intervals around the sun. To do this, the total number of tooth in the ring gear and sun gear mixed divided by the amount of planets must equal a complete number. Of program, the planets need to be spaced far enough from each other so that they do not interfere.

Fig.2: Equivalent and contrary forces around the sun equal no side force on the shaft and bearing in the center, The same can be shown to apply to the planets, ring gear and world carrier.

This arrangement affords several advantages over other possible arrangements, including compactness, the possibility for the sun, ring gear, and planetary carrier to use a common central shaft, high ‘torque density’ due to the load being shared by multiple planets, and tangential forces between your gears being cancelled out at the center of the gears due to equal and opposite forces distributed among the meshes between your planets and other gears.

Gear ratios of standard planetary gear sets
Sunlight gear, ring gear, and planetary carrier are usually used as insight/outputs from the gear set up. In your regular planetary gearbox, among the parts is normally held stationary, simplifying stuff, and giving you an individual input and an individual output. The ratio for just about any pair could be worked out individually.

Fig.3: If the ring gear is normally held stationary, the velocity of the earth will be as shown. Where it meshes with the ring gear it will have 0 velocity. The velocity boosts linerarly across the planet equipment from 0 compared to that of the mesh with the sun gear. Therefore at the centre it will be moving at half the rate at the mesh.

For instance, if the carrier is held stationary, the gears essentially form a standard, non-planetary, equipment arrangement. The planets will spin in the opposite direction from sunlight at a relative quickness inversely proportional to the ratio of diameters (e.g. if the sun has twice the diameter of the planets, the sun will spin at half the acceleration that the planets perform). Because an external gear meshed with an internal gear spin in the same path, the ring gear will spin in the same path of the planets, and once again, with a rate inversely proportional to the ratio of diameters. The rate ratio of the sun gear relative to the ring therefore equals -(Dsun/DPlanet)*(DPlanet/DRing), or just -(Dsun/DRing). That is typically expressed as the inverse, called the gear ratio, which, in this case, is -(DRing/DSun).

One more example; if the ring is kept stationary, the medial side of the planet on the ring aspect can’t move either, and the earth will roll along the inside of the ring gear. The tangential speed at the mesh with the sun equipment will be equal for both sun and world, and the guts of the planet will be shifting at half of that, being halfway between a spot moving at full rate, and one not moving at all. Sunlight will end up being rotating at a rotational rate in accordance with the swiftness at the mesh, divided by the diameter of sunlight. The carrier will be rotating at a swiftness relative to the speed at

the center of the planets (half of the mesh speed) divided by the diameter of the carrier. The apparatus ratio would thus be DCarrier/(DSun/0.5) or just 2*DCarrier/DSun.

The superposition method of deriving gear ratios
There is, nevertheless, a generalized way for determining the ratio of any kind of planetary set without having to figure out how to interpret the physical reality of every case. It really is known as ‘superposition’ and works on the basic principle that if you break a movement into different parts, and then piece them back again together, the effect will be the identical to your original motion. It is the same theory that vector addition works on, and it’s not a stretch to argue that what we are doing here is actually vector addition when you obtain right down to it.

In cases like this, we’re going to break the motion of a planetary arranged into two parts. The first is if you freeze the rotation of all gears in accordance with one another and rotate the planetary carrier. Because all gears are locked collectively, everything will rotate at the velocity of the carrier. The next motion is definitely to lock the carrier, and rotate the gears. As noted above, this forms a far more typical equipment set, and gear ratios can be derived as functions of the many gear diameters. Because we are merging the motions of a) nothing except the cartridge carrier, and b) of everything except the cartridge carrier, we are covering all motion taking place in the system.

The information is collected in a table, giving a speed value for each part, and the apparatus ratio when you use any part as the input, and any other part as the output can be derived by dividing the speed of the input by the output.