Planetary Gears – a masterclass for mechanical engineers

Planetary gear sets contain 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 input/outputs from a planetary equipment set
Typically, one part of a planetary set is held stationary, yielding an individual input and an individual output, with the entire 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 utilized mainly because inputs, with the single output being a function of both inputs
This could be accomplished in a two-stage gearbox, with the first stage traveling two portions of the next stage. A very high gear ratio could be noticed in a compact package. This type of arrangement is sometimes known as a ‘differential planetary’ set
I don’t think there is a mechanical engineer out there who doesn’t have a soft spot for gears. There’s simply something about spinning bits of metal (or some other material) meshing together that’s mesmerizing to watch, while checking so many options functionally. Particularly mesmerizing are planetary gears, where in fact the gears not merely spin, but orbit around a central axis as well. In this post we’re likely to look at the particulars of planetary gears with an eyesight towards investigating a specific category of planetary equipment setups sometimes known as a ‘differential planetary’ set.

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

Planetary Gears
Planetary gears normally consist of three parts; A single sun gear at the guts, an internal (ring) equipment around the outside, and some number of planets that move in between. Usually the planets will be the same size, at a common center length from the guts of the planetary gear, and kept by a planetary carrier.

In your basic setup, your ring gear will have teeth equal to the number of the teeth in sunlight gear, plus two planets (though there may be advantages to modifying this slightly), simply because a line straight over the center from one end of the ring gear to the other will span sunlight gear at the guts, and space for a planet on either end. The planets will typically be spaced at regular intervals around sunlight. To do this, the total amount of tooth in the ring gear and sun gear mixed divided by the amount of planets has to equal a complete number. Of course, the planets have to be spaced far plenty of from one another therefore that they don’t interfere.

Fig.2: Equivalent and opposite 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 employ a common central shaft, high ‘torque density’ because of the load being shared by multiple planets, and tangential forces between your gears being cancelled out at the center of the gears because of equal and opposite forces distributed among the meshes between the planets and other gears.

Gear ratios of standard planetary gear sets
Sunlight gear, ring gear, and planetary carrier are normally used as insight/outputs from the apparatus set up. In your standard planetary gearbox, among the parts is normally kept stationary, simplifying things, and giving you a single input and an individual output. The ratio for any pair can be worked out individually.

Fig.3: If the ring gear is certainly held stationary, the velocity of the earth will be while shown. Where it meshes with the ring gear it will have 0 velocity. The velocity increases linerarly over the planet equipment from 0 to that of the mesh with the sun gear. As a result at the centre it will be shifting at half the quickness at the mesh.

For example, if the carrier is held stationary, the gears essentially form a standard, non-planetary, gear arrangement. The planets will spin in the opposite direction from sunlight at a member of family quickness inversely proportional to the ratio of diameters (e.g. if sunlight provides twice the size of the planets, the sun will spin at half the velocity that the planets do). Because an external gear meshed with an interior equipment spin in the same direction, the ring gear will spin in the same path of the planets, and again, with a rate inversely proportional to the ratio of diameters. The quickness ratio of the sun gear relative to the ring thus equals -(Dsun/DPlanet)*(DPlanet/DRing), or just -(Dsun/DRing). This is typically expressed as the inverse, known as the apparatus ratio, which, in this case, is -(DRing/DSun).

One more example; if the band is held stationary, the medial side of the planet on the band aspect can’t move either, and the planet will roll along the within of the ring gear. The tangential speed at the mesh with the sun gear will be equal for both sun and planet, and the center of the earth will be moving at half of this, getting halfway between a point moving at full rate, and one not really moving at all. Sunlight will become rotating at a rotational acceleration relative to the rate at the mesh, divided by the size of sunlight. The carrier will become rotating at a velocity 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, however, a generalized method for figuring out the ratio of any planetary set without having to work out how to interpret the physical reality of each case. It really is known as ‘superposition’ and works on the principle that if you break a motion into different parts, and then piece them back together, the effect will be the same as your original motion. It is the same theory that vector addition functions on, and it’s not really a stretch to argue that what we are carrying out here is actually vector addition when you obtain right down to it.

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

The info 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 could be derived by dividing the speed of the input by the output.