Planetary Gears – a masterclass for mechanical engineers

Planetary gear sets contain a central sun gear, surrounded by many planet gears, held by a planet carrier, and enclosed within a ring gear
Sunlight gear, ring gear, and planetary carrier form three possible input/outputs from a planetary gear set
Typically, one part of a planetary set is held stationary, yielding a single input and an individual output, with the entire gear ratio based on which part is held stationary, which may be the input, and which the output
Instead of holding any part stationary, two parts can be utilized as inputs, with the single output being a function of both inputs
This is often accomplished in a two-stage gearbox, with the first stage traveling two portions of the second stage. An extremely high gear ratio can be understood in a compact package. This type of arrangement may also be called a ‘differential planetary’ set
I don’t think there exists a mechanical engineer away there who doesn’t have a soft place for gears. There’s just something about spinning items of metallic (or some other materials) meshing together that is mesmerizing to watch, while checking so many possibilities functionally. Especially mesmerizing are planetary gears, where the gears not only spin, but orbit around a central axis aswell. In this article we’re likely to consider the particulars of planetary gears with an eyes towards investigating a specific family of planetary equipment setups sometimes known 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 consist of three parts; A single sun gear at the guts, an internal (ring) equipment around the outside, and some quantity of planets that proceed in between. Generally the planets are the same size, at a common middle distance 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 the sun gear, plus two planets (though there might be benefits to modifying this slightly), due to the fact a line directly over the center in one end of the ring gear to the other will span sunlight gear at the guts, and room for a world on either end. The planets will typically become spaced at regular intervals around the sun. To do this, the total amount of teeth in the ring gear and sun gear mixed divided by the amount of planets has to equal a whole number. Of training course, the planets need to be spaced far plenty of from each other therefore that they do not interfere.

Fig.2: Equal and contrary forces around the sun equal no aspect pressure on the shaft and bearing in the centre, The same could 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 sunlight, ring gear, and planetary carrier to use a common central shaft, high ‘torque density’ because of the load being shared by multiple planets, and tangential forces between the gears being cancelled out at the center of the gears due to equal and opposite forces distributed among the meshes between the planets and other gears.

Gear ratios of regular planetary gear sets
The sun gear, ring gear, and planetary carrier are normally used as input/outputs from the gear set up. In your regular planetary gearbox, one of the parts is definitely held stationary, simplifying things, and giving you an individual input and a single output. The ratio for just about any pair could be exercised individually.

Fig.3: If the ring gear is held stationary, the velocity of the earth will be seeing that shown. Where it meshes with the ring gear it will have 0 velocity. The velocity raises linerarly over the planet equipment from 0 to that of the mesh with sunlight gear. Therefore at the center it will be shifting at half the rate at the mesh.

For example, if the carrier is held stationary, the gears essentially form a typical, non-planetary, gear arrangement. The planets will spin in the opposite direction from sunlight at a relative rate inversely proportional to the ratio of diameters (e.g. if the sun has twice the size of the planets, sunlight will spin at half the rate that the planets perform). Because an external gear meshed with an interior gear spin in the same path, the ring gear will spin in the same direction of the planets, and again, with a speed inversely proportional to the ratio of diameters. The quickness ratio of sunlight 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 instance, is -(DRing/DSun).

Yet another example; if the ring is held stationary, the medial side of the earth on the band side can’t move either, and the earth will roll along the inside of the ring gear. The tangential swiftness at the mesh with the sun gear will be equivalent for both sun and world, and the center of the planet will be moving at half of that, becoming halfway between a point moving at complete speed, and one not really moving at all. Sunlight will be rotating at a rotational velocity relative to the speed at the mesh, divided by the size of the sun. The carrier will end up being rotating at a rate relative to the speed at

the center of the planets (half of the mesh rate) divided by the diameter of the carrier. The gear ratio would therefore end up being DCarrier/(DSun/0.5) or simply 2*DCarrier/DSun.

The superposition method of deriving gear ratios
There is, however, a generalized way for figuring out the ratio of any kind of planetary set without having to figure out how to interpret the physical reality of every case. It is called ‘superposition’ and works on the theory that if you break a motion into different parts, and then piece them back again together, the result would be the same as your original movement. It’s the same basic principle that vector addition works on, and it’s not a stretch to argue that what we are carrying out here is in fact vector addition when you get right down to it.

In this case, we’re likely to break the motion of a planetary arranged into two parts. The foremost is in the event that you freeze the rotation of all gears in accordance with each other and rotate the planetary carrier. Because all gears are locked collectively, everything will rotate at the acceleration of the carrier. The next motion is certainly to lock the carrier, and rotate the gears. As mentioned above, this forms a more typical gear set, and equipment ratios can be derived as functions of the many equipment 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 movement taking place in the system.

The info is collected in a table, giving a speed value for each part, and the gear ratio by using 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.


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