Planetary Gears – a masterclass for mechanical engineers

Planetary gear sets include a central sun gear, surrounded by several planet gears, kept 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 portion of a planetary set is held stationary, yielding an individual input and a single output, with the overall gear ratio based on which part is held stationary, which is the input, and which the output
Instead of holding any part stationary, two parts can be utilized simply because inputs, with the single output being a function of the two inputs
This could be accomplished in a two-stage gearbox, with the first stage driving two portions of the next stage. A very high equipment ratio can be recognized in a compact package. This sort of arrangement may also be called a ‘differential planetary’ set
I don’t think there is a mechanical engineer away there who doesn’t have a soft spot for gears. There’s simply something about spinning items of metallic (or various other material) meshing together that is mesmerizing to view, while checking so many opportunities functionally. Particularly mesmerizing are planetary gears, where in fact the gears not only spin, but orbit around a central axis aswell. In this article we’re going to consider the particulars of planetary gears with an eyes towards investigating a specific family of planetary gear setups sometimes known as a ‘differential planetary’ set.

Components of planetary gears
Fig.1 Components of a planetary gear

Planetary Gears
Planetary gears normally consist of three parts; An individual sun gear at the center, an interior (ring) gear around the exterior, and some number of planets that go in between. Generally the planets are the same size, at a common middle distance from the guts of the planetary gear, and held by a planetary carrier.

In your basic setup, your ring gear could have teeth equal to the number of the teeth in sunlight gear, plus two planets (though there might be advantages to modifying this slightly), due to the fact a line straight over the center from one end of the ring gear to the other will span the sun gear at the guts, and room for a planet on either end. The planets will typically be spaced at regular intervals around sunlight. To accomplish this, the total number of teeth in the ring gear and sun gear mixed divided by the number of planets must equal a whole number. Of training course, the planets need to be spaced far more than 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 centre, The same can be shown to apply to the planets, ring gear and planet 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 your gears being cancelled out at the guts 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
The sun gear, ring gear, and planetary carrier are usually used as input/outputs from the gear set up. In your regular planetary gearbox, among the parts is definitely kept stationary, simplifying points, and giving you an individual input and a single result. The ratio for just about any pair can be exercised individually.

Fig.3: If the ring gear is certainly held stationary, the velocity of the planet will be while shown. Where it meshes with the ring gear it has 0 velocity. The velocity raises linerarly across the planet equipment from 0 to that of the mesh with the sun gear. Consequently at the centre it’ll be moving at half the quickness at the mesh.

For example, if the carrier is held stationary, the gears essentially form a typical, non-planetary, equipment arrangement. The planets will spin in the contrary direction from sunlight at a relative swiftness inversely proportional to the ratio of diameters (e.g. if the sun provides twice the size of the planets, the sun will spin at half the swiftness that the planets do). Because an external equipment meshed with an internal equipment spin in the same direction, the ring gear will spin in the same direction of the planets, and again, with a swiftness inversely proportional to the ratio of diameters. The speed ratio of the sun gear relative to the ring thus equals -(Dsun/DPlanet)*(DPlanet/DRing), or just -(Dsun/DRing). That is typically expressed as the inverse, known as the apparatus ratio, which, in cases like this, is -(DRing/DSun).

One more example; if the band is kept stationary, the side of the earth on the band aspect can’t move either, and the earth will roll along the within of the ring gear. The tangential swiftness at the mesh with the sun equipment will be equal for both the sun and world, and the guts of the planet will be shifting at half of this, being halfway between a point moving at complete quickness, and one not moving at all. Sunlight will be rotating at a rotational rate in accordance with the velocity at the mesh, divided by the size of the sun. The carrier will end up being rotating at a velocity in accordance with the speed at

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

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

In cases like this, we’re going to break the movement of a planetary set into two parts. The foremost is in the event that you freeze the rotation of all gears relative to one another and rotate the planetary carrier. Because all gears are locked together, everything will rotate at the speed of the carrier. The next motion is usually to lock the carrier, and rotate the gears. As mentioned above, this forms a more typical gear set, and equipment ratios could be derived as functions of the various equipment diameters. Because we are combining the motions of a) nothing at all except the cartridge carrier, and b) of everything except the cartridge carrier, we are covering all motion occurring in the system.

The information is collected in a table, giving a speed value for each part, and the apparatus 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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