Planetary gear sets include a central sun gear, surrounded by many planet gears, kept 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 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 depending on which part is held stationary, which is the input, and that your output
Instead of holding any part stationary, two parts can be utilized mainly 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 generating two portions of the second stage. An extremely high equipment ratio can be understood in a compact package. This sort 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 steel (or some other materials) meshing together that’s mesmerizing to view, while checking so many possibilities functionally. Especially mesmerizing are planetary gears, where in fact the gears not merely 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 particular category of planetary equipment setups sometimes known as a ‘differential planetary’ set.
The different parts of planetary gears
Fig.1 Components of a planetary gear
Planetary gears normally consist of three parts; A single sun gear at the center, an internal (ring) gear around the outside, and some quantity of planets that move in between. Generally the planets are the same size, at a common middle range from the center of the planetary gear, and kept by a planetary carrier.
In your basic setup, your ring gear could have teeth add up to the amount of the teeth in sunlight gear, plus two planets (though there might be advantages to modifying this somewhat), due to the fact a line straight across the center from one end of the ring gear to the other will span the sun gear at the guts, 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 teeth in the ring gear and sun gear mixed divided by the number of planets has to equal a whole number. Of training course, the planets need to be spaced far enough from one another therefore that they do not interfere.
Fig.2: Equivalent and opposite forces around sunlight equal no part drive 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 employ a common central shaft, high ‘torque density’ due to the load being shared by multiple planets, and tangential forces between the gears being cancelled out at the center of the gears because of equal and opposite forces distributed among the meshes between your planets and other gears.
Gear ratios of regular planetary gear sets
Sunlight gear, ring gear, and planetary carrier are usually used as insight/outputs from the gear set up. In your standard planetary gearbox, among the parts is usually kept stationary, simplifying factors, and providing you an individual input and a single result. The ratio for any pair could be exercised individually.
Fig.3: If the ring gear can be held stationary, the velocity of the planet will be seeing that shown. Where it meshes with the ring gear it has 0 velocity. The velocity boosts linerarly across the planet equipment from 0 compared to that of the mesh with sunlight gear. Therefore at the center it will be moving at fifty percent 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 member of family acceleration inversely proportional to the ratio of diameters (e.g. if sunlight provides twice the diameter of the planets, sunlight will spin at half the rate that the planets do). Because an external equipment meshed with an interior 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 acceleration ratio of the sun gear relative to the ring hence equals -(Dsun/DPlanet)*(DPlanet/DRing), or simply -(Dsun/DRing). That is typically expressed as the inverse, called the gear ratio, which, in cases like this, is -(DRing/DSun).
One more example; if the ring is held stationary, the side of the earth on the band aspect can’t move either, and the planet will roll along the within of the ring gear. The tangential acceleration at the mesh with sunlight gear will be equal for both sun and planet, and the guts of the earth will be moving at half of this, getting halfway between a point moving at complete quickness, and one not moving at all. Sunlight will be rotating at a rotational quickness in accordance with the speed at the mesh, divided by the size of sunlight. The carrier will be rotating at a swiftness relative to 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, nevertheless, a generalized method for determining the ratio of any planetary set without having to work out how to interpret the physical reality of every case. It is known as ‘superposition’ and works on the theory that in the event that you break a movement into different parts, and then piece them back again together, the result would be the identical to your original movement. It’s the same principle that vector addition works on, and it’s not a stretch to argue that what we are performing here is in fact vector addition when you get right down to it.
In cases like this, we’re likely to break the movement of a planetary set into two parts. The first is if you freeze the rotation of all gears in accordance with each other and rotate the planetary carrier. Because all gears are locked jointly, everything will rotate at the acceleration of the carrier. The second motion is usually 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 various 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 occurring in the system.
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.