Planetary gear sets contain a central sun gear, surrounded by several planet gears, held by a planet carrier, and enclosed within a ring gear
Sunlight gear, ring gear, and planetary carrier form three possible insight/outputs from a planetary gear set
Typically, one portion of a planetary set is held stationary, yielding a single input and an individual output, with the overall 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 used as inputs, with the single output being truly a function of both 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 could be recognized in a concise package. This type of arrangement may also be known as a ‘differential planetary’ set
I don’t think there exists a mechanical engineer away there who doesn’t have a soft spot for gears. There’s simply something about spinning bits of metal (or various other materials) meshing together that is mesmerizing to view, while checking so many possibilities functionally. Particularly mesmerizing are planetary gears, where in fact the gears not only spin, but orbit around a central axis aswell. In this post we’re going to look at the particulars of planetary gears with an attention towards investigating a specific category of planetary equipment setups sometimes referred to as a ‘differential planetary’ set.
The different parts of planetary gears
Fig.1 Components of a planetary gear
Planetary gears normally contain three parts; An individual sun gear at the guts, an internal (ring) gear around the exterior, and some number of planets that proceed in between. Generally the planets are the same size, at a common center length from the center of the planetary equipment, and held by a planetary carrier.
In your basic setup, your ring gear could have teeth add up to the number of the teeth in the sun gear, plus two planets (though there might be benefits to modifying this somewhat), simply because a line straight across the center from one end of the ring gear to the other will span the sun gear at the center, and area for a world on either end. The planets will typically be spaced at regular intervals around sunlight. To do this, the total amount of teeth in the ring gear and sun gear combined divided by the number of planets has to equal a complete number. Of training course, the planets need to be spaced far plenty of from each other so that they don’t interfere.
Fig.2: Equal and opposite forces around the sun equal no part force on the shaft and bearing at the center, The same could be shown to apply straight to the planets, ring gear and world carrier.
This arrangement affords several advantages over other possible arrangements, including compactness, the likelihood for the sun, 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 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
The sun gear, ring gear, and planetary carrier are usually used as input/outputs from the apparatus arrangement. In your regular planetary gearbox, among the parts can be kept stationary, simplifying things, and giving you an individual input and an individual result. The ratio for 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 increases linerarly over the planet gear from 0 to that of the mesh with the sun gear. Therefore at the centre it will be moving at half the swiftness at the mesh.
For example, 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 the sun 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 acceleration 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 direction of the planets, and again, with a speed inversely proportional to the ratio of diameters. The acceleration ratio of sunlight 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 instance, is -(DRing/DSun).
One more example; if the ring is held stationary, the medial side of the earth on the band part can’t move either, and the earth will roll along the within of the ring gear. The tangential quickness at the mesh with the sun gear will be equal for both sun and world, and the center of the earth will be moving at half of this, being halfway between a spot moving at complete velocity, and one not moving at all. Sunlight will become rotating at a rotational acceleration in accordance with the swiftness at the mesh, divided by the diameter of the sun. The carrier will become rotating at a speed in accordance with the speed at
the center of the planets (half of the mesh rate) divided by the size of the carrier. The apparatus ratio would therefore 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 needing to work out how to interpret the physical reality of every case. It is known as ‘superposition’ and functions on the theory that if you break a movement into different parts, and then piece them back together, the effect will be the identical to your original motion. It is the same basic principle that vector addition functions on, and it’s not really a extend to argue that what we are carrying out here is in fact vector addition when you get because of it.
In this case, we’re going to break the motion of a planetary arranged into two parts. The foremost is if you freeze the rotation of all gears relative to each other and rotate the planetary carrier. Because all gears are locked collectively, everything will rotate at the rate of the carrier. The second motion is definitely to lock the carrier, and rotate the gears. As observed above, this forms a more typical gear set, and gear ratios can be derived as features 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 occurring in the machine.
The information is collected in a table, giving a speed value for every part, and the apparatus ratio by using 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.