The planetary mechanism: calculation, diagram, synthesis

There are all sorts of mechanical devices. Some of them are familiar to us from childhood. This, for example, a watch, a Bicycle whirligig. Others, we know, as you get older. It's the engines, winches cranes and other. Each moving mechanism is any system that causes the wheels to spin, and the machine work. One of the most interesting and popular is the planetary gear. Its essence is that the car drives the wheels or gears that interact with each other in a special way. To view further details.

General information

The planetary gear and the planetary gear is so named by analogy with our Solar system, which conditionally can be represented as follows: in the center is the "sun" (a Central wheel mechanism). Around it move the "planet" (little wheels or pinions). All of these details in the planetary mechanism have outer teeth. Conventional solar system, its diameter has a border. Its role in the planetary mechanism performs a large wheel or epicycle. It also has teeth, only internal. A lot of work in this construction performs carrier constituting the linkage. The movement can be done in different ways: either the sun will rotate, or epicycle, but always in conjunction with satellites.

When the work of the planetary mechanism can be used and other structure, for example, two suns, satellites, and led, but without a epicycle. Another option - two of the epicycle, but without the sun. Carrier and the satellites should always be present. Depending on the number of wheels and positioning of the axes of rotation in space, the design can be simple or complex, flat or spatial. the

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To fully understand how this system operates, it is necessary to understand the details.

Locating elements

The simplest form of planetary mechanism includes three sets of gear with varying degrees of freedom. The above satellites rotate around their axes and simultaneously around the sun, remaining in place. The epicycle planetary mechanism connects the outside and also rotates through successive clutch teeth (and its satellites). This design is able in a single plane to change the torque (angular velocity).

In a simple planetary mechanism can rotate the sun and the satellites and the hub to remain fixed. In any case, the angular velocities of all components are not chaotic and have a linear dependence from each other. As the rotation of the carrier, is provided by the low speed output with high torque.

That is the essence of the planetary gear is that this design is able to change, to sort and stack torque and the angular velocity held. Rotational motion at the same place in the same geometric axis. A necessary element of the transmission of different vehicles and mechanisms.

Features of structural materials and diagrams

However, the fixed component is not always necessary. In differential systems, each element rotates. The mechanisms of the planetary such as this, include one output-managed (managing) two inputs. For example, the differential that drives the axle in the car, is a similar transmission.

Such systems operate on the same principle as the structure with parallel shaft. Even a simple planetary gear set has two entrances, fixed ring gear is a constant input of zero angular velocity.

Detailed device description

Mixed planetary design can have a different number of wheels, as well as various transmission, through which they are connected. The existence of such parts greatly extends the capabilities of the mechanism. Compound planetary designs can be assembled so that the shaft of the carrier platform moving at high speed. As a result, some problems with the reduction sun gear and the other can be eliminated in the process of improving the device.

Thus, as can be seen from the above information, the planetary gear works on the principle of transmission of rotation between the links, which is the Central and movable. While complex systems are more in demand than others.

Configuration Options

In a planetary mechanism, it is possible to use the wheels (gears) of various configurations. Standard fit with straight teeth, helical, worm, herringbone. Type gearing on the planetary gear will not be affected. Important to coincide the axis of rotation of the carrier and the Central wheel. But the axis satellites may be located in other planes (intersecting, parallel, intersecting). Example of skew - differential cross axle, which gears have a conical shape. Example of skew - differential, self-locking, which engages the worm gear (Torsen).

Simple and complex devices

As noted above, the scheme of the planetary mechanism always includes a carrier and two Central wheels. Satellites can be as much as necessary. This so-called simple or elementary device. In such arrangements, the construction can be such : "SAF", "SWE", "EVE", where:

• With the sun.
• In - carrier.
• E - hub.

Each set of wheels + satellites called planetary. In this case, all wheels should rotate in the same plane. Simple mechanisms are one - and two-row. In various technical devices and machines they are rarely used. An example would be a planetary mechanism of a Bicycle. According to this principle a bushing through which the traffic moves. Its design is built on a "BOO". Satellites not in 4 pieces. The sun is rigidly mounted to the axle of the rear wheel, and the epicenter is moving. To rotate it forces the cyclist pressing on the pedal. The transmission speed, hence the speed of rotation may vary.

It is Much more common to meet the complex planetary gear mechanisms. Their schemes can be very different, depending on what one or the other design. As a rule, the complex mechanisms consist of a few simple, established as a General rule for the planetary gear. Such complex systems are two-, three - or four-row. It is theoretically possible to create designs with a large number of rows, but in practice this is not found.

Planar and spatial device

Some people think that a simple planetary gear must be flat. This is only partly true. Complex devices can also be flat. This means that gear is, no matter how much was used in the device are in the same or in parallel planes. Spatial mechanisms are the planetary ranks in two or more planes. With own wheels can be smaller than in the first embodiment. Note that the flat planetary gear is the same as spatial. The only difference is occupied by the device area, that is, compactness.

Degrees of freedom

So is the set of coordinate rotation to determine the position of the system in space at a given time. In fact, each planetary gear has degrees of freedom not less than two. That is, the angular velocity of rotation of any part of such devices are not connected linearly, as in other gears. This allows you to output the angular velocity is not what you are at the entrance. This can be explained by the fact that in the differential when the planetary mechanism are three elements in any row and the rest related to it linearly by means of any one element of the range. It is theoretically possible to create a planetary system with three or more degrees of freedom. But in practice, they are unhealthy.

The Gear ratio of the planetary gear set

This is the most important characteristic of rotational motion. It allows you to determine how many times the increased torque on the driven shaft relative to the torque shaft. To determine the gear ratio by formulas:

I = d2/d1 =Z2/Z1 = M2/M1 = W1/W2 = n1/n2, where:

• 1 - link leading.
• 2 - link slave.
• D1, d2 - diameters of the first and second units.
• Z1, Z2 - number of teeth.
• M1, M2 - torque.
• W1 W2 - the angular velocity.
• N1 n2 - speed.

Thus, at a reduction ratio greater than one on the driven shaft increases the torque, and the frequency and the angular velocity decrease. This should always be considered when creating a design, because the gear ratio in the planetary mechanisms depends on how many teeth have wheels, and which element is leading.

Scope

In the modern world there are many different machines. Many of them work with the help of planetary mechanism.

They are used in automotive differentials, planetary gears, in the kinematic schemes of machine tools, reduction gears air engines airplanes, bikes, harvesters and tractors, tanks and other military equipment. The principles of the planetary transmission to a transmission to drive electric generators. Let's look at another one.

Planetary rotation mechanism

This design is used in some tractors, vehicles on tracks and tanks. A simple diagram of the device shown in the figure below. The working Principle of planetary rotation mechanism is: carrier (1) is connected with the brake drum (2) and the drive wheel located in the caterpillar. The epicycle (6) connected to the shaft of a transmission (position 5). The sun (8) is connected with the disk clutch (3) and the drum brake swivel (4). When you turn on the lock-up clutch and the band brake off the satellites rotate will not. They will become like the levers, as by means of teeth associated with the sun (8) and the epicycle (6). Why force them and led simultaneously to rotate around a common axis. The angular speed is the same.

When you turn off the lock-up clutch and the brake turn the sun will stop, and the satellites move around their axes. Thus, they create a torque on the carrier and rotates the driving wheel caterpillars.

Wear

With regard to service life and depreciation, in the linear mechanisms of planetary systems distribution of load considerably among the major components.

Thermal and cyclic fatigue may increase in them due to the limited load distribution and the fact that the planetary gear can rotate quitequickly on their axes. Moreover, at high speeds and transfer relations the planetary gear, the centrifugal force can significantly increase the amount of motion. It should also be noted that the lower accuracy of production and increasing the number of satellites the trend of imbalance increases.

These devices and their systems may even be subject to depreciation or amortization. Some designs will be sensitive to even small imbalances and is able to demand high-quality and expensive components of the Assembly. The exact location of the planetary pins around the axis of the sun gear can be key.

Other schemes of planetary mechanisms that help to balance the load include the use of floating subassemblies or “soft” of fixtures to provide maximum durability in the movement of the sun or the epicenter.

The Basics of synthesis planetary devices

This knowledge is useful when designing and creating the nodes of the machines. The concept of “synthesis of planetary mechanisms” is to calculate the number of teeth in the sun, hub and satellites. It is necessary to observe several conditions:

• Gear ratio must equal the specified value.
• Engage the teeth of the wheels should be correct.
• You Need to ensure the concentricity of the input shaft and the output.
• You want to ensure the neighborhood (satellites should not interfere with each other).

Also when designing you need to consider the dimensions of the future structure, its mass and efficiency.

If you set the ratio (n), the number of teeth on the sun (S) and planetary gears (P) must satisfy the equality:

n = S/P

If we assume that the number of teeth on the hub before (A), in a locked cage must be respected equality:

N = -S/A

If fixed epicenter, it is also true the following equality:

N = 1+ A/S

So is the calculation of the planetary mechanism.

Advantages and disadvantages

There are several types of transfers that are successfully used in various devices. Planetary among them the following advantages:

• It provides less load on each tooth of the wheel (of the sun and the epicenter, and satellites) due to the fact that the load on them is distributed more evenly. This positively affects the service life of the structure.
• At the same power planetary gear has smaller dimensions and mass than when using other types of transmission.
• The Ability to achieve more gear ratios with a lesser number of wheels.
• Providing a lower level of noise.

Disadvantages of planetary mechanisms:

• You Need higher precision in their manufacture.
• Small efficiency with a relatively large gear ratio.