# Planetary gears - Applied Mechanics

## Planetary gears

Planetary gears are called gears with gears with moving geometric axes. The movement of these wheels, called satellites, is similar to the motion of planets around the Sun. Therefore, these programs were called planetary. The satellites g are fixed to the mobile link - the carrier h and rotate along with it around the central axis 0. The satellites roll over the central wheels a and b, having external and internal meshing. The central wheels are called the solar wheel (a) and the reference wheel ( b) (Figure 4.39, a); - angular frequencies of rotation of the central wheel a, of the satellite and carrier; - the number of teeth of the central wheels and the satellite.

Mechanisms with planetary gears can be used as differentials, when all links are mobile. They have two degrees of mobility. For example, the differential in cars in which the cylindrical wheels are replaced by conical ones (Figure 4.39, b). The addition and decomposition of movements is possible, when the speeds of the shafts and the wheels K fixed on them are different, car. The most common transmission, in which one of the central wheels is fixed; then the mechanism has only one degree of mobility.

Fig. 4.39

Planetary gears refer to coaxial gears and are usually multi-threaded (two or three, depending on the number of satellites), thereby reducing the load on the teeth and reducing the size of the wheels.

Advantages of planetary gears in the presence of two or more satellites: smaller overall dimensions and mass, as the torque is transmitted over several flows; large gear ratios in one stage; smaller transverse forces act on the shafts.

Disadvantages, increased accuracy of manufacturing and assembly (not lower than the seventh degree of accuracy, but better the sixth and even the fifth); at high gear ratios the efficiency is reduced.

Planetary gears are widely used in transport, machine-tool construction, instrument making and other industries. A large number of planetary gear schemes have been developed. Consider the schemes of the most common transmissions (the designation determines the presence of two central wheels a and b and the carrier h), shown in Table. 4.13.

Scheme 1 is the simplest single-stage transmission. This transfer is most common due to high efficiency and manufacturability. Scheme 2 is used for large gear ratios. It includes two steps, each of which is made in scheme 1.

Table 4.13

 Number Schemas Schematic diagram Gear ratio Efficiency 1 2 3

It is also possible to use transmissions with a large number of stages. Scheme 3 is close to scheme 1, but on the carrier there is a block with a two-row satellite. This transfer is more complex and requires manufacturing with increased accuracy. The mass of this transmission is less than the transmission performed according to scheme 1.

In the designation of gear ratios, the superscript denotes the stopped link, and the lower indicates the transfer of rotation from the lead to the slave. For example, is the gear ratio from the driving wheel a to the driver h with the wheel b.

Kinematic calculation. The kinematic calculation of the planetary gear for a given gear ratio and the selected kinematic scheme (see Table 4.13) reduces to the selection of the number of teeth of the wheels. At the same time, it is necessary to observe three conditions: coaxiality, neighborhood and collection. Consider these conditions for a planetary transmission performed according to scheme 1.

The condition of coaxiality is necessary in order for the axes of the central wheels to coincide with the axis of rotation of the carrier. For this, the center distances a and g and the wheels g and b must be equal to:

(4.55)

The condition of neighborhood is necessary so that when setting the satellites their teeth do not touch each other. The condition can be satisfied by the expression

(4.56)

The condition of collecting requires the teeth of all satellites to coincide with the spacing between the teeth of the central wheels. The fulfillment of this condition is necessary to ensure assembly in the presence of several satellites:

(4.57)

where - the number of satellites; C is an arbitrary integer.

The design features of planetary gearing affect the load distribution between satellites. In an ideal design with several satellites they are equal. In the real transmission because of the errors in the manufacture of force are distributed unevenly. For load balancing, constructive measures are used: one of the central wheels is made floating, which is realized by connecting them to the shaft or body by means of gear clutches. The uneven distribution of the load among the satellites is taken into account by the coefficient K s. If there is an alignment mechanism , and if there is no

If the torque on the sun wheel is , then its share in meshing with one satellite and the circumferential force are respectively

(4.58)

The calculation of the planetary gear for the inner and outer gears of the satellite is carried out according to the formulas for cylindrical gears. Since the inner engagement is stronger than the outer one, then for the same wheel materials, the strength of only the outer gearing of the wheels is calculated a and g. When determining the number of loading cycles, the teeth are set for the sun wheel , and for the satellite

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