Planetary Gear Train
a mechanism for transmitting rotational motion by spur or bevel gears (less often by friction wheels) that include planet gears, or pinions that undergo coum-pound motion and have a moving axis of rotation. The moving element on which the axles of the planet gears are supported is called the carrier (Figure 1). The planets usually mesh with sun, or central, gears that rotate about the shaft of the mechanism or are fixed. The number of planets in a planetary gear train depends on the possibility of housing them in the mechanism, but in order to achieve a more uniform load distribution as a result
of the automatic adjustment of the gears it is preferable to have three planets. The compactness and small weight of a planetary gear train are due largely to the distribution of the transmitted power among the planets and to the use of internal gearing. A gear ratio in a planetary gear train is designated by the letter u and indicates the ratio of the angular velocities of the elements designated by a double subscript; a superscript shows which element of the mechanism is taken as fixed. If the directions of rotation of the driving and driven gears are identical, then the gear ratio is considered to be positive, but if the directions are different, it is taken as negative.
The simplest planetary gear train has one degree of freedom and one fixed sun gear. The properties and capabilities of such planetary gear trains depend largely on the sign of the gear ratio of the simple train—that is, the train in which the carrier is stopped and the gear train becomes an ordinary mechanism with fixed wheel axles. If the gear ratio in the simple train is negative, then
where ω1C and ω4C are the angular velocities of the sun gears. The gear ratio of the planetary train is then given by the formula
Here z1 and z4 are the numbers of teeth on the sun gears, and Z2 and Z3 are the numbers of teeth on the planets. Such planetary trains have a high efficiency (0.96–0.99) but do not permit the obtaining of high gear ratios. When there are three planets in a single-row planetary train (Figure 1,a), u can be no greater than 12 and is usually ≤ 8. For a two-row train (Figure l,b), usually u ≤ 15. In selecting the number of teeth on the gears, the rule governing the assembly of a planetary train must also be taken into account. In the simplest case, for a single-row planetary gear train it is sufficient that z1 and z4 be multiples of k, the number of planets. In order to obtain trains with a high efficiency and a high gear ratio, several single-row planetary trains of the type in Figure l,a are usually combined in series.
If the gear ratio in the simple train is positive (Figure 2),
then the gear ratio of the planetary train is given by the formula
Such planetary trains permit the obtaining of very high gear ratios, but they have a low efficiency.
If shaved gears are used and the number of teeth is selected so that (z2/z1)(z4/z3) is close to 1, it is possible to obtain planetary trains with an extremely high gear ratio. For example, when z1 = z3, z2 = z1 – 1, and z4 = z1 + 1, the planetary gear trains illustrated in Figure 2,a and 2,b give uC14 = Z12. In other words, when z1 = 100, u = 10,000. Here, however, the efficiency of the train is less than 0.01. For average gear ratios (of the order of 100), the efficiency of planetary gear trains with internal gearing is equal to 0.6–0.7. Such trains can therefore be used in power transmissions.
The fabrication of planetary gear trains is greatly simplified if
the planets are made single-crown and of extended width and are in mesh with sun gears that have different numbers of teeth (Figure 2,c).
Planetary gear trains of various functions and designs and with different characteristics are used in reduction gears to obtain compact coaxial designs and high gear ratios and in gear boxes, reversing gears, and clutch mechanisms to obtain convenient control by means of brakes and friction clutches. There exists a planetary gear train with a gear ratio of up to 2 X 106.
REFERENCES
Kudriavtsev, V. N. Planetarnye peredachi, 2nd ed. Moscow-Leningrad, 1966.Detali mashin: Raschet i konstruirovanie: Spravochnik, 3rd ed., vol. 3. Edited by N. S. Acherkan. Moscow, 1969.
N. IA. NIBERG
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