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91
Summary
Many different planetary gear arrangements can be obtained by
varying the positions and size of the driving, driven, and fixed gear
members. In each case, tooth mesh loss, efficiency, and power
developed by the gears can be readily determined by the approach just
discussed. Analysis of various planetary train types shows that
efficiencies of all simple and compound systems may be expressed by
one of four basic formulas; Equations 14, 23, 28 and 33.
Two basic conditions determine which one of these expressions
must be used for a given case: (1) Whether the input shaft of a planetary
train is connected to one of the sun gears or to the planet cage and (2)
whether the position of the input shaft of the planetary train coincides or
does not coincide with the position of the driving member of the
equivalent train obtained by stopping the planetary cage.
This last condition depends upon the train design and, in some
cases such as the differential systems, upon the diameter ratios of the
gears constituting the given train. The magnitude of R in these
expressions is a function of the type of planetary train and gear size
relationships. This value can be positive or negative. In all cases, the
absolute value of R must be used for calculation of tooth mesh losses
and efficiency. In the expressions developed here, tosses due to oil
churning, as well as those introduced by the support members, have not
been considered.
REFERENCES
1. M.P. Massot – “Influence du Frottement sur la Functionnement des Trains
Epicycloidaux,” Societe des Ingeniers Civils de France, 1986, pages 576-593.
2. H.E. Meritt – “Epicyclic Gear Trains No II,” The Engeneer (England). March 28.
1981.
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