Epicyclic Drive Trains: Analysis, Synthesis, and Applications

A. Symbols and Types

A. Symbols and Types Section 31. Symbols and Modifying Subscripts or Superscripts For compound drives, which consist of several epicyclic transmissions, the symbols /, 2, s, and/;, as defined in the previous part I (sec. 4), will be used to denote the gears or shafts of the first transmission. The corresponding gears or shafts of the second transmission are then denoted accordingly by the primed symbols, 7', 2', s'', pf and the gears or shafts of a third revolving drive train by the double primed symbols, /", 2", s", /?", etc. Analogously, the basic speed-ratios of these transmissions are denoted by * o > 'o > 'o a n d the basic efficiencies by rjOf rj^, r)£ . If, in general notation, the shafts of the individual revolving drives are symbolized by lowercase letters, we shall use a, b, c for the first transmission, a', b', c' for the second, etc. This type of notation permits us to analyze the individual component transmissions of a compound revolving drive, such as shown in fig. 109, by using directly, and without rethinking, the formulas which have been derived earlier for the simple epicyclic transmissions. If conventional reduction drives with fixed axes are combined with revolving drives, their gears and shafts are denoted by a sequence of numbers starting with 3 as shown in fig. 10. The shafts of two (or more) component transmissions which are rigidly coupled form a "coupling shaft." If a coupling shaft is also an external shaft, it is called a "connected coupling shaft"; if it is not connected to the outside, it is called "a free coupling shaft" (fig. 110). Shafts which are not coupled in this way, and either are the input or output shafts of a compound transmission, or are locked by a rigid connection with the housing, are called "connected monoshafts" and "fixed monoshafts," respectively (fig. 110). The coupling shafts and the remaining monoshafts of the revolving compound drive trains are denoted by uppercase letters or Roman numerals ("uppercase subscription"), the shafts of the component transmissions, however, by lowercase letters or arabic numerals ("lowercase subscription ") as described previously. In "simple bicoupled transmissions" (sec. 32), which consist of only two component transmissions, the connectedcoupling shaft is always denoted with S and the free coupling shaft with F; 169 170 / Compound Epicyclic Transmissions 2 2' 2" 1" n m b Fig. 109. Series-coupled revolving drive train consisting of three two-shaft transmissions which are connected in series: a> general symbolic representation; b> schematic representation of a typical transmission; c, symbolic representation of the transmission b. the two monoshafts, however, are labeled with the Roman numerals /and //(see fig. 110). If it is unknown or immaterial which of the shafts of the component transmissions of a simple bicoupled transmission should be the carrier shafts and which the central gear shafts, then these shafts are labeled with lowercase letters according to their functions in the bicoupled transmission. In fig. 110a, for example, m, m' are connected monoshafts, c, c' join to form the connected coupling shaft 5, and /, / ' join to form the free coupling shaft F. When the positions of the carrier shafts s, s', and the central gear shafts 1, 1', 2, 2' of the component transmissions are known, then these specific symbols, rather than lowercase letters, are used as shown in fig. 110b. The different component transmissions are distinguished by Roman numerals as shown in fig. 110. In the equations used to analyze compound or simple transmissions, the newly introduced symbols also are used as subscripts. This is consistent with our previous practice. Section 32. Types a) Derivation from Simple Revolving Drives If a compound revolving drive is constructed from a number of simple revolving drives, each of the shafts of these component transmissions can be connected as an input or output shaft, can be fixed in the housing, or can be 32. Types / 171 coupled to any shaft of another component transmission. The available simple transmissions, and the various types of compound epicyclic transmissions which result from their combinations, are shown in a series of schematic representations whose shafts are labeled with the chosen symbols (fig. HI). If exclusively two-shaft epicyclic transmissions (which always have one stationary shaft and, hence, only one degree of freedom) are coupled in series or parallel, the resulting compound transmission likewise has only one degree of freedom. This is illustrated in figs. 11 If and 11 Ig. The single degree of freedom also...