Epicyclic Drive Trains: Analysis, Synthesis, and Applications

B. Graphical Analysis

B. Graphical Analysis Section 16. Symbolic Representations of Epicyclic Transmissions According to Wolf In the previous chapter it has been shown that the function of a revolving drive can be analyzed without consideration of each detail of its design. Rather, a kinematic analysis can be performed when only the basic speedratio /o is known, which, according to worksheet 3, also determines the position of the summation shaft. Wolf [13], therefore, proposed a symbolic representation of the revolving drives which contains only the previously mentioned kinematical characteristics , as shown in fig. 53. A circle represents the transmission and three radial lines the three shafts. Because of their special importance, the summation shaft is symbolized by a double line, and the carrier shaft by an extension of the single or double line into the interior of the circle. According to worksheet 3, the location of the summation shaft also distinguishes negative-ratio drives from positive-ratio drives with /0 1. CrossFig . 53. Symbols for revolving drive trains according to Wolf [13]: a, negative-ratio transmission /o 1 . Fig. 54. Symbolic representation of the operating conditions of revolving drive trains: a, basic transmission with a positive speed-ratio; b-c, two-shaft transmissions ; dy basic transmission with an infinitely variable speed-ratio; e, three-shaft transmission with an infinitely variable basic speed-ratio /o, e.g., as shown in fig. 44; /, three-shaft transmission with unknown or freely selectable position of carrier and summation shaft. 83 84 / Simple Revolving Drive Trains a. b Fig. 55. Symbolic representation of a conventional transmission: a, with a constant speed-ratio /34; b, with an infinitely variable speed-ratio /34. hatching at a shaft flange, as shown in figs. 54a, b, and c, indicates that this shaft is fixed to the housing and, therefore, cannot rotate. If the carrier shaft is locked as shown in fig. 54a, then the Wolf symbol depicts a basic transmission. A locked central gear shaft as shown in figs. 54b and c represents a two-shaft revolving drive. When either the speed-ratio of a basic transmission or the basic speed-ratio of a three-shaft transmission is infinitely variable, an arrow is drawn across the transmission symbol as shown in figs. 54d and 54e respectively. A revolving drive train whose carrier and summation shafts have an unknown location, or can be freely chosen, is depicted with three equal shafts as shown in fig. 54f. In contrast to the practice for well-defined transmissions, these shafts are denoted by lower case letters (e.g., a, b, c) rather than by 1, 2, and s. A simple reduction drive with fixed axes may be symbolized by a circle with only two shafts as shown in fig. 55, although basically it should be represented by the symbols shown in figs. 54a or 54d. However, in practical applications of these transmission symbols it seems preferable that conventional transmissions with fixed axes, which are sometimes separately connected to the input or output shafts of revolving drive trains, be immediately identified as such. Simple reduction drives which are components of a compound revolving drive train should always by symbolized by fig. 54a, where the carrier shaft Fig. 56. Symbolic representation of the possible coupling conditions for three-shaft transmissions: a, transmission whose shaft / can be changed from freely rotating to locked, whose shaft 2 can be freely rotating or connected, and whose shaft s can be freely rotating, connected, or locked; b, change-gear, which consists of the two gear trains / and // and shows the following coupling conditions: A is rigidly connected (input or output); at D, s and 2' are rigidly coupled but not externally connected (free coupling shaft); C can be freely rotating (idle condition), connected (input or output), or locked; at B, if 2 and /' are coupled, the coupling shaft can be free, connected , or locked; if 2 and V are not coupled, shaft 2 may be either freely rotating or connected and shaft V may be either freely rotating or locked. 17. Kutzbach Speed Diagram for Planetary Transmissions / 85 corresponds to the housing (see sec. 2). The coupling conditions of the shafts can be symbolized as shown in fig. 56a. Especially for compound transmissions, the analysis of power-flow, shaft torques, and speeds is greatly simplified when the Wolf-symbols are inspected, rather than the actual layouts of the gear trains. As an illustration, fig. 56b shows a change gear whose...