Epicyclic Drive Trains: Analysis, Synthesis, and Applications

IV. DESIGN HINTS

IV. DESIGN HINTS Section 43. Geometric Conditions for Assembly of Planetary Transmissions The design of a new transmission usually begins with the determination of the basic speed-ratio and the selection of the most suitable gear train as explained in earlier sections. The calculation of the gear parameters and the arrangement of the gears relative to each other can then proceed according to the well-known methods established for conventional gear trains. To determine the number of teeth for the gear train with the minimum overall diameter, before the gearing is actually designed for the given torques and the available materials, the following procedure can be employed. a) Correlation between Number of Teeth and Gear Diameter In reverted planetary transmissions, the center distance between the meshing gears must be selected in such a way that the two central gears can be arranged coaxially. In this respect, transmission designs with meshing planets (figs. 22, 23, 36, and 37) cause the least problems. Their center distances initially need only be approximated and the gear sets can then be designed to meet cost and manufacturing requirements. Finally, the center distances can be adjusted to the correct values by "jaekknifing" the drive train to a greater or lesser degree. However, in transmissions with simple stepped planets of the types shown, (figs. 19, 21, 24, 34, and 39), the two series-coupled gear stages must, from the very beginning, be designed to have the same center distances . In general, the overall basic speed-ratio is given and must be split between the two stages: In standard involute gear trains without addendum modification which have the diametral pitches P{ + P2 the center distances are C lpi = 5 # pT (%>! + Z») ' a n d C 2p2 = 5 * pT d = - 190/ 13. tDi/mo over- dimensioned because ab Verb 1 indicates that stage // is overdesigned and ab {/ab 2 2 1 "t z2 ' ZP2 Z~~2~ - 1 361|3pl*2l 360 |. l^i Z2I + 361 \Zp\Z2\ 360 1 - \Z\Zpi\ DM + \ZlZp2\ Jpal \ZiZp2\ ' 3|«pil - ki^l kpiZal ' , (138) (139) This shows that for gear trains with stepped planets the two index angles (5s)ifixedan d (5S)afixed are not equal. If we develop the resulting carrier spacings and place them side by side as shown in fig. 168, then we observe that dsmin becomes even smaller than the smaller of the two calculated spac- 318 / Design Hints 'Vitad — ZF miii 0 ' 2 fixed Fig. 168. Development of the circumference of the carrier showing the possible index angles. ings. In the example of fig. 168, we can generate 5smin if we turn gear 2 by two teeth relative to the fixed gear 1 so that the arm turns by 2 (5s)lfixed, and then lock gear 2 and turn gear 1 back by three teeth, which causes the arm to move back by 3 (5S) 2fixed-Thus, we obtain Ssmin = 2(6s )l f l x e d - 3(6s)2fixed • The teeth of the stepped planet which are brought into mesh by these two motions do not have the same angular position relative to each other as the teeth which were in mesh before these two motions took place. Since, during this procedure, both central gears have been turned by an integer number of teeth, a new planet could be installed at the initial location of the first planet, provided its two stepped gears have precisely the same position relative to each other as those of the first planet. According to eqs. (136) and (137), or (138) and (139), the reduced ratio of the index angles 8S for a given gear train becomes )l fixed (^s) 2 fixed Jp2 (140) where t is the largest common divisor of the two numbers of teeth of the stepped planets andjpl andyp2 are simply the integer residues of the numerator and denominator. As fig. 168 and eq. (140) show, the index angles jp2(4) 1fixed= 7pl(*s)2fixed » are equal, and determine the angle at which a stepped planet can be inserted between the central gears, with the same teeth as were at the initial position fitting the meshes at the new position. For negative-ratio transmissions, the smallest index angle 6smin as shown in fig. 168, is obtained from eqs. (136) and (137). Thus, 43. Geometric Conditions for Assembly of Transmissions / 319 s )lfixed...