Gear Geometry and Applied Theory: Planetary Gear Trains

INTRODUCTION Planetary gear trains were the subject of intensive research directed at determination of dynamic response of the trains, vibration, load distribution, efficiency, enhanced design, and other important topics [Lynwander, 1983; Ishida & Hidaka, 1992; Kudrjavtzev et al ., 1993; Kahraman, 1994; Saada & Velex, 1995; Chatterjee & Tsai, 1996; Hori & Hayashi, 1996a, 1996b; Velex & Flamand, 1996; Lin & Parker, 1999; Chen & Tseng, 2000; Kahraman & Vijajakar, 2001; Litvin et al ., 2002e]. This chapter covers gear ratio, conditions of assembly, relations of tooth numbers, efficiency of a planetary train, proposed modification of geometry of tooth surfaces, determination of transmission errors, etc. Special attention is given to the regulation of backlash for improvement of load distribution. GEAR RATIO A planetary gear mechanism has at least one gear whose axis is movable in the process of meshing. Planetary Mechanisms of Figs. 23.2.1 (a) and (b) Figures 23.2.1(a) and (b) represent two simple planetary gear mechanisms formed by two gears 1 and 2 that are in external or internal meshing, respectively, and a carrier c on which the gear with the movable axis is mounted. Gear 1 is fixed and planet gear 2 performs a planar motion of two components: (i) transfer rotation with the carrier, and (ii) relative rotation about the carrier.