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C. Design and Operating Characteristics of Simple Planetary Transmissions Section 20- Practically Achievable Basic Speed-Ratios Theoretically, all the simple planetary transmission designs which are shown in figs. 19 to 43, could be designed with any basic speed-ratio. Practically , however, the range of the basic speed-ratios of each type is limited by the following aspects: a) For economical reasons, an external gear stage should not exceed a speed-ratio of i = - 4 to - 8 . For higher speed-ratios, multi-stage transmissions are smaller, lighter, and cheaper. This applies equally to planetary transmissions whose largest single-stage speed-ratio, therefore, should not normally exceed these values which thus also limit /0. b) If three or more planets are arranged as densely as possible around the circumference of the carrier, then the smallest possible sun gear, the largest ring gear and, thus, the largest possible ratio between their diameters results from the condition that the addendum circles of the planets may not touch each other. c) In specific cases, other restrictions, which shall not be discussed at this point, may be imposed by design conditions such as weight, volume, or loads on the planet bearings due to the centrifugal forces. The limits of the basic speed-ratios, as given in figs. 19 to 43, are valid for the most frequently encountered cases where three planets are arranged around the sun gear with a minimum distance between their addendum circles (which is equal to the reciprocal of the diametral pitch) and a sun gear with z = 17 teeth. For planetary transmissions with two sun gears it has been assumed that the smaller of the two sun gears has 17 teeth. In gear trains with stepped planets as shown, for example, in figs. 19 and 35, the pinion gears of each stage are geometrically similar and carry equal loads. Thus, the ratio between their (pitch circle) diameters equals the cube root of their torque ratio. For the most frequently encountered types of planetary transmissions (that is, for negative-ratio transmissions as shown in fig. 33, positive-ratio transmissions as shown in fig. 19, and open revolving drives as shown in figs. 29 and 43), the largest possible basic speed-ratios io are given in figs. 71 104 21. Efficiency of the Two-Shaft Transmission / 105 and 72 as functions of the number of planets which are arranged around the circumference of the sun gear. In a planetary transmission with bevel gears, as shown in fig. 41, an increasing basic speed-ratio i0 causes the planet's axis to become more nearly horizontal. Thus, the planetary gear train of fig. 33 can be considered as the limiting case of the bevel gear train of fig. 41 and, therefore, has the same maximum basic speed-ratio. Section 21. Efficiency of the Two-Shaft Transmission a) Influence of Design on Efficiency The following three measures are suited to achieve high efficiencies in planetary transmissions: 1. Try to achieve low tooth-friction losses by applying such well-known gear design methods as the use of high quality tooth profiles and the selection of suitable materials and lubrication methods. Especially, the sliding motion between the tooth profiles must be minimized by using annular gear stages and gear stages with as many teeth as possible [27]. 2. As indicated by eq. (10), the number of gear meshes which the powerflow must pass in series should be as small as possible in order to limit the sources of friction power-losses and thus obtain a high basic efficiency (parallel gear meshes which occur with power branching, theoretically, do not influence the efficiency). 3. Keep the rolling power PR and thus the tooth-friction losses low as compared to the input power Pin, since according to eq. (51) the efficiency increases with a decreasing power ratio PRAFV Fig. 15 shows that for uncorrected gear trains, the tooth-friction losses, which in power transmissions constitute the bulk of the losses, decrease substantially with an increasing number of teeth. It also shows that the toothfriction losses in internal gear meshes where i > 0 are much smaller than in external gear meshes where i 7st when - | ^ - = — . Fm 1.5 For all other speed-ratio ranges in which P^\n/Pm is smaller than these values, planetary gear trains under otherwise equal conditions should achieve a higher efficiency (rjF{ > r)St) than single stage external gear trains. For the three previously considered planetary gear trains, these speed-ratio ranges can be found from figs...

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