Planetary-gear transmissions are compact speed reductions which use parallel-load paths to transmit high power. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single-plane planetary transmission, the speed-reduction ratio must be greater than two for planet gears to exist. As the ratio increases, so does the size of the planets relative to the sizes of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a spur-gear planetary with a fixed size, speed-reduction ratio, input speed, power and materials. The planetary-gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the ball bearings and spur gears in the reduction. Planet-bearing life strongly influences the optimal reduction lives which point to an optimal planetary reduction ratio in the neighborhood of four to five.

1.
AGMA STANDARD, 1988, “Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth,” ANSI/AGMA 2001-B88, Alexandria, Virginia.
2.
Chin
H.
,
Danai
K.
, and
Lewicki
D. G.
,
1995
, “
Fault Detection of Helicopter Gearboxes Using the Multi-Valued Influence Matrix Method
,”
ASME Journal of Mechanical Design
, Vol.
117
, No.
2
, pp.
248
253
.
3.
Donley, Mark G., and Steyer, Glen C., 1992, “Dynamic Analysis of a Planetary Gear System,” Advancing Power Transmission into the 21st Century, ASME DE-VOL-43-l, pp. 117–127.
4.
Fox, Paul F., 1991, “Gear Arrangements,” Ch. 3, Dudley’s Gear Handbook, 2nd Ed., D. P. Townsend, ed. McGraw Hill, New York.
5.
Kahraman
A.
,
1994
, “
Planetary Gear Train Dynamics
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
116
, No.
3
, pp.
713
720
.
6.
Lynwander, Peter, 1983, Gear Drive Systems, Marcel Dekker, New York.
7.
Muller, Herbert W., 1982, Epicyclic Drive Trains, Wayne State University Press, Detroit, Mich.
8.
Rashidi, Majid, and Krantz, Timothy L., 1992, “Dynamics of a Split-Torque Helicopter Transmission,” Advancing Power Transmission into the 21st Century, ASME DE-VOL-43-1, pp. 19–33.
9.
Rubadeux, K. L., 1995, “PLANOPT—A Fortran Optimization Program for Planetary Transmission Design,” M.S. Thesis, The University of Akron, Akron, Ohio.
10.
Saada
A.
, and
Velex
P.
,
1995
, “
An Extended Model for the Analysis of the Dynamic Behavior of Planetary Trains
,”
ASME Journal of Mechanical Design
, Vol.
117
, No.
2
, pp.
241
247
.
11.
Savage
M.
,
Radil
K. C.
,
Lewicki
D. G.
, &
Coy
J. J.
,
1989
, “
Computerized Life and Reliability Modeling for Turboprop Transmissions
,”
AIAA Journal of Propulsion and Power
, Vol.
5
, No.
5
, pp.
610
614
.
12.
Savage
M.
, and
Lewicki
D. G.
,
1991
, “
Transmission Overhaul and Component Replacement Predictions Using Weibull and Renewal Theory
,”
AIAA Journal of Propulsion and Power
, Vol,
7
, No.
6
, pp.
1049
1054
.
13.
Savage
M.
,
Mackulin
B. J.
,
Coe
H. H.
, and
Coy
J. J.
,
1992
, “
Maximum-Life Spur-Gear Design
,”
AIAA Journal of Propulsion and Power
, Vol.
8
. No.
6
, pp.
1273
1281
.
14.
Savage
M.
,
Prasanna
M. G.
, and
Coe
H. H.
,
1993
, “
Maximum-Life Spiral-Bevel Reduction Design
,”
Gear Technology, The Journal of Gear Manufacturing
, Vol.
10
, No,
5
, pp.
24
40
.
15.
Savage, M., Rubadeux, K. L., Coe, H. H., and Coy, J. J., 1994, “Spur, Helical and Spiral-Bevel Transmission-Life Modeling,” NASA TM 106552, AIAA 94-3079, 30th Joint Propulsion Conference, Indianapolis, Indiana.
16.
Savage
M.
,
Lattime
S. B.
,
Kimmel
J. A.
, and
Coe
H. H.
,
1994
, “
Optimal Design of Compact Spur-Gear Reductions
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
116
, No.
3
, pp.
690
696
.
17.
Savage, M., Rubadeux, K. L., and Coe, H. H., 1995, “Bending-Strength Model for Internal Spur-Gear Teeth,” NASA TM 107012, AIAA 95-3049, 31st Joint Propulsion Conference, San Diego, California.
18.
Tsai
L. W.
,
1987
, “
An Application of the Linkage Characteristic Polynomial to the Topographical Synthesis of Epicyclic-Gear Trains
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS AND AUTOMATION IN DESIGN
, Vol.
109
, No.
3
, pp.
329
337
.
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