The concept of virtual power is first defined as the power measured, in a noninertial frame, in an epicyclic gear train. We then introduce the concept of virtual-power ratio, an invariant related to the power loss in an epicyclic system. It is shown that virtual-power flow and balance exist in an epicyclic gear train, based on which a novel algorithm to compute the gear-mesh powerloss and the train efficiency is formulated. This algorithm is general enough to be applied to any given epicyclic gear train. Our results are compared with previous work on the subject.
Issue Section:
Research Papers
1.
Pennestri
, E.
, and Freudenstein
, F.
, 1993, “The Mechanical Efficiency of Epicyclic Gear Trains
,” ASME J. Mech. Des.
1050-0472, 115
(3
), pp. 645
–651
.2.
Radzimovsky
, E. I.
, 1956, “A Simplified Approach for Determining Power Losses and Efficiency of Planetary Gear Drives
,” Mach. Des.
0024-9114, 28
(3
), pp. 101
–110
.3.
Radzimovsky
, E. I.
, 1959, “How to Find Efficiency, Speed, and Power in Planetary Gear Drives
,” Mach. Des.
0024-9114, 31
(12
), pp. 144
–153
.4.
Macmillan
, R. H.
, 1961, “Power Flow and Loss in Differential Mechanisms
,” J. Mech. Eng. Sci.
0022-2542, 3
(1
), pp. 37
–41
.5.
Macmillan
, R. H.
, and Davies
, P. B.
, 1965, “Analytical Study of Systems for Bifurcated Power Transmission
,” J. Mech. Eng. Sci.
0022-2542, 7
(1
), pp. 40
–47
.6.
Yu
, D.
, and Beachley
, N.
, 1985, “On the Mechanical Efficiency of Differential Gearing
,” ASME J. Mech., Transm., Autom. Des.
0738-0666, 107
(1
), pp. 61
–67
.7.
del Castillo
, J. M.
, 2002, “The Analytical Expression of the Efficiency of Planetary Gear Trains
,” Mech. Mach. Theory
0094-114X, 37
(2
), pp. 197
–214
.8.
Pennestrì
, E.
, and Valentini
, P. P.
, 2003, “A Review of Formulas for the Mechanical Efficiency Analysis of Two Degrees-of-Freedom Epicyclic Gear Trains
,” ASME J. Mech. Des.
1050-0472, 125
(3
), pp. 602
–608
.9.
Kahraman
, A.
, Ligata
, H. K. K.
, and Zini
, D. M.
, 2004, “A Kinematics and Power Flow Analysis Methodology for Automatic Transmission Planetary Gear Trains
,” ASME J. Mech. Des.
1050-0472, 126
(6
), pp. 1071
–1081
.10.
Salgado
, D. R.
, and del Castillo
, J. M.
, 2005, “Selection and Design of Planetary Gear Trains Based on Power Flow Maps
,” ASME J. Mech. Des.
1050-0472, 127
(1
), pp. 120
–134
.11.
Nelson
, C. A.
, and Cipra
, R. J.
, 2005, “Simplified Kinematic Analysis of Bevel Epicyclic Gear Trains With Application to Power-Flow and Efficiency Analyses
,” ASME J. Mech. Des.
1050-0472, 127
(2
), pp. 278
–286
.12.
Macmillan
, R. H.
, 1949, “Epicyclic Gear Efficiencies
,” Engineer
, 188
(4900
), pp. 727
–728
.13.
Truesdell
, C.
, 1966, The Elements of Continuum Mechanics
, Springer-Verlag
, New York.14.
Buckingham
, E.
, 1928, Spur Gears
, McGraw-Hill
, New York.15.
Freudenstein
, F.
, and Yang
, A. T.
, 1972, “Kinematics and Statics of a Coupled Epicyclic Spur-Gear Train
,” Mech. Mach. Theory
0094-114X, 7
(2
), pp. 263
–275
.16.
Angeles
, J.
, 2003, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms
, Springer-Verlag
, New York.17.
Harary
, F.
, 1969, Graph Theory
, Perseus Books
, Cambridge.18.
Tsai
, L. W.
, 2000, Mechanism Design: Enumeration of Kinematic Structures According to Function
, CRC Press
, Boca Raton.19.
Tuplin
, W. A.
, 1957, “Compound Epicyclic Gear Trains
,” Mach. Des.
0024-9114, 29
(7
), pp. 100
–104
.20.
Litvin
, F. L.
, Fuentes
, A.
, Vecchiato
, D.
, and Gonzalez-Perez
, I.
, 2004, “New Design and Improvement of Planetary Gear Trains
,” NASA Glenn Research Center Technical Reports.Copyright © 2007
by American Society of Mechanical Engineers
You do not currently have access to this content.
