The concept of potential power efficiency is introduced as the efficiency of an epicyclic gear train (EGT) measured in any moving reference frame. The conventional efficiency can be computed in a carrier-moving reference frame in which the gear carrier appears relatively fixed. In principle, by attaching the reference frame to an appropriate link, torques can be calculated with respect to each input, output, or (relatively) fixed link in the EGT. Once the power flow direction is obtained from the potential power ratio, the torque ratios are obtained from the potential power efficiencies, the particular expression of the efficiency of the EGT is found in a simple manner. A systematic methodology for the efficiency analysis of one and two degree-of-freedom (DOF) EGTs is described, and 14 ready-to-use efficiency formulas are derived for 2DOF gear pair entities (GPEs). This paper includes also a discussion on the redundancy of the efficiency formulas used for 1DOF GPEs. An incomplete in the efficiency formulas in previous literature, which make them susceptible to wrong application, is brought to light.
Issue Section:
Design of Direct Contact Systems
References
1.
Merritt
, H. E.
, 1947
, Gear Trains
, Sir Isaac Pitman & Sons Ltd.
, London
, pp. 123
–137
.2.
Macmillan
, R. H.
, 1961
, “Power Flow and Loss in Differential Mechanisms
,” J. Mech. Eng. Sci.
, 3
(1
), pp. 37
–41
.3.
Macmillan
, S. R. H.
, and Davies
, P. B.
, 1965
, “Analytical Study of Systems for Bifurcated Power Transmission
,” J. Mech. Eng. Sci.
, 7
(1
), pp. 40
–47
.4.
Pennestri
, E.
, and Freudenstein
, F.
, 1993
, “The Mechanical Efficiency of Epicyclic Gear Trains
,” ASME J. Mech. Des.
, 115
(3
), pp. 645
–651
.5.
Radzimovsky
, E. I.
, 1956
, “A Simplified Approach for Determining Power Losses and Efficiency of Epicyclic Gear Drives
,” Mach. Des.
, 9
, pp. 101
–110
.6.
Radzimovsky
, E. I.
, 1959
, “How to Find Efficiency, Speed and Power Losses in Epicyclic Gear Drives
,” Mach. Des.
, 11
, pp. 144
–153
.7.
Yu
, D.
, and Beachley
, N.
, 1985
, “On the Mechanical Efficiency of Differential Gearing
,” J. Mech. Transm. Autom. Des.
, 107
(1
), pp. 61
–67
.8.
del Castillo
, J. M.
, 2002
, “The Analytical Expression of the Efficiency of Epicyclic Gear Trains
,” Mech. Mach. Theory
, 37
(2
), pp. 197
–214
.9.
Chen
, C.
, and Angeles
, J.
, 2007
, “Virtual-Power Flow and Mechanical Gear-Mesh Power Losses of Epicyclic Gear Trains
,” ASME J. Mech. Des.
, 129
(1
), pp. 107
–113
.10.
Chen
, C.
, and Liang
, T. T.
, 2011
, “Theoretic Study of Efficiency of Two-DOFs of Epicyclic Gear Transmission Via Virtual Power
,” ASME J. Mech. Des.
, 133
(3
), p. 031007
.11.
Pennestri
, E.
, Mariti
, L.
, Valentini
, P. P.
, and Mucino
, V. H.
, 2012
, “Efficiency Evaluation of Gearboxes for Parallel Hybrid Vehicles: Theory and Applications
,” Mech. Mach. Theory
, 49
, pp. 157
–176
.12.
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.
, 125
(3
), pp. 602
–608
.13.
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.
, 127
(2
), pp. 278
–286
.14.
Mantriota
, G.
, and Pennestrì
, E.
, 2003
, “Theoretical and Experimental Efficiency Analysis of Multi-Degrees-of-Freedom Epicyclic Gear Trains
,” Multibody Syst. Dyn.
, 9
(4
), pp. 389
–408
.15.
Kahraman
, A.
, Ligata
, H.
, Kienzle
, K.
, and Zini
, D. M.
, 2004
, “A Kinematics and Power Flow Analysis Methodology for Automatic Transmission Epicyclic Gear Trains
,” ASME J. Mech. Des.
, 126
(6
), pp. 1071
–1081
.16.
Hsieh
, H. I.
, and Tsai
, L. W.
, 1998
, “The Selection of a Most Efficient Clutching Sequences Associated With Epicyclic-Type Automatic Transmission
,” ASME J. Mech. Des.
, 120
(4
), pp. 514
–519
.17.
Duan
, Q. H.
, and Yang
, S. R.
, 2002
, “A Study on Power Flow and Meshing Efficiency of 3K Type Epicyclic Gear Train
,” Mech. Sci. Technol.
, 21
(3
), pp. 360
–362
.18.
White
, G.
, 2003
, “Derivation of High Efficiency Two-Stage Epicyclic Gears
,” Mech. Mach. Theory
, 38
(2
), pp. 149
–159
.19.
Hsieh
, L.-C.
, and Chen
, T.-H.
, 2011
, “The Design and Efficiency Analysis of Epicyclic Gear Reducer
,” J. Adv. Mater. Res.
, 317–319
, pp. 2226
–2229
.20.
Hsieh
, L. C.
, and Chen
, T. H.
, 2012
, “On the Meshing Efficiency of 3K-Type Epicyclic Simple Gear Reducer
,” J. Adv. Sci. Lett.
, 12
(1
), pp. 34
–39
.21.
Hsieh
, L. C.
, and Tang
, H.-C.
, 2013
, “On the Meshing Efficiency of 2K-2H Type Epicyclic Gear Reducer
,” Adv. Mech. Eng.
, 2013
, p. 686187
.22.
Ayats
, J. G.
, Calvet
, J. V.
, Canela
, J. M.
, Diego-Ayala
, U.
, and Artes
, F. F.
, 2011
, “Power Transmitted Through a Particular Branch in Mechanisms Comprising Epicyclic Gear Trains and Other Fixed or Variable Transmissions
,” Mech. Mach. Theory
, 46
(11
), pp. 1744
–1754
.23.
Pennestrì
, E.
, and Valentini
, P. P.
, 2002
, “Dynamic Analysis of Epicyclic Gear Trains by Means of Computer Algebra
,” Multibody Syst. Dyn.
, 7
(3
), pp. 249
–264
.24.
Pennestrì
, E.
, and Freudenstein
, F.
, 1993
, “A Systematic Approach to Power-Flow and Static Force Analysis in Epicyclic Spur-Gear Trains
,” ASME J. Mech. Des.
, 115
(3
), pp. 639
–644
.25.
Vaidyanathan
, L. S.
, Harianto
, A.
, and Kahraman
, J.
, 2009
, “Influence of Design Parameters on Mechanical Power Losses of Helical Gear Pairs
,” J. Adv. Mech. Des., Syst., Manuf.
, 3
, pp. 146
–158
.26.
Esmail
, E. L.
, 2013
, “Nomographs for Synthesis of Epicyclic-Type Automatic Transmissions
,” Meccanica
, 48
(8
), pp. 2037
–2049
.27.
Massot
, M. P.
, 1936
, “Influence du Frottement sur la Fonctionnement des Trains Epicycloideaux
,” Soc. Ing. Civ. Fr.
, pp. 576
–593
.Copyright © 2016 by ASME
You do not currently have access to this content.
