An analytical expression for the total efficiency of the Simpson gear train is derived using virtual power analysis. This expression is consistent with intuition when the total efficiency is 100%. Power flow analysis shows that there are no internal power circulation and amplification in the Simpson gear train. Analysis based on the derived efficiency formula shows that the total efficiency of the Simpson gear transmission is more sensitive to the individual gear efficiencies when the speed reduction is higher.

References

References
1.
Rabindran
,
D.
, and
Tesar
,
D.
, 2008, “
Power Flow Analysis in Parallel Force/Velocity Actuators (PFVA): Theory and Simulations
,”
ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
New York
, Aug.
3
6
.
2.
Zhu
,
F.
,
Chen
,
L.
,
Yin
,
C.
, and
Tang
,
L.
, 2010, “
Scheme Design and Optimal Selection for Hybrid Electric Vehicle Planetary Gear Mechanism
,”
Zhongguo Jixie Gongcheng/China Mech. Eng.
,
21
(
1
), pp.
104
109
.
3.
Tsai
,
L. W.
, 2000,
Mechanism Design: Enumeration of Kinematic Structures According to Function
,
CRC
,
New York
.
4.
Radzimovsky
,
E. I.
, 1956, “
A Simplified Approach for Determining Power Losses and Efficiency of Planetary Gear Drives
,”
Mach. Des.
,
28
(
3
), pp.
101
110
.
5.
Pennestri
,
E.
, and
Freudenstein
,
F.
, 1993, “
The Mechanical Efficiency of Epicyclic Gear Trains
,”
ASME J. Mech. Des.
,
115
, pp.
645
651
.
6.
Radzimovsky
,
E. I.
, 1959, “
How to Find Efficiency, Speed, and Power in Planetary Gear Drives
,”
Mach. Des.
,
31
(
12
), pp.
144
153
.
7.
Macmillan
,
R. H.
, 1961, “
Power Flow and Loss in Differential Mechanisms
,”
J. Mech. Eng. Sci.
,
3
(
1
), pp.
37
41
.
8.
Macmillan
,
R. H.
, and
Davies
,
P. B.
, 1965, “
Analytical Study of Systems for Bifurcated Power Transmission
,”
J. Mech. Eng. Sci.
,
7
(
l
), pp.
40
47
.
9.
Yu
,
D.
, and
Beachley
,
N.
, 1985, “
On the Mechanical Efficiency of Differential Gearing
,”
J. Mech., Transm., Autom. Des.
,
107
, pp.
61
67
.
10.
del Castillo
,
J. M.
, 2002, “
The Analytical Expression of the Efficiency of Planetary Gear Trains
,”
Mech. Mach. Theory
,
37
, pp.
197
214
.
11.
Pennestri
,
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
, pp.
602
608
.
12.
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
, pp.
278
286
.
13.
Kahraman
,
K. K. A.
,
Ligata
,
H.
, and
Zini
,
D. M.
, 2004, “
A Kinematics and Power Flow Analysis Methodology for Automatic Transmission Planetary Gear Trains
,”
ASME J. Mech. Des.
,
126
, pp.
1071
1081
.
14.
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.
,
127
, pp.
120
134
.
15.
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
.
16.
Chen
,
C.
, and
Liang
,
T. T.
, 2011, “
Theoretic Study of Efficiency of Two-DOF of Epicyclic Gear Transmission via Virtual Power
,”
ASME J. Mech. Des.
,
133
(
3
),
p.
031007
.
17.
Buckingham
,
E.
, 1928,
Spur Gears
,
McGraw-Hill
,
New York
.
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