In this study, a two-dimensional (2D), steady-state, discrete dynamic model of a double-planet planetary gearset is proposed. The dynamic model is generalized such that it can consist of N number of planet branches and can operate under any operating conditions (load and speed). The contact between each external to external and external to internal gear pair is modeled to obtain stiffnesses and mesh displacement excitations using a generalized load distribution model. The natural modes are computed by solving the corresponding eigenvalue problem. The forced vibration response to gear mesh excitations is obtained by applying the modal summation technique. The model is capable of predicting gear mesh dynamic load and dynamic transmission error spectra for each gear mesh, dynamic bearing load spectra for each bearing as well as gear body dynamic displacements. Forced vibration response of an example system that consists of three double-planet branches is studied to demonstrate the influence of some of the key design parameters.

References

References
1.
Muller
,
W. H.
,
1982
,
Epicyclic Drive Trains
,
Wayne State University Press
,
Detroit, MI
.
2.
Lynwander
,
P.
,
1983
,
Gear Drive Systems
,
Marcel Dekker
,
New York
.
3.
Saada
,
A.
, and
Velex
,
P.
,
1995
, “
An Extended Model for the Analysis of the Dynamic Behavior of Planetary Trains
,”
ASME J. Mech. Des.
,
117
(
2A
), pp.
241
247
.
4.
Endo
,
H.
,
Ito
,
M.
, and
Ozeki
,
T.
,
2003
, “
Development for Toyota's Transaxle for Minivan Hybrid Vehicles
,”
JSAE Rev.
,
24
(
1
), pp.
109
116
.
5.
Miyata
,
S.
, and
Liu
,
D.
,
2007
, “
Study of a Control Mechanism of a Half-Toroidal CVT During Load Transmission
,”
ASME J. Mech. Des.
,
1
(
3
), pp.
346
357
.
6.
Singh
,
A.
,
2007
, “
Influence of Planetary Needle Bearings on the Performance of Single and Double Pinion Planetary Systems
,”
ASME J. Mech. Des.
,
129
(
1
), pp.
85
94
.
7.
Ericson
,
T. M.
, and
Parker
,
R. G.
,
2013
, “
Natural Frequency Clusters in Planetary Gear Vibration
,”
ASME J. Vib. Acoust.
,
135
(
6
), p.
061002
.
8.
Kahraman
,
A.
,
2001
, “
Free Torsional Vibration Characteristics of Compound Planetary Gear Sets
,”
Mech. Mach. Theory
,
36
(
8
), pp.
953
971
.
9.
Mohammadpour
,
M.
,
Theodessiades
,
S.
, and
Rahnejat
,
H.
,
2015
, “
Dynamics and Efficiency of Planetary Gearsets for Hybrid Powertrains
,”
Proc. Inst. Mech. Eng., Part C
, epub.
10.
Cao
,
Z.
,
Shao
,
Y.
,
Ming
,
J. Z.
, and
Liang
,
X.
,
2014
, “
Dynamic and Quasi-Static Modeling of Planetary Gear Set Considering Carrier Misalignment Error and Varying Line of Action Along Tooth Width
,”
Proc. Inst. Mech. Eng., Part C
,
229
(
8
), pp.
1348
1360
.
11.
Dhouib
,
S.
,
Hbaieb
,
R.
,
Chaari
,
F.
,
Abbes
,
M. S.
,
Fakhfakh
,
T.
, and
Haddar
,
M.
,
2008
, “
Free Vibration Characteristics of Compound Planetary Gearsets
,”
Proc. Inst. Mech. Eng., Part C
,
222
(
8
), pp.
1389
1401
.
12.
Inalpolat
,
M.
, and
Kahraman
,
A.
,
2008
, “
Dynamic Modeling of Planetary Gears of Automatic Transmissions
,”
Proc. Inst. Mech. Eng., Part K
,
222
(3), pp.
229
242
.
13.
Kahraman
,
A.
,
Ligata
,
H.
,
Kienzle
,
K.
, and
Zini
,
D. M.
,
2008
, “
A Kinematics and Power Flow Analysis Methodology for Automatic Transmission Planetary Gear Trains
,”
ASME J. Mech. Des.
,
126
(
6
), pp.
1071
1081
.
14.
Kwon
,
H. S.
,
Kahraman
,
A.
,
Lee
,
H. K.
, and
Suh
,
H. S.
,
2014
, “
An Automated Design Search for Single and Double-Planet Planetary Gear Sets
,”
ASME J. Mech. Des.
,
136
(
6
), p.
061004
.
15.
Kubur
,
M.
, and
Kahraman
,
A.
,
2004
, “
Dynamic Analysis of a Multi-Shaft Helical Gear Transmission by Finite Elements: Model and Experiment
,”
ASME J. Vib. Acoust.
,
126
(
3
), pp.
398
406
.
16.
Houser
,
D. R.
,
2003
,
LDP, Gear Load Distribution Program
,
Gear Dynamics and Gear Noise Research Laboratory, The Ohio State University
,
Columbus, OH
.
17.
Parker
,
R. G.
, and
Lin
,
J.
,
2004
, “
Mesh Phasing Relationships in Planetary and Epicyclic Gears
,”
ASME J. Mech. Des.
,
126
(
2
), pp.
365
370
.
18.
Kahraman
,
A.
, and
Blankenship
,
G. W.
,
1994
, “
Planet Mesh Phasing in Epicyclic Gearsets
,”
International Gearing Conference
, Newcastle, UK, pp.
99
104
.
19.
Ewins
,
D. J.
,
2000
,
Modal Testing: Theory, Practice and Application
,
Research Studies Press
,
Hertfordshire, UK
.
20.
Lin
,
J.
, and
Parker
,
R. G.
,
1999
, “
Analytical Characterization of the Unique Properties of Planetary Gear Free Vibration
,”
ASME J. Vib. Acoust.
,
121
(
3
), pp.
316
321
.
You do not currently have access to this content.