This article summarizes published journal articles on planetary and epicyclic gear dynamics and vibration. Research in this field has increased dramatically over the past two decades. The wide range of research topics demonstrates the technical challenges of understanding and predicting planetary gear dynamics and vibration. The research in this review includes mathematical models, vibration mode properties, dynamic response predictions including nonlinearities and time-varying mesh stiffness fluctuations, the effects of elastic compliance, and gyroscopic effects, among other topics. Practical aspects are also included, for example, planet load sharing, planet phasing, tooth surface modifications, and characteristics of measured vibration response.

References

References
1.
Chiang
,
T.
, and
Badgley
,
R. H.
,
1973
, “
Reduction of Vibration and Noise Generated by Planetary Ring Gears in Helicopter Aircraft Transmissions
,”
J. Eng. Ind.
,
95
(
4
), pp.
1149
1158
.10.1115/1.3438263
2.
Musial
,
W.
,
Butterfield
,
S.
, and
McNiff
,
B.
,
2007
, “
Improving Wind Turbine Gearbox Reliability
,”
NREL Technical Report No. NREL/CP-500-41548
.
3.
Rasmussen
,
F.
,
Thomsen
,
K.
, and
Larsen
,
T. J.
,
2004
, “
The Gearbox Problem Revisited
,” Riso Technical Report No. AED-RB-17(EN).
4.
Helsen
,
J.
,
Marrant
,
B.
,
Vanhollebeke
,
F.
,
De Coninck
,
F.
,
Berckmans
,
D.
,
Vandepitte
,
D.
, and
Desmet
,
W.
,
2013
, “
Assessment of Excitation Mechanisms and Structural Flexibility Influence in Excitation Propagation in Multi-Megawatt Wind Turbine Gearboxes: Experiments and Flexible Multibody Model Optimization
,”
Mech. Syst. Signal Process.
,
40
, pp.
114
135
.10.1016/j.ymssp.2012.12.001
5.
Struggl
,
S.
,
Berbyuk
,
V.
, and
Johansson
,
H.
,
2014
, “
Review on Wind Turbines With Focus on Drive Train System Dynamics
,”
Wind Energy
(in press).10.1002/we.1721
6.
Vijayakar
,
S. M.
,
2005
, “
Calyx Users Manual
,” http://ansol.us
7.
Özgüven
,
H. N.
, and
Houser
,
D. R.
,
1988
, “
Mathematical Models Used in Gear Dynamics—A Review
,”
J. Sound Vib.
,
121
(
3
), pp.
383
411
.10.1016/S0022-460X(88)80365-1
8.
Wang
,
J.
,
Li
,
R.
, and
Peng
,
X.
,
2003
, “
Survey of Nonlinear Vibration of Gear Transmission Systems
,”
ASME Appl. Mech. Rev.
,
56
(
3
), pp.
309
329
.10.1115/1.1555660
9.
Blankenship
,
G. W.
, and
Singh
,
R.
,
1992
, “
A Comparative Study of Selected Gear Mesh Interface Dynamic Models
,” ASME Power Transmission and Gearing Conference, Phoenix, AZ, pp. 137–164.
10.
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
.10.1115/1.2893982
11.
Cunliffe
,
F.
,
Smith
,
J. D.
, and
Welbourn
,
D. B.
,
1974
, “
Dynamic Tooth Loads in Epicyclic Gears
,”
J. Eng. Ind.
,
96
(
2
), pp.
578
584
.10.1115/1.3438367
12.
Botman
,
M.
,
1976
, “
Epicyclic Gear Vibrations
,”
J. Eng. Ind.
,
98
(
3
), pp.
811
815
.10.1115/1.3439034
13.
Gu
,
X.
, and
Velex
,
P.
,
2011
, “
A Lumped Parameter Model to Analyse the Dynamic Load Sharing in Planetary Gears With Planet Errors
,”
Appl. Mech. Mater.
,
86
, pp.
374
379
.10.4028/www.scientific.net/AMM.86.374
14.
Kahraman
,
A.
,
1994
, “
Planetary Gear Train Dynamics
,”
ASME J. Mech. Des.
,
116
(
3
), pp.
713
720
.10.1115/1.2919441
15.
Kahraman
,
A.
,
1994
, “
Natural Modes of Planetary Gear Trains
,”
J. Sound Vibration
,
173
(
1
), pp.
125
130
.10.1006/jsvi.1994.1222
16.
Cooley
,
C. G.
, and
Parker
,
R. G.
,
2012
, “
Vibration Properties of High-Speed Planetary Gears With Gyroscopic Effects
,”
ASME J. Vib. Acoust.
,
134
(
6
), p.
061014
.10.1115/1.4006646
17.
Kahraman
,
A.
,
2001
, “
Free Torsional Vibration Characteristics of Compound Planetary Gear Sets
,”
Mech. Mach. Theory
,
36
(
8
), pp.
953
971
.10.1016/S0094-114X(01)00033-7
18.
Kiracofe
,
D. R.
, and
Parker
,
R. G.
,
2007
, “
Structured Vibration Modes of General Compound Planetary Gear Systems
,”
ASME J. Vib. Acoust.
,
129
(
1
), pp.
1
16
.10.1115/1.2345680
19.
Inalpolat
,
M.
, and
Kahraman
,
A.
,
2008
, “
Dynamic Modelling of Planetary Gears of Automatic Transmissions
,”
Proc. Inst. Mech. Eng., Part K
,
222
(
3
), pp.
229
242
.10.1243/14644193JMBD138
20.
Guo
,
Y.
, and
Parker
,
R. G.
,
2010
, “
Purely Rotational Model and Vibration Modes of Compound Planetary Gears
,”
Mech. Mach. Theory
,
45
(
3
), pp.
365
377
.10.1016/j.mechmachtheory.2009.09.001
21.
Eritenel
,
T.
, and
Parker
,
R. G.
,
2009
, “
Modal Properties of Three-Dimensional Helical Planetary Gears
,”
J. Sound Vib.
,
325
(
1–2
), pp.
397
420
.10.1016/j.jsv.2009.03.002
22.
Abousleiman
,
V.
, and
Velex
,
P.
,
2006
, “
A Hybrid 3D Finite Element/Lumped Parameter Model for Quasi-Static and Dynamic Analyses of Planetary/Epicyclic Gear Sets
,”
Mech. Mach. Theory
,
41
(
6
), pp.
725
748
.10.1016/j.mechmachtheory.2005.09.005
23.
Abousleiman
,
V.
,
Velex
,
P.
, and
Becquerelle
,
S.
,
2007
, “
Modeling of Spur and Helical Gear Planetary Drives With Flexible Ring Gears and Planet Carriers
,”
ASME J. Mech. Des.
,
129
(
1
), pp.
95
106
.10.1115/1.2359468
24.
Wu
,
X.
, and
Parker
,
R. G.
,
2008
, “
Modal Properties of Planetary Gears With an Elastic Continuum Ring Gear
,”
ASME J. Appl. Mech.
,
75
(
3
), p.
031014
.10.1115/1.2839892
25.
Sondkar
,
P.
, and
Kahraman
,
A.
,
2013
, “
A Dynamic Model of a Double-Helical Planetary Gear Set
,”
Mech. Mach. Theory
,
70
, pp.
157
174
.10.1016/j.mechmachtheory.2013.07.005
26.
Kahraman
,
A.
,
1999
, “
Static Load Sharing Characteristics of Transmission Planetary Gear Sets: Model and Experiment
,” SAE Technical Paper Series No. 1999–01–1050.
27.
Ligata
,
H.
,
Kahraman
,
A.
, and
Singh
,
A.
,
2009
, “
A Closed-Form Planet Load Sharing Formulation for Planetary Gear Sets Using a Translational Analogy
,”
ASME J. Mech. Des.
,
131
(
2
), p.
021007
.10.1115/1.3042160
28.
Singh
,
A.
,
2010
, “
Load Sharing Behavior in Epicyclic Gears: Physical Explanation and Generalized Formulation
,”
Mech. Mach. Theory
,
45
(
3
), pp.
511
530
.10.1016/j.mechmachtheory.2009.10.009
29.
Singh
,
A.
,
2011
, “
Epicyclic Load Sharing Map—Development and Validation
,”
Mech. Mach. Theory
,
46
(
5
), pp.
632
646
.10.1016/j.mechmachtheory.2011.01.001
30.
Montestruc
,
A. N.
,
2010
, “
A Numerical Approach to Calculation of Load Sharing in Planetary Gears
,”
ASME J. Mech. Des.
,
132
(
1
), p.
014503
.10.1115/1.4000642
31.
Kahraman
,
A.
, and
Vijayakar
,
S. M.
,
2001
, “
Effect of Internal Gear Flexibility on the Quasi-Static Behavior of a Planetary Gear Set
,”
ASME J. Mech. Des.
,
123
(
3
), pp.
408
415
.10.1115/1.1371477
32.
Bodas
,
A.
, and
Kahraman
,
A.
,
2004
, “
Influence of Carrier and Gear Manufacturing Errors and Design Parameters on the Static Planet Load Sharing Behavior of Planetary Gear Sets
,”
JSME Int. J.
,
47
(
3
), pp.
908
915
.10.1299/jsmec.47.908
33.
Cheon
,
G.-J.
, and
Parker
,
R. G.
,
2004
, “
Influence of Bearing Stiffness on the Static Properties of a Planetary Gear System With Manufacturing Errors
,”
KSME Int. J.
,
18
(
11
), pp.
1978
1988
.10.1007%2FBF02990440
34.
Singh
,
A.
,
2005
, “
Application of a System Level Model to Study the Planetary Load Sharing Behavior
,”
ASME J. Mech. Des.
,
127
(
3
), pp.
469
476
.10.1115/1.1864115
35.
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
.10.1115/1.2359472
36.
Ligata
,
H.
,
Kahraman
,
A.
, and
Singh
,
A.
,
2008
, “
An Experimental Study of the Influence of Manufacturing Errors on the Planetary Gear Stresses and Planet Load Sharing
,”
ASME J. Mech. Des.
,
130
(
4
), p.
041701
.10.1115/1.2885194
37.
Ma
,
P.
, and
Botman
,
M.
,
1985
, “
Load Sharing in a Planetary Gear Stage in the Presence of Gear Errors and Misalignment
,”
ASME J. Mech. Des.
,
107
(
1
), pp.
4
10
.10.1115/1.3258694
38.
Singh
,
A.
,
Kahraman
,
A.
, and
Ligata
,
H.
,
2008
, “
Internal Gear Strains and Load Sharing in Planetary Transmissions: Model and Experiments
,”
ASME J. Mech. Des.
,
130
(
7
), p.
072602
.10.1115/1.2890110
39.
Prueter
,
P. E.
,
Parker
,
R. G.
, and
Cunliffe
,
F.
,
2011
, “
A Study of Gear Root Strains in a Multi-Stage Planetary Wind Turbine Gear Train Using a Three Dimensional Finite Element/Contact Mechanics Model and Experiments
,”
ASME Power Transmission and Gearing Conference
, Washington, DC, p. DETC2011–47451.10.1115/DETC2011-47451
40.
Hidaka
,
T.
, and
Terauchi
,
Y.
,
1976
, “
Dynamic Behavior of Planetary Gear (1st Report, Load Distribution in Planetary Gear)
,”
Bull. JSME
,
19
(
132
), pp.
690
698
.10.1299/jsme1958.19.690
41.
Hayashi
,
T.
,
Li
,
X. Y.
,
Hayashi
,
I.
,
Endo
,
K.
, and
Watanabe
,
W.
,
1986
, “
Measurement and Some Discussions on Dynamic Load Sharing in Planetary Gears
,”
Bull. JSME
,
29
(
253
), pp.
2290
2297
.10.1299/jsme1958.29.2290
42.
Kahraman
,
A.
,
1994
, “
Load Sharing Characteristics of Planetary Transmissions
,”
Mech. Mach. Theory
,
29
(
8
), pp.
1151
1165
.10.1016/0094-114X(94)90006-X
43.
August
,
R.
, and
Kasuba
,
R.
,
1986
, “
Torsional Vibrations and Dynamic Loads in a Basic Planetary Gear System
,”
ASME J. Vib. Acoust.
,
108
(
3
), pp.
348
353
.10.1115/1.3269349
44.
Gu
,
X.
, and
Velex
,
P.
,
2012
, “
A Dynamic Model to Study the Influence of Planet Position Errors in Planetary Gears
,”
J. Sound Vib.
,
331
(
20
), pp.
4554
4574
.10.1016/j.jsv.2012.05.007
45.
Gu
,
X.
, and
Velex
,
P.
,
2013
, “
On the Dynamic Simulation of Eccentricity Errors in Planetary Gears
,”
Mech. Mach. Theory
,
61
, pp.
14
29
.10.1016/j.mechmachtheory.2012.10.003
46.
Cheon
,
G.-J.
, and
Parker
,
R. G.
,
2004
, “
Influence of Manufacturing Errors on the Dynamic Characteristics of Planetary Gear Systems
,”
KSME Int. J.
,
18
(
4
), pp.
606
621
.10.1007%2FBF02983645
47.
Botman
,
M.
,
1980
, “
Vibration Measurements on Planetary Gears of Aircraft Turbine Engines
,”
J. Aircr.
,
17
(
5
), pp.
351
357
.10.2514/3.57912
48.
Krantz
,
T. L.
,
1991
, “
Gear Tooth Stress Measurements of Two Helicopter Planetary Stages
,” NASA Technical Report No. 91-C-038.
49.
Fuchun
,
Y.
,
Jutao
,
Z.
,
Xiaojun
,
Z.
, and
Hongqing
,
Z.
,
2011
, “
Axial Thrust Force of Compound Planetary Spur Gear Set
,”
ASME J. Mech. Des.
,
133
(
9
), p.
091004
.10.1115/1.4004806
50.
Boguski
,
B.
,
Kahraman
,
A.
, and
Nishino
,
T.
,
2012
, “
A New Method to Measure Planet Load Sharing and Sun Gear Radial Orbit of Planetary Gear Sets
,”
ASME J. Mech. Des.
,
134
(
7
), p.
071002
.10.1115/1.4006827
51.
Guo
,
Y.
,
Keller
,
J.
, and
LaCava
,
W.
,
2014
, “
Planetary Gear Load Sharing of Wind Turbine Drivetrains Subjected to Non-Torque Loads
,”
Wind Energy
(in press).10.1002/we.1731
52.
Hidaka
,
T.
,
Terauchi
,
Y.
, and
Nagamura
,
K.
,
1979
, “
Dynamic Behavior of Planetary Gear (7th Report, Influence of the Thickness of the Ring gear)
,”
Bull. JSME
,
22
(
170
), pp.
1142
1149
.10.1299/jsme1958.22.1142
53.
Montestruc
,
A. N.
,
2011
, “
Influence of Planet Pin Stiffness on Load Sharing in Planetary Gear Drives
,”
ASME J. Mech. Des.
,
133
(
1
), p.
014501
.10.1115/1.4002971
54.
Zhu
,
C. C.
,
Xu
,
X. Y.
,
Lim
,
T. C.
,
Du
,
X. S.
, and
Liu
,
M. Y.
,
2013
, “
Effect of Flexible Pin on the Dynamic Behaviors of Wind Turbine Planetary Gear Drives
,”
Proc. Inst. Mech. Eng., Part C
,
227
(
1
), pp.
74
86
.10.1177/0954406212447029
55.
Lin
,
J.
, and
Parker
,
R. G.
,
2000
, “
Structured Vibration Characteristics of Planetary Gears With Unequally Spaced Planets
,”
J. Sound Vib.
,
233
(
5
), pp.
921
928
.10.1006/jsvi.1999.2581
56.
Parker
,
R. G.
,
Agashe
,
V.
, and
Vijayakar
,
S. M.
,
2000
, “
Dynamic Response of a Planetary Gear System Using a Finite Element/Contact Mechanics Model
,”
ASME J. Mech. Des.
,
122
(
3
), pp.
304
310
.10.1115/1.1286189
57.
Ambarisha
,
V. K.
, and
Parker
,
R. G.
,
2007
, “
Nonlinear Dynamics of Planetary Gears Using Analytical and Finite Element Models
,”
J. Sound Vib.
,
302
(
3
), pp.
577
595
.10.1016/j.jsv.2006.11.028
58.
Ericson
,
T. M.
, and
Parker
,
R. G.
,
2013
, “
Planetary Gear Modal Vibration Experiments and Correlation Against Lumped-Parameter and Finite Element Models
,”
J. Sound Vibration
,
332
(
9
), pp.
2350
2375
.10.1016/j.jsv.2012.11.004
59.
Ericson
,
T. M.
, and
Parker
,
R. G.
,
2013
, “
Natural Frequency Clusters in Planetary Gear Vibration
,”
ASME J. Vib. Acoust.
,
135
(
6
), p.
061002
.10.1115/1.4023993
60.
Parker
,
R. G.
, and
Wu
,
X.
,
2010
, “
Vibration Modes of Planetary Gears With Unequally Spaced Planets and an Elastic Ring Gear
,”
J. Sound Vib.
,
329
(
11
), pp.
2265
2275
.10.1016/j.jsv.2009.12.023
61.
Kahraman
,
A.
,
Kharazi
,
A. A.
, and
Umrani
,
M.
,
2003
, “
A Deformable Body Dynamic Analysis of Planetary Gears With Thin Rims
,”
J. Sound Vib.
,
262
(
3
), pp.
752
768
.10.1016/S0022-460X(03)00122-6
62.
Bu
,
Z.
,
Liu
,
G.
, and
Wu
,
L.
,
2012
, “
Modal Analyses of Herringbone Planetary Gear Train With Journal Bearings
,”
Mech. Mach. Theory
,
54
, pp.
99
115
.10.1016/j.mechmachtheory.2012.03.006
63.
Qian
,
P.-Y.
,
Zhang
,
Y.-L.
,
Cheng
,
G.
,
Ge
,
S.-R.
, and
Zhou
,
C.-F.
,
2014
, “
Model Analysis and Verification of 2K-H Planetary Gear System
,”
J. Vib. Control
(in press).10.1177/1077546313496575
64.
Helsen
,
J.
,
Vanhollebeke
,
F.
,
Marrant
,
B.
,
Vandepitte
,
D.
, and
Desmet
,
W.
,
2011
, “
Multibody Modelling of Varying Complexity for Modal Behaviour Analysis of Wind Turbine Gearboxes
,”
Renewable Energy
,
36
(11), pp.
3098
3113
.10.1016/j.renene.2011.03.023
65.
Frater
,
J.
,
August
,
R.
, and
Oswald
,
F. B.
,
1983
, “
Vibration in Planetary Gear Systems With Unequal Planet Stiffness
,” NASA Technical Report No. TM-83428.
66.
Saada
,
A.
, and
Velex
,
P.
,
1995
, “
An Extended Model for the Analysis of the Dynamic Behavior of Planetary Trains
,”
ASME J. Mech. Des.
,
117
(
2
), pp.
241
247
.10.1115/1.2826129
67.
Lin
,
J.
, and
Parker
,
R. G.
,
1999
, “
Sensitivity of Planetary Gear Natural Frequencies and Vibration Modes to Model Parameters
,”
J. Sound Vib.
,
228
(
1
), pp.
109
128
.10.1006/jsvi.1999.2398
68.
Guo
,
Y.
, and
Parker
,
R. G.
,
2010
, “
Sensitivity of General Compound Planetary Gear Natural Frequencies and Vibration Modes to Modal Parameters
,”
ASME J. Vib. Acoust.
,
132
(
1
), p.
011006
.10.1115/1.4000461
69.
Perkins
,
N. C.
, and
Mote
,
C. D.
, Jr.
,
1986
, “
Comments on Curve Veering in Eigenvalue Problems
,”
J. Sound Vib.
,
106
(
3
), pp.
451
463
.10.1016/0022-460X(86)90191-4
70.
Lin
,
J.
, and
Parker
,
R. G.
,
2001
, “
Natural Frequency Veering in Planetary Gears
,”
Mech. Struct. Mach.
,
29
(
4
), pp.
411
429
.10.1081/SME-100107620
71.
Cooley
,
C. G.
, and
Parker
,
R. G.
,
2013
, “
The Geometry and Frequency Content of Planetary Gear Single-Mode Vibration
,”
Mech. Syst. Signal Process.
,
40
(
1
), pp.
91
104
.10.1016/j.ymssp.2013.04.009
72.
Gregory
,
R. W.
,
Harris
,
S. L.
, and
Munro
,
R. G.
,
1963
, “
Dynamic Behaviour of Spur Gears
,”
Proc. Inst. Mech. Eng.
,
178
(
1
), pp.
207
226
.10.1243/PIME_PROC_1963_178_018_02
73.
Blankenship
,
G. W.
, and
Singh
,
R.
,
1995
, “
A New Gear Mesh Interface Dynamic Model to Predict Multi-Dimensional Force Coupling and Excitation
,”
Mech. Mach. Theory
,
30
(
1
), pp.
43
57
.10.1016/0094-114X(94)00018-G
74.
Velex
,
P.
, and
Maatar
,
M.
,
1996
, “
A Mathematical Model for Analyzing the Influence of Shape Deviations and Mounting Errors on Gear Dynamic Behaviour
,”
J. Sound Vib.
,
191
(
5
), pp.
629
660
.10.1006/jsvi.1996.0148
75.
Eritenel
,
T.
, and
Parker
,
R. G.
,
2012
, “
An Investigation of Tooth Mesh Nonlinearity and Partial Contact Loss in Gear Pairs Using a Lumped-Parameter Model
,”
Mech. Mach. Theory
,
56
, pp.
28
51
.10.1016/j.mechmachtheory.2012.05.002
76.
Eritenel
,
T.
, and
Parker
,
R. G.
,
2012
, “
Three-Dimensional Nonlinear Vibration of Gear Pairs
,”
J. Sound Vib.
,
331
(
15
), pp.
3628
3648
.10.1016/j.jsv.2012.03.019
77.
Vijayakar
,
S. M.
,
Busby
,
H. R.
, and
Houser
,
D. R.
,
1988
, “
Linearization of Multibody Frictional Contact Problems
,”
Comput. Struct.
,
29
(
4
), pp.
569
576
.10.1016/0045-7949(88)90366-5
78.
Vijayakar
,
S.
,
Busby
,
H.
, and
Wilcox
,
L.
,
1989
, “
Finite Element Analysis of Three-Dimensional Conformal Contact With Friction
,”
Comput. Struct.
,
33
(
1
), pp.
49
61
.10.1016/0045-7949(89)90128-4
79.
Vijayakar
,
S.
,
1991
, “
A Combined Surface Integral and Finite Element Solution for a Three-Dimensional Contact Problem
,”
Int. J. Numer. Methods Eng.
,
31
(
3
), pp.
525
545
.10.1002/nme.1620310308
80.
Parker
,
R. G.
, and
Lin
,
J.
,
2004
, “
Mesh Phasing Relationships in Planetary and Epicyclic Gears
,”
ASME J. Mech. Des.
,
126
(2), pp.
365
370
.10.1115/1.1667892
81.
Guo
,
Y.
, and
Parker
,
R. G.
,
2011
, “
Analytical Determination of Mesh Phase Relations in General Compound Planetary Gears
,”
Mech. Mach. Theory
,
46
(12), pp.
1869
1887
.10.1016/j.mechmachtheory.2011.07.010
82.
Guo
,
Y.
, and
Parker
,
R. G.
,
2014
, “
Analytical Determination of Back-Side Contact Gear Mesh Stiffness
,”
Mech. Mach. Theory
,
78
, pp.
263
271
.10.1016/j.mechmachtheory.2014.03.011
83.
Harris
,
S. L.
,
1958
, “
Dynamic Loads on the Teeth of Spur Gears
,”
Proc. Inst. Mech. Eng.
,
172
(1), pp.
87
112
.10.1243/PIME_PROC_1958_172_017_02
84.
Velex
,
P.
, and
Ajmi
,
M.
,
2006
, “
On the Modelling of Excitations in Geared Systems by Transmission Errors
,”
J. Sound Vib.
,
290
(
3–5
), pp.
882
909
.10.1016/j.jsv.2005.04.033
85.
Liu
,
G.
, and
Parker
,
R. G.
,
2008
, “
Dynamic Modeling and Analysis of Tooth Profile Modification for Multimesh Gear Vibration
,”
ASME J. Mech. Des.
,
130
(
12
), p.
121402
.10.1115/1.2976803
86.
Seager
,
D. L.
,
1975
, “
Conditions for the Neutralization of Excitation by the Teeth in Epicyclic Gearing
,”
Proc. Inst. Mech. Eng.
,
17
(
5
), pp.
293
298
.10.1243/JMES_JOUR_1975_017_042_02
87.
Inalpolat
,
M.
, and
Kahraman
,
A.
,
2010
, “
A Dynamic Model to Predict Modulation Sidebands of a Planetary Gear Set Having Manufacturing Errors
,”
J. Sound Vib.
,
329
(
4
), pp.
371
393
.10.1016/j.jsv.2009.09.022
88.
Velex
,
P.
, and
Flamand
,
L.
,
1996
, “
Dynamic Response of Planetary Trains to Mesh Parametric Excitations
,”
ASME J. Mech. Des.
,
118
(
1
), pp.
7
14
.10.1115/1.2826860
89.
Parker
,
R. G.
,
Vijayakar
,
S. M.
, and
Imajo
,
T.
,
2000
, “
Non-Linear Dynamic Response of a Spur Gear Pair: Modelling and Experimental Comparisons
,”
J. Sound Vib.
,
237
(
3
), pp.
435
455
.10.1006/jsvi.2000.3067
90.
Lin
,
J.
, and
Parker
,
R. G.
,
2002
, “
Planetary Gear Parametric Instability Caused by Mesh Stiffness Variation
,”
J. Sound Vib.
,
249
(
1
), pp.
129
145
.10.1006/jsvi.2001.3848
91.
Parker
,
R. G.
, and
Wu
,
X.
,
2012
, “
Parametric Instability of Planetary Gears Having Elastic Continuum Ring Gears
,”
ASME J. Vib. Acoust.
,
134
(
4
), p.
041011
.10.1115/1.4005836
92.
Bahk
,
C.-J.
, and
Parker
,
R. G.
,
2011
, “
Analytical Solution for the Nonlinear Dynamics of Planetary Gears
,”
ASME J. Comput. Nonlinear Dyn.
,
6
(
2
), p.
021007
.10.1115/1.4002392
93.
Chen
,
Z.
, and
Shao
,
Y.
,
2013
, “
Dynamic Simulation of Planetary Gear With Tooth Root Crack in Ring Gear
,”
Eng. Failure Anal.
,
31
, pp.
8
18
.10.1016/j.engfailanal.2013.01.012
94.
Chen
,
Z.
, and
Shao
,
Y.
,
2013
, “
Dynamic Features of a Planetary Gear System With Tooth Crack Under Different Sizes and Inclination Angles
,”
ASME J. Vib. Acoust.
,
135
(3), p.
031004
.10.1115/1.4023300
95.
Shao
,
Y.
, and
Chen
,
Z.
,
2013
, “
Dynamic Features of Planetary Gear Set With Tooth Plastic Inclination Deformation Due to Tooth Root Crack
,”
Nonlinear Dyn.
,
74
(4), pp.
1253
1266
.10.1007/s11071-013-1038-x
96.
Liang
,
X.
,
Zuo
,
M. J.
, and
Pandey
,
M.
,
2014
, “
Analytically Evaluating the Influence of Crack on the Mesh Stiffness of a Planetary Gear Set
,”
Mech. Mach. Theory
,
76
, pp.
20
38
.10.1016/j.mechmachtheory.2014.02.001
97.
Blankenship
,
G. W.
, and
Kahraman
,
A.
,
1996
, “
Gear Dynamics Experiments Part I: Characterization of Forced Response
,”
ASME Power Transmission and Gearing Conference
, San Diego, CA.
98.
Ambarisha
,
V. K.
, and
Parker
,
R. G.
,
2006
, “
Suppression of Planet Mode Response in Planetary Gear Dynamics Through Mesh Phasing
,”
ASME J. Vib. Acoust.
,
128
(
2
), pp.
133
142
.10.1115/1.2171712
99.
Chen
,
Z.
,
Shao
,
Y.
, and
Su
,
D.
,
2013
, “
Dynamic Simulation of Planetary Gear Set With Flexible Spur Ring Gear
,”
J. Sound Vib.
,
332
(
26
), pp.
7191
7204
.10.1016/j.jsv.2013.07.026
100.
Yang
,
J.
, and
Yang
,
P.
,
2013
, “
Random Vibration Analysis of Planetary Gear Trains
,”
ASME J. Vib. Acoust.
,
135
(
2
), p.
021005
.10.1115/1.4023053
101.
Nikolajsen
,
J. L.
, and
Botman
,
M.
,
1983
, “
Dynamic Behavior of a Journal Bearing in a Planet Gear
,”
Tribol. Trans.
,
26
(
1
), pp.
87
93
.10.1080/05698198308981481
102.
Cheon
,
G. J.
,
Lee
,
D. H.
,
Ryu
,
H. T.
,
Kim
,
J. H.
, and
Han
,
D. C.
,
1999
, “
A Study on the Dynamic Characteristics of an Epicyclic Gear Train With Journal Bearing
,” SAE Technical Paper Series No. 1999–01–1052.
103.
Sun
,
T.
, and
Hu
,
H. Y.
,
2003
, “
Nonlinear Dynamics of a Planetary Gear System With Multiple Clearances
,”
Mech. Mach. Theory
,
38
(
12
), pp.
1371
1390
.10.1016/S0094-114X(03)00093-4
104.
Al-Shyyab
,
A.
, and
Kahraman
,
A.
,
2007
, “
A Non-Linear Dynamic Model for Planetary Gear Sets
,”
Proc. Inst. Mech. Eng., Part K
,
221
(4), pp.
567
576
.10.1243/14644193JMBD92
105.
Al-Shyyab
,
A.
,
Alwidyan
,
K.
,
Jawarneh
,
A.
, and
Tlilan
,
H.
,
2009
, “
Non-Linear Dynamic Behaviour of Compound Planetary Gear Trains: Model Formulation and Semi-Analytical Solution
,”
Proc. Inst. Mech. Eng., Part K
,
223
(
3
), pp.
199
210
.10.1243/14644193JMBD197
106.
Guo
,
Y.
, and
Parker
,
R. G.
,
2010
, “
Dynamic Modeling and Analysis of a Spur Planetary Gear Involving Tooth Wedging and Bearing Clearance Nonlinearity
,”
Eur. J. Mech. A/Solids
,
29
(6), pp.
1022
1033
.10.1016/j.euromechsol.2010.05.001
107.
Guo
,
Y.
, and
Parker
,
R. G.
,
2012
, “
Dynamic Analysis of Planetary Gears With Bearing Clearance
,”
ASME J. Comput. Nonlinear Dyn.
,
7
(
4
), p.
041002
.10.1115/1.4005929
108.
Bahk
,
C.-J.
, and
Parker
,
R. G.
,
2013
, “
Analytical Investigation of Tooth Profile Modification Effects on Planetary Gear Dynamics
,”
Mech. Mach. Theory
,
70
, pp.
298
319
.10.1016/j.mechmachtheory.2013.07.018
109.
Kim
,
W.
,
Lee
,
J. Y.
, and
Chung
,
J.
,
2012
, “
Dynamic Analysis for a Planetary Gear With Time-Varying Pressure Angles and Contact Ratios
,”
J. Sound Vib.
,
331
(
4
), pp.
883
901
.10.1016/j.jsv.2011.10.007
110.
Li
,
S.
,
Wu
,
Q.
, and
Zhang
,
Z.
,
2014
, “
Bifurcation and Chaos Analysis of Multistage Planetary Gear Train
,”
Nonlinear Dyn.
,
75
(1–2), pp.
217
233
.10.1007/s11071-013-1060-z
111.
Guo
,
Y.
,
Keller
,
J.
, and
Parker
,
R. G.
,
2014
, “
Nonlinear Dynamics and Stability of Wind Turbine Planetary Gear Sets Under Gravity Effects
,”
Eur. J. Mech. A/Solids
,
47
, pp.
45
57
.10.1016/j.euromechsol.2014.02.013
112.
Tamminana
,
V. K.
,
Kahraman
,
A.
, and
Vijayakar
,
S.
,
2007
, “
A Study of the Relationship Between the Dynamic Factors and the Dynamic Transmission Error of Spur Gear Pairs
,”
ASME J. Mech. Des.
,
129
(
1
), pp.
75
84
.10.1115/1.2359470
113.
Yuksel
,
C.
, and
Kahraman
,
A.
,
2004
, “
Dynamic Tooth Loads of Planetary Gear Sets Having Tooth Profile Wear
,”
Mech. Mach. Theory
,
39
(7), pp.
695
715
.10.1016/j.mechmachtheory.2004.03.001
114.
Schlegel
,
R. G.
, and
Mard
,
K. C.
,
1967
, “
Transmission Noise Control Approaches in Helicopter Design
,”
ASME Design Engineering Conference
, New York, p. 67-DE-58.
115.
Palmer
,
W.
, and
Fuehrer
,
R.
,
1977
, “
Noise Control in Planetary Transmissions
,” SAE Technical Paper No. 770561.
116.
Toda
,
A.
, and
Botman
,
M.
,
1980
, “
Planet Indexing in Planetary Gears for Minimum Vibration
,” ASME Design Engineering Technical Conference, St. Louis, MO, p. 79–DET–73.
117.
Hidaka
,
T.
,
Terauchi
,
Y.
, and
Nagamura
,
K.
,
1979
, “
Dynamic Behavior of Planetary Gear (6th Report, Influence of Meshing-Phase)
,”
Bull. JSME
,
22
(
169
), pp.
1026
1033
.10.1299/jsme1958.22.1026
118.
Kahraman
,
A.
, and
Blankenship
,
G. W.
,
1994
, “
Planet Mesh Phasing in Epicyclic Gear Sets
,”
Proceedings of the International Gearing Conference
, Newcastle, UK, pp.
99
104
.
119.
Parker
,
R. G.
,
2000
, “
A Physical Explanation for the Effectiveness of Planet Phasing to Suppress Planetary Gear Vibration
,”
J. Sound Vib.
,
236
(4), pp.
561
573
.10.1006/jsvi.1999.2859
120.
Hidaka
,
T.
,
Terauchi
,
Y.
, and
Ishioka
,
K.
,
1976
, “
Dynamic Behavior of Planetary Gear (2nd Report, Displacement of Sun Gear and Ring Gear)
,”
Bull. JSME
,
19
(
138
), pp.
1563
1570
.10.1299/jsme1958.19.1563
121.
Hidaka
,
T.
,
Terauchi
,
Y.
,
Nohara
,
M.
, and
Oshita
,
J.
,
1977
, “
Dynamic Behavior of Planetary Gear (3rd Report, Displacement of Ring Gear in Direction of Line of Action)
,”
Bull. JSME
,
20
(
150
), pp.
1663
1672
.10.1299/jsme1958.20.1663
122.
Velex
,
P.
,
Pichon
,
V.
,
Randrianarivo
,
L.
, and
Wittman
,
R.
,
1994
, “
Dynamic Behavior of Epicyclic Trains: Experimental and Numerical Analyses
,”
Proceedings of the International Gearing Conference
, Newcastle, UK, pp.
265
269
.
123.
Helsen
,
J.
,
Vanhollebeke
,
F.
,
De Coninck
,
F.
,
Vandepitte
,
D.
, and
Desmet
,
W.
,
2011
, “
Insights in Wind Turbine Drive Train Dynamics Gathered by Validating Advanced Models on a Newly Developed 13.2 MW Dynamically Controlled Test-Rig
,”
Mechatronics
,
21
(4), pp.
737
752
.10.1016/j.mechatronics.2010.11.005
124.
Wu
,
X.
, and
Parker
,
R. G.
,
2006
, “
Vibration of Rings on a General Elastic Foundation
,”
J. Sound Vib.
,
295
(
1–2
), pp.
194
213
.10.1016/j.jsv.2006.01.007
125.
Vangipuram Canchi
,
S.
, and
Parker
,
R. G.
,
2006
, “
Parametric Instability of a Circular Ring Subjected to Moving Springs
,”
J. Sound Vib.
,
293
(
1–2
), pp.
360
379
.10.1016/j.jsv.2005.10.007
126.
Vangipuram Canchi
,
S.
, and
Parker
,
R. G.
,
2006
, “
Parametric Instability of a Rotating Circular Ring With Moving, Time-Varying Springs
,”
ASME J. Vib. Acoust.
,
128
(
2
), pp.
231
243
.10.1115/1.2159040
127.
Vangipuram Canchi
,
S.
, and
Parker
,
R. G.
,
2008
, “
Effect of Ring-Planet Mesh Phasing and Contact Ratio on the Parametric Instabilities of a Planetary Gear Ring
,”
ASME J. Mech. Des.
,
130
(1), p.
014501
.10.1115/1.2803716
128.
Wang
,
S.
,
Huo
,
M.
,
Zhang
,
C.
,
Liu
,
J.
,
Song
,
Y.
,
Cao
,
S.
, and
Yang
,
Y.
,
2011
, “
Effect of Mesh Phase on Wave Vibration of Spur Planetary Ring Gears
,”
Eur. J. Mech. A/Solids
,
30
(6), pp.
820
827
.10.1016/j.euromechsol.2011.06.004
129.
Stockton
,
R. J.
,
1985
, “
Sun Gear Traveling Wave Vibration in a Sequential Planetary Gear Box
,”
ASME Design Engineering Technical Conference
, p. 85–DET–167.
130.
Meirovitch
,
L.
,
1974
, “
A New Method of Solution of the Eigenvalue Problem for Gyroscopic Systems
,”
AIAA J.
,
12
(
10
), pp.
1337
1342
.10.2514/3.49486
131.
Cooley
,
C. G.
, and
Parker
,
R. G.
,
2013
, “
Mechanical Stability of High-Speed Planetary Gears
,”
Int. J. Mech. Sci.
,
69
, pp.
59
71
.10.1016/j.ijmecsci.2013.01.025
132.
Cooley
,
C. G.
, and
Parker
,
R. G.
,
2013
, “
Unusual Gyroscopic System Eigenvalue Behaviour in High-Speed Planetary Gears
,”
J. Sound Vib.
,
332
(
7
), pp.
1820
1828
.10.1016/j.jsv.2012.09.043
133.
Inalpolat
,
M.
, and
Kahraman
,
A.
,
2009
, “
A Theoretical and Experimental Investigation of Modulation Sidebands of Planetary Gear Sets
,”
J. Sound Vib.
,
323
(
3–5
), pp.
677
696
.10.1016/j.jsv.2009.01.004
134.
Hidaka
,
T.
,
Terauchi
,
Y.
, and
Ishioka
,
K.
,
1979
, “
Dynamic Behavior of Planetary Gear (4th Report, Influence of the Transmitted Tooth Load on the Dynamic Increment Load)
,”
Bull. JSME
,
22
(
168
), pp.
877
884
.10.1299/jsme1958.22.877
135.
Hidaka
,
T.
,
Terauchi
,
Y.
, and
Nagamura
,
K.
,
1979
, “
Dynamic Behavior of Planetary Gear (5th Report, Dynamic Increment of Torque)
,”
Bull. JSME
,
22
(
169
), pp.
1017
1025
.10.1299/jsme1958.22.1017
136.
McFadden
,
P. D.
, and
Smith
,
J. D.
,
1985
, “
An Explanation for the Asymmetry of the Modulation Sidebands About the Tooth Meshing Frequency in Epicyclic Gear Vibration
,”
Proc. Inst. Mech. Eng., Part C
,
199
(
1
), pp.
65
70
.10.1243/PIME_PROC_1985_199_092_02
137.
Ericson
,
T. M.
, and
Parker
,
R. G.
,
2013
, “
Experimental Quantification of the Effects of Torque on the Dynamic Behavior and System Parameters of Planetary Gears
,”
Mech. Mach. Theory
74, pp. 370–389.
138.
McFadden
,
P. D.
, and
Smith
,
J. D.
,
1986
, “
Effect of Transmission Path on Measured Gear Vibration
,”
ASME J. Vib. Acoust.
,
108
(
3
), pp.
377
378
.10.1115/1.3269353
139.
Yu
,
S.
, and
Kaatz
,
S.
,
2005
, “
Asymmetric Gear Noise Sidebands and Application to Planetary Gear Noise Reduction
,” SAE Technical Paper Series No. 2005–01–2462.
140.
McFadden
,
P. D.
,
1991
, “
A Technique for Calculating the Time Domain Averages of the Vibration of the Individual Planet Gears and the Sun Gear in an Epicyclic Gearbox
,”
J. Sound Vib.
,
144
(
1
), pp.
163
172
.10.1016/0022-460X(91)90739-7
141.
McFadden
,
P. D.
,
1994
, “
Window Functions for the Calculation of the Time Domain Averages of the Vibration of the Individual Planet Gears and Sun Gear in an Epicyclic Gearbox
,”
ASME J. Vib. Acoust.
,
116
(
2
), pp.
179
187
.10.1115/1.2930410
142.
McNames
,
J.
,
2002
, “
Fourier Series Analysis of Epicyclic Gearbox Vibration
,”
ASME J. Vib. Acoust.
,
124
(
1
), pp.
150
153
.10.1115/1.1403735
143.
Blunt
,
D. M.
, and
Keller
,
J. A.
,
2006
, “
Detection of a Fatigue Crack in a UH-60A Planet Gear Carrier Using Vibration Analysis
,”
Mech. Syst. Signal Process.
,
20
(
8
), pp.
2095
2111
.10.1016/j.ymssp.2006.05.010
144.
Patrick
,
R.
,
Ferri
,
A.
, and
Vachtsevanos
,
G.
,
2012
, “
Effect of Planetary Gear Carrier-Plate Cracks on Vibration Spectrum
,”
ASME J. Vib. Acoust.
,
134
(
6
), p.
061001
.10.1115/1.4006651
145.
Chen
,
Z.
, and
Shao
,
Y.
,
2013
, “
Mesh Stiffness of an Internal Spur Gear Pair With Ring Gear Rim Deformation
,”
Mech. Mach. Theory
,
69
, pp.
1
12
.10.1016/j.mechmachtheory.2013.04.017
146.
Litvin
,
F. L.
,
Vecchiato
,
D.
,
Demenego
,
A.
,
Karedes
,
E.
,
Hansen
,
B.
, and
Handschuh
,
R.
,
2002
, “
Design of One Stage Planetary Gear Train With Improved Conditions of Load Distribution and Reduced Transmission Errors
,”
ASME J. Mech. Des.
,
124
(
4
), pp.
745
752
.10.1115/1.1515797
147.
Vecchiato
,
D.
,
2006
, “
Tooth Contact Analysis of a Misaligned Isostatic Planetary Gear Train
,”
Mech. Mach. Theory
,
41
(6), pp.
617
631
.10.1016/j.mechmachtheory.2005.10.001
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