In this paper, the progress in nonlinear dynamics of gear driven systems in the past twenty years is reviewed, especially the gear dynamic behavior, by considering the backlash and time-varying mesh stiffness of teeth. The basic concepts, the mathematical models and the solving methods for the non-linear dynamics of geared systems are then reviewed. The critical issues for further research on the nonlinear vibration in gear transmission systems are also discussed. There are 204 references cited in this review article.
Issue Section:
Review Articles
1.
Ozguven
HN
and Houser
DR
(1988
), Mathematical models used in gear dynamics—A review
, J. Sound Vib.
, 121
(3
), 383
–411
.2.
Li R and Wang J (1997), Geared System Dynamic—Vibration, Shock and Noise, Science Press, Beijing.
3.
Kahraman
A
and Blankenship
GW
(1997
), Experiments on nonlinear dynamic behavior of an oscillator with clearance and periodically time-varying parameters
, ASME J. Appl. Mech.
64
, 217
–226
.4.
Vinayak
H
and Singh
R
(1998
), Multi-body dynamics and modal analysis of compliant gear bodies
, J. Sound Vib.
210
(2
), 171
–214
.5.
Vinayak
H
, Singh
R
, and Padmanabhan
C
(1995
), Linear dynamic analysis of multi-mesh transmissions containing external rigid gears
, J. Sound Vib.
185
(1
), 1
–32
.6.
Benton
M
and Seireg
A
(1978
), Simulation of resonances and instability conditions in pinion-geared systems
, ASME J. Mech. Des.
100
, 26
–32
.7.
Benton
M
and Seireg
A
(1981
), Factors influencing instability and resonance in Geared systems
, ASME J. Mech. Des.
103
, 372
–378
.8.
Wang
KL
and Cheng
HS
(1981
), A numerical solution to the dynamic load, film thickness, and surface temperatures in spur gears, Part I—Analysis
, ASME J. Mech. Des.
103
, 177
–187
.9.
Kahraman
A
and Singh
R
(1990
), Non-linear dynamics of a spur gear pair
, J. Sound Vib.
142
(1
), 49
–75
.10.
Kahraman
A
and Singh
R
(1991
), Non-linear dynamics of a geared rotor-bearing system with multiple clearance
, J. Sound Vib.
144
(3
), 469
–506
.11.
Padmanabhan
C
and Singh
R
(1992
), Spectral coupling issues in a two-degree-of freedom system with clearance non-linearities
, J. Sound Vib.
155
(2
), 209
–230
.12.
Padmanabhan
C
, Barlow
RC
, Rook
TE
, and Singh
R
(1995
), Computational issues associated with gear rattle analysis
, ASME J. Mech. Des.
117
, 185
–192
.13.
Kahraman
A
and Singh
R
(1991
), Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system
, J. Sound Vib.
146
(1
), 135
–156
.14.
Cai
Y
(1995
), Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon (a new stiffness function of helical involute tooth pair
), ASME J. Mech. Des.
117
, 460
–469
.15.
Kahraman
A
and Blankenship
GW
(1996
), Interactions between commensurate parametric and forcing excitations in a system with clearance
, J. Sound Vib.
194
(3
), 317
–336
.16.
Theodossiades
S
and Natsiavas
S
(2000
), Non-linear dynamics of gear-pair systems with periodic stiffness and backlash
, J. Sound Vib.
229
(2
), 287
–310
.17.
Nakamura
K
(1967
), Tooth separations and abnormal noise on power transmission gears
, Bull. JSME
10
, 846
–854
.18.
Azar
RC
and Crossley
FRE
(1977
), Digital simulation of impact phenomenon in spur geared system
, ASME J. Eng. Ind.
99
, 792
–798
.19.
Wang
CC
(1978
), Rotational vibration with backlash Part 1
, ASME J. Mech. Des.
100
, 363
–373
.20.
Wang
CC
(1981
), Rotational vibration with backlash Part 2
, ASME J. Mech. Des.
103
, 387
–397
.21.
Yang DCH and Lin JY (1985), A rotary model for spur gear dynamics, ASME Paper 85-DET-2.
22.
Yang
DCH
and Lin
JY
(1987
), Herztian damping, tooth friction and bending elasticity in gear impact dynamics
, ASME J. Mech., Transm., Autom. Des.
109
, 189
–196
.23.
Blankenship
GW
and Singh
R
(1995
), A new gear mesh interface dynamic model to predict multi-dimensional force coupling and excitation
, Mech. Mach. Theory
, 30
(1
), 43
–57
.24.
Blankenship
GW
and Singh
R
(1995
), Dynamic force transmissibility in helical gear pairs
, Mech. Mach. Theory
, 30
(3
), 323
–339
.25.
Kahraman
A
(1994
), Dynamic analysis of a multi-mesh helical gear train
, ASME J. Mech. Des.
116
, 706
–712
.26.
Rook
TE
and Singh
R
(1995
), Dynamic analysis of a rever-idler gear pair with concurrent clearances
, J. Sound Vib.
182
(2
), 303
–322
.27.
Singh
R
, Xie
H
, and Comparin
RJ
(1989
), Analysis of automobile neutral gear rattle
, J. Sound Vib.
131
, 177
–196
.28.
Padmanabhan C, Rook TE, and Singh R (1992), Computational issues associated with gear rattle analysis, part I problem formulation, Proc of 6th Int Power Trans Gearing Conf, 1, 129–136.
29.
Barlow R, Padmanabhan C, and Singh R (1992), Computational issues associated with gear rattle analysis, Part II Evaluation criterion for numerical algorithms, Proc of 6th Int Power Trans Gearing Conf, 2, 505–512.
30.
Kucukay F (1984), Dynamic behavior of high speed gears, IMecH E. C317/84.
31.
Kuenkay F (1984), Dynamic loads in gear teeth, Proc of 3rd Conf Vib Rotating Machinery, Inst Mech Eng, 73–79.
32.
Neriya
SV
, Bhat
RB
, and Sankar
TS
(1988
), On the dynamic response of a helical geared system subjected to a static transmission error in the form of deterministic and filtered white noise inputs
, ASME J. Vib., Acoust., Stress, Reliab. Des.
110
, 501
–506
.33.
Fawzi
MA
and El-Saeidy
(1991
), Effect of tooth backlash and ball bearing beadband clearance on vibration spectrum in spur gear boxes
, J. Acoust. Soc. Am.
89
, 2766
–2773
.34.
Hill
GW
(1886
), On the part of motion of the lunar perigee which is a function of the mean motions of the sun and moon
, Acta Math.
8
, 1
–36
.35.
Nayfeh AH and Mook DT (1979), Nonlinear Oscillations, John Wiley and Sons.
36.
Mathieu
E
(1868
), memoire sur le mouvement vibratoire d’une membrane de forme elliptique
, J. Math. Pures Appl.
13
, 137
–203
.37.
Bolotin VV (1964), Dynamic Stability of Elastic System, Holden-Day, San Francisco.
38.
Pedersen
P
(1985
) On the stability diagrams for damped Hill equations
, Q. Appl. Math.
42
, 477
–495
.39.
Bollinger JG and Harker RJ (1967), Unsachen and answirkangen dymischer zahnkrafte in stirnadgetrieben, Indnstric Anzeigen, March.
40.
Bollinger
JG
and Harker
RJ
(1967
), Instability potential of high speed gearing
, J Indust Math Soc
, 17
(2
), 39
–55
.41.
Toridon
GV
and Gauvin
R
(1977
), Dynamic stability of a two-stage gear train under the influence of variable meshing stiffness
, ASME J. Eng. Ind.
99
, 785
–791
.42.
Kumer
AS
, Sanker
TS
, and Osman
MOM
(1985
), On dynamic tooth load and stability of a spur-geared system using the state-spacing approach
, ASME J. Mech., Transm., Autom. Des.
107
, 54
–60
.43.
Zadoks
RI
and Midha
A
(1987
), Parametric stability of a two-degree-of freedom machine system, Part I—Equations of motion and stability
, ASME J. Mech., Transm., Autom. Des.
109
, 210
–215
.44.
Zadoks
RI
and Midha
A
(1987
), Parametric stability of a two-degree-of freedom machine system, Part II—Stability analysis
, ASME J. Mech., Transm., Autom. Des.
109
, 216
–223
.45.
Matsuhisa H, Miyaji Y, and Sato S (1982), Parametrically excited vibration with external constant load and damping, Memoirs of the Faculty of Engineering, Kyoto Univ, 44, 158–167.
46.
Iwatsubo T, Arii S, and Kawai R (1984), The coupled lateral torsional vibration of a geared rotor system, Proc of IMechE Vibration in Rotating Machinery Conf, Paper C265/84, 59–66.
47.
Amabili
M
and Rivola
A
(1997
), Dynamic analysis of spur gear pairs: steady-state response and stability of the SDOF model with time-varying mesh damping
, Mech. Syst. Signal Process.
11
, 375
–390
.48.
Raghothama
A
and Narayanan
S
(1999
), Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method
, J. Sound Vib.
226
(3
), 469
–492
.49.
Raghothama A (1993), Bifurcation and chaos in gear and cam mechanisms with clearance type of nonlinearities, MS thesis, Indian Institute of Technology, Madras.
50.
Fu
FCL
and Nemat-Nasser
S
(1972
), Stability of solution of systems of Linear differential equations with harmonic coefficients
, AIAA J.
10
(1
), 30
–36
.51.
Hansen
JM
(1985
), Stability diagrams for coupled, Mathieu-equations
, Ingenieur-Archiv
55
, 463
–473
.52.
Lindh
KG
and Likins
PW
(1970
), Infinite determinant methods for stability analysis of periodic-coefficient differential equations
, AIAA J.
8
, 463
–473
.53.
Weyh
B
and Kostyra
H
(1991
), Direct Floquet method for stability limits determination—I. Theroy
, Mech. Mach. Theory
26
, 123
–131
.54.
Kostyra
H
and Weyh
B
(1991
), Direct Floquet method for stability limits determination—II. Application and phenomena
, Mech. Mach. Theory
26
, 123
–131
.55.
Seyranian
AP
, Solem
F
, and Pedersen
P
(2000
), Multi-parameter linear periodic systems: sensitivity analysis and applications
, J. Sound Vib.
229
(1
), 89
–111
.56.
Sinha
SC
and Wu
DH
(1991
), An efficient computational scheme for the analysis of periodic systems
, J. Sound Vib.
151
, 91
–117
.57.
Comparin
RJ
and Singh
R
(1990
), Frequency response characteristics of a multi-degree-of freedom system with clearances
, J. Sound Vib.
142
(1
), 101
–124
.58.
Dubowsky
S
and Freudenstein
F
(1971
), Dynamic analysis of mechanical systems with clearances, Part 1, Formulation of dynamic model
, ASME J. Eng. Ind.
93
, 305
–309
.59.
Dubowskey
S
and Freudenstein
F
(1971
), Dynamic analysis of mechanical systems with clearance, Part 2: dynamic response
, ASME J. Eng. Ind.
93
, 310
–316
.60.
Karagiannis
K
and Pfeiffer
F
(1991
), Theoretical and experimental investigations of gear-rattling
, Nonlinear Dyn.
2
, 367
–387
.61.
Shaw
SW
(1989
), The onset of chaos in a two-degree-of freedom impact system
, ASME J. Appl. Mech.
56
, 168
–174
.62.
Yakubovich VA and Starzhinskii VM (1975), Linear Differential Equations with Periodic Coefficients, John Wiley, New York.
63.
Comparin
RJ
and Singh
R
(1989
), Non-linear frequency response characteristics of an impact pair
, J. Sound Vib.
134
, 259
–290
.64.
Choi
HS
and Lou
JYK
(1991
), Nonlinear behavior and chaotic motions of an SDOF system with piecewise-nonlinear stiffness
, Int. J. Non-Linear Mech.
26
, 461
–473
.65.
Kim
YB
and Noah
ST
(1991
), Stability and bifurcation analysis of oscillators with piecewise-linear characteristics: a general approach
, ASME J. Appl. Mech.
58
, 545
–553
.66.
Wong
CW
, Zhang
WS
, and Lau
SL
(1991
), Periodic forced vibration of unsymmetric piecewise-linear system by incremental harmonic balance method
, J. Sound Vib.
149
, 91
–105
.67.
Kim
YB
(1998
), Multiple harmonic balance method for aperiodic vibration of a piecewise-linear system
, ASME J. Vibr. Acoust.
120
, 181
–187
.68.
Blankenship
GW
and Kahraman
A
(1995
), Steady state forced response of a mechanical oscillator with combined parametric excitation and clearance type non-linearity
, J. Sound Vib.
185
(5
), 743
–765
.69.
Wu
WT
, Wickert
JA
, and Griffin
JH
(1995
), Modal analysis of the steady state response of a driven periodic linear system
, J. Sound Vib.
183
(2
), 297
–308
.70.
Liu
K
(1999
), Extension of modal analysis to linear time-varying systems
, J. Sound Vib.
226
(1
), 149
–167
.71.
Lamarque
CH
and Janin
O
(2000
), Modal analysis of mechanical systems with impact nonlinearities: limitations to a modal superposition
, J. Sound Vib.
235
(4
), 567
–609
.72.
Natsiavas
S
, Theodossiades
S
, and Goudas
I
(2000
), Dynamic analysis of piecewise linear oscillators with time periodic coefficients
, Int. J. Non-Linear Mech.
35
, 53
–68
.73.
Ling
FH
(1983
), A numerical treatment of the periodic solutions of non-linear vibration systems
, Appl. Math. Mech.
4
, 525
–546
.74.
Foale
S
and Thompson
JMT
(1991
), Geometrical concepts and computational techniques of nonlinear dynamics
, Comput. Methods Appl. Mech. Eng.
89
, 381
–394
.75.
Awrejcewicz
J
and Someya
T
(1991
), Periodic, quasi-periodic and chaotic orbits and their bifurcations in a system of coupled oscillators
, J. Sound Vib.
146
, 527
–532
.76.
Sato
K
, Yamamoto
S
, and Kawakami
T
(1991
), Bifurcation sets and chaotic states of a geared system subjected to harmonic excitation
, Computational Mech., Berlin
7
, 173
–182
.77.
Padmanabhan
C
and Singh
R
(1995
), Analysis of periodically excited non-linear systems by a parametric continuation technique
, J. Sound Vib.
184
(1
), 35
–58
.78.
Padmanabhan
C
and Singh
R
(1995
), Dynamics of a piecewise non-linear system subject to dual harmonic excitation using parametric continuation
, J. Sound Vib.
184
(5
), 767
–799
.79.
Shahruz
SM
and Tan
CA
(1989
), Response of linear slowly varying systems under external excitations
, J. Sound Vib.
131
, 239
–247
.80.
Babitsky VI and Krupenin VL (2001), Vibration of Strongly Nonlinear Discontinuous Systems, Springer, Berlin (Translated from Russian, Nauka, Mosco, 1985).
81.
Kobrinsky AE (1969), Dynamics of Mechanisms with Elastic Connections and Impact Systems, Iliffe Books Ltd, London (Translated from Russian, Nauka, Moscow, 1964).
82.
Babitsky VI (1998), Theory of Vibro-impact Systems and Applications, Springer, Berlin (Translated from Russian, Nauka, Mosco, 1978).
83.
Krylov NM and Bogolyuov NM (1947), Introduction to Nonlinear Mechanics, Princeton Univ Press (Translated from Russian, Keiv AS USSR, 1937).
84.
Nakada T et al. (1956), The dynamic loads on gear caused by varying the elasticity of the mating teeth, Proc of 6th Japan Natl Congress for Applied Mechanics, 496–507.
85.
Gregory
RW
, Harris
SL
, and Munro
RG
(1963
), Dynamic behavior of spur gears
, Proc. Inst. Mech. Eng., IMechE Conf.
178
, 207
–226
.86.
Harris
SL
(1958
), Dynamic loads on the teeth of spur gears
, Proc. Inst. Mech. Eng., IMechE Conf.
172
(2
), 87
–112
.87.
Baron
J
et al. (1973
), Dynamic investigation of multi-degree gear transmission model with varying stiffness coefficient
, Nonlinear Vibration Program
,14
, 547
–559
.88.
Bollinger
JG
et al. (1964
), Instability potential of high speed gearing
, Ind. Math.
17
, Pt 2 (39
–55
).89.
Johson DC (1958), The excitation of resonant vibrations by gear tooth meshing effects, Proc. Int. Conf. On Gearing, London, 18–23.
90.
Utagawa
M
et al. (1962
), Dynamic loads on spur gear teeth having pitch error at high speed
, Bull. JSME
, 5
(18
), 374
–381
.91.
David JW (1985), Dynamic coupling in geared rotor systems, ASME Paper 85-DET-11
92.
Benton
MI
and Seireg
A
(1980
), The application of the Ritz averaging method to determining the response of systems with time-varying stiffness to harmonic excitation
, ASME J. Mech. Des.
102
, 384
–390
.93.
Li
J
(1986
), The stability analysis of gear vibration equation under dynamic load, J. Kumming Inst.
1986
(1
) 77
–82
.94.
Sato
T
, Umezawa
K
, and Ishikawa
J
(1983
), Effects of contact ratio and profile correction on gear rotational vibration
, Bull. JSME
, 26
, 2010
–2016
.95.
Terauchi
Y
, Nadano
H
, and Nohara
M
(1982
), On the effect of the tooth profile modification on the dynamic load and the sound level of the spur gears
, Bull. JSME
, 25
, 1474
–1481
.96.
Lin HH, Townsend DP, and Oswald FB (1989), Dynamic loading of spur gears with linear or parabolic tooth profile modifications, Proc of ASME 5th Int Power Trans Gearing Conf, Chicago IL 1, 409–419.
97.
Lin HH, Townsend DP, and Oswald FB (1989), Profile modification to minimize spur gear dynamic loading, Proc of ASME 5th Int Power Trans Gearing Conf, Chicago IL, 1, 455–465.
98.
Lin HH and Houston RL (1986), Dynamic loading on parallel shaft gears, NASA CR 179473.
99.
Yoon
KY
and Rao
SS
(1996
), Dynamic load analysis of spur gears using a new tooth profile
, ASME J. Mech. Des.
118
, 1
–6
.100.
Kahraman A and Blankenship GW (1996), Gear dynamics experiments, Part-III: effect of involute tip relief, ASME Power Transmission and Gearing Conf, San Diego, CA.
101.
Kasuba
R
and Ewans
JW
(1981
), An extended model for determining dynamic loads in spur gearing
, ASME J. Mech. Des.
100
, 69
–76
.102.
Staph
HE
(1976
), A parametric analysis of high-contact-ratio spur gears
, ASLE Trans.
19
, 201
–215
.103.
Lin
HH
, Huston
RL
, and Coy
JJ
(1988
), On dynamic loads in parallel shaft transmissions: partI-modeling and analysis
, ASME J. Mech., Transm., Autom. Des.
110
, 221
–225
.104.
Oswald FB, Rebbechi B, Zakrajsek JJ, and Townsend DP (1991), Comparison of analysis and experiment for dynamics of low contact ratio spur gears, NASA TM-103232.
105.
Liou
CH
, Lin
HH
, Oswald
FB
, and Townsend
DP
(1996
), Effect of contact ratio on spur gear dynamic load with no tooth profile modifications
, ASME J. Mech. Des.
118
, 439
–443
.106.
Kahraman
A
and Blankenship
GW
(1999
), Effect of involute contact ratio on spur gear dynamics
, ASME J. Mech. Des.
121
, 112
–118
.107.
Maatar
M
and Velex
P
(1996
), An analytical expression for the time-varying contact length in perfect cylindrical gears: some possible applications in gear dynamics
, ASME J. Mech. Des.
118
, 586
–589
.108.
Andersson
A
(2000
), An analytical study of the effect of the contact ratio on the spur gear dynamic response
, ASME J. Mech. Des.
122
, 508
–514
.109.
Kubo
A
and Kiyono
S
(1980
), Vibration excitation of cylindrical involute gears due to tooth form error
, Bull. JSME
, 23
, 1536
–1543
.110.
Umezawa
K
, Suzuki
T
, and Sato
T
(1986
), Vibration of power transmission helical gears (approximate equation of tooth stiffness
), Bull. JSME
, 29
, 1605
–1611
.111.
Kahraman A and Blankenship GW (1996), Gear dynamics experiments Part-II: Effect of involute contact ratio, ASME Power Transmission and Gearing Conf, San Diego, CA.
112.
Blankenship GW and Kahraman A (1996), Gear dynamics experiments Part-I: Characteristics of forced response, ASME Power Transmission and Gearing Conf, San Diego, CA, 373–380.
113.
Martin
KF
(1978
), A review of friction predictions in gear teeth
, Wear
, 49
, 201
–238
.114.
Benedict
GH
and Kelley
BW
(1961
), Instantaneous coefficients of gear tooth friction
, ASLE Trans.
4
, 59
–70
.115.
Flamand
L
, Berthe
D
, and Godet
M
(1981
), Simulation of Hertzian contacts found in spur gears with a high performance disk machine
, ASME J. Mech. Des.
103
, 204
–209
.116.
Johnson
KL
and Spence
DI
(1991
), Determination of gear tooth friction by disc machine
, Tribol. Int.
24
, 269
–275
.117.
Radzimovsky
EI
, Miraferi
A
, and Broom
WE
(1973
), Instantaneous efficiency and coefficient of friction of an involue gear drive
, ASME J. Eng. Ind.
95
, 1131
–1138
.118.
Yoshizaki
M
, Naruse
C
, Nemoto
R
, and Haizuka
S
(1991
), Study on frictional loss of spur gears (concerning the influence of tooth form, load, tooth surface roughness and lubricating oil
), Tribol. Trans.
31
, 138
–146
.119.
Rebecchi B, Oswald F, and Townsend DP (1996), Measurement of gear tooth dynamic friction, Proc of 7th ASME Int Power Transmission and Gearing Conf, San Diego, CA, 355–363.
120.
Wu
S
and Cheng
HS
(1991
), A friction model of partial-EHL contacts and its application to power loss in spur gears
, Tribol. Trans.
34
, 397
–407
.121.
Houser DR, Bolze VM, and Graber JM (1996), static and dynamic transmission error measurements and predictions for spur and helical gear sets, Proc of 7th ASME Int Power Transmission and Gearing Conf, San Diego, CA, 365–372.
122.
Borner
J
and Houser
DR
(1996
), Friction and bending moments on gear noise excitations
, SAE Trans.
105
, 1669
–1676
.123.
Iida
H
, Tamura
A
, and Yamada
Y
(1985
), Vibrational characteristics of friction between gear teeth
, Bull. JSME
, 28
, 1512
–1519
.124.
Shing TK, Tsai LW, and Krishnaprasad PS (1994), Dynamic model of a spur geared system with backlash and friction consideration, ASME Proc Machine Elements and Machine Dynamics Conf, DE-71, 155–163.
125.
Hochmann D (1997), Friction force excitations in spur and helical involute parallel axis gearing, PhD dissertation, Ohio State Univ, Columbus OH.
126.
Vedmar
L
and Henriksson
B
(1998
), A general approach for determining dynamic forces in spur gears
, ASME J. Mech. Des.
120
, 593
–598
.127.
Velex
P
and Cahouet
V
(2000
), Experimental and numerical investigations on the influence of tooth friction in spur and helical gear dynamics
, ASME J. Mech. Des.
122
, 515
–522
.128.
Vaishya
M
and Singh
R
(2001
), Analysis of periodically varying gear mesh systems with Coulomb friction using Floquet
, J. Sound Vib.
243
, 525
–545
.129.
Iida H and Tamura A (1984), Coupled torsional-flexural vibration of shaft in a geared system, Proc of Conf Vibr Rotating Mech, Institution of Mechanical Engineers, 67–72.
130.
Choy FK, Tu YK, Savage M, and Townsend DP (1989), Vibration signature analysis of multistage gear transmissions, ASME of Proc 5th Int Power Trans Gearing Conf, Chicago, 1, 383–387.
131.
Iida
H
, Tamura
A
, and Yamamoto
H
(1986
), Dynamic characteristics of a gear train system with softly supported shafts
, Bull. JSME
, 29
, 1811
–1816
.132.
Umezawa
K
, Ajima
T
, and Houjoph
H
(1986
), Vibrations of three axis geared systems
, Bull. JSME
, 29
, 950
–957
.133.
Velex P and Saada A (1991), A model for the dynamic behavior of multi-stage geared systems, Proc of 8th Int Federation Theory Mach Mech World Congress, Prague, 2, 621–625.
134.
Linke H and Borner J (1991), Dynamic loads on gear trains with idler gears, Proc of JSME Int Conf Motion Power Transm, Hiroshima, 31–36.
135.
Rashidi M and Krantz TL (1992), Dynamics of a split torque helicopter transmission, ASME Proc 6th Int Power Trans Gearing Conf, 1, 347–358.
136.
Lim TC and Houser DR (1997), Dynamic analysis of lay-shaft gears in automotive transmission, Proc of SAE Noise and Vib Conf, 739–749.
137.
Vinayak H (1995), Multi-body dynamics and modal analysis approaches for multi-mesh transmissions with compliant gear bodies, PhD dissertation, Ohio State Univ, Columbus OH.
138.
Raclot
JP
and Velex
P
(1999
), Simulation of the dynamic behaviour of single and multi-stage geared systems with shape deviations and mounting errors by using a spectral method
, J. Sound Vib.
220
(5
), 861
–903
.139.
Lim
TC
and Li
J
(1999
), Dynamic analysis of multi-mesh counter-shaft transmission
, J. Sound Vib.
219
(5
), 905
–919
.140.
Huang
KJ
and Liu
TS
(2000
), Dynamic analysis of a spur gear by the dynamic stiffness method
, J. Sound Vib.
234
(2
), 311
–329
.141.
Amirouche
FM
, Tajiri
GC
, and Valco
MJ
(1995
), Mathematical model of a time and position variant external load on a gear tooth using the modified Timoshenko beam equation
, Int. J. Numer. Methods Eng.
39
, 2073
–2094
.142.
Oda
S
, Koide
T
, and Miyachika
K
(1985
), Dynamic behavior of thin-rimmed helical gears with various web
, Bull. JSME
, 28
, 2434
–2441
.143.
Iwatsuk N, Hayashi I, and Maki H (1991), Estimation of noise power radiation from gear bodies, JSME Int Conf Motion and Power Trans, Hiroshima, Japan, 49–53.
144.
Cornejo G and Rakhit A (1996), Identification of spiking vibrations in gears and their effect on the performance of gearbox in high speed applications, ASME DE88, 195–203.
145.
Okamura H, Suzuki Y, and Nakano N (1996), Experiments and analysis of sound-damping rings for gears: application of snap rings, ASME DE 88, 345–354.
146.
Blankenship GW and Singh R (1992), A comparative study of selected gear mesh interface dynamic models, ASME Proc of 6th Int Power Trans Gearing Conf, DE43, 137–146.
147.
Vinayak
H
and Singh
R
(1996
), Eigensolutions of annular-like elastic disks with intentionally removed or added material
, J. Sound Vib.
192
, 741
–769
.148.
Parker
RG
, Vijayakar
SM
, and Imajo
T
(2000
), Non-linear dynamic response of a spur gear pair: modeling and experimental comparisons
, J. Sound Vib.
237
, 435
–455
.149.
Kahraman
A
(1994
), Planetary gear train dynamics
, ASME J. Mech. Des.
116
, 713
–720
.150.
Saada
A
and Velex
P
(1995
), An extended model for the analysis of the dynamic behavior of planetary trains
, ASME J. Mech. Des.
117
, 241
–247
.151.
Velex
P
and Flamand
L
(1996
), Dynamic response of planetary trains to mesh parametric excitations
, ASME J. Mech. Des.
118
, 7
–14
.152.
Parker
RG
, Agashe
V
, and Vijayakar
SM
(2000
), Dynamic response of a planetary geared system using a finite element/contact mechanics model
, ASME J. Mech. Des.
122
, 305
–311
.153.
Bapat
CN
, Popplewell
N
, and McLachlan
K
(1983
), Periodic motions of an impact pairs
, J. Sound Vib.
87
, 19
–40
.154.
Popplewell
N
, Bapat
CN
, and McLachlan
K
(1983
), Stable periodic vibroimpact of an oscillator
, J. Sound Vib.
87
, 41
–59
.155.
Shaw
SW
and Holmes
PJ
(1983
), A periodic forced impact oscillator with large dissipation
, ASME J. Appl. Mech.
50
, 849
–857
.156.
Shaw
SW
(1985
), The dynamics of a harmonically excited system having rigid amplitude constrains, Part 1: Subharmonic motions and local bifurcations
, ASME J. Appl. Mech.
52
, 453
–458
.157.
Shaw
SW
(1985
), The dynamics of a harmonically excited system having rigid amplitude constraints, Part 2: Chaotic motions and global bifurcations
, ASME J. Appl. Mech.
52
, 459
–464
.158.
Palej
P
and Niziol
J
(1986
), On a direct method of analyzing impacting mechanical system
, J. Sound Vib.
108
, 191
–198
.159.
Bapat
CN
and Popplewell
N
(1987
), Several similar vibro-impact systems
, J. Sound Vib.
113
, 17
–28
.160.
Lee
CH
and Byrne
K
(1987
), Impact statistics for a simple random rattling system
, J. Sound Vib.
119
, 529
–543
.161.
Whiston
GS
(1987
), The vibro-impact response of a harmonically excited and preloaded one-dimensional linear oscillator
, J. Sound Vib.
115
, 303
–319
.162.
Whiston
GS
(1987
), Global dynamics of a vibro-impacting linear oscillator
, J. Sound Vib.
118
(3
), 395
–429
.163.
Smith
CE
and Liu
PP
(1992
), Coefficients of resultation
, ASME J. Appl. Mech.
59
, 663
–669
.164.
Veluswami
MA
and Crossley
FRE
(1975
), Multiple impacts of a ball between two plates, Part 1: Some experiments observations
, ASME J. Eng. Ind.
97
, 820
–827
.165.
Veluswami
MA
and Crossley
FRE
(1975
), Multiple impact of a ball between two plates, Part 2: Mathematical modeling
, ASME J. Eng. Ind.
97
, 828
–835
.166.
Shaw
SW
and Holmes
PJ
(1983
), A periodically forced piecewise linear oscillator
, J. Sound Vib.
90
, 129
–155
.167.
Tomlinson
GR
and Lam
J
(1984
), Frequency response characteristics of structure with single and multiple clearance type non-linearities
, J. Sound Vib.
96
, 111
–125
.168.
Hunt
KH
and Crossley
FRE
(1975
), Coefficient of restitution interpreted as damping in vibroimpact
, ASME J. Eng. Ind.
42
, 440
–445
.169.
Whiston
GS
(1979
), Impacting under harmonic excitation
, J. Sound Vib.
67
, 179
–186
.170.
Munro RG (1962), The dynamic behavior of spur gears, PhD dissertation, Cambridge Univ.
171.
Kubo
A
, Yamada
K
, Aida
T
, and Sato
S
(1972
), Research on ultra high speed gear devices (reports 1–3
), Trans JSME
38
, 2692
–2715
.172.
Umezawa
K
, Sata
T
, and Ishikawa
J
(1984
), Simulation of rotational vibration of spur gears
, Bull. JSME
, 38
, 102
–109
.173.
Hayashi T, Nishi N, Ohno T, and Crossley FRE (1979), Multipe impacts of a cylinder between two planes and of the meshing teeth of a pair of gears, Proc. of 4th World Congress on Theory of Mechanics and Mechanisms, 350–353.
174.
Ozguven
HN
and Houser
DR
(1988
), Dynamic analysis of high speed gears by using loaded ststic transmission error
, J. Sound Vib.
125
, 71
–83
.175.
Galhoud
LE
, Masri
SF
, and Anderson
JC
(1987
), Transfer function of a class of nonlinear multidegree of freedom oscillator
, ASME J. Appl. Mech.
54
, 215
–225
.176.
Winter H and Kojima M (1981), A study on the dynamics of geared system—Estimation of overload on gears in system, Proc Int Symp Gearing and Power Trans, Tokyo, c-12.
177.
Gelb A and Vander Velde WE (1968), Multiple-Input Describing Functions and Nonlinear System Design, McGraw-Hill, New York.
178.
Comparin RJ (1988), A study of the frequency response of impact pairs with application to automative gear rattle, PhD dissertation, Ohio State Univ, Columbus OH.
179.
Comparin
RJ
and Singh
R
(1990
), An analytical study of automobile neutral gear rattle
, ASME J. Mech. Des.
112
, 237
–245
.180.
Johnson O and Hirami N (1991), Diagnosis and objective evaluation of gear rattle, SAE 911082.
181.
Sakai T, Doi Y, Yamatommo K, Ogasawara T, and Narita M (1982), Theoretical and experimental analysis of rattling noise of automotive gearbox, SAE Paper 810773.
182.
Ohnuma S, Shigetaro Y, Mineichi I, and Fujimoto T (1985), Research on the idling rattle of manual transmission, SAE Paper 850979.
183.
Pfeiffer
F
and Kunert
A
(1990
), rattling models of deterministic to stochastic processes
, Nonlinear Dyn.
1
, 63
–74
.184.
Kataoka
M
, Ohno
S
, and Sugimoto
T
(1991
), Forced torsional vibration of a two-degree-of-freedom system including a clearance and two-step-hardening spring
, JSME Int. J., Ser. III
34
, 345
–354
.185.
Theissen
J
(1995
), The effects of backlash on the dynamic load in gear transmission (in Chinese
), Gear
9
, 77
–82
.186.
Ozguven HN (1989), Further work on DYTEM computer code, Research Report, Ohio State Univ, Columbus OH.
187.
Retting
H
(1965
), Zahnkrafte und schwingungen in stirnradgetrieben
, Konstroruktion
,17
, 41
–53
.188.
Terauchi
Y
, Hidaka
T
, and Nagashima
M
(1967
), Dynamic loads on spur gear teeth
, Trans JSME
33
, 456
–472
.189.
Sato
K
, Kamada
O
, and Takatsu
N
(1979
), Jump phenomena in geared system to random excitation
, Bull. JSME
, 28
, 1271
–1278
.190.
Ozguven
HN
(1991
), A non-linear mathematical model for dynamic analysis of spur gear including shaft and bearing dynamics
, J. Sound Vib.
145
(2
), 239
–260
.191.
Richard JA (1983), Analysis of Periodically Time-Varying System, Springer-Verlay, New York.
192.
Padmanabhan
C
and Singh
R
(1996
), Analysis of periodically forced nonlinear Hill’s oscillator with application to a geared system
, J. Acoust. Soc. Am.
99
(1
), 324
–334
.193.
Lau
SL
and Zhang
WS
(1992
), Non-linear vibrations of piecewise linear systems by incremental harmonic balance method
, ASME J. Appl. Mech.
59
, 153
–160
.194.
Li R, Lin T, Tao Z, and Yang C (2001), Structure modal analysis of gearbox, Proc of ICMT-2001, 360–362
195.
Li R, Lin T, Tao Z, Han X (2001), Study on coupled vibration response of geared system Proc of MPT 2001-Fukuoka, 97–101.
196.
Li R, Lin T, and Tao Z (2001), Research on nonlinear vibration and impact for geared system, Proc. of ICME 2000, 76 (020114).
197.
Tao Z, Li R, and Lin T (2000), Prediction of coupled vibration response for geared system, Proc. of GTMS, 275–280.
198.
Lin T, Li R, and Tao Z (2001), Computerized simulation for three dimensional static and dynamic contact/impact problem of gear drives, ICMT 2001, 248–251.
199.
Chen
CS
, Natsiavas
S
, and Nelson
HD
(1997
), Stability analysis and complex dynamics of a gear-pair system supported by a squeeze film damper
, ASME J. Vibr. Acoust.
119
, 85
–88
.200.
Chen
CS
, Natsiavas
S
, and Nelson
HD
(1998
), Coupled lateral-torsional vibration of a gear-pair system supported by a squeeze film damper
, ASME J. Vibr. Acoust.
120
, 860
–867
.201.
Shiau
TN
, Rao
JS
, Chang
JR
, and Choi
ST
(1999
), Dynamic behavior of geared rotors
, ASME J. Eng. Gas Turbines Power
, 121
, 494
–503
.202.
Mitchell
LD
and David
JW
(1985
), Proposed solution methodology for the dynamical coupled, nonlinear geared rotor mechanics equation
, ASME J. Vib., Acoust., Stress, Reliab. Des.
107
, 112
–116
.203.
Lin
RM
et al. (1993
), Chaotic vibration of mechanical system with backlash
, Mech. Syst. Signal Process.
7
(3
), 257
–272
.204.
Liaw
CY
and Koh
CG
(1993
), Dynamical stability and chaos of system with piecewise linear stiffness
, ASCE J. Eng. Mech. Dv.
119
(8
), 1542
–1557
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