A review of planetary and epicyclic gear dynamics and vibrations research

Applied Mechanics Reviews

Volumn 66, Issue 4, 2014, Pages

  Cooley, Christopher G ^a   Parker, Robert G ^b  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b Virginia Polytechnic Institute and State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMIC RESPONSE; EPICYCLIC GEARS; MATHEMATICAL MODELS; MECHANICAL DRIVES; RESEARCH;

ELASTIC COMPLIANCE; GYROSCOPIC EFFECTS; JOURNAL ARTICLES; RESPONSE PREDICTION; TECHNICAL CHALLENGES; TIME-VARYING MESH STIFFNESS; TOOTH SURFACE MODIFICATIONS; VIBRATION RESPONSE;

VIBRATIONS (MECHANICAL);

EID: 84903145067     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.4027812     Document Type: Review

References (147)

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.
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.
5. Struggl, S., Berbyuk, V., and Johansson, H., 2014, "Review on Wind Turbines With Focus on Drive Train System Dynamics," Wind Energy (in press).
6. Vijayakar, S. M., 2005, "Calyx Users Manual," http://ansol.us
7. Ozguven, H. N., and Houser, D. R., 1988, "Mathematical Models Used in Gear Dynamics-A Review," J. Sound Vib., 121(3), pp. 383-411. (Pubitemid 18603605)
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. (Pubitemid 40205919)
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.
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.
12. Botman, M., 1976, "Epicyclic Gear Vibrations," J. Eng. Ind., 98(3), pp. 811-815.
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.
14. Kahraman, A., 1994, "Planetary Gear Train Dynamics," ASME J. Mech. Des., 116(3), pp. 713-720.
15. Kahraman, A., 1994, "Natural Modes of Planetary Gear Trains," J. Sound Vibration, 173(1), pp. 125-130.
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.
17. Kahraman, A., 2001, "Free Torsional Vibration Characteristics of Compound Planetary Gear Sets," Mech. Mach. Theory, 36(8), pp. 953-971. (Pubitemid 32776143)
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. (Pubitemid 46736040)
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.
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.
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.
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.
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. (Pubitemid 46736079)
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.
25. Sondkar, P., and Kahraman, A., 2013, "A Dynamic Model of a Double-Helical Planetary Gear Set," Mech. Mach. Theory, 70, pp. 157-174.
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.
28. Singh, A., 2010, "Load Sharing Behavior in Epicyclic Gears: Physical Explanation and Generalized Formulation," Mech. Mach. Theory, 45(3), pp. 511-530.
29. Singh, A., 2011, "Epicyclic Load Sharing Map-Development and Validation," Mech. Mach. Theory, 46(5), pp. 632-646.
30. Montestruc, A. N., 2010, "A Numerical Approach to Calculation of Load Sharing in Planetary Gears," ASME J. Mech. Des., 132(1), p. 014503.
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. (Pubitemid 33716227)
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. (Pubitemid 39519962)
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. (Pubitemid 40308929)
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. (Pubitemid 40843884)
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. (Pubitemid 46736078)
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.
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. (Pubitemid 15476384)
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.
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, 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.
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.
42. Kahraman, A., 1994, "Load Sharing Characteristics of Planetary Transmissions," Mech. Mach. Theory, 29(8), pp. 1151-1165.
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. (Pubitemid 16605949)
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.
45. Gu, X., and Velex, P., 2013, "On the Dynamic Simulation of Eccentricity Errors in Planetary Gears," Mech. Mach. Theory, 61, pp. 14-29.
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. (Pubitemid 39475316)
47. Botman, M., 1980, "Vibration Measurements on Planetary Gears of Aircraft Turbine Engines," J. Aircr., 17(5), pp. 351-357.
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.
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.
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).
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. (Pubitemid 10462192)
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.
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.
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.
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.
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.
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.
59. Ericson, T. M., and Parker, R. G., 2013, "Natural Frequency Clusters in Planetary Gear Vibration," ASME J. Vib. Acoust., 135(6), p. 061002.
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.
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.
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.
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).
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.
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.
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. (Pubitemid 129533144)
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.
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. (Pubitemid 16547152)
70. Lin, J., and Parker, R. G., 2001, "Natural Frequency Veering in Planetary Gears," Mech. Struct. Mach., 29(4), pp. 411-429. (Pubitemid 34055516)
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.
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.
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.
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. (Pubitemid 126368450)
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.
76. Eritenel, T., and Parker, R. G., 2012, "Three-Dimensional Nonlinear Vibration of Gear Pairs," J. Sound Vib., 331(15), pp. 3628-3648.
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.
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. (Pubitemid 20612451)
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.
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.
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.
82. Guo, Y., and Parker, R. G., 2014, "Analytical Determination of Back-Side Contact Gear Mesh Stiffness," Mech. Mach. Theory, 78, pp. 263-271.
83. Harris, S. L., 1958, "Dynamic Loads on the Teeth of Spur Gears," Proc. Inst. Mech. Eng., 172(1), pp. 87-112.
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. (Pubitemid 43006048)
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.
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.
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.
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. (Pubitemid 126698471)
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.
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. (Pubitemid 34090263)
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.
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.
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.
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.
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.
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.
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.
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.
100. Yang, J., and Yang, P., 2013, "Random Vibration Analysis of Planetary Gear Trains," ASME J. Vib. Acoust., 135(2), p. 021005.
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. (Pubitemid 13525282)
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.
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. (Pubitemid 350223602)
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.
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.
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.
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.
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.
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.
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.
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. (Pubitemid 46736077)
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.
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. (Pubitemid 10438818)
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.
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.
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. (Pubitemid 8590443)
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.
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. (Pubitemid 43765584)
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.
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.
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.
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.
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.
131. Cooley, C. G., and Parker, R. G., 2013, "Mechanical Stability of High-Speed Planetary Gears," Int. J. Mech. Sci., 69, pp. 59-71.
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.
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.
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.
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. (Pubitemid 10438817)
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. (Pubitemid 15477071)
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. (Pubitemid 16605953)
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. (Pubitemid 21671699)
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.
142. McNames, J., 2002, "Fourier Series Analysis of Epicyclic Gearbox Vibration," ASME J. Vib. Acoust., 124(1), pp. 150-153.
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. (Pubitemid 44205429)
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.
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.
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.
147. Vecchiato, D., 2006, "Tooth Contact Analysis of a Misaligned Isostatic Planetary Gear Train," Mech. Mach. Theory, 41(6), pp. 617-631.