A Review of Planetary and Epicyclic Gear Dynamics and Vibrations Research

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.

[1]  Geng Liu,et al.  Modal analyses of herringbone planetary gear train with journal bearings , 2012 .

[2]  Sandeep M. Vijayakar,et al.  Finite element analysis of three-dimensional conformal contact with friction , 1989 .

[3]  S. L. Harris,et al.  Dynamic Loads on the Teeth of Spur Gears , 1958 .

[4]  Avinash Singh,et al.  An Experimental Study of the Influence of Manufacturing Errors on the Planetary Gear Stresses and Planet Load Sharing , 2008 .

[5]  Alfred N. Montestruc.  A Numerical Approach to Calculation of Load Sharing in Planetary Gear Drives , 2010 .

[6]  Teruaki Hidaka,et al.  Dynamic Behavior of Planetary Gear : 4th Report, Influence of the Transmitted Tooth Load on the Dynamic Increment Load , 1978 .

[7]  Robert G. Parker,et al.  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 , 2011 .

[8]  Teruaki Hidaka,et al.  Dynamic Behavior of Planetary Gear : 2nd Report, Displacement of Sun Gear and Ring Gear , 1976 .

[9]  Yimin Shao,et al.  Dynamic simulation of planetary gear set with flexible spur ring gear , 2013 .

[10]  Ahmet Kahraman,et al.  A dynamic model to predict modulation sidebands of a planetary gear set having manufacturing errors , 2010 .

[11]  P. Velex,et al.  On the modelling of excitations in geared systems by transmission errors , 2006 .

[12]  Robert G. Parker,et al.  Parametric Instability of a Rotating Circular Ring With Moving, Time-Varying Springs , 2006 .

[13]  Xianghe Peng,et al.  Survey of nonlinear vibration of gear transmission systems , 2003 .

[14]  Robert G. Parker,et al.  Modal properties of three-dimensional helical planetary gears , 2009 .

[15]  Robert G. Parker,et al.  Planetary gear modal vibration experiments and correlation against lumped-parameter and finite element models , 2013 .

[16]  Ahmet Kahraman,et al.  Static Load Sharing Characteristics of Transmission Planetary Gear Sets: Model and Experiment , 1999 .

[17]  Avinash Singh,et al.  Internal Gear Strains and Load Sharing in Planetary Transmissions: Model and Experiments , 2008 .

[18]  Christopher G. Cooley,et al.  Unusual gyroscopic system eigenvalue behavior in high-speed planetary gears , 2013 .

[19]  W. LaCava,et al.  Planetary gear load sharing of wind turbine drivetrains subjected to non‐torque loads , 2015 .

[20]  Robert G. Parker,et al.  Analytical Solution for the Nonlinear Dynamics of Planetary Gears , 2011 .

[21]  Wim Desmet,et al.  Multibody modelling of varying complexity for modal behaviour analysis of wind turbine gearboxes , 2010 .

[22]  Robert G. Parker,et al.  Modal Properties of Planetary Gears With an Elastic Continuum Ring Gear , 2008 .

[23]  R. G. Munro,et al.  Dynamic Behaviour of Spur Gears , 1963 .

[24]  Ahmet Kahraman,et al.  Load sharing characteristics of planetary transmissions , 1994 .

[25]  Robert G. Parker,et al.  Analytical investigation of tooth profile modification effects on planetary gear dynamics , 2013 .

[26]  Ahmet Kahraman,et al.  A non-linear dynamic model for planetary gear sets , 2007 .

[27]  Robert G. Parker,et al.  A PHYSICAL EXPLANATION FOR THE EFFECTIVENESS OF PLANET PHASING TO SUPPRESS PLANETARY GEAR VIBRATION , 2000 .

[28]  M. Botman,et al.  Dynamic Behavior of a Journal Bearing in a Planet Gear , 1983 .

[29]  Ahmet Kahraman,et al.  Planetary gear train dynamics , 1994 .

[30]  Robert G. Parker,et al.  Parametric instability of a circular ring subjected to moving springs , 2006 .

[31]  D. L. Seager.  Conditions for the Neutralization of Excitation by the Teeth in Epicyclic Gearing , 1975 .

[32]  Robert G. Parker,et al.  Structured vibration characteristics of planetary gears with unequally spaced planets , 2000 .

[33]  Robert G. Parker,et al.  Influence of manufacturing errors on the dynamic characteristics of planetary gear systems , 2004 .

[34]  Philippe Velex,et al.  A dynamic model to study the influence of planet position errors in planetary gears , 2012 .

[35]  Robert G. Parker,et al.  Three-dimensional nonlinear vibration of gear pairs , 2012 .

[36]  M. Botman,et al.  Epicyclic Gear Vibrations , 1975 .

[37]  C. D. Mote,et al.  Comments on curve veering in eigenvalue problems , 1986 .

[38]  Robert G. Parker,et al.  An investigation of tooth mesh nonlinearity and partial contact loss in gear pairs using a lumped-parameter model , 2012 .

[39]  Iwao Hayashi,et al.  MEASUREMENT AND SOME DISCUSSIONS ON DYNAMIC LOAD SHARING IN PLANETARY GEARS , 1986 .

[40]  Tao Sun,et al.  Nonlinear dynamics of a planetary gear system with multiple clearances , 2003 .

[41]  Robert G. Parker,et al.  Sensitivity of General Compound Planetary Gear Natural Frequencies and Vibration Modes to Model Parameters , 2010 .

[42]  Ahmet Kahraman,et al.  A deformable body dynamic analysis of planetary gears with thin rims , 2003 .

[43]  Sandeep M. Vijayakar,et al.  Linearization of multibody frictional contact problems , 1988 .

[44]  Ji Yeong Lee,et al.  Dynamic analysis for a planetary gear with time-varying pressure angles and contact ratios , 2012 .

[45]  Teruaki Hidaka,et al.  Dynamic Behavior of Planetary Gear : 1st Report Load Distribution in Planetary Gear , 1975 .

[46]  P. Velex,et al.  A MATHEMATICAL MODEL FOR ANALYZING THE INFLUENCE OF SHAPE DEVIATIONS AND MOUNTING ERRORS ON GEAR DYNAMIC BEHAVIOUR , 1996 .

[47]  Christopher G. Cooley,et al.  Mechanical stability of high-speed planetary gears , 2013 .

[48]  James McNames,et al.  Fourier Series Analysis of Epicyclic Gearbox Vibration , 2002 .

[49]  Ahmet Kahraman,et al.  Dynamic Modelling of Planetary Gears of Automatic Transmissions , 2008 .

[50]  Håkan Johansson,et al.  Review on wind turbines with focus on drive train system dynamics , 2015 .

[51]  Robert G. Parker,et al.  Dynamic Analysis of Planetary Gears With Bearing Clearance , 2012 .

[52]  Avinash Singh,et al.  Epicyclic Load Sharing Map — Development and validation , 2011 .

[53]  Christopher G. Cooley,et al.  The geometry and frequency content of planetary gear single-mode vibration , 2013 .

[54]  R. Parker,et al.  Dynamic Response of a Planetary Gear System Using a Finite Element/Contact Mechanics Model , 2000 .

[55]  N P E Alfred Montestruc.  Influence of Planet Pin Stiffness on Load Sharing in Planetary Gear Drives , 2011 .

[56]  P. Velex,et al.  Modeling of Spur and Helical Gear Planetary Drives With Flexible Ring Gears and Planet Carriers , 2007 .

[57]  George Vachtsevanos,et al.  Effect of Planetary Gear Carrier-Plate Cracks on Vibration Spectrum , 2012 .

[58]  Robert G. Parker,et al.  Analytical Characterization of the Unique Properties of Planetary Gear Free Vibration , 1999 .

[59]  W. E. Palmer,et al.  Noise Control In Planetary Transmissions , 1977 .

[60]  Robert G. Parker,et al.  Purely rotational model and vibration modes of compound planetary gears , 2010 .

[61]  Robert G. Parker,et al.  Parametric Instability of Planetary Gears Having Elastic Continuum Ring Gears , 2012 .

[62]  Leonard Meirovitch,et al.  A New Method of Solution of the Eigenvalue Problem for Gyroscopic Systems , 1974 .

[63]  Zaigang Chen,et al.  Dynamic Features of a Planetary Gear System With Tooth Crack Under Different Sizes and Inclination Angles , 2013 .

[64]  Robert G. Parker,et al.  Analytical determination of mesh phase relations in general compound planetary gears , 2011 .

[65]  Faydor L. Litvin,et al.  Design of One Stage Planetary Gear Train With Improved Conditions of Load Distribution and Reduced Transmission Errors , 2002 .

[66]  Philippe Velex,et al.  A Lumped Parameter Model to Analyse the Dynamic Load Sharing in Planetary Gears with Planet Errors , 2011 .

[67]  Zhou Xiaojun,et al.  Axial Thrust Force of Compound Planetary Spur Gear Set , 2011 .

[68]  Kazuteru Nagamura,et al.  Dynamic Behavior of Planetary Gear : 6th Report, Influence of Meshing-Phase , 1978 .

[69]  Avinash Singh,et al.  A Closed-Form Planet Load Sharing Formulation for Planetary Gear Sets Using a Translational Analogy , 2009 .

[70]  Yimin Shao,et al.  Dynamic features of planetary gear set with tooth plastic inclination deformation due to tooth root crack , 2013 .

[71]  Avinash Singh.  Application of a System Level Model to Study the Planetary Load Sharing Behavior , 2005 .

[72]  Donald R. Houser,et al.  Mathematical models used in gear dynamics—A review , 1988 .

[73]  R. H. Badgley,et al.  Reduction of Vibration and Noise Generated by Planetary Ring Gears in Helicopter Aircraft Transmissions , 1973 .

[74]  P. Velex,et al.  Dynamic Response of Planetary Trains to Mesh Parametric Excitations , 1996 .

[75]  Ahmet Kahraman,et al.  A New Method to Measure Planet Load Sharing and Sun Gear Radial Orbit of Planetary Gear Sets , 2012 .

[76]  Sandeep M. Vijayakar,et al.  Effect of Internal Gear Flexibility on the Quasi-Static Behavior of a Planetary Gear Set , 2001 .

[77]  Robert G. Parker,et al.  PLANETARY GEAR PARAMETRIC INSTABILITY CAUSED BY MESH STIFFNESS VARIATION , 2002 .

[78]  Ahmet Kahraman,et al.  Influence of Carrier and Gear Manufacturing Errors on the Static Load Sharing Behavior of Planetary Gear Sets , 2004 .

[79]  Rajendra Singh,et al.  A new gear mesh interface dynamic model to predict multi-dimensional force coupling and excitation , 1995 .

[80]  Robert G. Parker,et al.  Suppression of Planet Mode Response in Planetary Gear Dynamics Through Mesh Phasing , 2006 .

[81]  Timothy L. Krantz.  Gear Tooth Stress Measurements of Two Helicopter Planetary Stages , 1992 .

[82]  Hitham M. Tlilan,et al.  Non-linear dynamic behaviour of compound planetary gear trains: Model formulation and semi-analytical solution , 2009 .

[83]  Robert G. Parker,et al.  Nonlinear dynamics and stability of wind turbine planetary gear sets under gravity effects , 2014 .

[84]  Scott Xiong Yu,et al.  Asymmetric Gear Noise Sidebands and Application to Planetary Gear Noise Reduction , 2005 .

[85]  Kazuteru Nagamura,et al.  Dynamic Behavior of Planetary Gear : 7th Report, Influence of the Thickness of the Ring Gear , 1978 .

[86]  Ahmet Kahraman,et al.  Free torsional vibration characteristics of compound planetary gear sets , 2001 .

[87]  Robert G. Parker,et al.  Effect of Ring-Planet Mesh Phasing and Contact Ratio on the Parametric Instabilities of a Planetary Gear Ring , 2008 .

[88]  Jonathan A. Keller,et al.  Detection of a fatigue crack in a UH-60A planet gear carrier using vibration analysis , 2006 .

[89]  Yimin Shao,et al.  Dynamic simulation of planetary gear with tooth root crack in ring gear , 2013 .

[90]  Robert G. Parker,et al.  NATURAL FREQUENCY VEERING IN PLANETARY GEARS* , 2001 .

[91]  J. D. Smith,et al.  Dynamic Tooth Loads in Epicyclic Gears , 1974 .

[92]  Robert G. Parker,et al.  Influence of bearing stiffness on the static properties of a planetary gear system with manufacturing errors , 2004 .

[93]  P. D. McFadden,et al.  Effect of transmission path on measured gear vibration , 1986 .

[94]  P. Velex,et al.  An Extended Model for the Analysis of the Dynamic Behavior of Planetary Trains , 1995 .

[95]  Teruaki Hidaka,et al.  Dynamic Behavior of Planetary Gear : 3rd Report, Displacement of Ring Gear in Direction of Line of Action , 1977 .

[96]  Sheng Li,et al.  Bifurcation and chaos analysis of multistage planetary gear train , 2014 .

[97]  Ahmet Kahraman,et al.  Natural Modes of Planetary Gear Trains , 1994 .

[98]  Ahmet Kahraman,et al.  A theoretical and experimental investigation of modulation sidebands of planetary gear sets , 2009 .

[99]  S. Butterfield,et al.  Improving Wind Turbine Gearbox Reliability , 2007 .

[100]  Wim Desmet,et al.  Assessment of excitation mechanisms and structural flexibility influence in excitation propagation in multi-megawatt wind turbine gearboxes: Experiments and flexible multibody model optimization , 2013 .

[101]  Ming J. Zuo,et al.  Analytically evaluating the influence of crack on the mesh stiffness of a planetary gear set , 2014 .

[102]  Ahmet Kahraman,et al.  Dynamic tooth loads of planetary gear sets having tooth profile wear , 2004 .

[103]  Christopher G. Cooley,et al.  Vibration Properties of High-Speed Planetary Gears With Gyroscopic Effects , 2012 .

[104]  M. Botman.  Vibration Measurements on Planetary Gears of Aircraft Turbine Engines , 1980 .

[105]  M. Botman,et al.  Load Sharing in a Planetary Gear Stage in the Presence of Gear Errors and Misalignment , 1985 .

[106]  Robert G. Parker,et al.  Dynamic modeling and analysis of a spur planetary gear involving tooth wedging and bearing clearance nonlinearity , 2010 .

[107]  Avinash Singh.  Influence of Planetary Needle Bearings on the Performance of Single and Double Pinion Planetary Systems , 2007 .

[108]  P. D. McFadden,et al.  A technique for calculating the time domain averages of the vibration of the individual planet gears and the sun gear in an epicyclic gearbox , 1991 .

[109]  P. D. McFadden,et al.  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 , 1994 .

[110]  Robert G. Parker,et al.  Analytical determination of back-side contact gear mesh stiffness , 2014 .

[111]  P D McFadden,et al.  An Explanation for the Asymmetry of the Modulation Sidebands about the Tooth Meshing Frequency in Epicyclic Gear Vibration , 1985 .

[112]  Zaigang Chen,et al.  Mesh stiffness of an internal spur gear pair with ring gear rim deformation , 2013 .

[113]  Ping Yang,et al.  Random Vibration Analysis of Planetary Gear Trains , 2013 .

[114]  Gang Cheng,et al.  Model analysis and verification of 2K-H planetary gear system , 2015 .

[115]  Ahmet Kahraman,et al.  A dynamic model of a double-helical planetary gear set , 2013 .

[116]  Avinash Singh,et al.  Load sharing behavior in epicyclic gears: Physical explanation and generalized formulation , 2010 .

[117]  Daniele Vecchiato.  Tooth contact analysis of a misaligned isostatic planetary gear train , 2006 .

[118]  Teik C. Lim,et al.  Effect of flexible pin on the dynamic behaviors of wind turbine planetary gear drives , 2013 .

[119]  Kazuteru Nagamura,et al.  Dynamic Behavior of Planetary Gear : 5th report, Dynamic Increment of Torque , 1978 .

[120]  Yimin Song,et al.  Effect of mesh phase on wave vibration of spur planetary ring gear , 2011 .

[121]  Robert G. Parker,et al.  Dynamic Modeling and Analysis of Tooth Profile Modification for Multimesh Gear Vibration , 2008 .

[122]  Robert G. Parker,et al.  Vibration modes of planetary gears with unequally spaced planets and an elastic ring gear , 2010 .

[123]  Sandeep M. Vijayakar,et al.  A study of the relationship between the dynamic factors and the dynamic transmission error of spur gear pairs , 2007 .

[124]  Robert G. Parker,et al.  Structured Vibration Modes of General Compound Planetary Gear Systems , 2007 .

[125]  Robert G. Parker,et al.  Nonlinear Dynamics of Planetary Gears Using Analytical and Finite Element Models , 2007 .

[126]  Philippe Velex,et al.  On the dynamic simulation of eccentricity errors in planetary gears , 2013 .

[127]  P. Velex,et al.  A hybrid 3D finite element/lumped parameter model for quasi-static and dynamic analyses of planetary/epicyclic gear sets , 2006 .

[128]  Robert G. Parker,et al.  Natural Frequency Clusters in Planetary Gear Vibration , 2013 .

[129]  Robert G. Parker,et al.  Vibration of rings on a general elastic foundation , 2006 .

[130]  Robert G. Parker,et al.  Mesh Phasing Relationships in Planetary and Epicyclic Gears , 2004 .

[131]  R. August,et al.  Torsional Vibrations and Dynamic Loads in a Basic Planetary Gear System , 1986 .

[132]  Robert G. Parker,et al.  NON-LINEAR DYNAMIC RESPONSE OF A SPUR GEAR PAIR: MODELLING AND EXPERIMENTAL COMPARISONS , 2000 .

[133]  S. Vijayakar.  A combined surface integral and finite element solution for a three‐dimensional contact problem , 1991 .

[134]  Wim Desmet,et al.  Insights in wind turbine drive train dynamics gathered by validating advanced models on a newly developed 13.2 MW dynamically controlled test-rig , 2011 .

[135]  Robert G. Parker,et al.  SENSITIVITY OF PLANETARY GEAR NATURAL FREQUENCIES AND VIBRATION MODES TO MODEL PARAMETERS , 1999 .