The geometry and frequency content of planetary gear single-mode vibration

Abstract The geometry and frequency content of single-mode vibrations of spur planetary gears are investigated in the rotating carrier-fixed and the stationary reference frames. Planetary gears with equally spaced or diametrically opposed planets have exactly three mode types, called planet, rotational, and translational modes. The properties of these vibration modes lead to response with well-defined geometry. The frequency content of the motion differs between the rotating carrier-fixed and stationary bases. The results from this work assist the analysis of experimental planetary gear measurements.

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

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

[3]  David J. Ewins,et al.  Modal Testing: Theory, Practice, And Application , 2000 .

[4]  E. F. Crawley,et al.  Analytical and Experimental Investigation of the Coupled Bladed Disk/Shaft Whirl of a Cantilevered Turbofan , 1986 .

[5]  L. Meirovitch A Modal Analysis for the Response of Linear Gyroscopic Systems , 1975 .

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

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

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

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

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

[11]  D. J. Ewins,et al.  Modal analysis and testing of rotating structures , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

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

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

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

[15]  Giancarlo Genta,et al.  Whirling of unsymmetrical rotors: A finite element approach based on complex co-ordinates , 1988 .

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

[17]  I. Y. Shen,et al.  Ground-Based Vibration Response of a Spinning, Cyclic, Symmetric Rotor With Gyroscopic and Centrifugal Softening Effects , 2009 .

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

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

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

[21]  J. Casey,et al.  A tensor method for the kinematical analysis of systems of ridid bodies , 1986 .

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

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

[24]  K. T. Chan,et al.  Revolving superposed standing waves in a spinning Timoshenko Beam , 2012 .

[25]  S. A. Tobias,et al.  The Influence of Dynamical Imperfection on the Vibration of Rotating Disks , 1957 .

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

[27]  James Casey,et al.  A Treatment of Rigid Body Dynamics , 1983 .

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

[29]  Chong Won Lee,et al.  MODAL CHARACTERISTICS OF ASYMMETRICAL ROTOR-BEARING SYSTEMS , 1993 .

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

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

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

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

[34]  P. C. Hughes,et al.  Dynamics of Gyroelastic Continua , 1984 .

[35]  P. J. Brosens,et al.  Whirling of Unsymmetrical Rotors , 1961 .

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

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

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

[39]  A. Galip Ulsoy,et al.  Vibration Localization in Rotating Shafts, Part 1: Theory , 1995 .