Vibration of Planetary Gears Having an Elastic Continuum Ring Gear

.............................................................................................................................. ii Dedication .......................................................................................................................... iv Acknowledgments............................................................................................................... v Vita ..................................................................................................................................... vi Table of

[1]  Jonathan A. Wickert,et al.  Spatial Modulation of Repeated Vibration Modes in Rotationally Periodic Structures , 2000 .

[2]  F. M. Detinko.  Free vibration of a thick ring on multiple supports , 1989 .

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

[4]  R. August,et al.  Gear mesh stiffness and load sharing in planetary gearing , 1984 .

[5]  Robert G. Parker,et al.  Nonlinear Dynamics of Planetary Gears With Equal Planet Spacing , 2007 .

[6]  G. V. Tordion,et al.  Dynamic Stability of a Two-Stage Gear Train Under the Influence of Variable Meshing Stiffnesses , 1977 .

[7]  Robert G. Parker,et al.  Mesh Phasing Relationships in Planetary and Epicyclic Gears , 2003 .

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

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

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

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

[12]  T. Y. Yang,et al.  Natural frequencies and modes of rings that deviate from perfect axisymmetry , 1986 .

[13]  R. Parker,et al.  Nonlinear dynamics of idler gear systems , 2008 .

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

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

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

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

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

[19]  Rajendra Singh,et al.  Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system , 1991 .

[20]  Rajendra Singh,et al.  Non-linear dynamics of a geared rotor-bearing system with multiple clearances , 1991 .

[21]  C. D. Mote,et al.  Exact Boundary Condition Perturbation Solutions in Eigenvalue Problems , 1996 .

[22]  V. R. Murthy,et al.  Dynamic characteristics of stiffened rings by transfer matrix approach , 1975 .

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

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

[25]  Marco Amabili,et al.  DYNAMIC ANALYSIS OF SPUR GEAR PAIRS: STEADY-STATE RESPONSE AND STABILITY OF THE SDOF MODEL WITH TIME-VARYING MESHING DAMPING , 1997 .

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

[27]  Robert G. Parker,et al.  Mesh Stiffness Variation Instabilities in Two-Stage Gear Systems , 2002 .

[28]  M. Savage,et al.  Effects of rim thickness on spur gear bending stress , 1991 .

[29]  A. K. Mallik,et al.  Free vibration of thin circular rings on periodic radial supports , 1977 .

[30]  Robert G. Parker,et al.  Exact boundary condition perturbation for eigensolutions of the wave equation , 1998 .

[31]  C.H.J. Fox,et al.  A simple theory for the analysis and correction of frequency splitting in slightly imperfect rings , 1990 .

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

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

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

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

[36]  Timothy L. Krantz.  Mechanical Systems Technology Branch research summary, 1985 - 1992 , 1993 .

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

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

[39]  B. L. Dhoopar,et al.  Free vibration of circular rings on radial supports , 1979 .

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

[41]  Fred B. Oswald,et al.  Influence of tooth profile modification on spur gear dynamic tooth strain , 1995 .

[42]  J.-G. Tseng,et al.  On the Vibration of Bolted Plate and Flange Assemblies , 1994 .

[43]  C. D. Mote,et al.  Vibration and parametric excitation in asymmetric circular plates under moving loads , 1987 .

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

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

[46]  Ahmet Kahraman,et al.  Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: sub-harmonic motions , 2005 .

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

[48]  R. Parker,et al.  Vibration and Coupling Phenomena in Asymmetric Disk-Spindle Systems , 1996 .

[49]  Jonathan A. Wickert,et al.  MEASUREMENT AND ANALYSIS OF MODULATED DOUBLET MODE RESPONSE IN MOCK BLADED DISKS , 2002 .

[50]  Robert G. Parker,et al.  Exact Perturbation for the Vibration of Almost Annular or Circular Plates , 1996 .

[51]  K. B. Sahay,et al.  Vibration of a stiffened ring considered as a cyclic structure , 1972 .

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

[53]  Jonathan A. Wickert,et al.  Response of modulated doublet modes to travelling wave excitation , 2001 .

[54]  Radoslaw Zimroz,et al.  Vibration condition monitoring of planetary gearbox under varying external load , 2009 .

[55]  Singiresu S. Rao,et al.  In-Plane Flexural Vibrations of Circular Rings , 1969 .

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

[57]  F. B. Oswald,et al.  Vibration in Planetary Gear Systems with Unequal Planet Stiffnesses , 1982 .

[58]  T. J. McDaniel.  Dynamics of Circular Periodic Structures , 1971 .

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

[60]  Ahmet Kahraman,et al.  Experiments on Nonlinear Dynamic Behavior of an Oscillator With Clearance and Periodically Time-Varying Parameters , 1997 .

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