PLANETARY GEAR PARAMETRIC INSTABILITY CAUSED BY MESH STIFFNESS VARIATION

Abstract Parametric instability is investigated for planetary gears where fluctuating stiffness results from the changing contact conditions at the multiple tooth meshes. The time-varying mesh stiffnesses of the sun–planet and ring–planet meshes are modelled as rectangular waveforms with different contact ratios and mesh phasing. The operating conditions leading to parametric instability are analytically identified. Using the well-defined properties of planetary gear vibration modes, the boundaries separating stable and unstable conditions are obtained as simple expressions in terms of mesh parameters. These expressions allow one to suppress particular instabilities by adjusting the contact ratios and mesh phasing. Tooth separation from parametric instability is numerically simulated to show the strong impact of this non-linearity on the response.

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

[2]  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 .

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

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

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

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

[7]  Ahmet Kahraman,et al.  INTERACTIONS BETWEEN COMMENSURATE PARAMETRIC AND FORCING EXCITATIONS IN A SYSTEM WITH CLEARANCE , 1996 .

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

[9]  A. Seireg,et al.  Factors Influencing Instability and Resonances in Geared Systems , 1981 .

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

[11]  A. Seireg,et al.  Simulation of Resonances and Instability Conditions in Pinion-Gear Systems , 1978 .

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

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

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

[15]  J. W. Evans,et al.  An Extended Model for Determining Dynamic Loads in Spur Gearing , 1981 .

[16]  A. Seireg,et al.  Normal Mode Uncoupling of Systems with Time Varying Stiffness , 1980 .