WANG Shu-guo, ZHANG Yan-bo, LIU Wen-liang, GUO Li-feng, LIAO Peng-tai, QI Li-mei. Nonlinear Vibration Bifurcation Characteristics of Multi-Clearance 2-Stage Gear Systems[J]. Applied Mathematics and Mechanics, 2016, 37(2): 173-183. doi: 10.3879/j.issn.1000-0887.2016.02.006
Citation: WANG Shu-guo, ZHANG Yan-bo, LIU Wen-liang, GUO Li-feng, LIAO Peng-tai, QI Li-mei. Nonlinear Vibration Bifurcation Characteristics of Multi-Clearance 2-Stage Gear Systems[J]. Applied Mathematics and Mechanics, 2016, 37(2): 173-183. doi: 10.3879/j.issn.1000-0887.2016.02.006

Nonlinear Vibration Bifurcation Characteristics of Multi-Clearance 2-Stage Gear Systems

doi: 10.3879/j.issn.1000-0887.2016.02.006
  • Received Date: 2015-09-16
  • Rev Recd Date: 2015-11-02
  • Publish Date: 2016-02-15
  • A 5-DOF nonlinear vibration model for multi-clearance 2-stage gear systems was established with the lumped-mass method. In view of transmission errors, time-varying meshing stiffness and multiple gear clearances, the dimensionless dynamic equations for the system were derived. By means of the Poincaré maps and bifurcation diagrams, the bifurcation properties of the system were discussed under the effects of the rotation rate and the damping ratio. Given the various nonlinear factors, the 2-stage gear system exhibits rich and complex bifurcation characteristics. With the changes of the related parameters, the system will be in short-period motion, or long-period motion, or quasi-periodic motion or chaotic motion. For different damping ratios, with the decrease of the rotation rate, the system state changes from stable period-1 motion into stable period-2 motion through period-doubling bifurcation; then the system state changes into quasi-periodic motion through the Hopf bifurcation, in turn changes into stable period-1 motion after a catastrophe; finally the system enters into chaos through the Hopf bifurcation-phase locking. Moreover, with the increase of the rotation rate, the system damping ratio range corresponding to chaotic motions reduces, and the system will be in stable period-1 motion, or long-period motion or quasi-periodic motion, while the damping ratio range corresponding to long-period motion and quasi-periodic motion shortens and that corresponding to period-1 motion lengthens.
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