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Nonsmooth Vibration Characteristic of Gear Pair System with Periodic Stiffness and Backlash

Author

Listed:
  • Minjia He
  • Shuo Li
  • Zhenjun Lin
  • Jinjin Wang
  • Shuang Liu
  • Ruolan Hao

Abstract

As the most widely used power transmission device in mechanical equipment, the vibration characteristics of gears have a very important influence on the working performance. It is of great theoretical and practical significance to study the vibration characteristics of gear system. In this paper, a gear transmission system model is set up in a forcefully nonlinear form; the continuity mapping and discontinuity mapping are utilized to analyze the nonsmooth vibration. Then, the sliding dynamics of separation boundaries is studied by using the perturbation method and the differential inclusion theory. In addition, the periodic response of gear pair system is illustrated and Floquet’s theory is presented to confirm the stability and bifurcation of periodic response. Concurrently, the maximal Lyapunov exponent is obtained to accurately determine the chaotic state in gear pair system, which is consistent with the bifurcation diagram and Poincare section. Finally, a reasonable explanation is given for the jump phenomenon in bifurcation diagram.

Suggested Citation

  • Minjia He & Shuo Li & Zhenjun Lin & Jinjin Wang & Shuang Liu & Ruolan Hao, 2018. "Nonsmooth Vibration Characteristic of Gear Pair System with Periodic Stiffness and Backlash," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-13, July.
    • Handle: RePEc:hin:jnddns:3498057
    DOI: 10.1155/2018/3498057
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