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Dynamic analysis of gear system under fractional-order PID control with the feedback of meshing error change rate

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Abstract

Based on the fractional-order proportional-integral-derivative (PID) control of the feedback of change rate of gear meshing error, the nonlinear dynamics problem of a spur gear pair is investigated. A model is established including backlash, time-varying stiffness, internal and external excitations and other factors, where the fractional-order PID control terms are also considered. The periodic solution is obtained based on the incremental harmonic balance method, and it is verified by the numerical solution. The effects of the coefficients and the orders of the fractional-order PID controller are analyzed in detail. The control performances of fractional-order PID controller and integer-order PID controller are compared. The results show that the fractional-order PID controller has good control performance for the gear meshing system. By changing the parameters of the controller, the resonance amplitude of the gear meshing system can be suppressed, and the resonance frequency of the gear meshing system can also be adjusted.

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Authors and Affiliations

  1. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Lei Liu & Jiangchuan Niu

  2. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Xianghong Li

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  1. Lei Liu
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  2. Jiangchuan Niu
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Correspondence to Jiangchuan Niu.

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Liu, L., Niu, J. & Li, X. Dynamic analysis of gear system under fractional-order PID control with the feedback of meshing error change rate. Acta Mech 229, 3833–3851 (2018). https://doi.org/10.1007/s00707-018-2194-3

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  • DOI: https://doi.org/10.1007/s00707-018-2194-3

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