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Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency Excitations

Author

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  • Li Jiang

    (School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China
    College of Intelligent Manufacturing, Chengdu Technological University, Chengdu 611730, China)

  • Tao Wang

    (College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, China
    Engineering Research Center of Advanced Metal Composites Forming Technology and Equipment of Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China)

  • Qing-Xue Huang

    (School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China
    College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, China
    Engineering Research Center of Advanced Metal Composites Forming Technology and Equipment of Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China)

Abstract

In this paper, the fractional order differential terms are introduced into a horizontal nonlinear dynamics model of a cold mill roller system. The resonance characteristics of the roller system under high-frequency and low-frequency excitation signals are investigated. Firstly, the dynamical equation of the roller system with a fractional order is established by replacing the normal damping term with a fractional damping term. Secondly, the fast-slow variable separation method is introduced to solve the dynamical equation. The amplitude frequency response characteristics of the system are analyzed. The study finds that there are three equilibrium points. The characteristics of the three equilibrium points and the critical forces causing the bifurcation are investigated. Due to the different orders of the fractional derivatives, various new resonant phenomena are found in the systems with single-well and double-well potentials. Additionally, the double resonance occurs while p = 0.3 or 1.0, and single resonance occurs while p = 1.8. Unlike integer order systems, the critical resonance amplitude of high-frequency signals in fractional order systems depends on the damping strength and is influenced by the fractional order damping. This study provides a broader picture of the vibration characteristics of the roll system for rolling mills.

Suggested Citation

  • Li Jiang & Tao Wang & Qing-Xue Huang, 2023. "Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency Excitations," Mathematics, MDPI, vol. 11(7), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1626-:d:1109198
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    References listed on IDEAS

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    1. Hashemizadeh, E. & Ebrahimzadeh, A., 2018. "An efficient numerical scheme to solve fractional diffusion-wave and fractional Klein–Gordon equations in fluid mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1189-1203.
    2. Yan, Zhi & Wang, Wei & Liu, Xianbin, 2018. "Analysis of a quintic system with fractional damping in the presence of vibrational resonance," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 780-793.
    3. Dang, Rongqi & Chen, Yiming, 2021. "Fractional modelling and numerical simulations of variable-section viscoelastic arches," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    4. Yang, Yongge & Xu, Wei & Gu, Xudong & Sun, Yahui, 2015. "Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 190-204.
    5. Ghayesh, Mergen H. & Amabili, Marco & Farokhi, Hamed, 2013. "Two-dimensional nonlinear dynamics of an axially moving viscoelastic beam with time-dependent axial speed," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 8-29.
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