Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency Excitations
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 equatio...
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MDPI AG
2023-03-01
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| Online Access: | https://www.mdpi.com/2227-7390/11/7/1626 |
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| author | Li Jiang Tao Wang Qing-Xue Huang |
| author_facet | Li Jiang Tao Wang Qing-Xue Huang |
| author_sort | Li Jiang |
| collection | DOAJ |
| description | 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 <i>p</i> = 0.3 or 1.0, and single resonance occurs while <i>p</i> = 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. |
| first_indexed | 2024-03-11T05:30:24Z |
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| language | English |
| last_indexed | 2024-03-11T05:30:24Z |
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| spelling | doaj.art-243dc61fd2e44eafb89a2574a2dd5b922023-11-17T17:08:20ZengMDPI AGMathematics2227-73902023-03-01117162610.3390/math11071626Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency ExcitationsLi Jiang0Tao Wang1Qing-Xue Huang2School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, ChinaCollege of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, ChinaSchool of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, ChinaIn 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 <i>p</i> = 0.3 or 1.0, and single resonance occurs while <i>p</i> = 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.https://www.mdpi.com/2227-7390/11/7/1626roller systemfractional-orderpitchfork bifurcationvibration resonance |
| spellingShingle | Li Jiang Tao Wang Qing-Xue Huang Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency Excitations Mathematics roller system fractional-order pitchfork bifurcation vibration resonance |
| title | Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency Excitations |
| title_full | Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency Excitations |
| title_fullStr | Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency Excitations |
| title_full_unstemmed | Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency Excitations |
| title_short | Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency Excitations |
| title_sort | resonance analysis of horizontal nonlinear vibrations of roll systems for cold rolling mills under double frequency excitations |
| topic | roller system fractional-order pitchfork bifurcation vibration resonance |
| url | https://www.mdpi.com/2227-7390/11/7/1626 |
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