Nonlinear Vibration Analysis Of Sink Roll In The Zinc Pot Of A Continuous Galvanizing Line

The vibration of a sink roll in the zinc pot of a continuous galvanizing line not only affects the quality of galvanized products, but also accelerates the wear of bearings in the ends of the roll. Based on nonlinear vibration analysis, this paper investigates the vibration mechanism of the sink roll in a hot-dip galvanizing line. Results lay a theoretical foundation for proposing the treatment scheme of the vibration of the sink roll. The main research is shown as follows:Firstly, the structure which contains a steel strip from No.4 hot tension roller to a correcting roll, a sink roll and sliding bearings is taken as research object. On the basis of comprehensive analysis of the motion and force, a mechanical model which contains whirl and rotational vibration is established. Furthermore, the D'Alembert principle is used to derive the nonlinear dynamic equations. By analyzing the system's equilibrium, the dynamic equations with respect to the static equilibrium position are developed.Then, without considering the case of external excitation, the stability analysis of the sink roll is performed by the Lyapunov stability theory. Then the stability criterion is deduced, which could provide the reference for regulating the initial tension of steel strip and the engagement of the correcting roll to achieve the stability of the sink roll. In combination with the production practice, stable operation ranges of initial tension of the steel strip and engagement of the correcting roll are obtained. Numerical method is applied to analyze the effects of working parameters on natural frequencies of the derived system. Results indicate that the two order natural frequencies show opposite variation trend with respect to the initial tension of the strip, engagement of the correcting roll and friction coefficient of the sliding bearing.Finally, by considering the excitation of the correcting roll, the nonlinear dynamic equation of the sink roll is established. Furthermore, multiple scales method and Runge-Kutta method are applied to analyze the vibration characteristics of the sink roll analytically and numerically. Results demonstrate that the forced linear coupling resonance of the sink roll occurs when the excitation frequency of the correcting roll is close to a certain order natural frequency of the derived system and the relationship of the two order natural frequencies is not 2 times. However, the forced nonlinear coupling resonance with one to two internal resonance will be activated when the excitation frequency of the correcting roll is close to one certain order natural frequency of the derived system and the relationship of the two order natural frequencies is 2 times. The other mode of the 2-degree-of-freedom system may be aroused, even if the external excitation acts on one certain order mode directly. Compared with the linear system, the forced vibration of the sink roll with 1:2 internal resonance has the following characteristics: Compared with the linear system, the forced vibration under 1:2 internal resonance has the following characteristics: 1) When two order natural frequencies of the system are close to two times and the ratio is certain, the amplitude frequency curves of two degrees of freedom have an anti-resonance point near the first order natural frequency. So that number of the peak of amplitude frequency curve changes from one to two. Besides, with the increase of the natural frequency ratio, the left and right peaks of the amplitude frequency curve showing the shift phenomenon: the left one drops, the right one rises. 2) Near the anti-resonance point, the system has three steady state structures, which means three stable periodic solutions coexist. Parametric resonance of the sink roll with one to two internal resonance could occur when the excitation frequency of the correcting roll approach two times of a certain order natural frequency of the derived system and the relationship of the two order natural frequencies is 2 times. The trivial solution is destabilized by pitchfork bifurcation and produces non-trivial solutions with the increase of the excitation amplitude. The increase of damping not only causes the rise of threshold of excitation amplitude that results in pitchfork bifurcation, but also leads to the decrease of vibration amplitude of the sink roll. Due to the existence of squares, positive and negative amplitudes of parametric vibrations of the sink roll deviate from the equilibrium position. In the process of actual production, internal resonance can be avoided by adjusting the initial tension of the strip and the engagement of the correcting roll, and the friction characteristics of the sliding bearing can be improved as well.