带钢及其支承系统的参数振动分析

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In this paper, a vibration model is presented with the consideration of interactions between sheet metal and its sup- porting system. The nonlinear coupled dynamics equations are derived. The muhiple scale method and the Runge-Kutta meth- od are introduced to analyze the characteristics of sheet＇s vibration. The resuhs show that the primary parametric resonance of system is evoked by the tension＇s fluctuation. In the region of resonance, it can cause large vibration of sheet metal. At the same time, as the ratio of the frequency of top roller and sheet steel is about 2 （ that is r ≈ 2 ） , the sheet＇s characteristic is sub- stantial difference from that when 7- is far from 2 in the primary parametric resonance region. At this time, the vibration re- sponse of top roller is also considerable, even if the initial disturbance of top roller is small.考虑带钢及其支承的协同作用，建立带钢及其支承系统的振动模型，通过Galerkin方法得到带钢系统的常微分方程组，并运用多尺度法和龙格库塔法进行了研究。结果表明带钢末端张力波动时，会激起系统的主参数共振，引起带钢的大幅振动。当塔顶辊固有频率与带钢某阶固有频率的比值约为2（即r≈2）时，主参数共振区域特性与，r值远离于2的有本质的区别；此时，即使塔顶辊的初始扰动很小，塔顶辊的振动响应也会很大。