惯性边界下带钢的非线性振动分析  

Nonlinear vibration of strip steel under inertial boundary conditions

作　　者：高崇一[1] 杜国君[1] 李建雄[2] 胡发科 

机构地区：[1]燕山大学河北省重型装备与大型结构力学可靠性重点实验室,河北秦皇岛066004 [2]燕山大学电气工程学院自动化系,河北秦皇岛066004

出　　处：《振动与冲击》2016年第1期5-10,共6页Journal of Vibration and Shock

基　　金：河北省教育厅科学研究计划重点项目(ZD2015077);河北省高等学校创新团队领军人才培育计划项目(LJRC013);国家自然科学基金资助项目(61403332)

摘　　要：根据连轧机轧制过程中带钢与轧辊的运动机理,将相邻两机架间的带钢简化为轴向运动的Euler梁,轧辊简化为定轴转动的惯性元件,建立Euler梁在惯性边界下的非线性振动力学模型。基于哈密顿原理建立轴向运动Euler梁的纵向和横向非线性振动微分方程,利用Kantorovich时间平均法简化运动方程和边界条件,并采用修正迭代法求解运动方程。最后通过数值计算获得了Euler梁非线性振动的幅频响应曲线,并讨论惯性边界条件下的轴向运动速度、长度和轧辊的转动惯量对Euler梁振动特性的影响。研究结果可为控制和分析连轧过程中带钢垂直振动提供重要的理论参考。According to the strip steel between two neighboring movement mechanism of strip steel and rollers in rolling process of a tandem mill, the stands was simplified to an axially moving Euler beam and rollers were simplified to inertia components rotating about a fixed axis, the nonlinear vibration mechanical model of the beam under inertial boundary conditions was established. The longitudinal and lateral Vibration equations of the beam were derived with Hamilton principle. Kantorovich averaging method was used to simplify the motion equations and the inertial boundaries, and the modified iteration method was employed to solve the motion equations. Finally, based on the results of numerical calculation, the amplitude-frequency response curves of the beam were obtained, and the influences of beam axial velocity, beam length and rotational inertia of roller on the vibration performance of the beam under conditions of inertial boundary were discussed. The results provided an important theoretical reference for controlling and analyzing the vertical vibration of strip steel in a continuous rolling process.

关 键 词：Euler梁 惯性边界 带钢 垂直振动 修正迭代法 

分 类 号：TH113.1[机械工程—机械设计及理论] TG333.11[金属学及工艺—金属压力加工]