波纹辊轧机辊系主共振时滞反馈控制

金属复合板波纹辊轧制成形是一项变革技术,在复合板轧制成形的过程中,轧制界面的非线性阻尼以及上下波纹辊之间的非线性刚度都可能导致主共振的发生,造成辊缝的波动.考虑了波纹辊轧机波纹界面间的非线性阻尼和非线性刚度,建立了波纹辊轧机两自由度垂直非线性数学模型.利用奇异值理论和相平面法讨论了波纹辊轧机辊系自治下的稳定性,运用多尺度法求解了波纹辊轧机辊系在波纹界面激励下主共振的解析近似解和幅频特性方程.分析了非线性刚度系数、非线性阻尼系数、系统阻尼系数、轧制力的幅值等参数对主共振的影响.设计了线性和非线性复合作用的时滞反馈控制器来对波纹辊系的主共振进行控制,并且通过数值仿真验证了控制器设计的正确性和可行性.

Principal resonance time-delay feedback control of roller system in corrugated rolling mills

The composite sheet corrugated roll rolling technology is a revolutionary technology, the roll shape curve of corrugated roller is a cosine function curve. During the rolling process of composite plate, the nonlinear damping of the rolling interface and the nonlinear stiffness between corrugated roll and flat roll may cause principal resonance, resulting in the fluctuation of roll gap. Considering the nonlinear damping and nonlinear stiffness within corrugated interface of corrugated rolling mill, establish the mathematical model of the two-freedom-degree vertical nonlinear of roller system in corrugated rolling mills. The stability of roller autonomous system of corrugated rolling mill is discussed by using singular value theory. The approximate analytical solution and amplitude-frequency characteristic equations of principal resonance of roller system excited by corrugated interface are carried out by using the multiple-scale method. The influences of nonlinear stiffness coefficient, nonlinear damping coefficient, system damping coefficient and rolling force amplitude on vibration are analyzed. The time-delay feedback controller with linear and nonlinear interactions is designed to control the principal resonance of the corrugated roll system, and the correctness and feasibility of the controller are verified by numerical simulation.