计及弯曲刚度的印刷运动薄膜横向振动控制研究

Transverse Vibration Control of Moving Printing Membranes With Bending Stiffness

研究了不同边界条件下,计及弯曲刚度的轴向运动薄膜横向振动的主动控制问题.建立计及弯曲刚度的印刷运动薄膜的计算模型.利用有限差分法,对轴向运动薄膜的振动微分方程进行离散,推导出轴向运动矩形薄膜横向振动控制系统的状态方程.采用次最优控制法,对不同边界条件下轴向运动矩形薄膜横向振动进行主动控制研究.计算结果表明:采用次最优控制法能够在短时间内迅速、有效地降低运动薄膜的振动强度,并使之衰减趋近于0.作动器作用在固定位置点处时,对运动薄膜施加控制后,四边简支边界条件下的控制效果好.作动器作用在不同位置点处时,两种边界条件下中心点处的控制效果最好.计算证明次最优控制法能够有效地抑制印刷过程中计及弯曲刚度的轴向运动薄膜的横向振动,从而提高印刷套印精度,保证精密印刷质量.

The active control of transverse vibration of axially moving rectangular membranes with bending stiffness was investigated during the printing process. A computing model for the moving printing membrane with bending stiffness was established. The discretized dynamic equations for the moving membrane were obtained with the finite difference method,and the state equations of the transverse vibration control system for the moving membrane were derived. The suboptimal control method was applied to conduct the active control of transverse vibration of the moving membrane under various boundary conditions of actual printing processes. The calculated results showthat the vibration of the moving rectangular membrane can be controlled effectively within a short time with the suboptimal vibration control method.The control effect will be better when the actuators act on some fixed nodes with 4 edges simply supported; when the actuators act on variable nodes,the control effect will be the best in the case of central point actuation under the 2 types of boundary conditions,where the dimensionless time of velocity attenuation to zero is shorter than those in the other cases of actuation at the rest nodes. It is indicated that the transverse vibration of axially moving rectangular membranes can be controlled effectively with the suboptimal control method,thus the printing precision can be promoted and the printing quality ensured.