基于P型法的中间支承运动纸带横向振动特性研究

Vibration of a moving web with intermediate supports by a P-type method

北人PRC250凹版印刷机,其承印物-纸带为200~300 g/m^(2)的薄型纸板,多色印刷中的支承滚筒对印刷薄纸板形成中间支承和简支约束,可用板壳理论研究其动力学特性。该研究提出采用新型P型高阶微分求积升阶谱法求中间支承运动纸带动力学特性。根据Hamilton原理,推导运动纸带的能量泛函变分式,利用新构C1单元混合插值正交张量积形函数,对给出的能量泛函变分式进行求解,分析中间支承和速度对运动纸带横向振动特性的影响。结果表明:在对边简支对边自由约束条件下,运动纸带的复频率随中间支承的设置而增大,随速度的增大稳定区域逐渐变小;通过CAE软件Hypermesh有限元对比试验,证明该研究提出的方法求解中间支承运动纸带动力学特性,比有限元软件具有更良好的数值稳定性、平滑性和收敛性。

The substrate material of Beiren PRC250 printing machine is web of the weight of 200-300 g/m^(2),the supporting roller in the multi-color printing process was used as the intermediate support.In this paper,a new P-type higher order differential quadrature method was proposed to solve the vibration of a moving web with intermediate supports.According to the Hamilton principle,the energy expression of the moving web was deduced,the shape function of the element was generated by the interpolation of the newly constructed C1 element.The influence of intermediate support and velocity on transverse vibration of the moving web was analyzed.The results show that complex frequency of the paper tape increases with the setting of the intermediate support,and the stable region becomes smaller with the increase of the speed under the constraint of the simple support and the opposite side free movement.The comparative was carried out by the CAE software,and it is proved that the new method to solve the vibration of the intermediate support moving paper tape is better than finite element software.