Stability analysis of the printing cardboard with moving speed
WU Jimei1，2, SHAO Mingyue1, WANG Yan3, WU Qiumin2, ZHU Libin2
1.Faculty of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an 710048, China;
2.Faculty of Printing. Packing and Digital Media Engineering, Xi’an University of Technology, Xi’an 710048, China;
3.School of Civil Engineering and Architecture, Xi’an University of Technology, Xi’an 710048, China
The printing cardboard substrate with gram weight of 250 g/m2 of Shaanxi Beiren PRC250 cigarette package special type of gravure printing unit was taken as the research object. The printing cardboard with a certain thickness and a certain flexural rigidity was simplified as a thin plate model based on the moving thin plate theory. The stability of the printing cardboard with moving speed was studied. The dynamic model of moving printing cardboard was established. The transverse vibration differential equation of moving printing cardboard was obtained by the energy method and the variational principle. The transverse vibration differential equation was discretized using the Galerkin meshless method. Then the complex characteristic equation was obtained. The effects of different boundary conditions on the dynamic stability region of the moving printing cardboard were discussed by numerical calculation. The divergence instability critical speed of the printing cardboard of PRC250 cigarette package special type of gravure printing unit was obtained, which conforms to the boundary conditions with two opposite edges simply supported and the other two opposite sides free. And the divergence instability critical speed is 27.55 m/s. This conclusion provides a theoretical basis for the determination of the stable working range and structural optimization of the printing equipments.
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