基于印版–承印物协同作用的柔性版印刷压力计算模型

A Flexographic Printing Pressure Calculation Model Based on the Synergy between Printing Plate and Substrate

摘要: 针对传统柔性版印刷压力计算模型中忽略承印物力学贡献导致计算精度不足的问题，提出了一种基于印版–承印物协同作用的压力计算修正方法。该方法基于赫兹非线性接触理论，将传统的“圆柱–圆柱”接触模型重构为“圆柱–薄板–圆柱”接触模型，创新性地提出了形变量分离法，将接触区域的总形变解耦为印版形变量与承印物形变量。通过引入文克勒地基模型，推导了包含承印物厚度与弹性模量参数的印刷压力解析式，并利用有限元仿真验证了模型的准确性。研究结果表明，尽管PET承印物的形变仅在微纳米级别，但其高弹性模量显著改变了接触区的等效刚度；引入承印物参数后，计算得出的印刷压力较传统模型明显增加。理论计算值与有限元仿真值在变化趋势上保持高度一致，相对误差在合理范围内。该研究揭示了薄承印物对印刷压力的非线性增益机制，为高精密柔性版印刷压力控制系统的设计提供了更精确的理论依据。

Abstract: To address the insufficient calculation accuracy of traditional flexographic printing pressure models caused by ignoring the mechanical contribution of the substrate, a modified pressure calculation method based on the synergy between the printing plate and substrate is proposed. This method, grounded in Hertzian nonlinear contact theory, reconstructs the traditional “cylinder-cylinder” contact model into a “cylinder-thin plate-cylinder” contact model, and innovatively introduces a deformation separation method to decouple the total deformation of the contact area into printing plate deformation and substrate deformation. By incorporating the Winkler foundation model, an analytical formula for printing pressure including parameters of substrate thickness and elastic modulus is derived, and the accuracy of the model is verified through finite element simulation. The results indicate that although the deformation of the PET substrate is only at the micro- to nanometer scale, its high elastic modulus significantly alters the equivalent stiffness of the contact area; after introducing substrate parameters, the calculated printing pressure is notably higher than that from traditional models. The theoretical calculation values are highly consistent with the finite element simulation results in terms of variation trend, and the relative error is within a reasonable range. This study reveals the nonlinear gain mechanism of thin substrates on printing pressure, providing a more accurate theoretical basis for the design of high-precision flexographic printing pressure control systems.