Continuous Manufacturing Process for Folded Sheet Materials

该项目的目标是开发一种连续生产制造过程，用于将平板折叠成复杂的三维图案，该图案使用基于数学对称的新型材料流。 调查将涉及机器的设计和建设，并仔细分析的数学理论的材料折叠机制。以往的探索性研究表明，金属、聚合物和纸张都可以通过折叠技术折叠成双周期曲面，并建立了解释一类DPFs折叠过程的数学理论，将这些方法推广到描述显式小平面几何和顶点位置的实用算法中。该项目的重点是从数学上描述材料如何在机器的主辊系统内转化为复杂的三维图案，并了解折叠折痕的迁移和设置，使我们能够简化制造过程，快速和高质量地生产这些多功能折叠结构。将数学和工程联系起来的跨学科努力将使这两个领域的教育受益，并为制造集成和应用数学探索的发展提供了许多机会。

The objective of this project is to develop a continuous production manufacturing process for folding flat sheets into complex three dimensions patterns that uses a novel material flow based upon mathematical symmetry. The investigation will involve machine design and construction, and a careful analysis of the mathematical theory of the material folding mechanisms. Previous exploratory research has demonstrated that metal, polymer and paper sheets can folded into doubly periodic surfaces by folding techniques alone, and established the matematical theory to explain the folding process for one class of DPFs and to extend these methods into practical algorithms describing the explicit facet geometry and vertex locations. The focus of this project is to describe mathematically how the material transforms into the intricate three dimensions patterns inside the main roller system of the machine, complete with the knowledge of the migration and instating of fold creases, to enable us to streamline the manufacturing process for rapid and high quality production of these versatile folded structures. The interdisciplinary effort linking mathematics and engineering will benefit education in both areas with numerous opportunities for advancement of manufacturing integration and applied mathematics exploration.