Continuous Manufacturing Process for Folded Sheet Materials

该项目的目标是开发一种连续的生产制造工艺，将平板折叠成复杂的三维图案，使用基于数学对称的新型材料流。研究将涉及机器的设计和构造，以及对材料折叠机制的数学理论的仔细分析。先前的探索性研究表明，金属、聚合物和纸张可以单独通过折叠技术折叠成双周期曲面，并建立了数学理论来解释一类dpf的折叠过程，并将这些方法扩展到描述显式面几何和顶点位置的实用算法中。这个项目的重点是用数学方法描述材料是如何在机器的主辊系统中转化为复杂的三维图案的，并结合折叠折痕的迁移和定位知识，使我们能够简化制造过程，以快速和高质量地生产这些多功能折叠结构。数学与工程的跨学科结合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进步提供了许多机会。

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.