Fundamental Development of Mathematical Techniques and Computational Metrology for Coordinate Metrology

坐标计量数学技术和计算计量学的基础发展

• 批准号: 9988664
• 负责人: Thomas Kurfess
• 金额: $ 28.29万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9988664&HistoricalAwards=false
• 关键词: Fundamental; Development; Mathematical; Techniques; Computational

The goal of this research project is to advance mathematical and computational geometry tools to effectively and efficiently determine if the geometry of an artifact meets the target geometry that is specified. To achieve this task two primary objectives will be pursued. The first is the development of point-to-surface assignment based on a linearly faceted geometric model using a modified Voronoi diagram technique. A mathematical proof demonstrating that the faceted model in conjunction with the computational metrology techniques developed in this research will be developed to prove that the point-to-surface assignment is correct for the true (non-faceted) model. The second major objective is to derive the analytic partial derivatives for spline surfaces of any order. These partial derivatives will be tested against both numerical derivatives as well as currently used approximation techniques for both speed and accuracy. Finally, to demonstrate that the fundamental developments in mathematics and computational metrology are realistic and of use, they will be implemented and tested on a variety of industrial applications. If successful, the results of this research will provide faster and more accurate analyses of manufactured parts. The mathematics developed in this research to precisely align points to complex geometric surface models will permit improved analysis of parts such as complex injection molds and airfoil geometries. Furthermore, the techniques to be developed will also substantially reduce the computational time necessary to inspect complex geometries that have been made feasible via new manufacturing techniques, such as rapid prototyping. It is anticipated that the accuracy and speed results of this research will provide the enabling technology to directly and economically integrate optical and tactile scanning technology into production facilities such as automotive and aerospace facilities for use in real-time feedback for quality control.

该研究项目的目的是推进数学和计算几何工具，以有效有效地确定工件的几何形状是否符合指定的目标几何形状。为了实现这项任务，将实现两个主要目标。首先是使用修改的Voronoi图技术基于线性的几何模型的点对面分配的开发。一项数学证明，表明该研究中开发的刻面模型与计算计量技术结合使用，以证明对真实（非面孔）模型的点对面分配是正确的。第二个主要目标是为任何顺序的样条表面得出分析部分衍生物。这些部分衍生物将针对数值衍生物进行测试，以及目前使用近似技术的速度和准确性测试。最后，为了证明数学和计算计量学方面的基本发展是现实的且使用的，它们将在各种工业应用上进行实施和测试。 如果成功，这项研究的结果将为制造零件提供更快，更准确的分析。在这项研究中开发的数学是确切地与复杂的几何表面模型保持一致，将允许对诸如复杂注入模具和翼型几何形状等零件的分析进行改进。此外，要开发的技术还将大大减少检查通过新制造技术（例如快速原型制造）可行的复杂几何形状所需的计算时间。可以预料，这项研究的准确性和速度结果将为有利的技术直接和经济地将光学和触觉扫描技术直接整合到生产设施中，例如汽车和航空航天设施，用于实时反馈以进行质量控制。