Manufacturing Maps: A New Math Model for 3-D Tolerance Analyses in Process Planning, CMM Inspection and Statistical Process Control

制造图：用于工艺规划、CMM 检查和统计过程控制中 3D 公差分析的新数学模型

• 批准号: 0700878
• 负责人: Joseph Davidson
• 金额: --
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0700878&HistoricalAwards=false
• 关键词: Manufacturing; Maps; New; Math; Model

The research objective of this award is to develop mathematical models for manufacturing variations. In these models, dimensional and geometric variations on manufacturing features will be mapped to points in convex bounded regions in higher dimensional space. When features or tolerances stack-up in an assembly, error accumulation corresponds to Minkowski sums of all contributing regions (Tolerance Maps), which then represent the entire population of assemblies conforming to the given design specification. This research will create a method for using these maps for manufacturing operations based worst-case calculation in process planning by fitting maps corresponding to manufacturing specification inside maps corresponding to design. Statistical analysis of tolerance accumulation for any combination of frequency distribution corresponding to characteristics of manufacturing machines producing the corresponding features will also be investigated. Methods for direct fitting of inspection data from coordinate measuring machines into these and a methodology for using them in statistical process control maps will also be developed.If successful, the results of this research will enable precise mathematical interpretation of the tolerance standards, consequently preventing errors in manufacturing planning and inspection. Maps use in statistical process control will provide an effective visualization and diagnostic tool, based not just on proximity to worst case limits, but also on full statistical analysis. There is potential for this new method to streamline the analysis of Coordinate Measuring Machine data to where it can be an integral part of the feedback for statistical process control. This work will also generate material suitable for teaching the theory of tolerancing and metrology. It is envisioned that these new math models will enable future research on correlations between parameters of a manufacturing process, such as tool wear, and the shape and size of the measured subset, together with its location within the map.

该奖项的研究目标是开发制造变化的数学模型。在这些模型中，制造特征的尺寸和几何变化将被映射到高维空间中的凸有界区域中的点。当特征或公差在装配体中叠加时，误差累积对应于所有贡献区域（公差图）的 Minkowski 总和，从而代表符合给定设计规范的整个装配体群体。这项研究将创建一种方法，通过将与制造规范相对应的地图拟合到与设计相对应的地图内，将这些地图用于工艺规划中基于最坏情况计算的制造操作。还将研究与产生相应特征的制造机器的特征相对应的任何频率分布组合的公差累积的统计分析。还将开发将坐标测量机的检测数据直接拟合到这些数据中的方法以及在统计过程控制图中使用它们的方法。如果成功，这项研究的结果将能够对公差标准进行精确的数学解释，从而防止错误制造计划和检查。统计过程控制中使用的地图将提供有效的可视化和诊断工具，不仅基于接近最坏情况限制，而且还基于全面的统计分析。这种新方法有可能简化坐标测量机数据的分析，使其成为统计过程控制反馈的一个组成部分。这项工作还将生成适合教授公差和计量理论的材料。 预计这些新的数学模型将有助于未来研究制造工艺参数（例如工具磨损）与测量子集的形状和尺寸及其在地图中的位置之间的相关性。