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

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凸有界区域中的点。当特征或公差在组件中叠加时，误差累积对应于所有贡献区域的Minkowski和（公差图），然后表示符合给定设计规范的整个组件群体。本研究将创造一种方法，使用这些地图的制造操作为基础的最坏情况计算工艺规划中的拟合地图对应的制造规范内对应于设计的地图。还将研究与生产相应特征的制造机器的特征相对应的频率分布的任何组合的公差累积的统计分析。同时，还将开发将三坐标测量机的检测数据直接拟合到这些数据中的方法，以及将其用于统计过程控制图中的方法。如果成功，本研究的结果将能够对公差标准进行精确的数学解释，从而防止制造计划和检测中的错误。在统计过程控制中使用地图将提供一种有效的可视化和诊断工具，不仅基于接近最坏情况的限制，而且基于完整的统计分析。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。这项工作也将产生适合教学的公差和计量学理论的材料。 据设想，这些新的数学模型将使未来的研究之间的相关性的制造过程中，如工具磨损，形状和尺寸的测量子集，连同其在地图中的位置。

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.