Mathematical Modeling of Geometric Variations to Integrate Parametric Computer Aided Design with Tolerance Analyses and Optimization

几何变化的数学建模，将参数化计算机辅助设计与公差分析和优化相结合

• 批准号: 9821008
• 负责人: Joseph Davidson
• 金额: $ 48.55万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-03-01 至 2002-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9821008&HistoricalAwards=false
• 关键词: Mathematical; Modeling; Geometric; Variations; Integrate

The objective of this project is to develop a new bi-level math model for geometric tolerances, that is, the range of variation in size and shape that can be permitted for a part to be acceptable when in use. At the local level, the new model would represent each tolerance zone for a plane or an axis (line) as a multidimensional region or map, and it would include the computational techniques that relate interdependencies between these regions and subregions within them. The mathematical model to be developed will include formulations for variations in size, form, orientation, position, and runout, and combinations of these, which can be modeled using points, lines, and planes. The primary method for the research is to use traditional mathematics for representing planes, lines, and points in a tolerance zone. At the global level, the proposed model interrelates all frames of reference on a part or an assembly. It will include a symbolic algebra that relates the degrees of freedom and constraints for a feature, such as a hole, to reference frames used when specifying dimensions and tolerances. In order to validate the integrated bi-level mathematical model and to demonstrate its feasibility and usefulness, a set of prototype software modules will be designed and implemented. If successful, the results of this research will impact the state-of-the-art for geometric tolerances and the productivity of designers who use the results. At the local level, the model will treat dimensional and geometric tolerances in three dimensions and in a manner consistent with the standard on tolerances that is universally accepted by practitioners, whereas existing models for tolerances are only partially satisfactory in being consistent with the standard. At the global level it is projected that the new model will provide a unique bridge between mathematical characterizations of features (planes, lines, and points) and existing parametric computer-aided design models and statistical tolerance software packages. It is projected that successful completion of the project will provide the designer with a tool for making better decisions about allocating geometric tolerances. The completed model also should permit designers to identify trade-offs and to optimize the allocation of tolerances. The impact should be a shorter design time, fewer iterations in the prototype phase of design, and hence lower cost.

该项目的目的是为几何公差开发新的双层数学模型，即，在使用时可以接受零件的大小和形状变化范围。 在本地级别，新模型将代表平面或轴（线）作为多维区域或地图的每个公差区，它将包括将这些区域与其中的子区域之间相互依存相关的计算技术。 要开发的数学模型将包括用于大小，形式，方向，位置和跳动的变化的配方，以及可以使用点，线和平面进行建模的这些模型。 该研究的主要方法是使用传统数学来代表公差区的平面，线和点。 在全球层面上，提出的模型将零件或组件上的所有参考框架相关联。 它将包括一个符号代数，该代数将特征的自由度和约束程度（例如孔）与指定尺寸和公差时使用的参考帧相关联。 为了验证集成的双层数学模型并证明其可行性和实用性，将设计和实施一组原型软件模块。 如果成功，这项研究的结果将影响使用结果的几何公差和设计师的生产力。 在本地层面，该模型将以三个维度对待维度和几何公差，并且与从业者普遍接受的公差标准相一致，而现有的公差模型仅在与标准一致的情况下部分令人满意。 在全球层面上，预计新模型将在功能（平面，线和点）的数学特征与现有参数计算机辅助设计模型和统计公差软件包之间提供独特的桥梁。 预计该项目的成功完成将为设计师提供一个关于分配几何公差的更好决策的工具。 完成的模型还应允许设计人员确定权衡并优化公差分配。 影响应该是一个较短的设计时间，在设计的原型阶段迭代较少，因此成本较低。