SBIR Phase I: Tolerance Analysis Using a Unifying Constraint Theory for Variational Geometric Modeling

这个小企业创新研究（SBIR）第一阶段项目致力于三维公差分析的统一数学框架，该框架可以量化基于设计规范和相关制造过程的产品变化流。这一创新的标志是一个几何约束方程系统，它是运动自由度（DOF）的函数。由于几何拓扑、公差和制造过程，这些约束定义了特征、组件和零件到零件（装配）关系的可行空间。求解特定的齐次变换矩阵的方程集，这些矩阵系统地改变了基于特征的装配模型的特征和组件，从而允许对尺寸要求进行准确的计算和评估。该创新将为特征、组件和装配级别的变分建模提供统一的演算，第一阶段强调关键的装配级别。这种创新的总体好处包括：建立应用程序基础、易用性和容忍度分析的吸引力，以及与计算机辅助工程（CAE）系统实现令人信服的同步。计算机辅助公差分析在机械和电气系统的设计和制造、稳健的产品和工艺设计、同步工程、快速原型制作和产品质量提高等方面的应用有望得到应用。

9860883 This Small Business Innovation Research (SBIR) Phase I project addresses a unifying mathematical framework for three-dimensional tolerance analysis which can quantify the flow of variation through a product based upon design specifications and associated manufacturing processes. The hallmark of this innovation is a system of geometric constraint equations that are a function of kinematic degrees of freedom (DOF). The constraints define the feasible space for features, components, and part-to-part (assembly) relationships due to geometric topology, tolerancing, and the manufacturing process. Sets of equations are solved for the particular homogeneous transformation matrices that systematically vary the features and components of the resultant feature-based assembly model, allowing for accurate calculation and assessment of dimensional requirements. The innovation will provide a unity calculus for variational modeling at the feature, component, and assembly levels, with Phase I emphaizing the crucial assembly level. Overall benefits of this innovation include boarding the application base, ease-of-use, and appeal of tolerance analysis, as well as enabling a compelling synchroneity with Computer-Aided Engineering (CAE) systems. Applications of computer-aided tolerance analysis are anticipated in the design and manufacture of mechanical and electrical systems, robust product and process design, simultaneous engineering, rapid prototyping, and product quality enhancement.