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

9860883 这个小型企业创新研究（SBIR）第一阶段项目解决了三维公差分析的统一数学框架，可以根据设计规范和相关的制造工艺量化产品的变化流程。 这一创新的标志是一个系统的几何约束方程是一个功能的运动自由度（DOF）。 这些约束定义了特征、零部件和零件到零件（装配）关系的可行空间，这些关系是由几何拓扑、公差和制造过程引起的。 方程组被求解为特定的齐次变换矩阵，该矩阵系统地改变所得到的基于特征的装配模型的特征和组件，从而允许精确计算和评估尺寸要求。 创新将提供一个统一的演算变分建模的功能，组件和装配水平，与第一阶段的关键装配水平。 这一创新的总体优势包括应用基础、易用性和公差分析的吸引力，以及与计算机辅助工程（CAE）系统的同步性。 计算机辅助公差分析的应用预计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，快速原型和产品质量的提高。

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.