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Tolerance analysis in mechanical design.

机译：机械设计中的公差分析。

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Products cannot be manufactured precisely. Some deviations from nominal design will always be present, no matter how good manufacturing processes become. The precision with which a product is manufactured affects its functionality. Higher precision results in higher manufacturing cost. Tolerances describe allowed deviations from nominal design to ensure that a product is functional. Unfortunately tolerances interact in complicated ways which are difficult and often impossible to analyze. The reason for it is that tolerances can describe a large variety of allowed geometric variations from nominal design. While individual variations can be parameterized and modeled easily, combinations of even a few variations may result in extremely complex multi-dimensional spaces.; In this thesis we develop a mathematical theory and a representation to express engineering tolerance constraints. This representation is then used to formulate problems of tolerance analysis and synthesis. The approach is illustrated with examples. Mathematical solutions to tolerance analysis and synthesis problems are discussed.; The representation is developed to satisfy the following requirements: (1) representation is independent of the underlying geometric modeler; (2) both representation and tolerance analysis and synthesis techniques are uniform for individual components and for assemblies; (3) representation is fully symbolic; (4) representation unifies current engineering standards, geometric modeling techniques and tolerance analysis techniques; (5) representation can be used to model errors in manufacturing processes.; The representation uses a graph of symbolic geometric entities and symbolic geometric constraints to model designs of constrained parts and assemblies. Geometric information which is not included explicitly in the model, but required for tolerance analysis, is computed symbolically by MAPLE, a symbolic manipulation package. The translation of ANSI constraints into symbolic geometric and algebraic constraints is fully automatic and is performed in such a way as to: (i) minimize the symbolic complexity of the resulting tolerance representation, and (ii) preserve the geometric intent of high level ANSI constraints on the low levels of representation.; One of the natural applications of our representation is modeling errors in manufacturing and inspection processes. We demonstrate the technique by modeling errors and estimating error parameters for the calibration of a coordinate measuring machine.
机译：产品无法精确制造。不论制造工艺如何变好，总是会出现与名义设计的偏差。产品的制造精度会影响其功能。更高的精度导致更高的制造成本。公差描述了与标称设计的允许偏差，以确保产品功能正常。不幸的是，公差以复杂的方式相互作用，很难且通常无法分析。其原因是，公差可以描述名义设计中允许的多种几何变化。尽管可以轻松地对单个变量进行参数化和建模，但即使是几个变量的组合也可能导致极其复杂的多维空间。在本文中，我们发展了数学理论和表示来表达工程公差约束。然后，该表示用于制定公差分析和综合问题。通过示例说明了该方法。讨论了公差分析和综合问题的数学解决方案。表示的开发是为了满足以下要求：（1）表示独立于基础几何建模器； （2）表示和公差分析以及综合技术对于单个零件和装配都是统一的； （3）表示完全是象征性的； （4）表示法统一了当前的工程标准，几何建模技术和公差分析技术； （5）表示可用于建模制造过程中的错误。该表示使用符号几何实体图和符号几何约束图来建模受约束零件和装配体的设计。模型未明确包含但公差分析所需的几何信息是通过MAPLE（一种符号处理程序包）进行符号计算的。将ANSI约束转换为符号几何和代数约束是完全自动的，并且执行以下方式：（i）最小化由此产生的公差表示的符号复杂性，以及（ii）保留高级ANSI约束的几何意图代表性较低。我们表示的自然应用之一是在制造和检查过程中建模错误。我们通过对误差进行建模并估计误差参数来对坐标测量机进行校准来演示该技术。

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