Tolerancing for an Apple Pie: A Fundamental Theory of Tolerances
Tolerancing for an Apple Pie: A Fundamental Theory of Tolerances
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苹果派的公差：公差的基本理论
DOI：
10.1115/1.4057040
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发表时间：
2023
影响因子：
3.3
通讯作者：
Hazelrigg, George A.
中科院分区：
文献类型：
--
作者：
Roland Campbell, Joshua;Hazelrigg, George A.
公差开始于对实现的零件的尺寸施加限制的概念，以保持功能几何尺寸，并使成本有效的零件制造和检查。然而，越来越多的部件制造取决于部件几何形状，因为许多部件是根据“配方”而不是材料添加或去除的尺寸指令制造的。被称为过程公差，例如，IC芯片就是这种情况。在公差优化的情况下，一个典型的目标是成本最小化，同时实现所需的功能或“质量”。这篇文章对公差有不同的看法，建议不仅仅是确保零件以最低成本实现所需的功能，产品设计的典型潜在目标是赚钱，越多越好，公差包括附加的设计变量，可以在决策理论框架中进行优化。我们进一步认识到公差引入了与产品特性相关的附加产品属性，如一致性、质量、可靠性和耐用性。这些重要属性使候选设计的预期效用的计算复杂化，需要额外的计算步骤来确定它们。由此产生的公差理论阐明了田口损失函数固有的假设和局限性。我们说明了理论使用的例子公差的苹果派，这方便地要求考虑公差的数量和过程，以及这些公差之间的相互作用。
Tolerancing began with the notion of limits imposed on the dimensions of realized parts both to maintain functional geometric dimensionality and to enable cost-effective part fabrication and inspection. Increasingly, however, component fabrication depends on more than part geometry as many parts are fabricated as a result of a “recipe” rather than dimensional instructions for material addition or removal. Referred to as process tolerancing, this is the case, for example, with IC chips. In the case of tolerance optimization, a typical objective is cost minimization while achieving required functionality or “quality.” This article takes a different look at tolerances, suggesting that rather than ensuring merely that parts achieve a desired functionality at minimum cost, a typical underlying goal of the product design is to make money, more is better, and tolerances comprise additional design variables amenable to optimization in a decision theoretic framework. We further recognize that tolerances introduce additional product attributes that relate to product characteristics such as consistency, quality, reliability, and durability. These important attributes complicate the computation of the expected utility of candidate designs, requiring additional computational steps for their determination. The resulting theory of tolerancing illuminates the assumptions and limitations inherent to Taguchi’s loss function. We illustrate the theory using the example of tolerancing for an apple pie, which conveniently demands consideration of tolerances on both quantities and processes, and the interaction among these tolerances.