Mathematical issues in mechanical tolerance analysis

The aim of this paper is to provide an overview of tolerance analysis. Tolerancing decisions can profoundly impact the quality and cost of product. There is a strong need for increased attention to tolerance design to enable high-precision assemblies to be manufactured at lower costs. Indeed, tolerance analysis is a key element in industry for improving product quality. Designers want tight tolerances to assure product performance; manufacturers prefer loose tolerances to reduce cost. There is a critical need for a quantitative design tool for specifying tolerances. Tolerance analysis brings the engineering design requirements and manufacturing capabilities together in a common model, where the effects of tolerance specifications on both design and manufacturing requirements can be evaluated quantitatively. Significant amount of literature is related to tolerancing methods. Summaries of state of the art, the most recent developments, and the future trends in tolerancing research can be found. This paper provides a classification of the issues from a mathematical point of view