Mathematical Model to Formalize Tolerance Specifications and Enable Full 3D Tolerance Analysis

Arizona State University, Scottsdale AZ

Investigators

Abstract

Tolerances specify the ranges of permissible imperfections so a manufactured part will be acceptable for assembly and use. Standards exist to define classes of tolerances and to ensure proper communication among engineers. The purpose of this research is to continue creating a mathematical model of geometric tolerances. The results from our earlier work show that the proposed math model is compatible with the standards, and that it provides three-dimensional relations for assemblies. At the local level, the method of the new model is to represent each tolerance-zone for a plane or a line as a hypothetical point-space, or map, and to combine these for assemblies of parts. At the global level, the model inter-relates all reference frames of an assembly using degrees of freedom. The project includes the implementation of a tolerance analysis system for comparison of the new model with existing software. Existing methods for analysing tolerances today are based strongly on ad-hoc conventions from engineering practice and less on mathematical principles. Consequently, full three-dimensional analysis of tolerances in assemblies is not done today, and contemporary design software is only partially compatible with existing standards. The outcome of this project will provide the tools to complete full three-dimensional statistical analyses of tolerances, and, thereby, it will improve quality and lower cost. This project will result in new teaching materials, which should make the subject easier to include in undergraduate and graduate engineering curricula. Based on our model, we are proposing to the American Standards Committee a new set of professional development classes and certification exams that are directed at engineers for tolerance analysis in the digital age.