Manufacturing Maps: A New Math Model for 3-D Tolerance Analyses in Process Planning, CMM Inspection and Statistical Process Control

Arizona State University, Scottsdale AZ

Investigators

Abstract

The research objective of this award is to develop mathematical models for manufacturing variations. In these models, dimensional and geometric variations on manufacturing features will be mapped to points in convex bounded regions in higher dimensional space. When features or tolerances stack-up in an assembly, error accumulation corresponds to Minkowski sums of all contributing regions (Tolerance Maps), which then represent the entire population of assemblies conforming to the given design specification. This research will create a method for using these maps for manufacturing operations based worst-case calculation in process planning by fitting maps corresponding to manufacturing specification inside maps corresponding to design. Statistical analysis of tolerance accumulation for any combination of frequency distribution corresponding to characteristics of manufacturing machines producing the corresponding features will also be investigated. Methods for direct fitting of inspection data from coordinate measuring machines into these and a methodology for using them in statistical process control maps will also be developed. If successful, the results of this research will enable precise mathematical interpretation of the tolerance standards, consequently preventing errors in manufacturing planning and inspection. Maps use in statistical process control will provide an effective visualization and diagnostic tool, based not just on proximity to worst case limits, but also on full statistical analysis. There is potential for this new method to streamline the analysis of Coordinate Measuring Machine data to where it can be an integral part of the feedback for statistical process control. This work will also generate material suitable for teaching the theory of tolerancing and metrology. It is envisioned that these new math models will enable future research on correlations between parameters of a manufacturing process, such as tool wear, and the shape and size of the measured subset, together with its location within the map.