Tentative title: Computational models for tolerance accumulation (stackup) in geometric tolerancing
Advisor: Prof. H. B. Voelcker, hbv1@cornell.edu
Essential qualification: Working knowledge of geometric tolerancing, obtained either through design experience in industry or completion of MAE 5200 or an equivalent course.
Number of students: 1 – 2
Description
Mechanical designers control spatial variability (variations in part shapes, sizes, and relative positions) with dimensional tolerances. Geometric Dimensioning and Tolerancing (GD&T) is the standard medium in modern industry. GD&T emerged after WW-II as a set of industrial best practices without theoretical foundations, and it has been refined almost continuously since its emergence.
One of GD&T’s major gaps is a lack of systematic means for calculating tolerance accumulation (“stackup”) in assemblies. This project addresses the problem using a two-stream strategy. The first stream is focused on ‘mathematizing’ stackup, initially through careful study of a few selected examples. The primary tool for modeling accumulation will be Minkowski summation of point sets defined by tolerance zones.
The second stream seeks computationally effective means for implementing (evaluating, “doing”) Minkowski operations. Reasonable methods are known for linear polyhedral zones, but they do not generalize to curved zones. A possible ‘endrun’ around the problem, based on fast 2-D and 3-D convolution, will be explored here, initially through Matlab implementations.
The two streams can be pursued independently until each has produced results worthy of transfer to the other. Significant results in either stream can satisfy M.Eng project requirements. Success in both is likely to be a genuinely important achievement.