Modeling and verification methods for the inspection of geometric tolerances using point data
Carr, Kirsten Marie
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Permalink
https://hdl.handle.net/2142/19517
Description
Title
Modeling and verification methods for the inspection of geometric tolerances using point data
Author(s)
Carr, Kirsten Marie
Issue Date
1995
Doctoral Committee Chair(s)
Ferreira, Placid M.
Department of Study
Mechanical Science and Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Industrial
Engineering, Mechanical
Language
eng
Abstract
The ability to specify, produce, and verify parts with sufficiently small variations such that they are functionally equivalent is vital to the success of mass production. The amount of allowable variation in a part is specified by tolerances. To ensure a part conforms to these tolerances, inspection methods are required. With the increase demand for flexibility on the factory floor, a programmable inspection tool, known as the coordinate measuring machine (CMM), has become popular. A CMM is programmed to collect point data information from the surface of a part. This data is analyzed by verification algorithms to determine if the part conforms to the tolerance specifications. Since CMMs determine the conformance of a part based on point data information, methods for reasoning about tolerances based on this type of information are required.
In this work, a framework is developed for reasoning about the inspection of geometric tolerances, which include form, size, orientation, and position tolerances. Methodologies are developed that give geometric and mathematical characterizations of tolerance zones. The geometric characterization provides an understanding of the shape of the zone and how it is allowed to move in space. The mathematical characterization defines a set of equations that the parameters of the zone and all enclosed points must satisfy. These characterizations provide a basis for defining search/optimization models of the inspection of geometric tolerances that can be solved using standard optimization techniques.
The ability of this framework to model the inspection of the commonly used geometric tolerances is demonstrated. The resulting verification algorithms are based on min-max optimization models and represent an important departure from current verification methods, which are based on least-squares algorithms. The algorithms developed in this work are shown to be correct, robust, stable, efficient, and capable of improving upon the least-squares solution by as much as twenty percent. This improvement can result in significant cost savings in mass production. With the improvement of part quality as the main motivation behind all efforts to understand, measure, and eliminate deviations in the manufacturing of parts, this framework represents an important step forward in the inspection of geometric deviations.
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