Conformable evaluation of geometric dimensioning and tolerancing using discrete measurement data.

Abstract

This dissertation presents a methodology to utilize discrete measurements and evaluate manufactured parts in conformance with the current Geometric Dimensioning and Tolerancing (GD&T) standard. This method enables the Coordinate Measuring Machines to check the functional requirements defined in the current standard. The thesis includes: (1) adaptive sampling and identification of feature deviation, (2) mathematical implementation of GD&T functional requirements, and (3) computer interpretation of GD&T specifications. The proposed adaptive sampling strategy uses a hypothesis test and a model update technique to identify feature deviations. The feature deviation includes both systematic and random errors. They are estimated by a major form deviation and an uncertainty zone respectively. The uncertainty zone is estimated by the prediction interval. The prediction interval theorem provides specific sample size for each individual model. During the model update, this sampling method adaptively takes additional measurements to provide the appropriate sample size. This process will continue until the updated model is adequate to represent the systematic error. Then the prediction interval can accurately represent the random error. This approach has been validated through simulations. The GD&T functional requirements defined in the ANSI standard are modeled by a minimax constrained optimization method. A proposed local feature coordinate transformation (LFCT) technique is added in this approach to reduce the formulation complexity. Every specific functional requirement can be formulated by generic equations. This optimization method formulates both tolerances for individual features and tolerances for related features. This implementation directly simulates the functional gaging process described in the standard. In addition, ambiguous definitions in the current standard are reviewed. Solutions from the inspection and evaluation view points are suggested and implemented. A proposed hierarchical structure enables computers to correctly interpret GD&T functional requirements according to the specification symbols. The structure links the relations between tolerance representations and functional (mathematical) interpretations. A full scheme, from tolerance interpretation, adaptive sampling, to computer optimization and evaluation, is clearly established. It gives a complete computer GD&T evaluation process which conforms to the current standard definitions.