Methods for evaluation of systematic geometric deviations in machined parts and their relationships to process variables

Abstract

Increasing demands for precision-machined parts put a greater emphasis on achieving a better understanding of the relationships between manufacturing process variables and deviations from perfect geometric forms. To achieve this understanding, it is important to have high-quality metrology data on part features, which (in some sense) span the range of variability in form for the process under study. The problem is complex, involving the machine tool itself, materials, fixtures, cutters, feeds, speeds, and many other factors. In this report, a method is introduced that can identify key deviations from perfect form and can elucidate their dependence on some of the factors enumerated above. This work presents two useful models for form errors of cylindrical features and develops special cases of those models to suit specific requirements. One is an analytical model based on Chebyshev polynomials to model the axial errors and Fourier series to model angular dependencies. The second modeling approach uses the techniques of principal component analysis to extract a basis set of characteristic shapes directly from the measurement data. This report includes a full development of the mathematical basis for the analysis and concludes with some application examples.