Investigation of Characteristic Measures for the Analysis andSynthesis of Precision - Machined Surfaces 1

Error prediction and control are key factors in precision machining. These factors rely on the development of formal approaches for analyzing and characterizing error sources in manufacturing. One such approach is the development of mathematical measures of precision, where precision, in this context, is deened as surface variations of manufactured part prooles. In this paper, we discuss a novel investigation of four mathematical measures. These four methods, namely the autocorrelation function, the Fourier spectrum, a fractal-wavelet representation, and the Karhunen-Lo eve expansion, are applied to surfaces produced from grinding processes. The rst two methods provide a basis for the investigation, as they are commonly used in the literature for qualitative signal characterization of manufacturing surfaces. However, the fractal-wavelet method and Karhunen-Lo eve expansion have never been applied to the analysis and synthesis of surface variations. While other fractal methods have been used to characterize surface-nish variations , a wavelet formalism is a new approach, especially at the scales of both surface nish and tolerances. A combination of the rst three techniques is shown to give a proper minimum set of characteristic precision measures for representing grinding surfaces. This combination is a clear contribution to the eld of analysis of surface characteristics. It is also shown that the Karhunen-Lo eve technique is a novel alternative to represent surface errors. The existence of characteristic measures of surface precision should aid designers in choosing process and design parameters and in comparing the precision between competing machining processes.