A Form Tolerancing Theory Using Fractals and Wavelets

Abstract

Tolerancing is a crucial problem for mechanical designers, as it has quality and cost implications on product design. Research in tolerancing has addressed specific areas of the problem, but lacks a theoretical basis. A formal approach for geometric tolerancing with fractal-based parameters has been recently developed. This paper presents an enhanced error profile analysis and synthesis method, based on wavelets, that maintains and extends the use of fractals for surface error abstraction. An overview of the theory of wavelets is provided, and the link between fractals and wavelets is established. Physical test data are used to illustrate the application of wavelet theory to surface profile reconstruction and synthesis. The synthesis methods are then implemented in the functional design of ball-bearing elements, demonstrating the utility of fractal-based tolerancing. Plans for further study and implementation conclude the paper.