FORM TOLERANCING THEORY USING FRACTALS AND WAVELETS

Tolerancing is a crucial problem for mechanical designers, as it has q uality and cost implications on product design. Research in tolerancin g 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 enhanc ed error profile analysis and synthesis method, based on wavelets, tha t maintains and extends the use of fractals for surface error abstract ion. An overview of the theory of wavelets is provided, and the link b etween fractals and wavelets is established. Physical test data are us ed to illustrate the application of wavelet theory to surface profile reconstruction and synthesis. The synthesis methods are then implement ed in the functional design of ball-bearing elements, demonstrating th e utility of fractal-based tolerancing. Plans for further study and im plementation conclude the paper.