Study on Fractal Characteristic of Surface Micro-Topography of Micro-WEDM

Abstract

The surface micro-topography of micro-WEDM is random, disordered and multi-scale and has been proved that it is fractal with the characteristic of self-affinity within a certain scale on the basic of the fractal geometry theory. According to the characterization of W-M fractal function, the principles of three evaluation methods about power spectrum method, structure function method and wavelet criterion have been described. The advantages and disadvantages of them evaluating the fractal property of the surface micro-topography of micro-WEDM have been compared in this paper. The experimental results indicate that the wavelet criterion is more stable and dependable than the other two methods, so the fractal dimension D of the surface micro-topography of micro-WEDM has been calculated using it. The result shows that the fractal dimension has the tendency of decrease with the increase of root mean square deviation (Sq) value while it is not absolutely monotonic, which can be used as a beneficial supplement to traditional evaluation parameters of surface roughness.

Modeling and Optimization of Fractal Dimension in Wire Electrical Discharge Machining of EN 31 Steel Using the ANN-GA Approach

“…Moreover, due to the stochastic nature of WEDM, mathematical as well as AI techniques have been employed to predict optimal machining parameters and to improve the surface roughness. However, the fractal dimension has been seldom used as a parameter to characterize surface roughness in WEDM [30,31,32]. The center line average surface roughness (R a ) is dependent on parameters such as the resolution of the instrument used and the sampling length.…”