Fractal Parameters Extraction and Fractal Modeling of Electrode Surface in Vacuum Interrupters

It is acknowledged that microscopic electric field enhancement on electrode surface in vacuum interrupters (VIs) is fundamental to the electrical breakdown of vacuum gaps according to the different breakdown initiating mechanism. The rough surface conditions would have a significant influence on the characteristics of the microscopic electric field on the electrode surface. The objective of this paper is to extract the typical fractal parameters and establish the electrode rough surfaces based on fractal theory and measurement. Firstly, the electrodes of the typical material CuCr25 were measured by Atomic Force Microscope (Bruker, Dimension Icon). The sampling interval was 2 nm and the sampling length was 1 μm. Secondly, the wavelet analysis method was used to extract the fractal dimension of the W-M function and the Daubechies wavelet function base with two orders (DB2) was determined to be the most suitable one for extracting the fractal dimension. Then, two methods were used to extract the fractal scaling constant of the W-M function and the wavelet analysis method was chosen to be the most suitable one. Finally, the fractal model was established and the surface roughness of both engineering surfaces and fractal surfaces has been calculated. The results may provide some useful reference to study the vacuum breakdown phenomena.