Fractal characterization and simulation of surface profiles of copper electrodes and aluminum sheets

Surface topography influences electrical contact resistance in resistance spot welding. With structure function analysis, the surface profiles of copper electrodes and aluminum sheets are analyzed and characterized. The result shows that all of the profiles considered are multifractal, the presence of oxide film complicates the multifractal property of aluminum sheet surface and pickling method helps to remove the oxide film. To evade the discrepancy in critical wave numbers, some special measures are taken and the derived critical wave numbers are given. With modified Weierstrass–Mandelbrot (W–M) function and the critical wave numbers, the multifractal profiles are simulated. There are strong similarities between simulated and measured profiles. The probability densities of simulated profiles are compared with the measured ones. The good agreement validates the correctness of methods for characterization and simulation.