A Computer Aided Fractal Calculation in Tribology Research

Using fractal in studying tribology is becoming more important. Although digitizing and processing the surface topography image of a friction surface and wear particle are the means for calculating of the respective fractal dimensions, they are extremely troublesome. To establish a method for calculating and analyzing the fractal phenomena of a surface, the use of computer software and hardware is rather essential. A computer program was developed for auto-calculating: (i) the profile of fractal dimension using the existing methods of yardstick, power spectrum, and structure function; (ii) surface fractal dimension using the methods of slit island and box counting. The program also used W-M standard fractal function curve to improve the accuracy of prediction. Values predicted by all these methods show a power law trance, and demonstrate the individual advantages and limitations on practical calculation. Predicted profile of fractal dimension suggested that the yardstick method gave large error when some pivotal points were abandoned. Generally, structure function method predicted relatively more precisely for surface profile of high fractal dimension. Power spectrum method gave relatively good precision in predicting surface profile of low fractal dimension. The accuracy of calculating the surface fractal dimension is also analyzed by auto-relation coefficient. Furthermore, examples of fractal analysis on TiN surface and/or wear particles were performed by the various methods.