THE PERTURBATION DIMENSION FOR DESCRIBING ROUGH SURFACES

We define global and local "perturbations" of roughness profiles, considered as rectifiable or non rectifiable curves. The method consists in measuring classical roughness parameters in tau - windows of various sizes. When tau-tends to zero a characteristic scaling exponent is evaluated. This exponent is related to the "perturbation dimension" d. In rectifiable cases d is an integer. Otherwise, d is a real number. As a practical application, we characterize the roughness evolution of a shot-blasted surface as a function of the abrasive particle size.