Surface Fractal Characterization of Granite Cut by Diamond Wire Saw

The surface quality of granite cut by diamond wire saw significantly impacts the cost of subsequent processes such as grinding and polishing. Traditional evaluation parameters like surface roughness (Ra) or peak-to-valley value (PV) face challenges in characterizing the surface morphology. This study introduces fractal dimension (FD) as a potential auxiliary parameter for evaluating the surface quality of sawn granite. Cutting experiments were conducted on Shanxi Black granite using varying wire speeds, feed speeds, and workpiece sizes. The box-counting method was employed to extract the three-dimensional fractal dimension (3D FD) of the granite surface, which characterizes the overall surface complexity, as well as the distribution of two-dimensional fractal dimensions (2D FD) for granite surface cross-sectional profiles at different angles. The results indicate that the granite-sawn surface exhibits complex micro-morphology featuring brittle micro-pits and wavelike saw marks along the feed direction. A strong negative correlation exists between the 3D FD and both surface roughness Ra and PV value, suggesting that 3D FD can serve as an indicator of granite surface quality, with higher FD values corresponding to better surface quality. Moreover, compared to the PV value constrained by material heterogeneity, 3D FD more effectively represents the true surface quality of the granite. Additionally, the distribution characteristics of 2D FD at different angles effectively reveal surface anisotropy and damage. The results suggest that a more symmetrical 2D FD distribution is associated with consistent surface integrity in the evaluated samples. This suggests that FD has the potential to serve as a meaningful auxiliary parameter for characterizing granite surface quality. The findings hold significant importance for the accurate evaluation of diamond wire-saw-cut granite surfaces and provide a basis for the formulation of subsequent grinding process.