Fractal Fract. 2025 , 9 , 123
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3.3. Surface Friction vs. Surface Roughness Figure 9 presents the relationship between surface friction and roughness. As shown in Figure 9a, the correlation between the two properties is weak, suggesting their indepen- dence. This highlights the importance of measuring both surface roughness and friction for comprehensively characterizing surface properties. To illustrate this point (Figure 10), surfaces A and B, which exhibit the same average roughness and COV, demonstrate distinct performance characteristics [12,28]. For example, in terms of wear resistance, sample A is expected to perform significantly better than sample B despite having similar surface roughness metrics.
Figure9. Comparison of MIU with RMAD ( a ) and FMAD with RMAD ( b ).
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Figure10. Surfaces with identical roughness but distinct contours.
Figure 9b shows the relationship between FMAD and RMAD , both of which represent the MAD of surface friction and roughness, respectively. The correlation between FMAD and RMAD is stronger than that between MIU and RMAD . 3.4. FD Analysis of Surface Roughness of Printing Paper Table 4 presents the FD values, along with the surface roughness and friction param- eters. In previous studies [17], FD values calculated using the variogram method [12,29] were typically too similar to effectively distinguish between different paper products. In contrast, this study employed the PSD method for FD analysis, yielding results (Table 4) that are significantly more distinguishable than those obtained using the variogram method. However, note that most printing paper products undergo a calendering process to enhance the smoothness and quality of the printed material. The calendering process involves pressing the paper against a smooth surface with sufficient force to deform the paper structure as it passes through one or more two-roll nips [8]. Because of this process, the paper surface becomes more uniform, with FD values approaching one. Figure 11 illustrates the relationship between FD and surface roughness ( RMAD ). The R 2 value of 0.342 indicates a weak correlation between FD and surface roughness, suggesting that the two parameters exhibit distinct and independent characteristics. This observation is consistent with the results presented in Figure 1, further supporting the notion that FD and surface roughness describe fundamentally different aspects of sur- face properties.
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