Fractal Fract. 2025 , 9 , 123
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3. Results and Discussion 3.1. Surface Roughness of Printing Paper
Table 2 summarizes the surface roughness parameters, including the COV in percent- age, of the printing paper samples based on 10 measurements for each sample. As shown in Table 2, the COV values of Ra and Rq were higher than those of RMAD . These findings are consistent with those reported by Park et al. [22] and Lee et al. [17], who found that Ra and Rq varied depending on measurement factors such as stylus size and instrument specifications. In contrast, during RMAD calculations, Ra is treated as a constant, allowing it to reflect the actual surface variation independently of the measurement conditions.
Table2. Surface roughness of printing paper samples.
Ra , μ m
Rq , μ m
RMAD , μ m
Sample
Mean
COV 15.4% 14.6% 13.6%
Mean
COV 15.4% 14.4% 16.1%
Mean
COV 9.5% 5.1% 5.8% 5.7% 5.6% 6.8% 6.4% 9.2% 7.6% 3.6% 6.9% 6.6%
P&W1 P&W2 P&W3 P&W4 P&W5 P&W6 P&W7 P&W8 P&W9 P&W10 P&W11 P&W12
1.40 2.09 1.88 1.27 1.80 1.25 2.32 1.95 1.96 2.17 1.87 1.54
1.46 2.19 2.05 1.30 1.95 1.32 2.37 2.20 2.10 2.55 2.03 1.68
0.32 0.50 0.45 0.30 0.44 0.30 0.53 0.49 0.51 0.51 0.42 0.35
7.5% 8.4%
6.5%
11.5% 13.0% 10.3% 19.9% 19.7% 24.8% 14.9% 18.1%
12.4% 10.5% 16.6% 17.2%
7.5% 9.4%
13.3%
In addition, by comparing P&W11 (uncoated) and P&W12 (coated), all surface rough- ness parameters were reduced, demonstrating that the effect of coating on a paper surface can be determined using surface profile parameters such as Ra , Rq , and RMAD . Similar results have been obtained by other investigators [14,17,22]. Figure 7 compares RMAD with Ra (Figure 7a) and RMAD with Rq (Figure 7b). The R 2 variation indicates strong correlations (0.949 in Figure 7a and 0.923 in Figure 7b). However, the slopes of the equations in both figures are significantly lower than 1, suggesting that Ra and Rq exhibit greater variability than RMAD . This indicates that RMAD provides more stable results, independent of the measurement conditions [17,22].
Figure7. Comparison of RMAD with Ra ( a ) and RMAD with Rq ( b ).
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