Fractal Fract. 2025 , 9 , 123
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The mean absolute deviation (MAD) from R a ( R MAD) can be defined as follows [19]:
1 N ∑
N 1 | R i − R a | .
(5)
RMAD =
Figure 4 shows a graphical representation of R a , R q , and RMAD . In the figure, RMAD is calculated by dividing the shaded area by the scan length, as indicated by the dotted lines. Note that when calculating RMAD , R a is treated as a constant similarly to how the thickness average is treated as a constant when calculating R a . RMAD has been established as an ISO standard method for determining the surface roughness of paper and paperboards in ISO 24118-1:2023 [21].
Figure4. Graphical representations of Ra , Rq , and RMAD.
2.2.2. Surface Friction Characterization The Kato Surface Tester can simultaneously generate surface roughness and friction profiles using the same stylus under the same operating conditions. Figure 5 shows the friction profiles of the sample in Figure 3.
Figure5. Surface friction profile of P&W1.
The surface friction parameters the average coefficient of friction (COF, MIU ) and the MAD from the average COF ( FMAD ) are calculated using Equations (6) and (7), respectively.
1 N ∑
N 1 μ i
(6)
μ =
1 N ∑
N 1 | μ i − μ |
(7)
FMAD =
where MIU denotes the average COF, N represents the number of data points from the scan length, μ i denotes the COF at point i , and FMAD denotes the MAD from the MIU [19,20]. Here, N is calculated using Equation (2). When calculating FMAD , the average COF is treated as a constant, as in the case of RMAD (Figure 4). FMAD has been established
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