Fractal Fract. 2025 , 9 , 123
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Figure3. Surface roughness profile of P&W1.
A conical stylus (Figure 2) with a tip radius of 0.5 mm was used to operate the surface profiler, which was designed in accordance with KS M 4057:2021 [20]. This type of stylus is also described in ISO 24118-1:2023 [21]. The conical stylus, with a tip radius of 0.5 mm, has been successfully used to characterize the surface roughness and friction of paper and tissue products [17,22,23]. Its rounded contact area minimizes damage to the sample surface, because it is not sharp. 2.2.1. Surface Roughness Characterization With a surface roughness profile (Figure 3), many surface parameters can be deter- mined according to ISO 21920-2:2021 [24]. Among the surface roughness parameters, the roughness average ( Ra ) has been widely used [22] and can be calculated as follows:
1 N ∑
N 1 | R i | ,
(1)
Ra =
where Ra denotes the roughness average ( μ m), R i denotes the roughness ( μ m) at a scanning point I , and N represents the number of data points in the scan length. Here, N is calculated as follows: N = DAR × L / V , (2) where DAR denotes the data acquisition rate (Hz or points/s), L represents the scan length (mm), and V represents the scan speed (mm/s) [17,22,23]. Then, the spacing distance (SD) between two adjacent points can be calculated as follows: SD =( L × V ) / ( V / dar )= V / dar . (3) SD may be interpreted as the measuring unit in a roughness profile, indicating that the shorter the SD , the shorter the measuring unit. However, note that, in Equation (3), SD should be independent of the stylus size and dependent only on the scan speed ( V ) and the data acquisition rate ( DAR) [14,17,22,23]. As a numerical illustration, at DAR =1000Hz, L =20mm, and V =1mm/s, SD =1micron. Another commonly used parameter, square roughness ( Rq ) is widely used to describe the standard deviation of surface height variations [25,26] and can be calculated as follows: Rq = 1 N ∑ N i = 1 R 2 i , (4) where R q denotes the root mean square roughness ( μ m).
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