Fractal Fract. 2025 , 9 , 123
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Conventional methods for analyzing paper properties typically involve tensile strength tests, which require precise thickness measurements [9–11], but ignore surface roughness, which significantly affects the accuracy of thickness measurements across various paper products [12]. Thickness directly affects the evaluation of tensile strength, which is a key physical property of paper; thus, surface roughness ultimately affects the reliability and consistency of tensile strength results [13]. This highlights the importance of considering surface roughness when analyzing paper properties to ensure accurate and meaningful assessments. Currently, thickness measurements are performed under applied loads, where the thicknesses of multiple samples are recorded to calculate the mean value, standard de- viation, and coefficient of variation (COV) [14]. These metrics are then used to evaluate the physical properties of the product. However, as illustrated in the following example, this method carries the risk of yielding inaccurate assessments, highlighting the need for careful consideration of measurement variability. Figure 1 shows surface roughness profiles with identical mean values of 0 but different FD values [4,12] generated using computer simulation methods [15,16]. As shown in Figure 1, even with identical mean values and standard deviations, the surface roughness profiles vary according to their FD values. This result demonstrates that surface profiles can be significantly different even when they exhibit the same average roughness. As the FD approaches 2, which corresponds to the areal dimension, the profile increasingly fills the surface area. This result demonstrates that surface roughness profiles that are indistinguishable using conventional measure- ments, such as the mean and standard deviation, can be effectively differentiated by fractal geometry dimension analysis.
Figure1. Surface roughness vs. FD.
In a previous study [17], FD analysis was performed to evaluate the surface roughness of paper and tissue products. However, this analysis failed to identify distinct characteristics specific to each product type, probably due to the versatility of the surface roughness scales of paper products [18]. To address this limitation, this study interprets the FD values of printing paper products using power spectral density (PSD) analysis. Furthermore, this study investigates the relationships between surface roughness, surface friction, and FD via contact profilometry.
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