The Influence of Woven Fabric Geometry on Its Surface-Mechanical Properties

Abstract

This study presents the influence of the type of weave and relative fabric density on surface roughness and the coefficient of friction in raw cotton woven fabrics. Relative fabric density, which represents how full a fabric is compared to the maximum packing density allowed by its weave, provides a more accurate basis for comparison than absolute fabric density. Analysis revealed that both the type of weave and relative fabric density have a statistically significant effect on surface roughness, while neither factor significantly impacts the coefficient of friction. Notably, increasing relative fabric density consistently reduces surface roughness in plain, 2/2 twill, and, to some extent, 5-end satin fabrics, with plain fabrics showing the highest roughness overall. At high densities, 2/2 twill fabrics exhibit greater structural stability, yielding smoother surfaces than 5-end satin fabrics, reversing trends detected at lower densities. Furthermore, the relationship between surface roughness and friction was decoupled in plain and 2/2 twill fabrics—specifically, increased density leads to smoother surfaces and higher friction. 5-end satin fabrics were unique in showing a simultaneous reduction in both surface-mechanical properties as fabric density increased. These findings highlight that relative fabric density is a critical parameter for engineering fabrics with tailored performance properties.

1. Introduction

The development of advanced textile materials has become a focal point of modern materials science, with increasing attention given to surface-mechanical properties of fabrics such as surface roughness and the coefficient of friction. These characteristics are crucial in determining the performance, functionality, and end-use applications of fabrics. Surface roughness influences tactile properties, protective properties, wear behaviour, aesthetic appeal and even the interaction of fabrics with human skin (comfort properties). At the same time, the coefficient of friction affects properties such as drape, handle, abrasion resistance, sound absorption, sewing performance, and others [1,2,3,4,5,6].

Recent studies in textile engineering have explored these surface-mechanical properties across various domains, including the development of smart textiles [7,8], high-performance sportswear [9], medical fabrics, and protective clothing [10,11].

Increased surface roughness affects the tactile properties of fabrics, reducing slipperiness and evenness while enhancing the perception of roughness. This directly impacts sensorial comfort [12]. Surface roughness also impacts the thermophysiological comfort of fabrics, influencing properties such as thermal conductivity, moisture management, and air permeability. Fabrics with increased roughness demonstrate improved moisture management, which is vital for wearable comfort in sportswear [8]. Furthermore, the interplay between surface roughness and other textile properties influences the adhesive characteristics between fabrics and skin, affecting sensory comfort under diverse conditions [13]. LaBarre et al. [10] found that higher surface roughness increases inter-yarn friction, which is critical for energy dissipation during impact and affects tensile properties by altering yarn modulus and elongation. Surface roughness can enhance fabric durability and functional properties, including flammability resistance, hydrophobicity or hydrophilicity, and dyeability [14,15,16,17,18,19]. The surface roughness also influences the shedding of microfibers during laundering, impacting the fabric’s longevity and environmental footprint [20].

Likewise, controlling frictional behaviour is crucial for enhancing fabric hand and tactile comfort, wear and abrasion resistance, sewing and processing performance, garment fit and drape, and impact resistance [1,2,21,22,23]. The coefficient of friction directly influences fabric tactile perception, and a higher value often indicates a rougher surface [22]. Fabrics with optimised friction coefficients are more resistant to wear during use, washing, and handling, thus maintaining appearance and integrity over time [21]. During manufacturing, fabrics with extreme friction coefficients (high or low) can cause cutting, sewing, and handling issues, whereas a balanced coefficient of friction ensures smoother processing and better seam quality [21]. Friction also governs fabric interactions with other materials and the body, influencing how garments drape, cling, or slide, which is crucial for aesthetics and functionality [22]. In technical textiles, such as ballistic fabrics, optimised friction enhances energy absorption and failure resistance under stress or impact [22].

The close relationship and nuanced differences between surface roughness and the friction coefficient necessitate studying these properties in tandem. Surface roughness captures the topographical variation—the micro-peaks and valleys—of a fabric’s surface, directly influencing how the fabric interacts with skin or other surfaces. The friction coefficient, meanwhile, quantifies the resistance to sliding motion across a fabric surface. While rougher fabrics often have higher friction coefficients, exceptions can occur, especially when factors such as fibre chemistry or finishing treatments come into play. Researching these properties in tandem provides a more holistic understanding of fabric tactile properties and performance. Both significantly influence tactile comfort (the tactile sensation of fabric in contact with the skin), wearability (ease of donning, draping, and movement), and functional outcomes such as pilling resistance or durability. Understanding both parameters helps guide material selection, yarn design, and constructional decisions before finishing, ensuring that downstream processes can more precisely tailor fabrics for specific end-uses such as apparel, upholstery, or technical applications. To fully comprehend and control the variation in surface roughness and the coefficient of friction in woven fabrics, it is essential to develop a deep understanding of the structural parameters that influence these surface-mechanical characteristics. Neither surface roughness nor friction is an intrinsic property—they are strongly dependent on the fabric’s construction and material composition. By systematically manipulating these constructional parameters, it is possible to tailor the surface behaviour of fabrics to specific functional, aesthetic, or performance-related purposes. Key constructional factors that influence both surface roughness and the coefficient of friction of woven fabrics include [17,18,24,25,26,27,28,29,30,31,32,33,34,35].

(a)

Fibre type and cross-sectional shape: natural versus synthetic fibres, along with the geometry of their cross-section (e.g., trilobal, hollow, or flat shapes), which affect contact area and surface texture, influencing both roughness and friction;

(b)

Yarn construction: yarn structure significantly influences a fabric’s surface-mechanical properties. A fundamental distinction lies between staple and filament yarns. Staple yarns, composed of short fibres like cotton, exhibit greater hairiness due to protruding fibre ends and increased mechanical interlocking, increasing surface roughness and friction [10,23,27]. In contrast, filament yarns, composed of continuous strands like polyester, are naturally smoother without hairiness, reducing surface roughness and friction [10,23]. Other structural parameters include fineness and uniformity; finer, more uniform yarns (e.g., combed yarns) produce flatter surfaces with reduced surface roughness and friction [23,27,29]. Yarn twist also matters: higher twist levels bind fibres tightly, decreasing hairiness and smoothing the surface [12,27]. Multi-ply yarns can increase surface unevenness compared to single-ply yarns [27];

(c)

Fabric geometry: the type of weave defines the interlacing pattern and surface contact points, significantly altering both tactile perception and frictional resistance. At an equivalent warp and weft density, fabrics with a greater number of interlacement points (i.e., fewer floats) tend to have a more textured surface and a higher coefficient of friction. A greater crimp in the warp or weft increases yarn undulation, which accentuates surface irregularities and raises both roughness and friction. Conversely, reducing crimp flattens the fabric surface, thereby lowering these properties [4,27]. Fabric density, defined as the number of yarns per unit length, significantly influences surface-mechanical properties. Higher thread density compacts yarns, reducing surface undulations and thereby decreasing both roughness and friction. Conversely, lower fabric density results in more prominent peaks and valleys, elevating these properties [4,27,29]. For instance, Akgun et al. [4] demonstrated that increasing weft density in polyester fabrics directly reduces surface roughness, associating denser fabrics with smoother and less frictional surfaces. A well-balanced fabric (similar properties in warp and weft, optimum crimp) produces a more uniform, even surface with lower roughness and friction. Imbalance causes irregular topography and higher friction [4]. Thicker fabrics usually arise from coarser, less dense constructions and manifest more pronounced surface undulations, leading to higher roughness and friction. Thinner, denser fabrics have a flatter surface [13];

(d)

Finishing processes: mechanical (brushing, calendaring) or chemical (enzyme, resin, softener, durable press) treatments can level or roughen the fabric surface, affecting roughness and friction [10]. Softeners or enzyme treatments reduce surface protrusions by smoothing or partially removing fibre ends, resulting in a smoother, less frictional hand. Resin and durable press finishes can alter flexibility and surface structure; antipilling or easy-care finishes may also affect roughness and friction [10,11]. Surface treatments and coatings, including plasma treatment, micro- and nano-scale structuring, and polymeric or carbon-based coatings, significantly modify the surface roughness and tactile properties by filling micro-gaps or imparting hydrophobic properties, often resulting in a smoother surface with reduced roughness and friction coefficient [36].

In conclusion, mastering the relationship between structural parameters and surface-mechanical properties ensures the precise engineering of textile materials. Ongoing investigations of these relationships are not only scientifically valuable but also essential for industrial manufacturing and critical to reducing environmental impact, making them indispensable for the future of advanced fabrics. Several research teams have systematically studied how both weave type (the pattern of yarn interlacement) and fabric density (number of threads per unit length) influence surface roughness and friction in raw (unfinished) woven fabrics. Akgun et al. [4] investigated how weave patterns (plain 1/1, twill 1/2, satin 1/5) and weft density influence surface roughness of polyester fabrics, specifically using raw (pretreated but undyed and unfinished) samples. They demonstrated that surface roughness increases from plain 1/1 to satin 1/5 weaves, with higher weft density reducing roughness and yielding smoother surfaces. They also found that satin weaves, with fewer interlacements and longer floats, exhibit greater surface roughness than plain weaves with frequent interlacements. Similarly, Beyene and Kumelachew [24] analysed cotton woven fabrics of different weave types (plain 1/1, twill 1/3, sateen 8/3) at constant density, showing that surface roughness increases with looser weaves due to longer floats, and is higher in the weft direction, due to lower thread density.

Although these studies have compared different types of weaves and absolute fabric densities, there is a significant limitation: absolute fabric density comparisons can favour certain fabrics artificially. For instance, a plain fabric and a satin fabric at the same ends/cm and picks/cm may not represent truly equivalent structures in terms of openness, robustness, or real-life applicability, as different weave geometries utilise space differently. Fabric geometry influences not only properties such as air permeability and cover factor, but also yarn float exposure, which affects roughness, friction, and even tensile strength. Relative fabric density, defined as the degree of yarn packing relative to the maximum density allowed by the weave, provides a more accurate basis for comparing fabrics than absolute density. Fabrics with different weaves but equivalent relative density (e.g., 90% of maximum density) exhibit comparable fabric openness, areal mass, and weave tightness, enabling consistent assessment of surface-mechanical properties, such as surface roughness, coefficient of friction, and tensile strength. Using relative fabric density as a comparison metric enables textile engineers to gain insights more predictive of manufacturing outcomes, as fabrics with a given weave type are typically designed with optimised relative density rather than absolute density. Additionally, studies based solely on absolute density may overestimate the influence of weave type, as they neglect density limitations with fabric geometry. Nevertheless, all existing studies have used absolute fabric density, not relative, when comparing weaves. However, further research that uses relative fabric density as a controlling parameter when comparing woven fabrics is needed, as this approach provides more scientifically robust and meaningful results for textile engineering and practical applications. Such studies are crucial for making realistic, actionable recommendations tailored to woven fabrics’ performance properties.

This paper aims to contribute to the field of new product development by analysing the effects of the type of weave and relative fabric density on surface roughness and friction coefficient of developed raw cotton woven fabrics designed for shirts. According to Kinebaum’s setting theory, we engineered and produced nine cotton woven fabrics made from combed yarns of 14 tex, incorporating three weave patterns and three relative density levels to evaluate their effects on surface-mechanical properties. Additionally, we compare the behaviour of surface roughness and friction coefficient with absolute fabric density to highlight differences in fabric performance.

2. Materials and Methods

For the experimental analysis, 100% cotton shirting woven fabrics were constructed, with their structural design guided by Kienbaum’s theory of boundary fabric geometry [37]. In order to isolate the effect of woven fabric structure on surface-mechanical properties, only raw, untreated samples woven on Picanol looms under consistent technological settings were selected. All fabrics were produced using combed cotton yarns with a linear density of 14 tex. These yarns had a twist of 928 turns per metre in the Z direction, a packing coefficient and flexibility factor of 0.8, a specific density of 1.2 g/cm³ and a diameter of 0.122 mm. Their tensile strength and elongation at break were 21.2 cN/tex and 5.7%, respectively. The average fibre length was 22.7 mm, and the fibre fineness was 144.5 mtex. The research included three weave types: plain (10-01 01-01-00), 4-end Z-twill (20-02 02-01-01) and 5-end Z-satin (31-01 04-01-03). Within each weave type category, fabrics were produced at three levels of relative fabric density—Level I (55–65%), Level II (65–75%) and Level III (75–85%)—to ensure realistic and representative fabric structures. The theory of boundary fabric geometry establishes that plain weave typically allows for lower maximum fabric densities than twill or satin weaves. This theoretical constraint is reflected in the actual thread densities achieved in the woven samples (

Table 1. The structural parameters of cotton woven samples.

Fabric Code	Type of Weave	Warp Density (Ends/cm)	Weft Density (Picks/cm)	Limit Density (Threads/cm)	Relative Fabric Density (%)
1	plain	38.7	18.2	42.8	62
2	plain	39.4	23.0	42.8	70
3	plain	39.5	32.5	42.8	84
4	twill	51.1	24.0	56.3	62
5	twill	50.2	30.8	56.3	70
6	twill	51.6	39.6	56.3	80
7	satin	56.9	26.5	65.3	59
8	satin	56.9	35.7	65.3	69
9	satin	57.1	46.6	65.3	79

). The equations used to calculate the relative fabric density are given below:

$$t=\sqrt{t_1{\times t}_2}$$

(1)

$$t_1={\displaystyle \frac{G_1}{G_{lim}}}\times 100 t_2={\displaystyle \frac{G_2}{G_{lim}}}\times 100$$

(2)

$$G_{lim}=g\times V\times \sqrt{{\displaystyle \frac{1000}{T}}}$$

(3)

$$g=5.117\times \sqrt{{\rho }_{fib} i}$$

(4)

$$V={\displaystyle \frac{1.732\times R}{R+\frac{a\times (2.6-0.6\times z)}{f}\times 0.732}}$$

(5)

where t represents the relative fabric density expressed as a percentage, G denotes the actual thread density (threads/cm), and G_lim refers to the theoretical maximum thread density achievable for a given type of weave. The symbol g indicates the nominal or base thread density (threads/cm), while V stands for the weave-specific structural coefficient known as the weave factor. T is the linear density of the yarn in tex, and ρ_fib is the volumetric density of the fibre material in g/cm³. The parameter i corresponds to the yarn compactness or packing coefficient. R signifies the total number of warp or weft threads within one full weave repeat, and a indicates the number of yarn bends (passes from fabric’s front to back and back again) per repeat. The variable z defines the minimal shift in the weave pattern, and f characterises the yarn’s flexibility or bending capability. Subscripts 1 and 2 are used to distinguish between warp and weft yarns, respectively.

The surface-mechanical properties of woven samples, such as surface roughness (SMD) and coefficient of friction (MIU), were obtained using a Kawabata Evaluation System for Fabrics (KES-FB4 AUTO), a surface analysing tester manufactured by Kato Tech Co., Ltd. in Kyoto, Japan. All tests were conducted under standard atmospheric conditions (20 °C ± 2 °C, 65% ± 2% RH), with specimens preconditioned for 24 h before analysis. Cotton woven fabrics were prepared as 20 cm × 20 cm samples. Each sample was mounted on the KES-FB4 platform, and the surface to be tested was facing upwards. A 5 mm-wide U-profile measurement head with a 0.5 mm radius and a constant force of 10 cN was used to automatically measure vertical displacement (for SMD calculation) and tangential force (for MIU calculation) over a 3 cm fabric path in a single test. Fabric movement speed was set to 1 mm/s, with an initial fabric tension of 4 N, and the tests were performed separately for the warp and weft directions. Surface roughness (SMD), expressed in μm, was calculated as the mean absolute deviation of surface height from the average surface height (Equation (6)) over the range of fabric path between 0.5 and 2.5 mm (e.g., 2 cm), and the coefficient of friction (MIU) was derived from Equation (7).

$$SMD={\displaystyle \frac{1}{L}}{\int }_0^X\left|h\left(x\right)-\overline{h}\right|dx$$

(6)

$$MIU={\displaystyle \frac{F_f}{F_n}}$$

(7)

Here, h(x) is the vertical displacement at position x in metres, $\overline{h}$ is the mean height over the measured fabric length (L), F_f is the mean friction force in cN, and F_n is the normal force (10 cN). Each measurement was repeated three times in both principal directions (warp and weft), and the mean values were used for further analysis.

To assess potential differences in surface-mechanical properties among the samples based on the type of weave and relative fabric density, an analysis of variance (ANOVA) was conducted. This statistical analysis aimed to evaluate the null hypothesis, which assumes there are no significant differences between groups concerning the aforementioned factors. The ANOVA procedure was performed using IBM SPSS Statistics 26, with a predefined significance level of 0.05 corresponding to a 95% confidence interval.

3. Results and Discussion

To elucidate the relationship between fabric geometry and its surface-mechanical properties, we incorporated the fundamental physical mechanisms of yarn deformation and yarn-to-yarn contact. Changes in surface roughness (SMD) and coefficient of friction (MIU), presented in the following sections, were a direct consequence of how individual yarns responded to the constraints imposed by the weave type and fabric density.

3.1. Statistical Analysis for Woven Fabric Surface Roughness and Coefficient of Friction

Table 2. Results of the ANOVA analysis for woven fabric surface roughness and coefficient of Rriction.

Dependent Variable: Surface roughness
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
intercept	224.640	1	224.640	12.821	0.044
type of weave—W	29.419	2	17.709	45.438	0.002
relative fabric density—RD	6.272	2	3.136	9.687	0.029
W and RD	1.295	4	0.324	-	-
Dependent Variable: Coefficient of friction
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
intercept	0.108	1	0.108	12,807.95	0.959
type of weave—W	19.744 × 10−5	2	9.872 × 10−5	0.614	0.586
relative fabric density—RD	14.120 × 10−5	2	7.060 × 10−5	0.439	0.672
T and W	0.001	4	0.000	-	-

shows the results of the variance analysis (ANOVA) for surface roughness and the coefficient of friction. These results suggest that structural parameters affect surface-mechanical properties differently. Both structural parameters (e.g., type of weave and relative fabric density) had a statistically significant effect on surface roughness. However, none of the structural parameters had a statistically significant effect on the coefficient of friction. The influence of the structural parameters on these properties will be discussed in the following subchapters.

3.2. Analysis of Surface Roughness in Relation to the Direction of the Thread System

The surface roughness of the woven samples was measured in the warp and weft directions. For economic reasons, all samples were constructed with a significantly higher warp density than weft density. However, the increase in relative fabric density was achieved by ensuring that the samples had approximately the same density of warp threads for each fabric group relative to the type of weave, while varying the density of weft threads (see Table 1). Consequently, surface roughness varied significantly based on the direction of the sensor movement in the measuring device. The fabrics exhibited different behaviours depending on the weave type. The plain fabric, which had the strongest interlacing of warp and weft threads, was the most stable and behaved differently from less stable fabrics, such as 2/2 twill and 5-end satin, which had floating threads.

Based on Figure 1a, which represents the measured surface roughness of plain fabrics at the I level of relative fabric density, the warp direction (blue line) showed a higher amplitude in surface roughness than the weft direction (orange line). Higher amplitude in the warp direction indicated greater vertical deviations in the surface profile—the peaks and valleys were more pronounced. As the sensor moved along the warp direction (i.e., across the weft threads), it captured height differences between adjacent weft yarns. Due to the lower weft density (fewer picks per unit length), the spacing between weft yarns was greater, resulting in a coarser surface profile. This led to higher surface roughness in the warp direction. In contrast, the surface profile in the weft direction was smoother and more uniform. Here, the sensor moved across the warp threads, which were typically present in higher density. The increased frequency of thread intersections led to a finer micro-topography, with lower amplitude deviations. The tightly packed warp threads contributed to a more stable and even surface, minimising undulations. Additionally, the tension and overlapping of warp yarns helped flatten the surface, further reducing surface irregularities. Figure 1a also shows the difference in frequency of the peaks in the warp and weft directions. Due to the higher number of warp threads per unit length, the weft direction had a higher frequency of peaks and valleys. The warp direction showed lower frequency variations, consistent with fewer weft threads.

In warp-dense 2/2 twill woven fabrics (Figure 1b), surface roughness was greater in the weft direction than in the warp direction—a reversal of the trend observed in warp-dense plain weave under similar structural asymmetry (warp density was much greater than weft density). This phenomenon occurred as the high warp density caused the weft yarns to form a pronounced crimp curvature. Concurrently, the 2/2 float system allowed extended segments of minimally constrained weft yarns to form isolated arches between interlacing points. When measured perpendicular to the warp (i.e., in the weft direction), the sensor traversed these amplified crimp peaks, yielding periodic roughness maxima (e.g., 29 µm at 1,9 cm displacement, corresponding to float centres). Conversely, measurements taken parallel to the warp direction followed the flatter, tensioned warp floats, yielding a near-neutral, lower roughness (0–7 μm). This fundamentally contrasted with the warp-dense plain weave, where frequent 1:1 interlacing distributed weft crimp into smaller, more numerous peaks that elevated roughness in the warp direction instead. The combination of float length and yarn crimp asymmetry, therefore, reversed the directional roughness behaviour in 2/2 twill structures. With its smoother profile, the warp direction in 2/2 twill fabrics may have been advantageous for applications requiring low-friction surfaces. In contrast, the rougher weft direction may have enhanced tactile or frictional properties where desired.

In the warp-dense 5-end satin fabric with 56.9 warp threads and 26.5 weft threads per centimetre (Figure 1c), the surface roughness values reflected a topography characterised by weft depressions. At the binding points, where the warps passed under the wefts, the high tension in the warp lifted the floats upwards. This created an elevated plane with a lower roughness in the warp direction. Conversely, the exposed weft yarns at the binding points were relatively recessed due to the dominance of the warp floats. The tightly packed warps formed a nearly continuous surface plane, raising the neutral reference level. Weft compression and geometric shadowing occurred concurrently. The wefts (26.5 picks per cm) were crimped downwards by the adjacent warp floats as there was little structural support between the sparse binding points (one per five yarns). At the binding points, the warps dove below the wefts. However, the wefts—constrained by high warp density—could not rise to match the float plane height. This created net depressions. Directional measurements and photographs (see Figure 2) confirmed that, in the warp direction, the sensor glided along the elevated floats, resulting in a lower detected roughness. In the weft direction, the sensor traversed the floats and binding points, resulting in detected weft recessions caused by uneven reed dent. The conclusions for the II and III levels of relative fabric densities showed similar fabric behaviour regarding the direction of the thread system.

3.3. Analysis of Surface Roughness in Relation to the Type of Weave

In woven structures, surface roughness is significantly influenced by the type of weave, relative fabric density and the direction of observation. Figure 3 illustrates the surface roughness at the first level of relative fabric density for samples according to the type of weave used, separately for the warp and weft directions. In the warp direction, distinct differences were observed among weave types. The plain fabric, with the highest number of interlacements per unit area, exhibited maximum yarn crimp and minimum thread density (warp/weft density: 38.7/18.2 threads/cm). This frequent interlacing caused pronounced undulations in the yarn path, resulting in a highly textured surface with a surface roughness of 11 μm (with a maximal amplitude of ±30 μm). This was a direct result of the high degree of yarn crimp imposed by the frequent 1/1 interlacements, where each yarn underwent pronounced undulations as it passed over and under the opposing yarn set, creating a dense pattern of small peaks and valleys. In contrast, the 2/2 twill fabric introduced a diagonal pattern with fewer interlacements and a greater warp/weft density (50.2/24 threads per cm), allowing the yarns to float over two threads before interlacing. This reduced crimp and led to moderate surface roughness of 2 μm (with maximal amplitude ±7 μm). While the reduced crimp created a smoother profile along the tensioned warp floats, the structure’s mechanics differed in the weft direction. The 2/2 float system allowed extended segments of minimally constrained weft yarns to form isolated arches between interlacing points, which resulting in periodic roughness maxima. The 5-end satin fabric had the highest thread density (warp/weft density: 56.9/26.5 threads per cm) and the longest warp floats (over four threads). This type of weave minimised interlacements and crimp and allowed a smooth, flat surface with roughness typically below ±3 µm (with a maximal amplitude of ±14 µm). Due to weft depressions, the 5-end satin fabric exhibited slightly higher surface roughness in comparison to the 2/2 twill fabric. The primary form of yarn deformation in this structure was not crimp, but rather the formation of “weft depressions”. The high tension in the densely packed warp yarns elevated the long floats to form a raised plane, while the sparsely supported weft yarns were pushed downward into recesses, creating a distinct topography of elevated plateaus and valleys. Progressing from plain to 2/2 twill/5-end satin weaves revealed an inverse relationship between interlacement frequency and surface smoothness. The fabric surface became progressively smoother as interlacement frequency decreased, and yarn float length increased. This finding contrasts with studies [4,24], which compared woven fabrics based on absolute fabric density.

There was little difference in surface roughness among the fabrics in the weft direction based on type of weave. The plain fabric had the lowest thread density (warp/weft density: 38.7/18.2 threads per cm) and the highest interlacement frequency, resulting in the maximum yarn crimp. This caused a greater undulating yarn path and a rougher surface texture. Despite its structural roughness, the plain weave exhibited an average surface roughness of 6.5 μm, slightly higher than that of the 5-end satin weave (6.0 μm) but lower than that of the 2/2 twill weave (7.1 μm).The 2/2 twill fabric (warp/weft: 50.2/24 threads per cm) featured a diagonal interlacing pattern that reduced the number of interlacements and crimp compared to the plain fabric. However, due to the nature of its diagonal floats and intermediate thread density, it exhibited the highest surface roughness of 7.1 μm. This suggests that, although the structure is theoretically smoother, the diagonal floats may introduce localised surface irregularities. This was evident in the examined sample, where uneven reed dent (see Figure 2b) caused greater vertical height differences in the weft direction. The 5-end satin fabric exhibited the highest thread density (warp/weft density: 56.9/26.5 threads per cm) and the lowest interlacement frequency. This structure featured the longest warp floats, pronounced weft recessions, and minimal crimp, resulting in the smoothest and flattest surface. This was reflected in the surface roughness of 6.0 μm—the lowest among all weave types.

These findings suggest that despite structural crimp and interlacement frequency being the key determinants of surface texture, average surface roughness is also influenced by float distribution, orientation, and reed irregularities. Indeed, these factors can introduce subtle variations in the surface profile, even in weaves with fewer interlacements.

3.4. Analysis of Surface Roughness in Relation to Relative Fabric Density

The woven fabric samples were constructed by maintaining a constant warp density within each fabric group for a given weave type, while increasing the weft density to achieve three distinct levels of relative fabric density, following the theory of limit fabric construction. Figure 4 illustrates the effect of relative fabric density on total surface roughness, calculated as the average of warp and weft direction measurements, representing the overall surface roughness of the woven fabric. Error bars indicate the standard deviation from three replicate measurements.

The results clearly demonstrate that increasing the relative fabric density consistently reduces surface roughness in plain, 2/2 twill, and, to some extent, 5-end satin fabrics, with plain fabrics showing the highest roughness overall. This was due to tighter yarn packing and fewer surface irregularities. The physical mechanism driving this was yarn compression; as density increased, the peaks of the crimped yarns were forcibly flattened and interstitial gaps were minimised, reducing the overall amplitude of the surface topography and thus lowering the measured SMD. Plain fabrics exhibited the highest surface roughness (9.1 µm at around 60% RD, decreasing to 6.1 µm at around 80% RD), as their frequent interlacings created a more uneven texture. In contrast, the 2/2 twill fabrics exhibited intermediate roughness (4.6 µm at around 60% RD, decreasing to 2.5 µm at around 80% RD), due to their diagonal float pattern, which more evenly distributed yarn intersections. The 5-end satin fabrics exhibited the lowest surface roughness values (4.5 µm at around 60% RD, decreasing to 3.4 µm at around 70% RD, and increasing to 3.6 µm at around 80% RD), as their long floats minimised interlacing points, creating a smoother surface. As relative density increased from approximately 60% to 80%, the plain fabrics exhibited a 33% reduction in surface roughness, while the 2/2 twill fabrics showed a 45.7% decrease. Although the plain fabric’s total surface roughness remained higher, it was highly responsive to density changes, nearly proportional to the twill’s improvement. The plain weave’s frequent interlacements amplified yarn compaction: at lower fabric density, pronounced yarn crimp and interstitial gaps increased surface roughness, but at higher density, these irregularities were flattened, reducing roughness. The 2/2 twill fabric benefited from density-induced yarn compaction and its inherent float structure, which synergistically enhanced surface smoothness. Thus, while the 2/2 twill fabric achieved greater total smoothness, the plain weave’s relative improvement was comparably sensitive to density changes. The 5-end satin fabrics demonstrated the lowest sensitivity to density changes among the three weaves, reducing total surface roughness by only 24.4% (from first to second level of RD). This limited improvement suggested that the satin fabric’s long floats and minimal interlacings already provide near-optimal surface smoothness at lower densities, leaving little room for enhancement through compaction alone. On the contrary, at the third level of RD, the surface roughness was raised slightly, as the reduction in surface roughness only reached 20%. At the third level of relative fabric density (highest compression), the 2/2 twill fabric exhibited significantly lower surface roughness (2.5 µm), which was a reversal of the performance hierarchy observed at lower densities. This phenomenon arose from fundamental structural differences: the shorter floats (two threads) and frequent diagonal interlacings of 2/2 twill fabric provide superior resistance to yarn deformation under high compression, distributing stresses evenly and minimising surface irregularities. In contrast, the extended floats of 5-end satin fabric (spanning four yarns) and sparse binding points concentrated compressive forces, promoting localised buckling and yarn displacement that increased roughness, despite the fabric’s inherent smoothness advantage at lower densities. Essentially, the long, unsupported floats of the 5-end satin were susceptible to localised buckling, which introduced new surface irregularities under intense compaction. The 2/2 twill’s structure provided superior stability, resisting this deformation and allowing it to achieve a smoother surface. This density-dependent inversion, where 2/2 twill’s structural stability outperforms 5-end satin’s long-float system, highlights the critical role of weave-density interactions in optimising surface topography. These findings emphasise the importance of selecting the correct type of weave and relative fabric density to engineer surface smoothness. 5-end satin and 2/2 twill weaves are preferable for applications requiring low roughness, particularly at relative fabric density levels exceeding 60%.

3.5. Analysis of Surface Roughness and Coefficient of Friction in Relation to the Absolute Fabric Density

Since surface roughness is a basic material characteristic that affects friction, we included an analogy between the two in the study. Figure 5 shows the relationship between total surface roughness (SMD), the coefficient of friction (MIU), and absolute thread density in the fabric. The absolute thread density was calculated as the arithmetic mean of the warp and weft thread densities.

We should acknowledge that ANOVA did not confirm any statistically significant influence of weave type or relative fabric density on the friction coefficient (p > 0.05). Nevertheless, graphical trends revealed distinct practical relationships across weaves. Firstly, comparing all three weaves revealed distinct patterns. Higher density smoothed all fabrics relative to the type of weave, yet it impacted friction in different ways. SMD in plain, 2/2 twill, and 5-end satin fabrics decreased with higher absolute fabric density. The friction coefficient (MIU) exhibited divergent behaviour: it rose with increasing absolute fabric density in plain and 2/2 twill fabrics but decreased in 5-end satin fabrics. The ANOVA’s lack of statistical significance for the friction coefficient (p > 0.05) warrants further explanation, as graphical analysis in Figure 5 reveals clear practical trends. This outcome stems from the ANOVA’s structure, which tests main effects of weave type and relative fabric density independently across the dataset. However, a strong interaction effect was observed, where fabric density’s influence on friction varies significantly—and oppositely—by weave type. Specifically, for plain and 2/2 twill fabrics, a higher friction coefficient was caused by increased fabric density due to intensified yarn-on-yarn jamming. Conversely, for the 5-end satin fabric, a decrease in friction was caused by increasing density as the long floats were flattened and contact points were minimised. When the ANOVA model assesses the overall main effect of ‘fabric density’, these divergent responses are averaged. The positive trend in the plain and twill fabrics is effectively cancelled out by the negative trend in the satin fabric, resulting in a net effect that is too weak to be statistically significant. Similarly, the main effect of ‘weave type’ is non-significant, as no single weave type exhibited higher or lower friction across all densities; the performance rankings reversed with changing density. Graphical analysis is thus critical, as it reveals these interaction-driven relationships masked by a main-effects ANOVA, providing valuable insights for practical fabric engineering that would otherwise be missed.

Plain fabrics exhibited a 33% reduction in surface roughness across the absolute fabric density range of 285–360 threads/cm and a 14% increase in coefficient of friction due to shear resistance from yarn crimp intensification at densely packed crossover points. This decoupling of roughness and friction was governed by yarn-to-yarn contact mechanics. While the surface’s macro-structure was smoothed by flattening the yarn crimp, the higher density packed yarns tightly, increasing the normal forces at crossover points. This led to intensified yarn-on-yarn jamming and greater shear resistance, causing friction (MIU) to rise even as the surface became geometrically smoother (SMD decreased). 2/2 twill fabrics showed a 45,7% SMD decline across the absolute fabric density range of 376–456 threads/cm, and a 14% increase in coefficient of friction arose from intensified yarn-on-yarn jamming at crossover points under higher density. 5-end satin fabrics demonstrated coordinated 20% SMD and 22% MIU reductions across the absolute fabric density range of 417–518 threads/cm, as compressed long floats minimised contact points. The physical mechanism was related to the total contact area. The 5-end satin fabric’s sparse interlacement points allowed compression to flatten long floats into a more uniform plane, minimising the real contact area with a surface. Unlike the plain and 2/2 twill fabrics, which exhibited significant yarn-on-yarn jamming, the satin fabric showed reduced surface roughness and friction coefficient in tandem with increasing fabric density. These trends imply that while the type of weave mediates the magnitude of crossover point constraints—amplifying shear resistance in plain/2/2 twill versus reducing it in 5-end satin—higher actual fabric density universally enhances surface roughness. The consistent decoupling of SMD and MIU in plain and 2/2 twill fabrics—where surface roughness coincides with rising friction—contrasts sharply with 5-end satin’s coupled reductions. The results underscore the dominant role of fabric geometry.

4. Conclusions

This research examined the influence of woven fabric geometry—specifically, the type of weave and relative fabric density—on two key surface-mechanical properties: surface roughness and the coefficient of friction. Conclusions of this study are as follows:

• The type of weave and the relative fabric density exhibited a statistically significant effect on surface roughness. The coefficient of friction, however, was not statistically influenced by either the type of weave or relative fabric density (confirmed by ANOVA);
• Plain fabrics exhibited the highest surface roughness due to frequent warp-weft interlacements and pronounced crimp height. 2/2 twill fabrics exhibited intermediate surface roughness, where diagonal floats mitigated the influence of structural density. In contrast, 5-end satin fabrics yielded the lowest overall surface roughness, attributable to extended longitudinal floats and minimal interlacement points, which produced the smoothest and flattest surface profile at the first and second levels of relative fabric density. At the third level of relative density (highest compression), the 2/2 twill fabrics exhibited significantly lower surface roughness (2.5 µm), which is a reversal of the performance hierarchy observed at lower densities;
• Increasing relative fabric density reduced surface roughness in all weave types due to tighter yarn packing and fewer surface irregularities. The degree of this reduction depended on the type of weave: plain and 2/2 twill fabrics showed the greatest relative improvements, while the 5-end satin fabrics were less responsive, maintaining smoothness even at lower densities;
• Although one might expect higher surface roughness to indicate higher friction, the study found that this was not necessarily true, especially for plain and 2/2 twill fabrics. In this case, increasing the warp/weft density smoothed the surface, but did not reduce friction due to the intensified yarn-on-yarn interaction at high densities. 5-end satin fabrics were distinct in this matter as they exhibited a simultaneous reduction in both surface roughness and coefficient of friction as warp/weft density increased;
• Both 5-end satin and 2/2 twill fabrics can be used for applications that demand low surface roughness or higher smoothness, particularly at relative fabric density levels exceeding 60%;
• The findings revealed that while the type of weave and relative fabric density directly influenced surface roughness, frictional behaviour was governed by the more complex yarn-level contact mechanics and jamming effects that were unique to each weave structure as density changed.

Mastering the interplay between the type of weave and relative fabric density allows textile engineers to control the surface-mechanical behaviour of woven fabrics more precisely. This understanding is essential for optimising comfort, appearance, and durability in apparel, interior and technical textiles. A key contribution of this research is the demonstration that relative fabric density is a critical—and superior—parameter for evaluating the surface-mechanical properties of woven fabrics. Traditional comparisons using absolute fabric density can be misleading, as they overlook the inherent geometric constraints of different weaves, which can lead to flawed conclusions. By normalising for the maximum packing potential of each structure, relative fabric density provides a standardised and more scientifically robust foundation for analysis, allowing for true “apples-to-apples” comparisons between different fabric types. This study’s findings—particularly the density-dependent performance inversion where 2/2 twill became smoother than 5-end satin at high densities—would likely remain hidden if only absolute fabric density were considered. Using relative fabric density as a controlled variable represents a notable innovation, offering valuable guidance for future woven fabric engineering. Therefore, this paper strongly advocates adopting relative fabric density as a standard metric in textile research. Its integration is not merely an incremental improvement, but a necessary step toward generating more accurate, comparable, and practically applicable insights into woven fabric performance.

Further studies that use relative, rather than absolute, fabric density as the primary parameter for comparing weaves are needed. Expanding this approach to a broader range of weave types and applications would generate scientifically robust and meaningful results for real-world manufacturing and product development. Additionally, there is significant potential to develop more realistic in situ testing methodologies and to integrate surface analysis with computational modelling and machine learning to predict performance and guide the design of advanced woven fabrics.