Abstract
Loop length is one of the most relevant variables to control while producing knitted fabrics because the final characteristics of the finished fabric depend on it to a great extent. The procedure followed to calculate it is based on standard UNE-EN 14970, and it is cumbersome, time-consuming and requires yarn-measuring equipment. This study investigated several single jersey and 1 × 1 rib structures produced with different yarn counts and 100% cotton yarns, and a 1 × 1 rib structure that was half-plated in alternating courses by defining four relaxation states of the different fabrics: two knits (knitting and dry relaxation and knitting and wet relaxation) and two dyed (dyed and dry relaxation and dyed and wet relaxation). The most significant dimensional variables were characterized in all the relaxation states and models were presented that explain the variability of the yarn length absorbed by the loop using other variables that are much simpler to analyze.
Manufactured knitted fabrics are popular given their excellent adaption capacity, hence this technology is used to manufacture underwear and sportswear. Weft-knitted fabrics also present a high degree of dimensional instability, which makes working with this fabric type throughout the manufacturing process complicated. To ensure dimensional stability throughout the lifetime of such garments, it is necessary to control the dimensional parameters during the entire production process and to confer the final garment with a minimum energy state to thus make it dimensionally stable.
Obtaining stable knitted fabrics is a purpose that has long since been a matter of concern. In 1926, Chamberlain 1 presented the first mathematical model to determine the knitted fabric loop configuration. Since then, other research works have undertaken relevant studies which conceptualise, define and mathematically formulate the dimensional behaviour of knitted fabrics.2–18
For years, Münden's equations19–21 have been applied to calculate the K factors that determine fabric dimension and loop rules. Doyle 22 discovered that knit density depended on loop length (SL). Nutting and Leaf 23 introduced another variable into Münden's equations, namely yarn count. Knapton et al.24,25 demonstrated that dimensional stability in plain-knitted fabrics can be achieved by mechanical means, relaxation techniques or chemical treatments. Fletcher and Roberts26–31 studied the geometry, relationship and dimensional stability of knits fabrics. The Starfish project32–37 is a long-term program of applied research whose basic aim is to create a comprehensive and systematic database describing the dimensional properties of finished cotton knits, and hence to derive a simple, rational and reliable system for predicting finished dimensions starting from the knitting and finishing specifications. The study by Ulson et al. 38 was based on determining the own K factors of each production process, based on differences between the K factors obtained in fabrics treated during a continuous bleaching process or an exhaustion bleaching process. Saravana and Sampath 39 predicted the dimensional properties of a double cardigan-type fabric using an “artificial neural network system.” Mobarock 40 proposed some mathematical ratios to predict the weight (GSM), width and final shrinkage of a finished cotton knitted fabric. Eltahan et al. 41 and Eltahan 42 determined the SL, tightness factor and porosity of a single jersey knitted fabric using mathematical equations. Sitotaw 43 and Sitotaw and Adamu 44 studied the dimensional characteristics of five knitted fabric structures made with 100% cotton and 95% cotton/5% elastane (EA). They concluded that the presence of EA significantly varied the outcome of the dimensional variables. Llinares et al. 45 proposed a procedure to calculate the SL of interlock fabrics by means of linear regression models to avoid applying standard UNE-EN 14970.
Objectives
This study is of great relevance for the technical textile industries, since it greatly simplifies the productive calculations for weft-knitted fabric companies. It offers an effective method for the estimation of the SL in the knitted fabrics in single jersey and 1 × 1 rib structures, after the knitting, dyeing and finishing processes. From the knowledge of the variables it is much easier to calculate, such as measurements as the wales per centimeter (WPCM) and courses per centimeter (CPCM) in the fabrics obtained in the knitting machines, without the need to perform a subsequent analysis based on the standard UNE-EN 14970.
In this way the quality control of the knitted fabrics is streamlined, being able to adjust the desired final characteristics of them more quickly contributes to the improvement of the increase in the quality of the final product.
The procedure employed by Llinares et al. 45 to calculate the SL of interlock fabrics can be applied to 1 × 1 rib and single jersey structures in cotton fabrics.
Experimental details
Materials and methods
The circular machines used to produce the knitted fabrics with 1 × 1 rib 100% cotton, 1 × 1 rib plated with elastane and 100% plain-knitted cotton structures
In the 1 × 1 rib structure, two different fabric types were obtained: a cotton fabric with a yarn count of 26.96 Ne and another cotton fabric with a yarn count of 30.26 Ne. From each fabric, 20 pieces were produced with the diameter of each machine as shown in Table 1 (14”, 16”, 18” and 20”), which gave 80 pieces with a yarn count of 26.96 Ne and 80 more with a yarn count of 30.26 Ne.
With the 1 × 1 rib structure, whose composition is 95% cotton-5% EA, plated cotton with a yarn count of 50.24 Ne with elastomer with a yarn count of 22 dtex half-plated in alternating courses were obtained. This gave 20 pieces of each selected machine diameter (16” and 18”) and 40 pieces were obtained.
For the single jersey structure, fabrics were produced with yarn counts of 26.96, 30.26 and 37.39 Ne using the machine diameters (17”, 18”, 22” and 24”), as indicated in Table 1. In all, 80 pieces were obtained from each employed yarn with yarn counts of 26.96, 30.26 and 37.39 Ne (corresponding to 20 pieces of diameter 17”, 20 of diameter 18”, 20 of diameter 22” and 20 of diameter 24”).
Two fabric relaxation states were distinguished after the knitting process ended.
Knitting and dry relaxation (KDR). Once the fabric had been produced, it was left in a conditioning atmosphere until a constant weight was obtained. Knitting and wet relaxation (KWR). The conditioned fabric was left until a constant weight was obtained and was submitted to a dimensional stability analysis according to standard UNE EN ISO 6330, of September 2012,
46
procedure 9N.
It is necessary to bear in mind that during the KWR relaxation process, no scouring fabric is obtained because this process does not remove peptine from cotton and, therefore, fibers continue to perform hydrophobically. However, this process manages to eliminate the stresses that accumulate during the knitting process and provides a dimensionally stable fabric, but the results of the dimensional variables having nothing to do with those corresponding to a scouring and bleaching process. This relaxation state can be used as an intermediate state between the KDR state and that obtained after the scouring process, and it helps to predict the dimensional properties of the finished fabric.
The pieces identified in each lot were placed in a conditioning atmosphere until a constant weight was obtained. Then two samples of each piece were cut to analyze them in relaxation states KDR and KWR. This analysis consisted of establishing the number of loops per length unit and area unit (WPCM, CPCM and stitch density) in line with standard UNE-EN 14971 47 to determine the laminar weight according to standard UNE-EN 14970 48 and the factors (K c , K w and K r ) by applying Münden's equations.
The lots are bleached by the exhaustion process. The dyeing conditions and the added products are respectively indicated in Figure 1 and Table 2.
Process diagram of scouring and bleaching fabrics. Products employed for scouring and bleaching process
After completing hydroextraction and then drying the lots, the pieces to be analyzed were identified, a sample of them was taken and they were left in a conditioning atmosphere.
Two relaxation states were distinguished after the dyeing process.
Dyed and dry relaxation (DDR). The dyed knitted fabric was left in a conditioning atmosphere until a constant weight was obtained. Dyed and wet relaxation (DWR). The dyed and conditioned knitted fabric was left until a constant weight was obtained. Then a dimensional stability test was run with it according to regulation UNE EN ISO 6330, of September 2012,
46
procedure 4N.
The relaxation states distinguished in the knitting and dyeing processes are represented in Figure 2.
Relaxation states in the knitting and dyeing processes. KDR: knitting and dry relaxation; KWR: knitting and wet relaxation; DDR: dyed and dry relaxation; DWR: dyed and wet relaxation.
Results and discussion
Variables of interest are represented by a boxplot. A boxplot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile and maximum. The term “boxplot” comes from the fact that the graph looks like a rectangle with lines extending from the top and bottom.
Figures 3–6 show the corresponding results of the variables WPCM, CPCM, stitch density/cm2 (SD) and SL from analyzing the 1 × 1 rib pieces with yarn counts 26.96 and 30.26 Ne of 100% cotton and 50.24 Ne 100% of cotton with EA and 22 dtex (half-plated in alternating courses), in relaxations states KDR, KWR, DDR and DWR.
Number of courses per centimeter (CPCM) for 1 × 1 rib fabrics. EA: elastane; KDR: knitting and dry relaxation; KWR: knitting and wet relaxation; DDR: dyed and dry relaxation; DWR: dyed and wet relaxation. Number of wales per centimeter (WPCM) for 1 × 1 rib fabrics. EA: elastane; KDR: knitting and dry relaxation; KWR: knitting and wet relaxation; DDR: dyed and dry relaxation; DWR: dyed and wet relaxation. Stitch density/cm2 (SD) for 1 × 1 rib fabrics. EA: elastane; KDR: knitting and dry relaxation; KWR: knitting and wet relaxation; DDR: dyed and dry relaxation; DWR: dyed and wet relaxation. Loop length (SL) for 1 × 1 rib fabrics. EA: elastane; KDR: knitting and dry relaxation; KWR: knitting and wet relaxation; DDR: dyed and dry relaxation; DWR: dyed and wet relaxation.



Figures 7–10 show the corresponding results of the variables WPCM, CPCM, SD and SL in the analysis done with the single jersey pieces with yarn counts of 26.96, 30.26 and 37.39 Ne of 100% cotton in relaxation states KDR, KWR, DDR and DWR.
Number of courses per centimeter (CPCM) for single jersey fabrics. KDR: knitting and dry relaxation; KWR: knitting and wet relaxation; DDR: dyed and dry relaxation; DWR: dyed and wet relaxation. Number of wales per centimeter (WPCM) for single jersey fabrics. KDR: knitting and dry relaxation; KWR: knitting and wet relaxation; DDR: dyed and dry relaxation; DWR: dyed and wet relaxation. Stitch density/cm2 (SD) for single jersey fabrics. KDR: knitting and dry relaxation; KWR: knitting and wet relaxation; DDR: dyed and dry relaxation; DWR: dyed and wet relaxation. Loop length (SL) for single jersey fabrics. KDR: knitting and dry relaxation; KWR: knitting and wet relaxation; DDR: dyed and dry relaxation; DWR: dyed and wet relaxation.



Having analyzed the fabrics in relaxation states KDR, KWR, DDR and DWR, the intention was to observe the relation linking the variables to obtain models that predict the SL of all the aforementioned relaxation states.
Valid models proposed by linear regression for all the studied 1 × 1 rib fabrics in relaxation states knitting and dry relaxation (KDR) and knitting and wet relaxation (KWR)
DV: dependent variable; IV: independent variable; WPCM: wales per centimeter; CPCM: courses per centimeter; SD: stitch density/cm2; SL: loop length (cm).
Valid models proposed by linear regression for all the studied single jersey fabrics in relaxation states knitting and dry relaxation (KDR) and knitting and wet relaxation (KWR)
DV: dependent variable; IV: independent variable; WPCM: wales per centimeter; CPCM: courses per centimeter; SD: stitch density/cm2; SL: loop length (cm).
Valid models proposed by linear regression for all the studied 1 × 1 rib in relaxations states dyed and dry relaxation (DDR) and dyed and wet relaxation (DWR)
DV: dependent variable; IV: independent variable; WPCM: wales per centimeter; CPCM: courses per centimeter; SD: stitch density/cm2; SL: loop length (cm).
Valid models proposed by linear regression for all the studied single jersey fabrics in relaxation states dyed and dry relaxation (DDR) and dyed and wet relaxation (DWR)
DV: dependent variable; IV: independent variable; WPCM: wales per centimeter; CPCM: courses per centimeter; SD: stitch density/cm2; SL: loop length (cm).
Figures 11–13 illustrate the linear regression models adjusted for the single jersey fabrics in relaxation state DWR.
Linear regression model for single jersey fabrics (relation between courses per centimeter and loop length in the dyed and wet relaxation state). Linear regression model for single jersey fabrics (relation between wales per centimeter and loop length in the dyed and wet relaxation state). Linear regression model for single jersey fabrics (relation between stitch density/cm2 and loop length in the dyed and wet relaxation state).


For relaxation states KDR and KWR, it was possible to predict the SL variable by the models proposed for the analyzed 1 × 1 rib fabrics (Table 2) and single jersey fabrics (Table 3). The same can be stated for the models proposed in Tables 4 and 5 for the 1 × 1 rib and single jersey fabrics in relaxation states DDR and DWR, respectively. To this end, it was necessary to know some independent variables, such as the CPCM, WPCM and SD. These variables can be obtained quite quickly by applying standard UNE-EN 14971 47 and by simply using a thread counter. Nevertheless, in order to calculate SL according to standard UNE-EN 14970, 48 an apparatus that measures yarn length, and that must be used in a laboratory, is necessary. By using the models herein presented it is possible to avoid the whole process set out in the standard, which speeds up the process followed to obtain the SL.
All the proposed models had an R2 that exceeds 95%, which accounted for optimum variability from the existing linearity with the independent variables CPCM, WPCM and SD.
The proposed models underwent a cross-validation process, which consisted of validating the models for a test data set, which comprised a collection of lots of each fabric and machine diameter. This analysis included calculating the SL of each lot in relaxation states KDR, KWR, DDR and DWR. In parallel, the values estimated by the proposed models were calculated. The estimated error was the difference between the estimated value and the actual value.
The errors estimated with the models proposed to estimate the SL in relaxation states KDR and KWR for the 1 × 1 rib fabrics (Table 2) fell within the 0.015–0.075 cm range. Applying the models that use the independent variables WPCM in relaxation state KDR (with a maximum estimated error of 0.015 cm) and CPCM in relaxation state KWR (with a maximum estimated error of 0.007 cm) is recommended because it is more accurate. In the single jersey fabrics (Table 3), the minimum estimated error was 0.004 cm, and the maximum estimated error was 0.011 cm. Given its better accuracy, using the models that estimate the SL from the independent variable WPCM is recommended.
The errors estimated with the models proposed to make estimations in relaxation states DDR and DWR for the 1 × 1 rib knitted fabrics (Table 4) fell within a minimum value of 0.010 cm and a maximum of 0.041 cm. Using the models that predict the SL with the variables WPCM or CPCM is recommended, regardless of being in relaxation state DDR, and for state DWR, which uses the variable WPCM. The models proposed for the single jersey fabrics (Table 5) in relaxation states DDR and DWR gave errors that ranged between 0.005 and 0.009 cm, and the most accurate models were those that used the independent variables WPCM and CPCM.
Conclusions
This study investigated the dimensional properties of two groups of fabrics: one formed by three single jersey fabrics and another by three 1 × 1 rib fabrics. Linear regression models are proposed to predict SL in relaxation states KDR, KWR, DDR and DWR for the following fabrics.
1 × 1 rib fabrics: two fabrics made with yarn lengths 26.96 and 30.26 Ne 100% cotton and a third one made with yarn length 50.24 Ne half-plated cotton in alternating courses, 22 dtex EA (Tables 2 and 4). Single jersey fabrics made with yarn lengths 26.96, 30.26 and 37.39 Ne in 100% cotton (Tables 3 and 5).
When validating the models, the estimated errors made when using them for each structure were very small. So, it can be concluded that these models account for the variability obtained in all the proposed models.
What this demonstrates is that the proposed models can be suitably used to calculate the SL of the analyzed structures based on knowledge about some dimensional variables, for example, WPCM, CPCM and stitch density, in any relaxation state: KDR, KWR, DDR or DWR. This avoids having to follow the conventional procedure used to analyze them in line with standard UNE-EN 14970, and avoids operations to identify wales, the direction that samples unweave in, cutting a long a column, counting the number of loops along a given length, removing yarn from knitted fabric, placing the measuring machine pincers by foreseeing loss of twist to measure its length and repeating this whole process 10 times to then calculate its mean. By running this procedure, and depending on the structure to be analyzed, it may be necessary to invest a considerable amount of time. The proposed models speed up this process.
At the same time, the present work demonstrates that the same procedure followed to predict the SL in interlock fabrics (2020) is valid to calculate the SL of the 1 × 1 rib and single jersey structures in any of the proposed relaxation states: KDR, KWR, DDR and DWR. To do so, the specific models for all three single jersey, 1 × 1 rib and interlock structures can be used.
This study propose to the reader an alternative procedure to find the value of the variable SL without the need to apply the standard UNE-EN 14970, in order to speed up the adjustment of the machines as much as possible for obtaining the desired fabric.
Footnotes
Declaration of conflicting interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The authors received no financial support for the research, authorship and/or publication of this article.
