Determining the structure parameters that affect overall properties of warp knitted fabrics using cluster analysis

Determining the structure parameters that affect overall properties of warp knitted fabrics using cluster analysis

Yoon, Hye-Shin

ABSTRACT

Two-bar warp knitted structures are grouped by cluster analysis of mechanical and physical properties, and the resulting classified groups show distinctive characteristics. The first group represents highly smooth, full and soft properties compared with other groups, and the characteristics of the second group are less smooth, full and soft. The fabrics of the third group are very stiff and smooth, and those of the last group are the least stiff, smooth, full, and soft. By analyzing the structures within and between groups, the structural parameters affecting the overall properties of warp knitted fabrics are determined. The results show that the formalized factors affecting the characteristics of warp knitted fabrics are the run-in ratio, pillar-lapping movement, direction of mutual guide bar movement with parallel or counter lapping, and closed or open lap type.

A knitted structure consists of interlacing loops, and the properties of these fabrics depend on the relationships and production methods of these loops. In particular, a warp knit structure differs from both woven and weft knitted fabrics in that its physical properties are very much a function of its structure [29]. Therefore, investigating the characteristics of warp knitted fabrics by structure is helpful when engineering fabrics for end– use.

Unfortunately, there are few studies about the relationship between a warp knitted fabric’s properties and its structure. Other works have focused only on geometry [2, 4, 6-7, 11-14] or the relationship between only one or two mechanical and physical properties, such as thickness and weight in fragments [5, 8, 9, 14]. We therefore intend to conduct an experimental and mathematical investigation of the overall properties of warp knitted fabrics as a function of their structures. In this investigation, our approach is to determine the structural parameters affecting the overall properties of warp knitted fabrics, because the relationship is never revealed until the structural parameters are defined.

The complex structures of warp knitted fabrics make research on this subject difficult. To solve this problem, we have classified the complex structures into groups depending on their mechanical and physical properties using cluster analysis. The resulting classified groups present differentiated characteristics. By analyzing the structures within and between the groups, we can determine the parameters of the structures that affect the characteristics of warp knitted fabrics.

Materials and Method

Eighteen kinds of two-bar warp knitted fabrics were produced, and their structures are given in Table I. We knitted the specimens using a warp knitting machine (Karl Mayer) with a 28 gauge electronic guide bar, with 20 courses/cm density in the machine state. The yarn chosen for this investigation was 75 denier/36 filament semi-dull PET filament yarn.

The two-bar warp knitted fabrics were selected for this study because they are the most common fabrics in warp knit technology. Two-bar structures are suggested for determining fabric characteristics in most cases. Although single bar structures are much more useful for investigating the elementary properties of loop structures, they are not suitable for most commercial applications. Moreover, the characteristics of the warp knitted fabrics depend on ground structures, which are generally made of two guide bars. Knitted fabrics with three or more guide bars are mainly used as pile fabrics rather than common knits, and the underlap structures from pile guide bars are brushed or raised.

In this study, we knitted a range of different structures using two fully threaded guide bars, as shown in Table I. These specimens were dry relaxed when removed from the machine for more than two weeks in standard conditioning at 20 +/- 2 deg C and 65 +/- 2% RH. They were heat-set in a laboratory drying and curing machine (CH– 815, Swiss Werner Mathis AG) at 180 deg C for 30 seconds. All fabrics were then measured after conditioning for 48 hours in standard conditions.

PHYSICAL AND MECHANICAL PROPERTIES

The surface images of specimens were analyzed by image analysis (Olympus optical, zoom stereo microscope), and densities were measured to examine the state of specimens after conditioning.

Mechanical properties were measured on eighteen different warp knitted specimens with the KES-FB system (Kato Tech Co., Ltd.) with knit standard conditions. For each knit structure, measurements were taken on three separate samples cut from the center of the specimen, and the three resulting values were averaged.

Mechanical properties such as tensile, bending, shear, and surface were measured for both wale and course directions. Three compression properties (LC, WC, RC) and two physical properties (weight, thickness) were also tested.

In our study, we used separated wale and course mechanical values [17] because our specimens were knitted fabrics with known differentiated properties between wales and courses. Moreover, as shown in Table 1, although they were knitted at the same density from the same materials, the specimens represented much different densities for wales and courses when they were removed from the machine. The resultant densities after dry relaxation are presented in Table I.

Mathematical Principles

Mathematical principles have the advantage in objective sorting of fabric characteristics from mechanical and physical properties because they can eliminate some subjectivity existing in the sensory perception of hand evaluation [10, 16, 17-25]. In addition, they should be also employed in categorizing fabrics according to a number of mechanical and physical properties. We tested as many properties as we could measure that were representative of fabric characteristics, because there has not yet been any established definition about what properties are related to fabric characteristics and how many properties should be chosen to explain the overall characteristics. But it was impossible for us to evaluate and classify characteristics of fabrics from twenty-nine mechanical and physical properties by intuition. So the data set needed to be processed, reduced, and interpreted by a mathematical method.

In this paper, we use cluster analysis to solve the problem of classifying fabric properties objectively [1, 3, 30]. The method is employed to discover the structure in the data set that is not readily apparent from visual inspection, and it is introduced to divide fabrics into groups, each representing a particular fabric performance and end-use characteristics. But different clustering methods can produce different results when applied to the same data, that is, certain methods have inherent biases in them [1]. Therefore, to confirm the validation of the classification, we have examined the similarity of the results from seven clustering methods when applied to the same data. We then classifly the groups of fabrics using a hierarchical agglomerative and iterative partitioning cluster analysis.

Results and Discussion

The twenty-nine variables of each specimen were measured instrumentally. The clustering calculation involved this multivariate framework. As shown in the summary of the data set in Table III, there was a large range of values for each of the properties measured.

Hierarchical Agglomerative Cluster Analysis: Through the SAS statistical computer program and the parameters of the sample set, we have obtained the results corresponding to these methods, and we show them in Figures 1-6.

From the similar results of the six methods of hierarchical clustering, we believe we have validated the classification of warp knitted fabrics in this investigation. But these results don’t provide the definite sorting result for practical sorting problems. The clustering trees of the various approaches only give a configuration for every number of clusters from one, the entire data set, up to the number of entities in which each cluster has only one member. Therefore, to determine the number of clusters present, two basic approaches of heuristic procedures and formal tests have evolved and are considered [1, 15, 27]. Using the pseudo F and t^sup 2^ statistics, the cubic clustering criterion, and an approximate expected R^sup 2^, we limit the number of clusters to four or five here.

From Figures 1-6, all six hierarchical clustering trees can be divided into two groups. The single, the centroid, and the median linkage method, whose cluster number is five, compose the first group. The complete, the average linkage, and Ward’s method, whose number is group four, belong to the second group.

After taking the six hierarchical methods into consideration and investigating the relationship between fabrics, we can create an illustration representing the relationship of warp knitted fabrics based on Ward’s method in Figure 7.

This investigation suggests, however, that not only defining the number of clusters, but also exploring the general pattern of the relationships between entities as represented by a hierarchical tree, is of paramount importance.

We cluster these fabric samples based on the mechanical and physical parameters thought to determine fabric handle, so the results suggest a similarity to fabric hand sorting. For example, four groups could correspond to four kinds of fabrics, that is, all members have similar mechanical and physical properties within each group, and they may have a similar hand. Besides, the subgroups could exist under main groups determined by the hierarchical tree. We also think there is a closer relationship within the subgroup.

Iterative Partitioning Cluster Analysis: Table IV lists the results of the clustering computation and the fabric samples included in each cluster. It can provide useful information on fabric properties related to a specific classification. Compared with the results from hierarchical cluster analysis, four clusters seem to be more similar to hierarchical analysis.

Effectiveness of Hierarchical and Iterative Procedures: Compared with different hierarchical clustering methods, it seems that complete, average linkage, and Ward’s method are more effective in discriminating the groups, and their results are also close to the iterative cluster method when the number of clusters is fixed at four. The iterative method presents simple, good results but the right number of clusters must be determined before.

CLASSIFYING WARP KNITTED FABRics

Considering both hierarchical and iterative cluster analysis, four clusters seem to be more appropriate to classification of warp knitted fabrics. We therefore provide four fabric groups representing specific characteristics, as shown in Figure 7.

Fifteen fabrics are allotted in two main groups, A and B. The A group, includes denbigh, atlas, locknit, cord, satin, and laying-in structures, and the B group comprises denbigh, reverse locknit, sharkskin, and queens cord. What is more, the two main groups can be divided into a few subgroups, and the fabrics of these subgroups are expected to have more similar characteristics than those of the main groups.

But information about the characteristics possessed by each group can not be obtained from cluster analysis. What we do know is that only the groups of warp knitted fabrics are reported as having similar characteristics. Therefore, to support the results from cluster analysis and to identify the characteristics of the groups, we compare the hand properties of warp knitted fabrics among groups through Kawabata’s HV equation (KN– 402-KT). The result is shown in Figure 8.

In that figure, the fabrics within the same group are gathered together, apart from others, thus confirming that the fabrics classified through cluster analysis have similar hand properties within the same group but dissimilar properties between groups.

From these results, the fabrics of group A represent high smooth, full and soft properties compared with the other groups. They also possess medium stiffness. The characteristics of the fabrics in group B are less smooth, full and soft than those in group A, but there is little difference in stiffness between A and B. The fabrics of group C show smoother properties than B and D, but above all, they have higher stiffness than any other groups. Finally, the fabric in the D group, a laying-in structure with closed chain stitch, is a peculiar case. It shows the lowest value of all three hand properties, stiffness, smoothness, and fullness and softness.

FORMALIZING STRUCTURAL PARAMETERS

To formalize the factors affecting the classification, we show the groups with structure in Figure 9.

Run-in Ratio: By analyzing the structures in groups A and B, we find that most structures with the same or longer run-in at the front guide bar than back guide bar are gathered in group A, and those with the shorter or same run-in are gathered in B. Figure 10 shows the relationship of run-in between the front and back guide bars, which we believe has paramount importance in dividing the fifteen fabrics into two groups.

The reason the run-in ratio makes a difference between the two groups is that the guide bar with the shorter run-in has a more decisive effect on basic mechanical properties. The passage and length of the front guide yam could have a greater effect on the hand properties of warp knitted fabrics because the front guide yam covers and anchors the back one. Thus, when the run-in ratio is larger than 1, that is to say, the run-in of the back guide bar is shorter than that of the front one, the pattern of the back one is thought to be more of a determinant of fabric performance. Similarly, when the run-in ratio is smaller than 1, the pattern of the front guide bar is considered to be conclusive. In this case, however, the properties of the fabrics seem to be more affected by the run-in of another bar than the former, because tension is given to the underlap of the front yarn while the front guide yam locks up the back one.

Pillar-Lapping Movement: In Figure 9, the diagram shows that the structures with pillar lapping movement tend to be separate from the two main groups. The pillar lapping movement is therefore considered to be the parameter showing singular characteristics.

When working a pillar stitch, the thread is always lapped around the same needle, and there is no lateral connection between the wales [26]. Therefore the structures with pillar stitch seem to have more stability in the longitudinal direction and a much greater difference between wale and course directions of the fabrics.

In addition, the pillar lapping movement can be open, closed, or a combination of closed and open laps. Among the pillar constructions, the closed pillar stitch is less common because of undesirable false twist [26]. The properties of the warp knitted fabrics with pillar stitch thus seem to be affected by the chain notation of closed or open pillar lapping movement.

Direction of Mutual Guide Bar Movement with Parallel or Counter Lapping: From Figures 1-6 and 7-9, we also see that the structures with parallel guide bar movement are grouped ahead of the other structures. This means that the structures with equal lap have more characteristics similar to each other, compared with those of similar pattern and run-in ratio. We think this might be due to loop stabilization and density variation. The shape of loops formed through the parallel guide bar movement tends to tilt after dry relaxation, and the slanted loops make the wale density smaller than erect loops. It seems to make a difference in the characteristics of warp knitted fabrics compared with other structures. So we suggest that the direction of mutual guide bar movement is an important parameter affecting the characteristics of warp knitted fabrics as well.

Closed or Open Lap Types: The closed or open lapping types are thought to affect the classification of warp knitted fabrics, because the structures with open lap are gathered together-denbigh (CO) and reverse locknit (CO) in group B of Figure 9. The reason for this is that the relaxation of warp knitted fabrics is as affected by the closed or open lap type as the direction of the mutual guide bar movement.

Conclusions

The essence of cluster analysis is to sort the samples into groups, and this method has the advantage of requiring little or no knowledge about the category structures in a sample set. All that is needed is a collection of measured parameters. From the resulting groups, the degree of “property association” is high between members of the same group and low between members of different groups. Therefore, this could be a useful approach for objective evaluations of fabric hand and for formalizing parameters.

In this investigation, we have found that warp knitted structures can be grouped by cluster analysis, and the resulting classified groups show distinctive characteristics between groups. By analyzing the structures within and between groups, we can determine the parameters affecting the characteristics of warp knitted fabrics. The results provide formalized factors of the run-in ratio, pillar-lapping movement, direction of mutual guide bar movement with parallel or counter lapping, and closed or open lap types.

AcKNOWLEDGMENT

We gratefully acknowledge the 2002 financial support provided for this study by the Inha University and the Industrial Technology Research Institute Foundation.

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Manuscript received August 1, 2001; accepted March 26, 2002.

HYE-SHIN YOON AND SHIN-WOONG PARK

Department of Textile Engineering, Inha University, Inchon 402-751, South Korea

Copyright Textile Research Institute Nov 2002

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