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A New Apparatus for the Study of Fabric Drape CHIYOMI MIZUTANI1 Heian Jogakuin (St. Agnes’) University, Takatsuki, Osaka 569-1092, Japan

TOSHIHIKO AMANO Mukogawa Women’s University, Nishinomiya, Hyogo, 606-8585, Japan

YOSHIYUKI SAKAGUCHI Digital Fashion Ltd, 2-2-7 Honmachi, Chuo-ku, Osaka, 541-0053, Japan ABSTRACT A new drape elevator is developed to analyze the drape generation mechanism. The drape elevator can measure drape shape, including node generation at various stages during drape formation. The drape elevator method indicates better reproducibility of the drape coefficient of the fabrics than the conventional method. The drape formation process is experimentally found to consist of three stages, seeds generation, their development, and the final stabilizing stages. A new parameter R, evaluating the shape of the drape, is defined in terms of the drape projection. Both the R parameter and the drape coefficient are expected to be useful parameters for the quantitative analysis of fabric drape formation.

Fabric drapability is an important factor from both aesthetic and practical points of view. A lot of studies of drape properties have considered the silhouette formation of clothing and fabric evaluations [1, 2, 8, 9, 11]. Recently computer simulations of fabric drape were rather successful [2, 4, 5]. These results indicate that the relationship between mechanical properties and drape formation is becoming clear to some extent [7, 13, 15]. To evaluate fabric drapability, the fabric research liberating method (FRL) has been widely used. However, we are concerned that the drape formation process can be disturbed by the rotation of the sample during measurements. Moreover, no information during the process of drape formation can be obtained with any conventional methods. However, in order to improve computer aided apparel design, much more information is needed on the drape of fabrics, especially the initial behavior, which probably plays an important role in analyzing the drape shape of fabrics and the number of nodes. There are still many unclear points in the fundamental mechanism of drape appear-

1 Correspondence: Chiyomi Mizutani, Faculty of Human Life and Enviroment, Heian Jogakuin (St. Agnes’) University, 5-81-1, Nanpeidai, Takatsuki, Osaka 569-1092, Japan, phone ⫹81-72-696-4924, fax ⫹81-72-696-4919, email : [email protected]

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ance. To solve these problems, it is necessary to make clear which fundamental mechanisms affect fabric drapability. We are interested in the process and mechanism of how draping can generate beautiful shapes. In order to study drape formation, we have developed a new apparatus called the drape elevator, which can be used to evaluate drape properties continuously during the whole process of drape formation. In this study, we compare the accuracy of measurements from the drape elevator with those of the conventional method (FRL). The drape generation of various sample fabrics is analyzed on the basis of direct observations of drape formation. The generation of nodes and the developing process are considered in relation to the mechanical properties of the sample fabrics.

Experimental We used various kinds of woven fabrics, including cotton, linen, wool, silk, and polyester blended with wool. We selected these samples because they are common in clothing fabrics, and commercially available. The details and physical properties of the sample fabrics are shown in Table I.

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TEXTILE RESEARCH JOURNAL TABLE I. Construction of sample fabrics.

Sample

Thickness, mm

Mass per unit area g/m2

Yarn density number/cm, warp/weft

Yarn count, tex warp/weft

Cotton Linen Wool 1 Wool 2 Silk PET/wool

0.22 0.21 0.28 0.32 0.15 0.50

120 127 154 160 83 222

59/29 33/27 24/22 32/25 48/38 36/21

14/14 20/20 32/32 25/25 9.5/9.5 35/35

plain plain plain plain plain twill

Ad ⫺ S1 ⫻ 100 S2 ⫺ S1

,

EVALUATING DRAPABILITY To evaluate the drapability of fabrics, we adopted both the drape elevator and FRL method. We close the FRL method because it is the Japan Industrial Standard. Drape Elevator Method The drape elevator was devised to evaluate the drape formation process. A construction diagram of this apparatus is shown in Figure 1. The drape elevator is equipped with a fixed round sample holder 12.7 cm in diameter, and an elevator table 6 cm wide surrounding the fixed sample holder. The elevator table can move up and down vertically at 1.0 cm by a rotation of the lever. At the onset of the measurement, both the sample holder and the moving table are adjusted on the flat level at the same height. First, the circular sample fabric 25.4 cm in diameter is set on the sample holder. As the elevator table is moved downward by operating the lever, the sample fabric gradually hangs and forms drapes by itself due to its own weight. During the process, a digital camera set just above the apparatus records the vertical projections of the fabrics. Characteristics such as the drape coefficient are calculated by using the values measured on the picture. The drape coefficient is calculated by the same formula as the conventional method:

FIGURE 1. Construction of drape elevator.

Drape coefficient ⫽

Weave type

(1)

where Ad, S1, and S2 are the area of the vertical projection of the draping sample fabric (cm2), the area of the round sample holder (cm2), and the area of the sample (cm2), respectively. The measured samples were prepared in the same manner as for the conventional method. Conventional Method (JIS L-1096 1999) The drape tester (YD-100, Daiei Science Ltd.) was used in the conventional method. A sample 25.4 cm in diameter was placed on the sample table and then rotated for 10 seconds at 120 rpm, disregarding the initial disturbances of the sample setting. After rotation stopped, the sample fabric hung down naturally by its own weight. The vertical projection of the hanging sample fabric was automatically recorded by a photoelectric tracing method, and the related parameters were calculated on the basis of these projections. Mechanical properties such as bending and shearing of the fabrics were estimated by the KES method, FB1-2 [6].

Results and Discussion COMPARISON

WITH

CONVENTIONAL METHOD

Drape is an important characteristic of textile fabrics. Several methods such as the FRL and the MIT (Massachusetts Institute of Technology) method for evaluating drapability have been developed and used in practical tests. Among them, the FRL method is widely known and has been adopted as a textile testing method in the Japanese Industrial Standard (JIS L 1096). On the other hand, there is little research on the MIT method [3]. Therefore, in this experiment, the FRL method was represented as the conventional method for comparison with the drape elevator method. In both methods, characteristics such as the drape coefficient were obtained on the basis of the vertical projection of a hanging fabric sample. Additionally, drape formation could be observed at any point during the process using the drape elevator method.

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The drape coefficient is a measure for characterizing the drapability of fabrics, and is confirmed as a stable and easily reproducible parameter. First, we compared the measuring accuracy of both methods. The drape coefficients and their standard deviations of various samples obtained by both methods are shown in Table II. The measurements were performed five times for each sample. Drape coefficients obtained with the drape elevator were somewhat larger than those with the conventional method. However, the standard deviation of the drape coefficients obtained by the drape elevator method became smaller, so the relative errors of the drape elevator method were less than half those of the conventional method. The results were similar for the reproducibility of the drape coefficients, as shown in Table III. This table shows the drape coefficients and their standard deviations of the repeat measurements using the same sample. A problem with the conventional method is the rotation of the hanging sample to adjust the initial condition after placement on the sample holder. Such rotation can possibly affect the hanging shape of the sample. Since the hanging of the sample results from a falling movement with some inertia of the rotation, drape may form under unstable complex conditions. On the other hand, there is no rotation process with the new drape elevator. In

TABLE II. Experimental results of the drape coefficient by the JIS method and drape elevator method. Drape coefficient, % Drape elevator

JIS method

Sample

Average

Standard deviation

Average

Standard deviation

Cotton Linen Wool 1 Wool 2 Silk PET wool

64.0 69.6 45.4 23.8 38.0 91.3

2.4 1.3 1.3 0.2 0.7 0.8

63.0 62.7 45.1 19.5 34.8 86.4

3.4 3.5 5.5 0.5 1.3 3.3

contrast, with the drape elevator drape gradually forms as the elevator table descends, so there is little disturbance during drape formation. DRAPE FORMATION PROCESS Figure 2 shows the vertical projections during drape formation of the cotton fabric obtained with the drape elevator. Although there were no changes at a descending distance of 1 cm, some seeds of nodes began to appear at 2 cm, and the drapes grew more clearly in the range of 3– 4 cm. The drapes were further completed and became stable at a distance of 6 –7 cm. Changes in the drape coefficients during drape formation are shown in Figure 3. The drape coefficients of polyester blended with wool (PET wool) remained almost constant throughout the whole process. On the other hand, the drape coefficients of cotton and linen fabrics changed greatly and lowered linearly in the range of 3–5 cm. In the following range, the drape coefficients remained almost constant. The sample fabrics hung free from the elevator table at a certain height depending on their mechanical properties. Due to the system geometry, any sample fabric is completely free of the elevator table at a descending distance of 6.4 cm. The drape coefficients of the silk and wools 1 and 2 changed greatly in the range of 3– 6 cm and became stable in the range of more than 6 cm. These results indicate that the drape formation process of the fabrics consists of three stages: node appearance in the early stage, drapes growing from these nodes in the next stage, and stabilized drapes in the final stage. Therefore, we have proved that the drape elevator can be effectively used to measure every stage of drape generation. NODE GENERATION

ON THE

FABRICS

Figure 4 shows the nodes in the early stages for various fabric samples. As is obvious in the figure, the nodes of wool 2 and silk tended to appear in the bias

TABLE III. Comparison of the drape coefficient with cycle measurement evaluated by the drape elevator and JIS methods. Cotton

Silk

Wool 2

Measurement number

Drape elevator

JIS

Drape elevator

JIS

Drape elevator

JIS

1 2 3 4 5 Average Standarddeviation

65.2 66.0 61.1 65.9 61.3 63.9 2.5

60.2 66.0 61.3 67.6 61.0 63.2 3.3

37.4 38.6 37.0 38.3 38.7 38.0 0.7

33.5 36.3 36.2 33.9 34.3 34.8 1.3

24.1 23.7 23.8 23.5 23.8 23.8 0.2

18.7 20.0 19.9 19.5 19.5 19.5 0.5

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FIGURE 2. Change in drape shape of cotton fabrics estimated by the drape elevator (number shows distance of descent).

direction of each fabric. Woven fabrics are generally anisotropic in their mechanical properties. To analyze these node generations, we measured the angular dependence of the bending properties, bending rigidity B and recovery 2HB, of the fabrics in the warp (0°), weft (90°), and both bias (45° and 135°) directions. The results are shown in Table IV. The values of B and 2HB in the bias directions of the fabrics were somewhat smaller than

FIGURE 3. Change in drape coefficient of fabrics at various stages.

those of the warp and weft directions. These results may indicate that the nodes tend to appear in specific regions such as along the bias directions on the fabrics. As the elevator table moves down, nodes form near the portion of small B and 2HB owing to fabric bending deformation due to forces within the fabric surface caused by its own weight. This process has already been discussed in theoretical studies using computer simulations. Our experiments with the drape elevator directly indicated the node generation process in the course of drape formation. The number of nodes did not change during the process for cotton, shown in Figure 2. The fundamental features of the drape were determined at the time of node generation in the early stage. However, the behavior of wool 2, shown in Figure 5, was quite different. Nodes appeared in the early stage and formed the drapes, but the number of nodes and the complete determination of drape shapes were achieved at the final stage. The drape shape and the number of nodes were finally determined when the hanging fabrics completely left the elevator table at approximately 6 cm of descending distance. These differences in drape formation are considered to occur due to the interrelationship of the sample weight and the bending properties, and they also seem to be affected by the friction between the sample fabrics and the surface of the elevator table.

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FIGURE 4. Nodes appearing on the various fabrics at early stages.

TABLE IV. Bending properties of samples at various angles. B, g/cm2/cm

2HB, g/cm/cm Angle, degrees

Sample

0

45

90

135

0

45

90

135

Cotton Linen Silk Wool 1 Wool 2 PET wool

0.066 0.212 0.034 0.075 0.030 0.197

0.054 0.144 0.023 0.067 0.021 0.257

0.075 0.245 0.024 0.087 0.023 0.576

0.048 0.159 0.026 0.064 0.021 0.277

0.041 0.106 0.024 0.025 0.008 0.305

0.038 0.071 0.022 0.028 0.007 0.483

0.041 0.110 0.015 0.026 0.010 0.796

0.039 0.075 0.019 0.026 0.007 0.473

FIGURE 5. Time dependence of drape shape of the wool 2 fabric (number shows distance of descent).

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Conclusions

EVALUATING DRAPE FORMATION The drape coefficient is relevant to the drapability of fabrics [12, 14], but it is not sufficient for characterizing drape formation. Fabrics with the same drape coefficients are able to form different drape shapes. In order to describe the draping features of the fabrics, another parameter relating to the shape of the drape projection is required. As a measure of the shape of the drape projection, a new parameter R other than the drape coefficient is defined by R⫽

冑共r ⫺ r 兲 0

r0 ⫺ rs

2

,

(2)

where (r ⫺ r0)2 is the average of (r ⫺ r0)2 along the whole contour of the drape projection, and r, r0 , and rs are radial coordinates of the drape projection, the radius of a circle with an area equal to that of the drape projection, and the radius of the sample holder, respectively. Using this parameter, the drape shape can be expressed at a point on R and the drape coefficient coordinate system. The R value is a measure expressing the simplicity or evenness of the drape projection. The larger the value, the smaller the simplicity of the shape. Thus, the shape of the drape can be distinguished even for samples with the same drape coefficient. Figure 6 shows the R-drape coefficient plots of cotton, wool, and silk fabrics. The slopes of these plots indicate certain features of drape formation. A different character in the drape formation process can be found for these samples. Thus, the R values suggest a measure available to characterize drape formation.

FIGURE 6. Relationship between R factor and drape coefficient.

We have studied drape formation by using the newly developed drape elevator. When measuring drape coefficients, the reproducibility of the new method is higher than that of the conventional method. Drape formation can be directly observed at any time throughout the process. Consequently, the process, including seed generation, will be useful in creating more realistic computer simulations of fabric drapablilty and drape shape. The new parameter R is defined as a shape factor of the fabrics other than the drape coefficient. The R and drape coefficient plots allow us to analyze fabric drape features. The drape elevator can be expected to be a useful tool for studies of fabric drape.

Literature Cited 1. Amano, T., Takada, K., and Kawanishi, S., Evaluation of Fabric Drapability, J. Jpn. Res. Assn. Textile End-Uses 35 (10), 570 –576 (1994). 2. Ascough, J., Bez, H. E., and Bricis, A. M., A Simple Beam Element, Large Displacement Model for the Finite Element Simulation of Cloth Drape, J. Textile Inst. 87 (1), 152–165 (1996). 3. Bao, L., Takatera, M., Sawada, K., Sakurai, M., Nakazawa, M., and Shinohara, A., Effect of Mechanical Properties on MIT Drape Behaviors of Fabrics, Sen-i Gakkaishi 58 (3), 77– 83 (2002). 4. Collier, J. R., Collier, B. J., O’Toole, G., and Sarggand, S.M., Drape Prediction by Means of Finite-element Analysis, J. Textile Inst. 82 (1), 96 –107 (1991). 5. Gan, L., Ly, N. G., and Steven G. P., A Study of Fabric Deformation Using Nonlinear Finite Elements, Textile Res. J. 65 (11), 669 – 675 (1995). 6. Kawabata, S., H. E. S. C. Standard of Hand Evaluation, J. Textile Mach. Soc. Jpn. (1975). 7. Niwa, M., and Seto, F., Relationship between Drapability and Mechanical Properties of Fabrics, J. Textile Mach. Soc. Jpn. 39 (11), T161–T168 (1986). 8. Suda, N., Kobayashi, S., and Ohira, M., Studies on Drapability of Fabrics, Relation between Hamburger’s Drape Coefficient and Lateral Drape Coefficient, J. Jpn. Res. Assn. Textile End-Use 11 (6), 312–317 (1970). 9. Suda, N., and Ohira, M., Studies on Drapability of Fabrics, The Physical Meaning of Hamburger’s Drape Coefficient, J. Jpn. Res. Assn. Textile End-Uses 13 (11), 475– 482 (1972). 10. Suda, N., and Ohira, M., Study on Drapability of Fabrics, Analysis of the Mechanism of Drape Formation by Using the Mechanical Models, J. Jpn. Res. Assn. Textile EndUses 15 (5), 164 –169 (1974). 11. Suda, N., and Ohira, M., Study on Drapability of Fabrics, Analysis of the Mechanism of Drape Formation by Using

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the Mechanical Models (2), J. Jpn. Res. Assn. Textile End-Uses 18 (2), 68 –73 (1977). 12. Yang, M., and Matsudaira, M., Measurement of Drape Coefficients of Fabrics and Description of Hanging Shapes of Fabrics, Part 2 : Description of Hanging Shapes About Anisotropic Fabrics, J. Textile Mach. Soc. Jpn. 51 (4), T65–T71 (1998). 13. Yamada, T., Nakazato, Y., Akami, H., and Suh, J., Flexural Rigidity and Drapability of Fabrics, J. Jpn. Res. Assn. Textile End-Uses 36 (7), 495–501 (1995). 14. Yang, M., and Matsudaira, M., Measurement of Drape

Coefficients of Fabrics and Description of Hanging Shapes of Fabrics, Part 3: The Effect of Fabric Parameters on Drape Shapes, J. Textile Mach. Soc. Jpn. 51 (9), T182– T191 (1998). 15. Zhang, R., and Matsudaira, M., Bending Vibrational Properties of Fabrics, Part 4 : Relationship between Parameters of Bending Vibration and Drape Coefficient of Fabric by Grey Relationship Analysis, J. Textile Mach. Soc. Jpn. 51 (5), T87–T91 (1998). Manuscript received March 20, 2003; accepted July 28, 2003.

A Linear Dynamic Model for Two-Strand Yarn Spinning JI-HUAN HE,1,2,3,5 YAN-PING YU,4 JIAN-YONG YU,2,4,5 WEI-RU LI,2,4,5 2,4,5 AND SHAN-YUAN WANG DongHua University, Shanghai 200051, People’s Republic of China

NING PAN Division of Textiles and Clothing, Department of Biological and Agricultural Engineering, University of California, Davis, California 95616, U.S.A. ABSTRACT A linear dynamic model is established for two-strand or Sirospun yarn processing. Approximate oscillating frequencies in the vertical and horizontal directions are obtained. By suitable choice of certain processing parameters, the mixture construction after the convergence point can be optimally matched.

Two-strand spun or Sirospun yarns are now widely used in the worsted industry. The strands are textured to improve the bulk of the resultant yarns, which possess more desirable properties. For example, the weaveability of fabrics formed by Sirospun yarns is significantly improved compared to their counterpart yarns. Lately, many static models have been established to describe Sirospun yarn processing with the aid of

1 Corresponding author: P.O. Box 471, 1882 Yan’an Xilu Road, Shanghai 200051, P.R. China. 2 Center of Physics of Fibrous Materials. 3 College of Science. 4 College of Textiles. 5 Key Lab of Textile Technology, Ministry of Education, China.

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experimental data to make the models closed [1, 2, 4, 5]. Yet our recent study [3] reveals that no experimental data are needed to definitely identify such system parameters as the strand convergence point or the convergence angles. The system should obey not only the force balance, which has been studied extensively in the open literature, but also all the conservation equations (i.e., conservation of mass, momentum, and energy), so the quasistatic model thus suggested by our group [3] is self-closed. In this paper, we develop a dynamic model for this problem. The characteristics of two-strand spun yarns depend mainly on how the two strands are combined and mixed, and the different oscillating frequencies of the convergence points in both the vertical and horizontal directions prove to be the dominant factors. 0040-5175/$15.00