No title

IJCST 8,1/2

12

Low-stress fabric testing for process control in garment assembly Application of robotics P. Potluri and I. Porat Department of Textiles, University of Manchester Institute of Science and Technology, Manchester, UK, and

J. Atkinson Department of Mechanical Engineering, University of Manchester Institute of Science and Technology, Manchester, UK

International Journal of Clothing Science and Technology, Vol. 8 No. 1/2, 1996, pp. 12-23. © MCB University Press, 0955-6222

Introduction Low-stress mechanical properties of fabrics have established themselves as an objective measure of quality and performance, replacing traditional subjective hand assessment. Test systems such as KES (Kawabata Evaluation System)[1] and FAST (fabric assurance by simple testing)[2] were developed for conducting tests on fabric samples in the low-stress region. The KES system consists of four semi-automatic test instruments for conducting compression, bending, shear, tensile and surface tests. An operator has to align the fabric sample, parallel to a principal direction, and clamp it in each instrument. A continuous stress-strain cycle is automatically applied to the fabric sample, until a pre-set limit is reached. The stress-strain curves are plotted using an x-y plotter. Sample alignment and mounting are the main sources of error in using the KES system. An individual skilled operator may achieve a reasonable degree of accuracy but measurements vary from operator to operator[3]. The FAST system consists of three instruments for conducting compression, bending, tensile and shear (bias extension) tests. These instruments are simple to use, but evaluate only a limited number of fabric properties because the tests are conducted at a specific load rather than as a continuous stress-strain relation. The correlation between low-stress fabric properties and fabric hand has been the subject of investigation by several researchers in the last two decades, with a significant contribution came from Kawabata[4] and his colleagues. With objective fabric hand evaluation well established, the attention of various researchers shifted to control and automation of garment assembly. Application of low-stress properties to garment assembly lies in two distinct areas: (1) process control in garment making-up; (2) automation of garment assembly.

Measurement of fabric low-stress properties

Figure 1 is a conceptual indication of the fabric low-stress properties in relation to garment assembly.

Application of robotics to fabric testing 13

Simulation of fabric behaviour during handling

Automated garment assembly

Setting of machine parameters

Garments are produced by a making-up process which involves sewing fabric panels in to a three-dimensional assembly, using sewing machines. As early as 1960, Lindberg[5] considered the relationship between fabric properties and problems encountered in garment construction. Shishoo[6] extended Lindberg’s work by relating KES properties, such as extensibility, bending rigidity and shear hysteresis. Stylios et al.[7] developed an expert system for predicting fabric sewability and setting of optimum sewing machine parameters, based on fabric properties. The concept of automatic overfeed control, using fabric properties in sewing machines was reported by Kawabata et al.[8]. Fabrics, being limp materials, pose considerable problems in automated handling. Gunner and Taylor[9] identified bending rigidity and coefficient of friction as two important fabric properties which control fabric behaviour during handling by a robot or any automated handling device. Computer simulation of fabric behaviour during automated handling, based on mechanical properties, has been reported by various researchers[10-12]. These simulations can be used for trajectory control of fabric handling devices. The KES and FAST test systems were developed primarily for objective hand evaluation. They work on relatively rigid test procedures ideally suited to hand evaluation. However, these tests do not adequately represent the stresses applied to a fabric panel during handling and making-up. A fully automated fabric test system, involving a robot, has been developed by the present investigators. The main feature of this system is its flexibility to change the test conditions. This paper looks at the possibility of using the robotic test system for process control in garment assembly.

Figure 1. Fabric low-stress properties related to garment assembly

IJCST 8,1/2

14

An industrial robot for automated fabric testing The robotic test system is based on an IBM SCARA robot[13], which is a precision assembly robot. The following features of the robot are important from the view point of automated testing: • The robot arm is horizontally articulated, having four degrees of freedom. This configuration is better suited for manipulating a fabric panel on a horizontal surface, than a vertically articulated robot arm. • The robot has a position repeatability of better than ± 0.05 mm. • The robot has linear and circular path capability, which is required for applying continuous test cycles. Speed and acceleration are programmable which are important for an accurate control of strain rate. • There are 48 programmable input and output ports available for communicating with external sensors and actuators. • An advanced programming language (AML/2) with multitasking facility is used for robot control. In the robotic test system, the tests cycles are applied by the robot in addition to fabric handling. The robot is equipped with a mechanically decoupled threeaxis load cell, a pneumatic gripper and an automatic tool changer. The mechanical design of this equipment has been reported elsewhere[14]. Automated handling and alignment of a fabric sample For automated handling during testing, the techniques should be compatible with those used for garment automation. Movement of a fabric panel on a smooth surface using pressure pads (velcro pads) has been reported[15,16]. A device, based on a rubber lining, for manipulating fabric samples on a horizontal surface has been developed in the present work (Figure 2). This device is attached to the robot arm using an electromagnetic tool changer. The fabric edge is detected by the two infrared diffuse sensors (Figure 2). The digital status of each sensor is communicated to robot controller through DI (digital input) ports. A fabric sample is aligned parallel to an edge or a clamping device through a series of translations and rotations. Fabric testing The main feature of the robotic system is to apply stress-strain cycles on a fabric sample by the robot itself, rather than using electromechanical devices. A compression test is conducted by a circular head attached to the robot arm (Figure 3(a)). The fabric sample is compressed at a predetermined strain rate (typically 0.02mm/s) until a preset pressure limit is attained. A bending test has been implemented using a cantilever method as this test requires fabric manipulation in a horizontal plane, compared to a pure bending test which needs positioning of the sample in a vertical plane. The fabric sample is drooped continuously as a cantilever and the fabric edge is detected by a bending angle sensor (Figure 3(b)).

Application of robotics to fabric testing

Robot arm Alignment sensors Manipulation device

15

Reflective tape

Figure 2. Fabric manipulation and alignment

Strain

Compression force

Robot arm

Electro-magnet attachment Compression head

Fabric sample (a)

Fabric sample

Manipulation device

Bending angle sensor

Stepper motor (b)

A shear test is conducted by clamping the fabric sample between a fixed clamp and the robot gripper. The robot is moved along a circular trajectory, keeping the gripper parallel to the fixed clamp. This is to ensure a constant tension in the fabric. The test is typically conducted between a shear limit of ±8˚ (Figure 4(a)). A tensile test is conducted by clamping the fabric sample, similar to a shear test, and moving the robot at a predetermined rate (0.1mm/s) until a preset tension limit is reached. A friction test may be conducted by dragging a friction contactor of known weight, attached to the robot arm (Figure 4(b)) on fabric surface and measuring

Figure 3. Compression and bending tests

IJCST 8,1/2

Robot arm

Sh ea rf or st ce ra in

Robot arm Fixed clamp

16

Friction contactor Clamp

Tool changer

Tensile force strain Force sensor (three axes)

Figure 4. Shear, tensile and friction tests

Displacement Friction force

Fabric panel

Robot gripper

(a)

(b)

the resulting force in the horizontal direction. This sensor is, at present, under development. Measurement of forces and deformations An important aspect of the present work is to compute fabric deformations from robot co-ordinate information, and use these data for plotting stress-strain relations in real time. This has been possible with the availability of advanced software features of AML/2 such as multi-tasking and dynamic position determination. Multi-tasking facilitates parallel running of several tasks and I/O functions in a time window of 18ms. A task for computing fabric deformations is running parallel to the main program. As soon as a digital sensor changes state or a handshake signal arrives, a software function “qposition (axis)” computes current robot position. A three-axis force sensor, which is mechanically decoupled, has been developed. This permits the measurement of relatively small forces, without cross-coupling[14]. A 12-bit A/D converter is used for acquiring force information into a computer. Figure 5 shows a typical force (pressure) deformation curve plotted during a compression test. Measurement in the presence of static and dynamic variations Test instruments are designed to keep the structural deformations to a minimum. But robot arms are compliant structures and deflect during testing. The deformation value computed from the robot internal sensors, through a software function, includes robot arm deformations. Compliance tests conducted on the robot showed that the load-deformation characteristics are

Application of robotics to fabric testing

Pressure (cN/cm2) 60

50

17

40

30

20

10

0

0 0.1 0.2 0.3 0.4 Thickness compression (mm)

0.5

0.6

Figure 5. Compression recovery curve

0.7

repeatable, within an accuracy limit specified for fabric tests. Load deflection characteristics of the robot arm, along the tensile and shear test directions, are measured accurately and compensated for in the software (Figure 6). Deflection (mm) 1.6

Deflection (mm) 0.16

1.4

0.14

1.2

0.12

1

0.1

0.8

0.08

0.6

2

0.4

1

Force

0.06

deflection

0.04

0.2

0.02

0

Force deflection 2 1 Timing belt

0 0 2 4 6 Force ( × 1,000cN)

8

10

12

(a) Robot compliance during a tensile test

0 100 200 300 400 500 600 Load (cN) (b) Robot compliance during a shear test

Key Loading Unloading

Figure 6. Robot arm compliance

IJCST 8,1/2

18

A good correlation with KES tensile tests was obtained, even for relatively stiff fabrics whose tensile deformations are comparable to robot arm deformations (Figure 7). Tensile force (cN/cm) 600 Corrected data

Measured data

500 400 300 200 100 Figure 7. Tensile deformation of a fabric

0 0

2

4 6 8 Tensile strain (per cent)

10

12

If the robotic test system is placed in a manufacturing environment, there are induced vibrations due to other machinery such as sewing machines or compressors. Acceleration or deceleration of the robot arm also induces vibrations. The problem of vibration is more pronounced in the case of a robot because the robot arm is a cantilever structure. While conducting shear tests it was noticed that the shear force variation, due to vibrations is unacceptable (Figure 8a). Typical vibration patterns within a sampling window of 200ms, used for shear tests, are shown in Figure 9, which exhibit a characteristic natural frequency of 85Hz. It was found that by averaging the data over a period of 160ms, collected at a sampling rate of 500Hz, reduced the range of variation from ±70cN to ±4cN. Figure 8b shows the shear force versus shear strain curve, after implementing this strategy. The robot controller has an I/O sampling window of 18ms, which limits the sampling rate to 18Hz. A sampling rate of 500Hz is required for the present application. A distributed control strategy, with two control nodes (robot controller and an PS/2 computer) has been implemented. The robot controller under AML/2 supervision, controls the test cycle, sequence, actuation of electropneumatic clamps and checking the status of digital sensors. The PS/2 computer controls data acquisition and analysis, using programs written in C. The computers exchange information through parallel digital lines, using a handshake routine.

Shear force (cN/cm)

Application of robotics to fabric testing

Shear force (cN/cm)

20

20

15

15

10

10

5

5

0

0

–5

–5

–10

–10

–15

–15

–20 –8 –6 –4 –2 0 2 4 6 Shear strain (degrees)

8

19

–20 –8 –6 –4 –2 0 2 4 6 Shear strain (degrees)

(a)

8

(b)

Figure 8. Shear force-strain curves without and with averaging

Force (cN) 60

Force (cN) 60

40

40 Mean value

20 0

Mean value

20 0 –20

–20

–40

–40

–60

–60

–80

–80

–100 0

50

100

150

Time (milliseconds)

200

0

20 40 60 80 100 120 140 160 Time (milliseconds)

Continuous bending test The traditional cantilever bending test involves measurement of a fabric cantilever length at a specific bending angle of 41.5˚. In the present work, a continuous cantilever test has been developed in which cantilever lengths are measured continuously at several bending angles. As soon as the fabric cantilever (Figure 10) intercepts the bending angle sensor (infrared retro-reflective sensor), the robot x-axis co-ordinate position is determined: Cantilever length = qposition(x)bending sensor – qposition(x)alignment sensor.

Figure 9. Typical shear force variations due to external vibrations

IJCST 8,1/2

The robot controller increments the stepper motor to the next position. The cantilever length for a given step is transmitted to the PS/2 computer through parallel lines. The bending angle is calibrated for each step. Using a finite element-based numerical technique, developed by the authors, bending angle versus cantilever length is converted to a moment-curvature relation (Figure 11).

20 Robot arm

Fabric panel

Figure 10. Bending test on a fabric panel

Stepper motor

Bending angle sensor

Testing as part of an automated clothing environment The KES and FAST systems are developed primarily for fabric hand evaluation, under controlled environmental conditions. However, the stresses applied to fabric panels during automated handling and making-up vary considerably from the standard tests. Fabric properties vary from one roll to another and there is also a variation within each roll. Environmental conditions in the manufacturing site vary from those of a test laboratory. The robotic test system facilitates integration of fabric tests into an automated clothing environment. It is possible to conduct low-stress fabric tests on a real fabric panel. Thickness of a single ply or an assembly can be easily measured, using a compression head attached to the robot. A cantilever bending test can be

Application of robotics to fabric testing

Moment (cN.cm/cm) 0.12

0.1

21

0.08

0.06

0.04

0.02

0 0

0.2

0.4 0.6 0.8 Curvature (1/cm)

0

1.2

conducted on a fabric panel as shown in Figure 10. The geometry of the panel, represented as a CAD file, is used in computing the moment-curvature relation. Greshon and Porat[15] developed robotic feeding of fabric panels to sewing machines under a feedback control of tension. Tension variations during sewing are detrimental to seam quality. The sensitivity of seam quality to tension variations varies enormously for different fabrics. If sewing is done along a bias, fabric is more extensible. A knitted panel is even more flexible and hence has a tendency to buckle. Feedback control of tension while feeding fabric panels to a sewing machine requires setting of system gain parameters, depending on fabric tensile stiffness, between sewing head and robot gripper. Figure 12 shows tensile testing of a panel under actual sewing conditions. Greshon and Porat use friction pads for feeding fabric panels to sewing machines. A tensile test, involving table friction, may be conducted as shown in Figure 13a. Friction between table surface and fabric panel may be tested by placing a weight and moving it horizontally. The friction force can be measured using the load cell mounted on the robot. Conclusions A robotic system equipped with a three-axis force sensor and a gripper has been successfully employed for testing fabrics in the low-stress region. Unlike existing test systems such as the KES, which was primarily developed for hand

Figure 11. Moment-curvature relation of a fabric

IJCST 8,1/2

22

Robot arm

Sewing head

Tensile force Tensile strain Figure 12. Tension test

Robot arm Friction pad

Sewing head

Weight

Tensile force

Friction

Tensile strain

Displacement

Figure 13. Tension and friction tests (a)

(b)

evaluation, the present robotic system is designed to test fabrics under varied conditions. Test conditions such as sample size, strain rate, etc. can be changed through the software. This creates the possibility of including fabric testing into an automated clothing environment. References 1. Manuals for the Kawabata Evaluation System, Kato Tekko Ltd, Kyoto, Japan, 1986. 2. Manuals for the Fabric Assurance by Simple Testing, CSIRO Division of Wool Technology, Australia, 1988. 3. Mahar, T.J., Dhingra, R.C. and Postle, R., “Measuring and interpreting low stress mechanical and surface properties, part 1: precision of measurement”, Textile Research Journal, Vol. 57 No. 6, 1987, pp. 357-69. 4. Kawabata, S., The Standardization and Analysis of Hand Evaluation, HESC, Textile Machinery Society of Japan, 1980. 5. Lindberg, J., Waestraberg, L. and Svenson, R., “Wool fabrics as garment construction materials”, Journal of the Textile Institute, Vol. 51, 1960, p. T1475.

6. Shishoo, R.L., “Relation between fabric mechanical properties and garment design and tailorability”, First International Clothing Conference, Bradford, 1991. 7. Stylios, G., Fan, J, Sotomi, J.O. and Deacon, R., “Introducing a new concept in garment manufacture, ‘the sewability integrated environment’, incorporating automated objective measurement systems”, 2nd International Clothing Conference, Bradford, 1992. 8. Kawabata, S., Niwa, M., Ito, K. and Nitta, M., in Stylios, G. (Ed.), Textile Objective Measurement and Automation in Garment Manufacture, Ellis Horwood, New York, NY, 1991. 9. Gunner, M.B. and Taylor, P.M., in Stylios, G. (Ed.), Textile Objective Measurement and Automation in Garment Manufacture, Ellis Horwood, New York, NY, 1991. 10. Brown, P.R., Buchanan, D.R. and Clapp, T.G., “Large-deflexion bending of woven fabric for automated material handling”, Journal of the Textile Institute, Vol. 81 No. 1, 1990, pp. 1-14. 11. Clapp, T.G. and Peng, H., “A comparison of linear and non-linear bending models for predicting fabric deformation in automated handling”, Journal of the Textile Institute, Vol. 82 No. 3, 1991, pp. 341-52. 12. Seyam, A. and Sun, F., “Manufacturing technology for apparel automation – layup module part II”, International Journal of Clothing Science and Technology, Vol. 6 No. 1, 1994, pp. 5-13. 13. IBM 7576 manufacturing system, IBM corporation, Boca Raton, FL, 1988. 14. Potluri, P., Atkinson, J. and Porat, I., “A robotic flexible test system (FTS) for fabrics”, Mechatronics, Vol. 5 No. 2/3, 1995, pp. 245-78. 15. Greshon, D. and Porat, I., “Robotic sewing using multisensory feedback”, 16th International Symposium on Intelligent Robots, Brussels, 1986. 16. Taylor, P.M. and Gunner, M.B., “Mechatronics in automated garment manufacture”, Mechatronics in Textile Industries Seminar, Loughborough, 1993.

Application of robotics to fabric testing 23

IJCST 8,1/2

Thread motion ratio used to monitor sewing machines J. Lewis Dorrity and L. Howard Olson

24

School of Textile and Fiber Engineering, Georgia Institute of Technology, Atlanta, USA Introduction The sewing machine operator is considered the first line of effort in the quality control of sewing operations. With advances in sewing machine automation, both fully and semi-automated sewing processes, that first line operator effort is removed or distracted by the nature of the automated processes. The US Department of Defense, Defense Logistics Agency, sponsored research to find means of automating the quality control function performed by the operator as part of a broad programme to support the US apparel industry and its homebased suppliers of sewn products. Its view is that improved competitiveness through automation is an admirable goal, but not if quality is sacrificed. Research leading to this paper[1] considered sewing defects and their origin as seen by sewing plant managers. For example, there is interest in detecting an improperly formed multi-ply bottom seam[2], known commonly as a “busted” seam. The effort included using a piezo-electric pick-up designed for acoustic emission research to determine whether acoustic signature analysis yields reliable information in sewing. Variability in sewing from cycle to cycle is the largest problem[3] to be surmounted in this approach to measurement of sewing parameters. The needle strikes the fabric structure differently with each cycle, and the thread has varying diameter and finish level along its length. Clear relationships between acoustic amplitude at certain frequencies and the number of plies of fabric have been found in sequential sets of data, only to have further sets of data contradict the results[4]. Acoustic analysis is unreliable as a general tool, even at one false indication per thousand cycles, although consistent results have been obtained for detection of broken or dulled sewing needles. Needle uniformity in modulus (due to metal composition) and shape (due to manufacturing tolerances) give the tightly controlled bandwidth and the consistency. A parallel research effort using another piezo-electric device to sense thread motion of the top thread in a lockstitch seam has overcome the reliability problem. This work is ongoing, with support from the National Textile Center.

International Journal of Clothing Science and Technology, Vol. 8 No. 1/2, 1996, pp. 24-32. © MCB University Press, 0955-6222

The authors appreciate the support given by the US National Textile Center for continuation of this work. Research leading to this effort has been sponsored by the US Defense Logistics Agency. Additionally, the co-operation of a number of industrial concerns has been vital to the success of this work, as has that of Rob Schoenborn and students at Georgia Institute of Technology.

Piezo element contact is made through a ceramic guide to the sewing thread. Convolutions due to twist and hairiness provide the deformations which the transducer senses and transforms to electrical signals. The time period of thread motion, obtained from these signals is influenced by factors which change the length of thread consumed, such as the number of plies of fabric under the needle, bobbin thread to top thread balance, and bobbin thread or top thread breaks. Presentation of the research effort leading to adoption of the thread motion ratio (TMR) and research results with various stitch types is the purpose of this paper. Points to be presented are first, that stitch length generally is a good indicator of stitch quality. Second, time of motion of thread is related to stitch length at constant speed. Third, the TMR, a normalized value, reduces the influence of speed. Finally, statistical analysis of data, slightly modified for varying stitch types, provides reliability in the use of the resultant values. This work is summarized below. Thread motion research The thread motion research has as its concept the timing of thread motion pulses. Piezo-electric transducer-based yarn motion systems have found a permanent place in the design of yarn break stop motion devices for weaving machines. The transducer relies on contact with the yarn or thread and senses vibration caused by motion over a ceramic guide. This report is directed to pulse width measurement for the period of thread motion and its reliability as a sewing defect indicator. Initial efforts in this research found that abnormalities in thread line motion point to several sewing defects. Because of the higher speed of sewing over weaving, the transducer is modified for faster time constants over those used in weaving. (Sensors and modifications to sensor electronics were provided by Torsten Carlsson, Eltex of Sweden, Greer, South Carolina.) Large changes in thread consumption and, particularly, any abrupt changes would indicate an abnormal or defective stitch, requiring a technician’s assistance to correct. Analysis of thread motion The type 301 lockstitch[5] is the stitch on which the research was conducted initially. Recent efforts reported below include type 504 overedge and type 406 chain stitches. The lockstitch requires that about 75mm of thread be passed around the bobbin and bobbin case under the bed of the machine during each stitch formation cycle while forming a stitch which may be only 2.5mm long. The additional yarn needed on each stitch is intermittently withdrawn from the yarn package at a high velocity. A machine running at 6,000rpm, which is 10ms per cycle, withdraws the new or additional yarn for a single stitch in about 1.0ms for a stitch length of 2.5mm in a lightweight fabric. Average thread velocity is 130 metres per minute during its motion.

Thread motion ratio

25

IJCST 8,1/2

26

Top thread consumed in a moderate weight fabric would be about 5.5mm for two-ply sewing, which includes the hidden stitch forming loops and the visible stitch yarn. The average rate of withdrawal is therefore 300 metres per minute in this example. The point is that low inertia or no inertia sensing is a requisite in monitoring sewing thread because of the rapid, intermittent withdrawal of thread. A complicating factor to this research effort is that yarn withdrawal is not constant from one stitch to another, and varies with machine speed. Figure 1 shows a typical pulse train. 7 6 5 4 3 2 1 0 –1 –2

Figure 1. Thread motion and sync pulses

–3 Key Eltex Sync

The pulse train of Figure 1 arises from sewing two plies of denim. The pulse period is about 30ms, whereas normally it would be about 10ms. Pulse width is 4 to 7ms. The variability is largely unexplained, but is probably due to thread unevenness, thread finish variation, differences in needle penetration (interstitial space versus striking a yarn), and fabric construction variability. Experiments performed to find optimum sewing tension levels with denim and a non-woven fabric demonstrate that a minimal bobbin loop is desirable for both reducing bobbin change frequency and decreasing the level of top thread tension. The assumption is that reduced thread tension yields fewer thread breaks. Thread motion ratio The next effort is to compare thread consumption with time of motion. Initial experiments using the piezo-electric transducer clearly show that the time during which the needle thread is being drawn by the take-up lever is about onetenth of the machine cycle. Specifically, for a 2,100 rpm speed of the sewing machine, one cycle takes about 28.6ms. While sewing one and three plies of a

utility trouser fabric, the corresponding times of thread pull versus machine cycle were 10.1 per cent and 12.9 per cent, respectively. TMR is defined as time of thread motion over total single sewing cycle time, such as the percentages given above. The initial experiments involving TMR included changes in stitch length using the standard adjustment on the sewing machine. A microprocessor board and other tools were used to collect these data[4-6]. Three settings were used which resulted in stitch lengths nominally of 2, 3, and 4mm. The percentage change in top thread consumption from one stitch setting to the other is about 20 per cent. The amount of variation in these pulse widths is considerable. In explaining this, note is made that the yarn diameter for the fabric used for this work is about 0.59mm. This is about 15 per cent of the stitch length. Realizing that the needle tends to be deflected rather than penetrate the yarn, the variation seen in the distributions might be explained by varying the stitch one yarn diameter in a random fashion. Variation determines sample size for the decision process. Data collected from sewing the denim gives a standard deviation of 0.31. Based on this, statistics show the sample size for various probabilities of error. Errors result in a wrong decision, where the decision may be to signal an error when in fact conditions are not in error (type I) or to fail to signal an error when error conditions do exist (type II). A high degree of certainty exists with a sample size of 19 for denim sewn with a type 301 stitch. Recent results show that other stitches (types 406 and 504) require as few as five as a sample size. For the level chosen, an error would be made only about once in 6 hours of operation at 4,000rpm with 70 per cent duty cycle. Correlation studies of TMR versus actual thread consumed show a correlation coefficient squared of 0.994 (R2). This is seen in Figure 2. This suggests that those defects which can alter thread consumption may be detectable by TMR analysis. There is some scatter to the data, and not every data set will correlate as well as this. Therefore, the design of a system which includes statistical certainty is necessary. This has been incorporated into the design of the research system by having a “learn” feature in which a technician, having ascertained that sewing is normal, requests that the system determine the appropriate statistical limits. These limits follow standard formulae. Figure 3 then illustrates results from the measurement of TMR for sewing a two-ply denim seam. This shows data from normal sewing occasionally going out of range, but this was due to the limits being set too tightly. More importantly, when the bobbin thread break occurred, there was a significant drop in TMR value. This was well beyond four sigma control limits. TMR has a non-zero value when there is a bobbin thread break because the feed dogs drive the fabric along, pulling top thread along the surface of the fabric.

Thread motion ratio

27

Thread motion ratio

IJCST 8,1/2

30

28

20

y = 3.5891×R x ^ 2 = 0.994

These data show the effect when the check spring is not adjusted properly

10

0 0 Figure 2. Thread motion ratio correlation to measured thread usage

2

4 Thread usage (mm)

6

Key High sewing tension Low sewing tension Check spring test

Thread motion ratio 15.00

12.00

9.00

6.00

Figure 3. Thread motion ratio data showing bobbin thread break

3.00

0

Loss of bobbin thread

8

Incidentally, if there is a top thread break, then the TMR value does drop to zero. This too is an easily detected condition. To illustrate the usefulness of TMR further one more example is given in Figure 4.

Thread motion ratio

Thread motion ratio

29

30 4mm

25 3mm

20 15

2mm 1mm

10

Figure 4. Thread motion ratio values – varying stitch lengths

5 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Figure 4 is generated by turning the stitch length knob on the sewing machine while measuring TMR. These data suggest another use for the TMR measurement. That is to determine when settings are out of limits during sewing machine set-up. In addition to this curve there are data for top thread tension, not presented here, which show a regular change in TMR value as tension changes. Machine set-up can have a large impact on defect generation, and while this prospect was not considered initially, there is user confirmation that this is a tool needed by sewing plants. Results with type 406 chainstitch The type 406 chainstitch is formed with two top threads and one lower looper thread. Thread consumption is greatest on the looper thread. Therefore, experiments are done with TMR monitoring of this thread. Results of tests are illustrated in Figure 5. The looper thread passes through both left and right needle thread loops. The change in TMR with any thread break well exceeds four sigma limits and reflects the change in magnitude of stitch geometry. A left or right needle break occurring first produced about the same magnitude drop in TMR. The value changes from 40 per cent to about 23 per cent. A problem with this type of machine is that the looper shaft under the bed parallels the looper thread path. Occasional wrapping of looper thread around the shaft, if undetected as in automated sewing, can destroy the sewing head. The effect of broken looper thread and a wrapping looper thread is that TMR is zero in both cases. While a wrapping thread is in theory represented by TMR of 1.0, in practice, the measurement circuit awaits a pulse edge that does not occur during wrapping. Thus it never records a thread motion time during the period of a machine cycle, resulting in zero TMR value.

IJCST 8,1/2

Thread motion ratio (per cent) 45 40

Left needle thread breaks

35 30

30

Thread motion ratio: 406 stitch at 4,300rpm double needle stitch

Normal sewing

25 20 15 10 5

Figure 5. Thread breaks with type 406 stitch

Right needle thread breaks

0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 Data points (average of 20 stitches per data point)

The alternative to monitoring the single looper thread is to monitor all three threads. Research will look into the matter of benefit in terms of additional defect detection versus the cost of a triple head monitoring system. The loss of both needle threads results in a looper TMR value of just above zero. In Figure 5 it was about 2 per cent. This represents the thread motion imparted by the feed dogs as the fabric advances with no stitch being formed, but with the looper thread anchored to the last stitch formed. Results with type 506 overedge stitch The type 506 stitch is formed with both a top and bottom looper thread and a single top needle thread. Both looper threads pass over the edge of a trimmed fabric edge to prevent ravelling. The looper threads predominate in thread consumption. Experiments placing the monitor on each thread showed that the needle thread has the smallest change when either looper thread breaks. The next two figures illustrate TMR for various break conditions based on sensing top looper or bottom looper threads. Typically, a break is followed by repair and a different type of break. First, Figure 6 illustrates data for monitoring the top looper thread. Note that loss of bottom looper thread or needle thread results in near zero TMR values. While a sample size of 20 is used here, clearly it is not necessary that it be as large. This machine may be monitored with a sample size of four or five. Tests of one or two sample sizes will be conducted in the near future. As shown in Figure 6, a top looper thread break results in a TMR of 0.0. The needle and bottom looper thread breaks gave low TMR values in the 13 per cent range as opposed to 23 per cent for normal sewing. This is the best arrangement of the three possibilities. Figure 7 gives results of monitoring the bottom looper during top looper and needle breaks.

Note that the loss of top looper thread does not greatly disturb the thread consumed by the bottom looper. The loss of either other thread, needle or bottom looper, is significant.

Thread motion ratio

Thread motion ratio (limits are set at 4 sigma)

31

25 20 15 10

Loss of needle thread

Loss of bottom looper thread

Loss of top looper thread

5 0

Figure 6. Monitoring the top looper thread (best monitoring condition)

Data points (average of 20 stitches per data point taken at 5,000 spm)

Thread motion ratio (limits are set at 4 sigma) 35

Bottom looper thread snag and break

30 Top looper thread snag and break 25 Loss of bottom looper thread 20 15 10 Loss of top looper thread 5 Loss of needle thread 0

Nevertheless, the inability to detect top looper loss is why use of TMR on the top looper thread is recommended over its use on bottom looper thread. Conclusions The piezo-electric device tested does detect certain sewing defects which cause significant changes in sewing thread consumption on types 301, 406 and 504 sewing machines. One limitation of using TMR is that a single stitch

Figure 7. Overedge: monitoring bottom looper

IJCST 8,1/2

32

measurement is too variable for reliable error indication, particularly with a type 301 stitch. TMR may be practical with one or very few measurements with both types 406 and 504 stitches. An average of a number of stitches gives statistical grounds for inferring that a change was due to a true error condition. The reliability of the transducer has been proven in manufacturing environments which are more severe than those expected in apparel plants. Thus, it is expected to function well in an apparel environment. Typically, a false stop is likely to be predicted wrongly once per million stitches if samples of 19 stitches each are taken on a lockstitch machine. As few as five stitches averaged may be used on type 504 and type 406 machines. References 1. Dorrity, J.L. and Olson, L.H., In-process Quality Control in Apparel Production: Sewing Defects, final report to Defense Logistics Agency, DLA 9000-87-D-0018-CLIN 0007, US Department of Defense, October 1991. 2. Murray, C.J., “Simple electronics to determine chained thread”, Design News, Vol. 45 No. 7, July 1989, pp. 124-5. 3. Matthews, B.A. and Little, T.J., “Sewing dynamics”, Textile Research Journal, Vol. 58, July 1988, pp. 383-91. 4. Dorrity, J.L. and Olson, L.H., “In-process quality control”, Proceedings of the 18th International Apparel Research Conference (ARC-AAMA), Atlanta, GA, 13 November 1991. 5. US Federal Standard 751a, Stitches, Seams, and Stitchings, General Services Administration, Washington, DC, January 1965. 6. Dorrity, J.L. and Olson, L.H., “System design for sewing defect detection”, International Journal of Clothing Science and Technology, Vol. 4 No. 5, 1993.

An XY-Theta manipulator for flexible fabric part positioning George R. Barrett, Carlos E. Farrington and Timothy G. Clapp

An XY-Theta manipulator

33

College of Textiles, North Carolina State University, Raleigh, North Carolina, USA Introduction The assembly of apparel garments has historically been a labour-intensive process. An analysis of the breakdown of the labour functions has shown that approximately 80 per cent of the labour to produce a garment is related to material handling[1]. The operator has to grasp the flexible fabric part, position it, and often combine two parts for assembly. One can break these manual handling tasks into identifiable functions. These functions include grasping, transporting, positioning, placement, and feeding. In order to reduce the manual labour in the apparel assembly process, automated equipment must be developed to perform these functions within the design constraints posed by the apparel assembly process. This paper focuses on the positioning function required to position a garment part for assembly accurately. Once a garment part has been separated from a multi-layered stack and transported to a general location, accurate positioning is required. The mechanical movements require the ability to move the part in two linear directions (X, Y ) and the ability to rotate the part (Θ)[2]. An XY-Theta (XYΘ) system for positioning garment parts is described in this paper. Prior work[3] deals with a specific device to place at a sewing station; however, the work described here is for a generic placement system. Engineering design constraints that guide the XYΘ development involve three general areas. These constraints are: (1) system cost; (2) geometrical variation of the part; and (3) the absence of a uniform edge to sense. The positioning system must be low-cost to be incorporated as part of a larger automated system. Garment parts vary in geometry when there are designed size changes. Loose yarns and rough edges around the perimeter of garment parts make edge detection difficult. The authors wish to acknowledge the support for this research by the United States Department of Defense through the Defense Logistics Agency contract No. 900-87-C-0509P22.

International Journal of Clothing Science and Technology, Vol. 8 No. 1/2, 1996, pp. 33-43. © MCB University Press, 0955-6222

IJCST 8,1/2

34

The described generic XYΘ positioning device satisfies all of the given design constraints and has the flexibility to be adapted for various specific applications. XYΘ description The generic XYΘ is composed of three major modules: (1) vision module; (2) positioning module; (3) control module. The vision module is designed to acquire information concerning the workspace. The control module contains the intelligence and, so, determines what is to be done given information from the vision module. The positioning module consists of the actuators and feedback switches. The control module commands both the vision and positioning modules, and the vision and positioning modules feed back vital information concerning the workspace and actuator status to the control module. The system block diagram is shown in Figure 1. Each of the XYΘ modules in Figure 1 and components in Figure 2 will be discussed in more detail. Vision module

Control module

Figure 1. System block diagram

Positioning module

Vision module The vision module is composed of two components: the linear charge-coupled device (CCD) arrays (Fairchild CCD 143) and the digitizing board. The linear arrays provide a low-cost (each array costs approximately US$150.00), compact vision system for the positioning module. Usually three arrays are necessary to establish the position and orientation of a part (a pocket). Light is projected from the top onto the arrays. As the fabric covers the linear arrays a shadow is produced over the array. The digitizing board uses the change in contrast to determine the location of the edge of the fabric. A benefit of this vision system is that it is not sensitive to the colour of the fabric. The quality of the edge, in terms of loose yarns, does complicate assessment of the fabric edge; however, software has been developed to distinguish loose yarns from the actual fabric edge.

An XY-Theta manipulator

Clock circuitry Line clock

Pixel clock Video signal

20 MHz AD/DC converter

4092 FIFO

8-bit

35 Interface

PLC controller Interface

8-bit

Microprocessor

OCD linear array

Pocket

XYΘ manipulator Figure 2. Overall positioning system block diagram

The digitizing board is composed of four basic elements: the clock circuit, the A/D conversion circuit, the data storage circuit and the microprocessor interface circuit. The first of these elements is the circuit responsible for creating the synchronizing clock pulse for the linear array. Binary counters are the basic building blocks for this circuit. The master clock is fed to a 2-bit binary counter. The first output of the binary counter yields the pixel clock, making the pixel clock half the frequency of the master clock, with a 50 per cent duty cycle. The second part of the clock circuitry is devoted to the line scan clock. The line scan clock is also based on binary counters; however, the circuit is slightly more complicated than the pixel clock circuit. The line scan clock circuit is more complicated because its period is directly related to the number of pixels in the linear array. The carry bit of the pixel 2-bit counter is fed into a 12-bit counter. This 12-bit counter is reset at the end of the scan, synchronizing the period of the line clock to the linear array line scan period. Adjusting the line scan period of the clock is done by a 3-bit decoder, which resets the 12-bit counter each time the pixel clock, bit 10 and bit 12 of the counter are high. The Fairchild CCD143 linear array requires that the offset between the rising edge of the pixel clock and the rising of the line scan clock is at least half of the pixel cycle. The half cycle delay is accomplished by using a 4-bit shift register. In this circuit the clock pin of the shift register is tied to the master clock and the

IJCST 8,1/2

Main clock

Pixel clock

Q2 2-bit counter

36

Figure 3. Clock circuit block diagram

Carry Clock

Q8 Reset

12-bit counter

3-bit decoder

DA

Q1

Line clock

4-bit shift register Q3

Q10

input pin DA is connected to the output of the of the 3-bit decoder. As a result the output Q1 of the shift register produces the desired line scan clock. Output Q2 of the shift register is used to reset the 12-bit counter. This assures that the counter is not reset before the end of line clock pulse is created (Figure 3). The line scan and pixel clock pulses are used widely throughout the vision system. The first point at which they are used is to synchronize the scan of the CCD array. Each pixel clock pulse yields a pixel intensity in the CCD array. Each line scan pulse signals the end of a line scan. These clocks are also used to synchronize the sampling of the A/D converters. The pixel clock is fed the A/D converter as the sampling clock. In addition, the clocks are used to control the information storage in the FIFO (first in, first out) (Figure 4). Pixel clock

Enable

Write

Read

Sampling clock AC/DC converter Figure 4. Digitizing circuit block diagram

Video signal

8-bit

FIFO

8-bit

FIFO empty

For all practical purposes it can be said that the pixel clock controls the data flow throughout the vision system up to the vision/microprocessor interface. As has been discussed above, the pixel clock is synchronized with the CCD array video signal output. The A/D converter, therefore, uses the pixel clock as the sampling rate for the A/D conversion. The A/D converter is a level triggered flash converter which samples the signal as long as the sampling clock is a high. The digitized value is temporarily kept in a latch for one pixel clock cycle. Hence, each pixel clock pulse causes the A/D converter to output a digitized value. As a result, the pixel clock is also used to control the data transfer rate between the A/D converter and the FIFO. The FIFO serves as a temporary storage facility in the vision system. This temporary storage facility is aimed at lowering the requirements on the microprocessor in terms of speed, access time and number of interface ports. If the processor transfer speed is slower than the sampling rate, the FIFO serves as a buffer to allow the microprocessor to catch up. If the transfer speed of the microprocessor is comparable to or faster than that of the sampling rate, the FIFO would seem transparent during the data transfer and acts as a SAM (sequential access memory). This feature reduces the memory requirements of the microprocessor. In either case the FIFO will allow the system designer to maximize the transfer rate and, therefore, makes the vision system very versatile. The use of FIFOs helps to lower the number of lines required on the vision/microprocessor interface, since a FIFO requires only a pulse to increment the storage address eliminating the need for an address bus (Figure 5). The interface circuitry links the FIFO and the low-cost microprocessor. There is no need to have an interface beyond this point because the linear array and A/D converter are operating in a continuous operation mode. Data are stored in Start to convert

An XY-Theta manipulator

37

Done

Line clock Q2

T flip-flop with reset

4-bit counter

Q3

Enable Pixel clock

Write

AC/DC converter 8 bits data

FIFO read reset

Read

FIFO

8 bits output

FIFO empty

Figure 5. FIFO-microprocessor interface circuit block diagram

IJCST 8,1/2

38

the FIFO only when the microprocessor generates a request signal. Further, operating the A/D converters in continuous mode alleviates the problem of waiting to ensure that the output of the CCD array and the A/D converter is under steady state. Therefore, interface circuitry is responsible for synchronizing the storage of data with the beginning of a new line. This is important, because the only way for the microprocessor to distinguish the beginning of a new scanned data line from the CCD array is if the data in the first FIFO register correspond with the digitized voltage level of the first pixel of the CCD array. To begin a scan the microprocessor signals the vision system to commence a scan by sending a pulse through the “start to convert” line. To synchronize the data storage, the interface circuit waits until the next line scan in the CCD to signal the FIFO to begin storing information. This results in a small delay between the start scan signal from the microprocessor and the actual storage of information into the FIFO; however, the CCD clock rate is usually much higher than that of the microprocessor. On writing the first byte of data to the FIFO, the FIFO drops of the “FIFO empty” line. A drop in the “FIFO empty” line signals to the microprocessor that it is clear to begin to read data from the FIFO. The “FIFO empty” line is low as long as the write pointer of the FIFO is greater than the read pointer. By using the combination of the “FIFO empty” line and the “start to convert” line the vision system can operate with two control lines and eight lines for data transfer. A “FIFO read pointer” reset is included in the interface circuit to allow the microprocessor to re-examine the data. This option is important, since one of the vision system design constraints is that the microprocessor data storage capacity may be limited. This feature allows the microprocessor to re-examine the data stored on the FIFO in case a second data processing stage is necessary. The data stored in the FIFO are not overwritten until the microprocessor signals the vision system to “start to convert” again. An example of a typical fabric edge as viewed by the linear array is shown in Figure 6. Positioning module The positioning module is built on a general purpose frame shown in Figure 7. This general construction allows the use of an assortment of motor types depending on the specific application. For example, the authors used a synchronous motor for the belt driven linear x transport, a dc motor driven cylinder for the linear y motion, and geared stepping/synchronous motor for angular Θ positioning. The fabric in this prototype is held between the head of the XYΘ and the workspace table by the weight of the head. Linear feedback controllers[4,5] could be used to increase the positioning accuracy of the motors used. Once the fabric is positioned, air cylinders are used to raise the positioning head. Other types of gripping include (but are not limited to) vacuum, electrostatic, and pneumatic or electrical picking devices[6,7]. The specific application

An XY-Theta manipulator

Amplitude 200

150

39

Fabric edge

100

50

0

50 Sample number ( × 10)

100

Figure 6. Typical fabric edge as seen by linear array

Figure 7. XYΘ manipulator

IJCST 8,1/2

40

would simply require the specialized gripping tool to be mounted on the XYΘ positioning head. Most microprocessors operate on a 5-volt supply, while most motor controllers operate at 24 volts and higher. This difference in operating current and voltage levels requires that an interface be used between the microprocessor and the motors. This interface will generally consist of some type of isolation circuit between the microprocessor and the motor controllers. Operational amplifiers can be used as isolation devices but do not yield true electrical isolation. Low-cost optical isolation relays are produced that provide several thousands of volts of true electrical isolation between the delicate microprocessor and the motor controllers. An example interface is shown in Figure 8. X motor controller

Microprocessor

Interface circuitry

Limit switches

Y motor controller Θ motor controller

Output isolation Figure 8. Control/positioning interface Input isolation

Control module The control module is implemented using a microprocessor with sufficient number of I/O lines for data transfer and control. Because of the use of FIFOs in the vision module, microprocessor speed is primarily dictated by the control operations required by the positioning module. Programming of the microprocessor can be performed using high-level languages like C, but where memory constraints are of concern programming at lower levels such as with Assembly usually yields more efficient code generation. Of primary concern during the placing of fabric parts in an automated environment is the prevention of collisions in the workspace. Collisions occur when two or more operations are attempted within a finite workspace[2]. The term “collision” indicates that two or more fabric parts or operation devices come into contact when such contact is destructive or causes interference to the operation. An example of this might be when positioning a fabric part at a sewing machine within an automated assembly station. It seems obvious that the XYΘ should not attempt to position a new part until the sewing machine

has completed a prior sewing task and the prior part has been removed from the sewing workspace. If the XYΘ does attempt a place operation a collision will occur because both the XYΘ and the sewing machine are utilizing the same workspace. In this case two modes of the process will simply interfere with each other. Other cases may result in damage to the assembly station. In any event, the detection and prevention of collisions should be managed either through a hierarchical control structure or within the modules themselves. The control module described only detects possible interdevice collisions occurring at the extremes of XYΘ travel. This is done through the use of limit switches shown in Figure 8. Workspace collisions are prevented using a hierarchical structure governed by a master controller which provides correct scheduling of parts throughout the automated process. The control sequence in the controller module is designed to ensure the timely and accurate placement of flexible fabric parts. The main program (low level) for placing the part is shown in Figure 9.

BEGIN

JSR INIT JSR HOME JSR PLACE BRA BEGIN

INITIALIZE CONTROLLER SEND XYTHETA TO HOME POSITION GRAB PART AND PLACE IT ON LINEAR ARRAYS

An XY-Theta manipulator

41

Figure 9. Main program (low level) for placing the part

Each of the routines in the main program handles the details of its specified task. For example, the jump to sub-routine INIT sets up the data direction for the microprocessor ports. INIT also sets up a table in RAM which is used when communicating with the vision module. An example pseudo-code for an INIT routine is shown in Figure 10. INIT

SET POINTER TO FIFO MASK TABLE STORE FIFO1 MASK STORE FIFO2 MASK STORE FIFO3 MASK STORE FIFO1 EDGE THRESHOLD STORE FIFO2 EDGE THRESHOLD STORE FIFO3 EDGE THRESHOLD SET PORT A DATA DIRECTIONS SET PORT C DATA DIRECTIONS INITIALIZE PORT C OUTPUT BITS STORE NUMBER OF FIFOS SET UP FABRIC EDGE TABLE FIFO 1 LOWER EDGE LIMIT FIFO 2 LOWER EDGE LIMIT FIFO 3 LOWER EDGE LIMIT FIFO 1 UPPER EDGE LIMIT FIFO 2 UPPER EDGE LIMIT FIFO 3 UPPER EDGE LIMIT STORE BASE ADDRESS STORE FIFO THRESHOLD ADDRESS OFFSET STORE FIFO EDGE ADDRESS OFFSET RTS

Figure 10. An example pseudocode for an INIT routine

IJCST 8,1/2

42

Once the controller has been initialized, a software loop encapsulates actions which must be done on each place operation. This is apparent by the BRA (branch always) to BEGIN in the main program. The main sequence of events for placing a part begins (or ends) with the control module commanding the positioning module to return to a standard position known as “home” where the XYΘ can wait for a part to position. This allows the position of the XYΘ to be known at least once to the hierarchical controller during each place operation. An example pseudo-code for the HOME routine is shown in Figure 11. HOME

Figure 11. An example pseudocode for the HOME routine

MAKE SURE ALL MOTORS ARE OFF TELL SUPERVISORY CONTROLLER XYTHETA IS READY RAISE POSITIONING HEAD OFF OF WORKSPACE CHECK X AND ENSURE XYTHETA IS IN HOME X POSITION CHECK Y AND ENSURE XYTHETA IS IN HOME Y POSITION WAIT FOR SUPERVISORY CONTROLLER TO TELL XYTHETA TO GO RTS

Notice that the HOME routine informs the hierarchical controller that the XYΘ is ready for a new part before the XYΘ is actually at the “home” position. This allows the hierarchical controller to bring a new part to the XYΘ as soon as possible without having to wait for the XYΘ actually to get home. This adds speed to the automated process without compromising collision resolution ability of the hierarchical controller. The XYΘ then waits at the “home” position for the hierarchical controller to tell the control module that a new part is ready and that the workspace is empty. Thus the hierarchical controller can halt the placing process to manage possible collisions. Once a “go” signal is sent to the control module from the supervising controller, the control module jumps to the PLACE routine. Pseudo-code for this routine is shown in Figure 12. PLACE

Figure 12. An example pseudocode for the PLACE routine

SET READY LINE TO LOW, I.E., XYTHETA IS BUSY LOWER XYTHETA POSITIONING HEAD ONTO FABRIC PART MOVE FABRIC PART INTO WORKSPACE POSITIONING FABRIC OVER LINEAR ARRAYS { GRAB FRAME FROM LINEAR ARRAYS FIND EDGES DETERMINE CONTROL ACTION } RTS

When the fabric part is placed correctly over the linear arrays, the control module jumps to the HOME routine which releases the part and tells the supervisory controller that the XYΘ has finished placing. The XYΘ positioning system is capable of consistently aligning a pocket in 3.2 seconds with an accuracy of ± 1/16 inch. The alignment time and accuracy of the system can be improved in two ways:

(1) the complexity of the control algorithm can be increased slightly; and (2) different types of motor drives can be chosen for each axis of motion. The type of motor drive plays an important role in the speed and accuracy of the system. The authors design a system which employs different types of drives in each of the axis. This was done to demonstrate the flexibility of the positioning system. In practical applications, however, the XYΘ mechanism should be designed with only one type of motor drive system. A single motor drive type in the XYΘ mechanism will simplify considerably the control algorithm. The type of motor drive should be chosen on the basis of cost and the desired positioning accuracy of the system. Discussion The positioning accuracy within this type of XYΘ manipulator is generally governed by the accuracy of the cut of the fabric. Frayed fabric edges reduce the positioning accuracy by moving the visible edge. Any simple edge detection method of placement will fail to give optimal results. In such cases requiring very accurate placement, the XYΘ should read a lensed two-dimensional CCD array, i.e. a CCD camera, and generate a least squares fit to an “ideal” fabric part. Positioning in this manner uses the entire fabric part and, therefore, is more robust against distorted or frayed fabric edges. The placement time of the XYΘ will, of course, depend on initial transport time to the linear arrays, initial deviation from final placement, motor speed, etc.; however, the authors have developed a prototype generic XYΘ and obtained excellent results. The prototype operates within an automated pocket sewing station moving fabric parts from one sewing operation and positioning for another. The prototype has a placement time of approximately three seconds for its specific application. References 1. Hoffman, K. and Rush, H., Micro-electronics and Clothing, the Impact of Technical Change on a Global Industry, Praeger, New York, NY, 1988. 2. Paul, R.P., Robot Manipulators, Mathematics, Programming, and Control, The MIT Press, Cambridge, MA, 1981. 3. Digital XYΘ, US Patent 5,290,027. Ark, New York, NY. 4. Brogan, W.L., Modern Control Theory, 3rd ed., Prentice-Hall, Englewood Cliffs, NJ, 1991. 5. Doyle, J.C., Francis, B.A. and Tannenbaum, A.R., Feedback Control Theory, Macmillan, New York, NY, 1993. 6. Sarhadi, M., Nicholson, P.R. and Simmons, J.E., “Advances in gripper technology for apparel manufacturing”, Proceedings of the Institution of Mechanical Engineers: UK Research in Advance Manufacture, paper C372/86, 1986. 7. Taylor, P.M., Taylor, G.E., Wilkinson, A.J. and Gibson, I., “Mechatronics in automated apparel manufacture”, Mechatronics: Designing Intelligent Machines, Proceedings of the Institute of Mechanical Engineers, 1990, pp. 1-4.

An XY-Theta manipulator

43

IJCST 8,1/2

44

Thinking sewing machines for intelligent garment manufacture G. Stylios and J.O. Sotomi Department of Industrial Technology, University of Bradford, Bradford, UK Introduction To conform to the shape of a three-dimensional body, fabrics have to be stitched, as in a garment, by needle and thread. This form of sewing, having survived for centuries, is the only means of joining acceptable to consumers. Detailed and exhaustive definition of fabrics, as with metals, is very complex, if not impossible. Fabric properties may interact with one another and possibly change with processing. On the other hand, the processing equipment, mainly sewing machines, have inherent problems in the engineering sense, predictably because of the complex mechanisms necessary for the many different types of stitches which they have to perform. Optimization of sewing machine settings has been, and still is, one of the most important requirements for the textile, garment and retailing industries, and for the sewing machinery manufacturing industry. The complex interactions at the fabric/machine interface have been a theme of study for some years[1,2]; the scientific deliverables which have formed the foundations for research into the new discipline are called “intelligent textile and garment manufacture”. This paper is concerned with the methodology applied to overlock sewing the lockstitch findings having been published elsewhere[3]. Problems associated with joining “limp materials” Arguably there is reasonable progress in relating fabric properties to sewing machine settings and stitching quality but, there are still areas that have not been numerically defined because of the complexity of the dynamic interactions between needle-fabric-machine parameters. The influence of a physical or mechanical property on the behaviour of a textile material is often non-linear and, in general, the interactions between the material and the sewing machine and needle tend to be highly non-linear. Owing to incomplete mathematical understanding of these non-linear interactions, the behaviour of each material cannot be effectively modelled using conventional techniques.

International Journal of Clothing Science and Technology, Vol. 8 No. 1/2, 1996, pp. 44-55. © MCB University Press, 0955-6222

The authors would like to acknowledge the support of the EPSRC Directorate of the SERC for funding this research, Bellow Machine Co. UK, Pegasus Machine Co. of Japan, Claremont plc. and Berburry of London Ltd for their collaboration.

Seam quality itself can have many definitions which are still subjective and, Thinking sewing even if measured, have to retain the analogous subjective understanding: machines unbalanced stitch, without seam pucker, with no seam slippage, no holes, etc. Furthermore, during the sewing machine operation a discrete problem may occur which cannot be modelled, such as, for example, pulling the fabric – inducing undue thread tension. Solutions to all these problems have to be 45 provided for effectively in the design of a new control model. Such control algorithms need to be robust enough to function successfully where no transfer function exists, or it has not been acceptably determined. The fabric properties/machine settings interface Overlock seams are primarily used for joining knitted fabrics of the single/double jersey types for underwear and outerwear. Since knitting gauges are becoming higher, the density of those fabrics is increased, rendering them prone to sewability problems. From the results of an earlier study into the effect of knitted fabric properties on sewing[4-7], the following properties have been found to interact with the sewing process: fabric thickness, fabric compression, fabric bending, fabric and yarn tensile strength and yarn friction. These properties can be measured automatically using specially developed measurement systems[4]. For a predetermined fabric type, a central rotatable experimental design of Box and Hunter[8] for three variables was used to determine the effect of foot force (gf), sewing speed (rpm) and needle size and shape. Table I shows the levels for these variables. Sewing was performed on the Orion Rimold sewing machine, and two sets of experiments were carried out with two different types of knitted fabrics, single and double jersey. Twenty combinations of needle size, foot force and speed were used in the experiments[8]. For each of the experimental combinations of the testing methodology, the stitching quality was assessed (including sewing damage) by means of counting the sewing holes under a microscope. Figures 1 and 2 show the contours of sewing damage in single jersey and double jersey respectively. Analysis of the results[7] (see Figures 1 and 2) established the theoretical sewing model and the appropriate rules for the

Experimental variables Foot force for single jersey (gf) Foot force for double jersey (gf) Sewing speed (rpm) Needle size (SES)

–1.682 388.2 529.4 1,644.6 60

Experimental levels –1 0 +1 419.12 598.4 2,240.3 66.07a

464.6 700.0 3,116.4 75

510.07 801.54 3,992.5 83.9a

+1.682 541.0 870.6 4,588.2 90

Note: a Means the closest needle size will be selected. For example, needle size 66.07 means the needle size 65 will be used in this experiment

Table I. Experimental set-up

IJCST 8,1/2

Foot force (experimental levels) 2 1.5 1

46

0.5 0 –0.5 –1 –1.5

2 34 1.

6 00 1.

67 0.

32 0.

38 –0

.6

.3

74

1 –0

–1

.0

46 .3 –1

–1

Figure 1. Contours of sewing damage for single jersey (needle size 80, y is the number of holes)

.6

8

–2

Sewing speed (experimental levels) Key

y=1 y=3

Foot force (experimental levels) 2 1.5 1 0.5 0 –0.5 –1 –1.5

Sewing speed (experimental levels) Key

y=1

y=3

y=5

y=7

2 34 1.

6 00 1.

67 0.

4 33 0.

02 .0

78 –0

–0

.3

74 .6

1 .0 –1

–0

46 .3 –1

–1

Figure 2. Contours of sewing damage for double jersey (needle size 80, y is the number of holes)

.6

8

–2

sewing machine fuzzy control system. It has been revealed that sewing machine Thinking sewing speed, foot force and needle type and size all affect the optimum settings of the machines sewing machine for any particular fabric, for consistent quality and damagefree sewing. Sewing damage was considered as one of the most important attributes during the overlocking operation of single and double knitted fabrics. The results of an earlier investigation[3,7] presented, in part, in Figures 1 and 47 2 show that: •

low foot forces are optimum at low sewing speeds;

•

high foot forces are optimum at high sewing speeds;

•

optimum foot forces should be higher for single jersey fabrics relative to the settings for double jersey fabrics;

•

optimum disc forces should be higher for thicker fabrics over the range of sewing speeds.

The sewability index for any given fabric was pre-determined prior to input into the fuzzy system. This pre-processing was performed by an artificial neuron and a weight on the connection between the neuron and each fabric property, trained using gradient descent methods (in error back propagation), to predict the sewability index accurately from the relevant physico-mechanical properties of the fabric. Fuzzification of inputs was carried out at the inputs layer while defuzzification was performed at the outputs layer (Figure 3).

Fuzzy logic

Fabric properties (input)

Machine speed W1

Optimum foot force

W2

W3

W4

Optimum disc force

Fabric sewability index

W5

Sewability prediction

Input layer

Rules

Output layer

Figure 3. Architecture of the fuzzy-neural network

IJCST 8,1/2

48

Triangular membership functions may be completely described by two parameters; centre and area, or by three parameters; namely, the centre, left and right spreads, to allow for asymmetry. By replacing the standard sigmoid function f(z) = (1 + e–z)–1 employed in forward propagation of neural networks by another function that incorporates these parameters in a network which implements the fuzzy system, automatic tuning was enabled[8]. For linear functions, µ (x) = (1 – |(x – c)/s|), where c is the centre of the membership function, s is sL for left spread or sR for right spread and x is a value of the output variable. Furthermore, the learning capabilities of the neural network and a complementary critic network will be used to optimize the output membership functions of the fuzzy system for implementation as an adaptive fuzzy system for closed loop feedback control. Implementation and validation In this investigation, all the input membership functions (Figures 4 and 5) were left unchanged and automatic tuning was performed on output membership functions (Figures 6 and 7) only. The membership functions representing low optimum outputs (Figures 9 and 10) were the most severely affected by the tuning, in terms of magnitude of change, and the direction of tuning, i.e. they

Low

Low/medium

Medium

Medium/high

High

1,500

2,250

3,000

3,750

4,500

Figure 4. Membership functions of first input – speed of sewing machine (rpm)

Low

Medium

High

0

0.5

1.0

Figure 5. Membership functions of second input – fabric sewability index

Low

Low/medium

Medium

Medium/high

Thinking sewing machines

High

49

DJ 1,739.0 SJ 2,371.5

Very very low

2,081.25 3,135.75

Very low

Low

Medium

Figure 6. Untuned membership functions of first output – foot force (steps of motor)

2,423.5 3,900.0

High

Very high

Very very high

Figure 7. Untuned membership functions of second output – disc force (steps of motor) 400

425

Fuzzy associative memories Sewability Optimized index/fabric parameter thickness Optimum foot force

Low Medium High

Optimum disc force

Low Medium High

Note: V = very; VV = very, very

450

475

500

525

Low

Speed of sewing machine Low/medium Medium Medium/high

Rule 1 Low Rule 6 Low Rule 11 Low Rule 1 VVHigh Rule 6 High Rule 11 Low

Rule 2 Low Rule 7 Low Rule 12 Low Rule 2 VVHigh Rule 7 High Rule 12 Low

Rule 3 Low Rule 8 Medium Rule 13 High Rule 3 VVHigh Rule 8 High Rule 13 VLow

Rule 4 High Rule 9 High Rule 14 High Rule 4 VVHigh Rule 9 High Rule 14 VLow

550

High Rule 5 High Rule 10 High Rule 15 High Rule 5 VVHigh Rule 10 Table II. High The set of fuzzy rules Rule 15 VVLow relating fabric sewability index and sewing speed to optimum machine settings

IJCST 8,1/2

50

Sewing speed

1

1

Low

Lowmedium

2

Medium

Medium

3

High

Mediumhigh

4

High

5

Foot force

6

Low

7

8

9

Very very high

10

Very high

11

High

12

Med

13

Low

14

Very low

High

15

Very very low

Antecedents

Rules

Consequents

Sewability index Medium

Figure 8. Fuzzyneural system for overlock sewing of knitted fabrics Inputs

Disc force

Output

were reduced. The membership functions (except low) of the output foot force Thinking sewing were increased in size while the sizes of all membership functions of the output machines disc force decreased in size after tuning. The fuzzy control system has been implemented on a prototype Pegasus industrial overlock sewing machine (Plate 1) which has shown considerable promise in the progress towards eliminating the learning curve introduced by a 51 new fabric to sewing machine control personnel before acceptable seam quality can be achieved. The prototype sewing machine was manufactured with stepping motors cast into its body to control the three thread tensions individually. The foot force is pneumatically controlled. The three thread tensions and presser foot force were controlled through an IBM-compatible personal computer. The control system receives two inputs, one from the processed fabric properties, and the other, machine speed. The system then specifies the optimum settings and these are achieved by the stepping motors and pneumatic pressure. Figures 11-14 show the simulated control surfaces and the actual surfaces followed by the fuzzy control system. There is good agreement between the actual disc force and simulated control surfaces, developed mainly from expert

Low

Medium

DJ 1,739.0 SJ 2,371.5

Very very low

Very low

2,081.25 3,135.75

Low

Medium

High

High

Figure 9. Membership functions of the optimum foot force after tuning

2,423.5 3,900.0

Very high

Very very high

Figure 10. Membership functions of the optimum disc force after tuning 400

425

450

475

500

525

550

IJCST 8,1/2

52

Plate 1. The intelligent sewing system (overlock machine)

Optimum foot force 1

0.5

0 1 0.8

1 0.8

0.6

Figure 11. The control surface of the foot force (simulated)

Sewability index

0.6

0.4 0.4 0.2

0.2 0

Sewing speed

0

experience and experimental fine tuning for knitted fabrics. The role played by thread tension after achieving seam balance in such fabrics is not critical and is practically insignificant when compared to the role of thread tension in woven fabrics especially on the lockstitch machine. However, the thicknesses of fabrics (knitted and woven) have been observed to have a significant effect on seam balance, although more so in knitted fabrics. The foot force, however, involved

Thinking sewing machines

Optimum foot force 1

53

0.5

0 1 0.8

1 0.8

0.6 0.6

0.4

Sewability index

Figure 12. The control surface of the foot force (achieved)

0.4 0.2

0.2 0

Sewing speed

0

Optimum disc force 1

0.5

0 1 0.2

0 0.2

0.4 0.4

0.6 Fabric thickness

0.6 0.8

0.8 1

Sewing speed

1

extensive tests as described earlier, and the actual control surface is also very acceptable. Although further tuning could have improved the comparison, it was felt that it would not yield significant improvement. Preliminary industrial trials carried out in collaboration with garment manufacturers such as Bentwood Brothers revealed that the system was capable of reducing the learning curve of control personnel about a new fabric by at least four weeks. Further work is therefore being carried out into more testing and training of the system in order to achieve a possible complete

Figure 13. The control surface of the disc force (simulated)

IJCST 8,1/2 Optimum disc force 1

54

0.5

0 1 0.2

0 0.2

0.4

Figure 14. The control surface of the disc force (achieved)

0.4

0.6 Fabric thickness

0.6 0.8

0.8 1

Sewing speed

1

elimination of the learning curve. Ongoing research is investigating the incorporation of reinforcement based unsupervised learning or adaptive fuzzy system as mentioned earlier. Discussion and conclusion The synergism of a combination of neural and fuzzy logic approach has been found most successful for modelling the control of sewing machinery for complex interactions with limp materials. It is now possible to optimize sewing machinery settings automatically for both static and dynamic conditions, for a given material to be stitched. This research establishes the next generation of intelligent sewing machines in the newly developed area of intelligent textile and garment manufacturing systems. The good agreement between the target and achieved control surfaces for the foot and disc forces verify the accuracy of the control system. References 1. Stylios, G., “Prognosis of sewability problems in garment manufacture using computer based techniques”, Proceedings of the IEEE International Conference on Systems Engineering, 9-11 August 1990, Pittsburgh, PA. 2. Stylios, G. and Fan, J., “An expert system for fabric sewability and optimisation of sewing and fabric conditions in garment manufacture”, Proceedings of the 1st International Clothing Conference “Textile Objective Measurement and Automation in Garment Manufacture”, 9-11 July 1990, Ellis Horwood, Chichester, 1991. 3. Stylios, G. and Sotomi, J., “A neuro-fuzzy control system for intelligent sewing machines”, Proceedings of the IEE International Conference on Intelligent Systems Engineering, Conference Publication Number 395, IEE, 1994, pp. 241-6.

4. Stylios, G., Fan, J., Sotomi, O.J. and Deacon, R., “Introducing a new concept in garment manufacture; the sewability integrated environment incorporating automatic objective measurement systems”, 2nd International Clothing Conference, July 1992 and International Journal of Clothing Science and Technology, Vol. 4 No. 4, 1992. 5. Stylios, G. and Zhu, R., “The mechanism of sewing damage in knitted textiles”, submitted for publication. 6. Stylios, G. and Sotomi, O.J., “Automatic settings of optimum sewing machine conditions for the manufacture of high quality garments made of lightweight synthetic fibre fabric”, Proceedings of the 21st Textile Research Symposium on Basic Properties of Fibres and Fibre Assemblies, Performance and Design of New Fibrous Materials, 7-9 August 1992, Japan. 7. Stylios, G. and Zhu, R., “Sewing dynamics; the interaction of speed, foot force and needle on sewing damage”, submitted for publication. 8. Box, G.E.P. and Hunter, J.S., “Statistics for experiments: an introduction to design, data analysis and model building”, Annals of Mathematical Statistics, 1957, p. 28. 9. Jamshidi, M., Vadiee, N. and Ross, T.J. (Eds), Fuzzy Logic and Control: Software and Hardware Applications, Prentice-Hall Publishers, Englewood Cliffs, NJ, 1993. 10. Berenji, H.R. and Khedkar, P., “Learning and tuning fuzzy logic controllers through reinforcements”, IEEE Transactions on Neural Networks, Vol. 3 No. 5, 1992, pp. 724-40. 11. Kosko, B., Neural Networks and Fuzzy Systems, A Dynamical Systems Approach to Machine Intelligence, Prentice-Hall International, Englewood Cliffs, NJ, 1992. 12. White, D.A. and Sofge, D.A. (Eds), Handbook of Intelligent Control: Neural, Fuzzy and Adaptive Approaches, Multiscience Press, 1992.

Thinking sewing machines

55

IJCST 8,1/2

56

Automatic faults detection and recognition for static plain fabrics Applying the theorem of texture “tuned” masks Shaw-Jyh Shin, I-Shou Tsai and Po-Dong Lee Feng Chia University, Taichung, Taiwan, Republic of China Introduction In recent years, work has been carried out on the faults detection and recognition of textiles. For example, Ribolzi and Gresser[1] used an optoelectronic processing technique to analyse the diffraction spectrum responses of fabrics in order to detect whether faults of weft-lacking or warp-lacking exist. Shimizu et al.[2] used the methods of co-occurrence matrix and comparison to inspect the existence of minute faults, etc. The methods mentioned above are restricted to identifying faults which are minute and with small variance. It is very difficult to analyse the feature points of fabrics with variable structure or tone by using opto-electronic processing; the method used by Shimizu et al. cannot inspect faults with variable structure, and it may cause great errors if fabrics do not have a uniform structure. In other words, these methods only detect simple faults and neglect faults with variable structure or grey-level differences. In this paper detection and recognition of faults such as filling bars, weft-lacking, oil stains and holes are discussed. Since faults of filling bars and weft-lacking have a variable structure, the fault of oil stains has grey-level differences, variable shapes and variable sizes, and holes have simple feature of irregular shapes, it is very difficult to identify these four faults with regular image segmentation, classification or simple diffraction spectrum analysis. The theorem of the texture “tuned” mask[3] was modified and used in this paper to solve the problems encountered in automatic faults detection and recognition of plain woven fabrics.

International Journal of Clothing Science and Technology, Vol. 8 No. 1/2, 1996, pp. 56-65. © MCB University Press, 0955-6222

Texture structure analysis Normal texture structure analysis From the process of image fining of the structure and the measurement of the distances between yarns, it is evident that the texture structure is not quite regular, and three variable phenomena are seen in normal texture structure. They are:

(1) the variability of the yarn thickness; (2) the distance change between yarns; and (3) the bend in yarns caused by lack of tension. Faults texture structure analysis Four different kinds of faults of plain fabrics were studied for detection and recognition. These are filling bars, oil stains, weft-lacking and holes. Holes are the simplest faults because they have almost the same tone, and change in areas or in sizes but with no variation in texture structure; filling bars are considered when the density of the wefts is higher than that of normal texture structure; the fault of weft-lacking occurs when yarns are bent due to tension; oil stains cause tone differences in the fabric. Of the four faults mentioned above, weft-lacking has the most variation in the texture structure; filling bars have a structure close to normal texture structure and are often mistaken for the normal texture. During the process of detection and recognition of the four faults, the following three problems are encountered: (1) inner texture structure variation between faults and faults, and faults and normal structure; (2) the grey-level differences in the faults of oil stains; and (3) the faults of variable shapes and sizes. These problems cannot be solved by using the method of image classification such as the co-occurrence matrix method, which extracts the structure features from structure image and sorts them into different texture structure images, by using contrast, roughness from different images or other features. The image classification process cannot solve the issue when faults exist in a part of the inspection samples. Basic principles of the method used From the above, we know that the method of image classification cannot solve the problem when faults exist in a part of the inspection samples. However, if the method of image segmentation is used, the faults existing in a part of the inspection area can be separated from the normal texture structure. The modified theorem of the texture “tuned” mask is used to segment and identify faults because faults and normal texture have different features in the structure variation. The theorem of the texture “tuned” mask on the classification and segmentation of rotated and scaled texture images was submitted by You and Cohen in 1993[3]. Since it is derived from the measurement of texture energy, some basic concepts of the measurement of the texture energy will be introduced, and ways to modify the “tuned” mask in order to solve the three problems mentioned before and to achieve the goal of automatic faults detection and recognition will also be discussed.

Theorem of texture “tuned” masks 57

IJCST 8,1/2

58

The measurement of structure energy Laws[4] derived four 5 × 5 convolution masks. These masks were intended to be sensitive to visual structure such as edges, ripples and spots, and to convert the images into texture energy images. This method characterizes different structure images, and the values of the texture energy obtained from this method will not change when the luminance changes. The process of the texture energy conversion can be described as follows: to take the convolution operation of the image I(i, j), i, j = 1 to N, with mask A(i, j). (In most cases the size of the mask A(i, j) is 5 × 5.) That is: F (i , j ) =

2

2

∑ ∑ A (k ,

l ) I (i + k , j + 1).

(1)

k=–2 l =–2

The deviation of F(i, j) is given by  1  E (i , j ) =    2n + 1 

2

i+n

∑

j +n

∑ | F (k ,

l ) – M (i , j )|

(2 )

k=i–n l = j –n

where M(i, j) is the mean of F(i, j) and given by  1  M (i , j ) =    2n + 1 

2

i+n

∑

j +n

∑

F (k , l ).

(3 )

k=i–n l = j –n

If the window of the image is large enough and the image is regular, the mean M(i, j) approaches zero, and equation (2) becomes  1  E (i , j ) =    2n + 1 

2

i+n

∑

j +n

∑

F (k , l )

(4 )

k=i–n l = j –n

which Laws[4] called the texture energy measure, which is used in his test as the texture feature. Adaptive convolution mask The theorem of the structure adaptive (or “tuned”) mask from You and Cohen[3] is to find dynamically an adaptive mask which is used to segment or classify different texture energy images under the circumstances of rotation and scaling. The generation of the texture adaptive mask from You and Cohen can be explained from following steps: (1) To create a dynamic texture sample set from different structure images obtained from different rotation and scaling. (2) To create several performance indexes of the adaptive mask. These performance indexes are explained in the following: • Index 1. This is to adjust the value of the adaptive mask which makes very close average texture energy when rotation and scaling change within a certain range.

• Index 2. This is to enlarge the differences of the average texture energy in different structures and to make it easier to segment and classify the images. • Index 3. From this index, there is a minimum square error of the average texture energy existing between every fault and discriminant function, as well as between normal structure and discriminant function. The discriminant function is to separate and to fix the distribution range of the average texture energy between faults and normal structure. • Index 4. This index is to reduce the distribution range of the texture energy in the faults and normal structure. (3) To find the optimum structure adaptive mask by using the gradient search and random search. The modification of the structure and adaptive mask The use of the structure adaptive mask is mainly to solve problems of segmentation and classification when images are rotated and scaled. It is not designed to solve the problem when the structure in the same texture changes, as in the case of four faults mentioned before. Therefore, the theorem of the structure adaptive mask is modified as follows to detect and recognize the faults for static plain fabrics. Modification of sample set According to the structure difference in faults, a dynamical sample set is established as shown in Figure 1. In this sample set, the faults of filling bars, oil stains and weft-lacking as well as normal texture structure are considered. As for holes, they are not considered in this sample set because they do not bear structure change. Modification of performance indexes in the structure adaptive mask Index 1. The convergence of the inner texture structure change in faults is expressed as:  ABS( E ( x , qx ) – E ( x , qy ))  P1 = max  (5 )   E ( x , qx ) + E ( x , qy )  where: X = 1 to 4 represents certain fault or the normal structure; QX and QY represent certain structure change and E(X, QX) represents the average texture energy of certain sample in the sample set. Index 2. The separation between normal structure, filling bars, oil stains and weft-lacking is expressed as:  ABS( E ( x ) – E ( y ))  P2 = min (6 )   E ( x ) + E ( y ) 

Theorem of texture “tuned” masks 59

IJCST 8,1/2

Fault 1

Fault 1

Fault 1

Variation 1

Variation 2

Variation N

Fault 2

Fault 2

Fault 2

Variation 1

Variation 2

Variation N

Fault M

Fault M

Fault M

Variation 1

Variation 2

Variation N

Normal structure

Normal structure

Normal structure

Variation 1

Variation 2

Variation N

60

Figure 1. Sample set of structure images

where E(x) or E(y) is the abbreviation for Ex(i, j) or Ey (i, j) as defined in equation (4), and is the average energy in certain structure x or y. This index is used to enlarge the difference between different structures. As for the discriminant function, f(x) = 1.2x is used instead of f(x) = x in J. You’s thesis is just to enlarge the distance between the four different average texture energy. The coefficient 1.2 is chosen for three reasons: (1) it can adequately enlarge the distance between normal texture and the faults; (2) it is difficult to converge for the standard error of texture energy when the coefficient is above 1.3; (3) it will reduce the faults recognition speed when the coefficient is too large. The square error between the average texture energy and the discriminant function is: e =

N

∑ ( E ( x ) – kf ( x ))2

x =1

where k is a constant which makes e minimum.

(7 )

Theorem of texture “tuned” masks

The index for the square error is: m

∑ E ( x) – e

n_error =

x =1 m

.

(8 )

∑ E ( x)

61

x =1

Index 3. The normalized texture energy difference is given by: 2

 E (i , j ) – AVE ( x )  Sdv( x ) = ∑ ∑  (9 )  . AVE ( x )  i = 1 j = 1   The maximum normalized texture energy difference is defined as max_Sdv = max{Sdv(x)}, where E(i, j) is the texture energy of certain point; AVE(x) is the average texture energy of this sample set. The size of the sample set is N × N. N is the number of all samples of normal structure or oil stains in the sample set. This index has great influence on the precision and resolution of faults recognition because it controls the distribution range of the texture energy on faults and normal structure. Index 4. The average deviation of the texture energy is given by: N

N

ave_dev(t1 , k ) = Sdv(t1 , k )0.5 E (t1 , k )

(10 )

where E(t1, k) is the average texture energy of normal structure or oil stains in certain samples. The index ave_dev(t1 , k ) – ( E (t1 , k ) – E (t1 )) P4 = 1 – (11) E (t1 ) – E (t2 ) is for normal structure and oil stains; that is P41 for normal structure and oil stains, P42 for oil stains and filling bars because these two cases have less distance in the average texture energy. t1 represents normal structure or oil stains, E(t2) is the average texture energy of certain fault. Finally, the final index f is modified to be f =

P2 ⋅ P41 ⋅ P42 ⋅ n _ error P1 ⋅ max_ Sdv

.

(12 )

Recognition flow-chart Assume the area of the detected texture image is small enough that two faults existing on the same sample at the same time can be neglected, and a structure adaptive mask can be found from the search logic of You[3], the texture energy for faults or normal structure should have a distribution range from the texture energy’s image histogram. That means the boundary values of the average texture energy can be set between faults and faults or faults and normal

IJCST 8,1/2

62

structure. If the fabric has a certain fault, the summation of the energy in this distribution range should be higher than that of the others, so that the specific fault can be detected. In order to detect the faults and to recognize them, a flowchart (shown in Figure 2) is designed. In this flow chart, SUM(A), SUM(B), SUM(C), and SUM(D) represent respectively the total points that the texture energy falls into a certain fault range. BAD_SUM is the sum of SUM(A), SUM(B), SUM(C), and SUM(D); THRESHOLD(X) is the threshold of each fault; THRESHOLD(N ) represents the threshold. between normal structure and each fault. The process of recognition is to calculate SUM(A), SUM(B), SUM(C) and SUM(D) first, then to judge which one is higher than its threshold in order to judge the existence of the certain fault. If none is higher than its threshold, then see if BAD_SUM is greater than or equal to THRESHOLD(N ). It is said to have a certain unknown fault existing if BAD_SUM is greater or equal to THRESHOLD(N ); otherwise, the detected sample is a normal structure.

Calculate SUM(A), SUM(B), SUM(C), SUM(D)

SUM(X) > Threshold(X)

Yes

Fault x

No BAD_SUM > Threshold(N)

No

Normal structure

Yes Figure 2. Recognition flow chart

Fault existing but do not know which kind

Process of automatic faults detection and recognition The process of automatic faults detection and recognition is summarized as follows: (1) Find a structure adaptive mask which makes the final index maximum. (2) Take the convolution operation in the image sample and the optimum adaptive mask. (3) Calculate the variance of the filtered image in order to get the texture energy image. (4) Detect or recognize the faults by using the different texture energy distribution in the faults and in normal structure.

Experiment Sampling Sampling is the first step in image analysis and it has great influence on the accuracy of analysis. Images of 512 × 512 pixels were grabbed from the CCD camera, and then filtered by a lowpass filter to filter out the high frequency noise. These image samples were taken from normal structure and the faults of oil stains, filling bars, weft-lacking and holes. Then six images of each different structure in every fault were taken (the size is 62 × 62 pixels) to form the sampling set.

Theorem of texture “tuned” masks 63

Sampling set The sampling set was as follows: • Fabrics detected: white static plain fabrics. • Faults: filling bars, weft-lacking, oil stains and holes. • Warp density: 24 ends/cm. • Weft density: 19 ends/cm. • Enlarging factor: 2. Finding the optimum adaptive mask From the sample set, the optimum adaptive mask which makes the final index f maximum can be found by using “gradient search” combined with “random search” methods[3]. The coefficients of this mask are confined below 100. The size of the shifting window is 9 × 9 when searching, and 15 × 15 when detecting.

–22.28 –15.36 –5.48 2.19 –38.81

Weft-lacking Normal structure Oil stains Filling bars MAX Notes: Final index: 0.9376 P41: 0.301 P42: 0.4319

39.48 27.28 8.90 25.85 47.78

–67.50 9.41 –37.42 –33.30 2.19

16.96 –13.64 43.02 –28.07 9.79

33.33 –7.69 –9.02 33.33 –20.95

SD

P1

P2

ave-E

N-error

0.1020 0.0636 0.0487 0.1090 0.1090

0.0979 0.1063 0.0756 0.1537 0.1537

0.1350

879.15 612.55 466.88 345.59 879.15

0.8960

Table I. The optimum adaptive mask

Table II. Index values and the average texture energy

IJCST 8,1/2

64

The coefficients of the optimum adaptive mask were obtained by calculating on a supercomputer to make the final index f maximum. This is shown in Table I and the value of each index calculated by using the optimum adaptive mask is shown in Table II. From Table II, the average texture energy from the top down are weft-lacking, normal structure, oil stains and filling bars. From the practical sampling sets of filling bars, weft-lacking, oil stains and holes, the average texture energies are obtained. Four boundary values are chosen by averaging adjacent average texture energy in Table II to classify those faults and normal structure: •

weft-lacking – normal structure: 745;

•

normal structure – oil stains: 539;

•

oil stains – filling bars: 405;

•

filling bars – holes: 191.

Thresholds in faults From analysing the distribution of the structure energy for filling bars, oil stains, weft-lacking, holes and normal structure, the thresholds are set to be 978, 1,204, 808, 0 and 1,360 for weft lacking, oil stains, filling bars, holes and normal structure respectively. Detection of samples Take ten samples from filling bars, weft-lacking, and oil stains respectively; five of them are samples with partly existing defects; two samples from the fault of holes, sample sizes are 76 × 76 pixels, detecting area is 58 × 58 pixels. Table III shows the distribution of points fall in every fault. Conclusions From the results of the recognition and detection, it can be seen that the optimum texture “tuned” (i.e. adaptive) mask found from the modified theorem of the texture “tuned” mask can be used satisfactorily to identify different faults under variable structure, shapes and sizes. However, there are two misjudgements during the detection: the sixth sample in the fault of filling bars and the seventh sample of oil stains. The former happened because the density of this sample is sparse and this makes the average texture energy shift to the range of oil stains instead of filling bars. The latter happened because the undertone of this sample makes the average texture energy move to the range of the normal structure. From the results, it can be seen that this method still has some restrictions which need to be studied and solved: •

oil stains of undertone cannot be detected;

•

the fault of filling bars is sometimes recognized as that of oil stains;

Weft-lacking

Filling bars

Oil stains

Holes

• •

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2

Weft-lacking

Normal structure

Oil stains

3,122 2,342 2,928 2,509 3,181 2,146 2,238 1,755 2,286 2,185 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 184 91 104 0 1,306 1,278

240 941 436 757 183 1,218 796 1,159 1,007 1,105 0 0 0 0 0 631 716 707 484 628 1,170 1,144 86 202 87 1,995 1,991 1,413 1,459 778 1,493 1,489

2 81 0 92 0 0 314 444 71 74 829 684 533 682 899 1,458 1,052 938 1,145 954 2,067 2,160 2,871 2,522 2,802 1,345 1,189 1,847 1,749 2,269 441 184

Filling bars 0 0 0 6 0 0 0 6 0 0 2,535 2,680 2,831 2,682 2,465 1,275 1,596 1,719 1,735 1,782 127 63 407 640 475 15 0 13 55 307 88 223

Holes 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 36 190

the minimum diameter of the detected fault is no less than the width of two ends; it cannot detect several faults existing on the same detecting area at the same time.

References 1. Ribolzi, J. and Gresser, J., “Real-time fault detection on textiles using opto-electronic processing”, Texture Research Journal, February 1993, pp. 61-9. 2. Shimizu, Y., Ishikawa, T., Furukawa, T., Kayama, N., Toba, E. and Kondon, A., “Expert system to inspect fabric defects by pattern recognition”, SEN-I GAKKAISHI, Vol. 46 No. 10, 1990, pp. 460-69. 3. You, J. and Cohen, H.A., “Classification and segmentation of rotated and scaled textured images using texture ‘tuned’ mask”, Pattern Recognition, Vol. 26 No. 2, 1993, pp. 245-58. 4. Laws, K.I., “Textured image segmentation”, PhD thesis, University of Southern California, January 1979. 5. Haralick, R.M., Shanmugam, K. and Dinstein, I., “Textural features for image classification”, IEEE Transaction on Systems Management of Cybernetics, Vol. SMC-3 No. 6, November 1993.

Theorem of texture “tuned” masks 65

Table III. The distribution of points in every fault

IJCST 8,1/2

66

Image processing as a tool to improve machine performance and process control D. Veit, I. Hormes, J. Bergmann and B. Wulfhorst Department of Textile Technology (ITA), RWTH Aachen, Germany Determination of trash content in cotton webs – introduction Raw cotton contains various trash particles, which get into the material during harvesting or the ginning process. In order to determine the trash content of cotton, these particles are currently weighed after a cleaning process or counted manually. By using the gravimetrical method, it is not possible to distinguish between different kinds of particles, although this is the crucial point in order to predict the behaviour of the cotton in the processes to follow and the characteristics of the final product. Furthermore, neps cannot be detected using this method. Although manually counting the trash particles distinguishes between different kinds of particles, the results are subject to considerable variation depending on the operator carrying out the measurements, and are, therefore, not reproducible. For these reasons, it is important to develop a method providing users with reproducible results which enable them to distinguish between various kinds of particles in order to predict the behaviour of the cotton material regarding its cleanability in the subsequent processes.

International Journal of Clothing Science and Technology, Vol. 8 No. 1/2, 1996, pp. 66-72. © MCB University Press, 0955-6222

Web production With digital image processing it is possible to detect and differentiate trash particles such as neps, seed coat particles, leaf and wooden fragments and extraneous fibres. To start with, the trash particles must be arranged in a thin fibre web for two reasons. First, it must be guaranteed that the particles are not lying one on the other and second, the web must be translucent in order to a allow transillumination. In that case, all sorts of particles can be detected without difficulty. At the Department of Textile Technology (ITA), a machine has been developed for producing thin fibre webs from about 2gm of raw cotton. Before making the web, it is possible to mount a cleaning device in order to clean the cotton of as many trash particles as possible. The web takes approximately 15 minutes to make and results in a fibre web of 500 × 500mm in size. This web is then arranged between two thin glass frames and put on to the scanning device. For the image-taking process, the web is virtually divided into segments of 15 × 15mm. Each image (taken using transillumination) then consists of 512 × 512 dots while using 256 different shades of grey (the value 0 represents black and the value 255 represents white). The images are taken row after row while the process of detecting the trash particles within the scanned image has to be completed before the next image is taken.

Detection of trash particles and classification First, all trash particles in the image are marked. All further analysis is applied only to these areas of the image in order to save computing time and memory. During the marking process, all medium to dark grey parts are set to blue and all dark grey to black regions are set to red, in order to simplify the subsequent classification process. Second, different parameters are calculated for each particle detected. These are: (1) mean grey value and standard deviation of the medium to dark grey areas; (2) mean grey value and standard deviation of the dark grey to black areas; (3) mean value and standard deviation of the differentiation coefficients on the edges of the particles; (4) size-independent form factor; (5) particle circumference; (6) size of the medium to dark grey areas; (7) size of the dark grey to black areas. The differentiation coefficients on the edges of the particles are calculated as follows: Differentiation coefficient = Grey value of the surroundings/grey value of the particle’s edge. This coefficient is needed when evaluating the “sharpness” of the particle’s edges. The size-independent form factor is used because although trash particles of the same kind can differ in their respective sizes, they are usually of a similar shape. When using a neural network for the classification of trash particles it is useful to have a form factor which describes the particle in question regardless of its size. This simplifies the training process of the neural network. The particle circumference is necessary in order to establish the real size of the particle. After computing these parameters, the particle is then classified, according to two different algorithms, as a nep, seed coat particle, leaf or wooden fragment or an extraneous fibre. This can be done with a neural network or using a nearest-neighbour-algorithm. For the nearest- neighbour-algorithm, all of the parameters are compared with all parameter combinations of all the other already classified particles and then classified by the particle that comes closest to the one in question. Alternatively, it is possible to classify the unknown particle by the three or five nearest neighbours. This can lead to better classification results but requires more computing time. Another method of classification is the use of a neural network. At the ITA a back propagation algorithm in connection with a fuzzy module is used[1]. The neural network applied uses 10 input knots, three hidden layers with 20, 15 and 10 hidden knots respectively and 5 output knots (there are five different classes of particles). All transfer functions are sigmoid functions.

Image processing as a tool 67

IJCST 8,1/2

68

These values have turned out to be the most suitable after comparing various parameter combinations. The fuzzy-module can improve the classification quality. Both algorithms – the nearest neighbour and the neural network – have to be trained before carrying out serial measurements with a set of about 1,500 particles which have been classified manually during the image-taking process. At that stage the nearest-neighbour algorithm is much quicker (it takes minutes) than the neural network (two to three days), but the application of its knowledge on the classification of dozens or hundreds of fibre webs is considerably quicker with the neural network. The classification quality of both algorithms is about 89 per cent which means that only 11 per cent of all the particles are classified wrongly. This value is calculated by classifying all particles which were used for training the respective system (nearest neighbour or neural network) using this system. The percentage of correctly classified particles is then called “classification quality”. Application on various kinds of cotton and results The trash content of the cotton webs can be determined with regard to the number of particles in the web, their size and their massive size (the proportion of the particle which is solid). The latter is the dark grey to black region within the particle, which represents, for instance, core fragments of seed coat particles or wooden components of leaf fragments. Figure 1 depicts the relation between different kinds of trash particles and their sizes. It is obvious that seed coat particles, neps and wooden fragments are much bigger in size than all the other particles. In Figure 2 the number of trash particles of each detected type is shown for several kinds of cotton. Neps represent the biggest share with about 40-50 per cent of all particles, followed by seed coat particles, leaf and wooden fragments

Leaf Wood Extraneous fibre Seed coat particle Nep Figure 1. Trash particle sizes (in mm2 per web of 500 × 500mm2)

Undefined 0

20

40

60

80

100

120

140

160

Image processing as a tool

Argentina Burkina Faso Mali

69 Paraguay Central Asia Zimbabwe 0

20

40 60 Trash content (per cent)

80

100

Key Undefined Extraneous fibre

Nep

Seed coat particle Wood

Leaf

with about 20 per cent, extraneous fibres make up less than 5 per cent of all particles. In Figure 3 the massive size of several particles in per cent per gramme of the particle is shown. For example, the solid areas of wooden particles make up about 55 to 80 per cent of the whole particle, for seed coat particles this value is between 40 and 50 per cent. In contrast, the massive sizes of neps, leaf fragments and extraneous fibres represent less than 2 per cent of the whole size of these particles. In order to determine the cleanability of cotton in the cleaning processes, webs were produced with and without a cleaning device. Figure 4 shows an example of the results of these experiments. The graph shows the reduction in massive sizes of seed coat particles and wooden fragments for cottons from a range of countries. It can be seen that cleaning reduces the massive sizes of seed coat and wood particles by between 70 and 85 per cent. Comparison with other measurements The results obtained from the analysis of the webs can be used for predicting certain yarn characteristics. Figure 5 shows the relation between the number of seed coat particles and the USTER-Imperfections of an OE-Rotoryarn. In Figure 6, the relation between the number of seed coat particles and the number of USTER –50 per cent thick places is shown. Figure 7 depicts the analogous relation for USTER +50 per cent thin places. A similar correlation can be obtained by looking at the summed up massive size of seed coat particles. These correlations indicate that mainly seed coat particles are responsible for

Figure 2. Content of various trash particles (per cent)

IJCST 8,1/2

Argentina

Burkina Faso

70

Mali

Paraguay

Central Asia

Zimbabwe 0

Figure 3. Relation between solid area and particle size (per cent)

50

100

Key Nep

Seed coat particle

Extraneous fibre

Wood

Leaf

Argentina Burkina Faso Mali Paraguay Central Asia Figure 4. Cleanability of trash particles regarding their solid parts (per cent)

Zimbabwe 0

10

20

30

40

50

60

70

80

90

Solid parts (per cent)

thick and thin places in OE-Rotoryarns since other particles do not show a similar correlation. These results are the basis of further investigations currently being carried out at the ITA. Their aim is to reach the degree of cleanability of the particles mentioned above in various cleaning machines. In order to achieve that, fibre webs are produced before and after each cleaning device and their trash content is then analysed using image processing. This may lead to an improved

Image processing as a tool

Imperfections 600 500 400

71

300 200 100 0 0

50

100

150

200

250

Figure 5. Correlation between USTER-imperfections and number of seed coat particles

200

250

Figure 6. Correlation between thick places and number of seed coat particles

Number of seed coat particles Key Measured Regression USTER + 50 per cent thick places 150

100

50

0 0

50

100

150

Number of seed coat particles Key Measured Regression

adjustment of these units with regard to their efficiency of cleaning out certain kinds of particles. Summary Within a project of research carried out at the ITA and sponsored by AiF Gesamttextil (committee for industrial research organizations, Frankfurt am Main), a system was developed which provides a tool to detect the trash content of cotton webs. The reproducible results enable the user to distinguish between

IJCST 8,1/2

USTER –50 per cent thin places

150

72

100

50

0 0 Figure 7. Correlation between thin places and number of seed coat particles

50

100

150

200

250

Number of seed coat particles Key Measured Regression

different kinds of trash particles like neps, seed coat particles, leaf and wooden fragments and extraneous fibres and furthermore to determine the exact composition of cotton regarding these particles. This allows the prediction of the degree of cleanability of the cotton and the number of USTER thick and thin places to be expected in the yarn. The results show that the seed coat particles are responsible for most yarn imperfections. This leads to the conclusion that the seed coat particle content is the most important factor regarding raw cotton quality and not the leaf and wooden fragment content. This is because leaf and wooden fragments could be easily removed during the cleaning process, whereas the seed coat particles could not. Furthermore, this new analysis method is suitable for the optimization of various cleaning devices, experiments in this area are currently under way at the ITA[1-4]. References 1. Hormes, I., Using Image Processing for Classification of Raw Cotton with Regard of Trash Content and Cleanability, AiF research report 8769, RWTH Aachen, 1994. 2. Hormes, I., “A system for analysing trash particles in cotton using digital image processing”, doctoral thesis, RWTH Aachen, 1994. 3. Hormes, I. and Wulfhorst, B., “Erkennen von Störpartikeln im Vlies von Baumwollfasern mit Hilfe der digitalen Bildverarbeitung”, Melliand Textilberichte 70, 1989, pp. 887-9. 4. Wulfhorst, B. (Ed.), Quality Insurance in the Textile Industry, RWTH Aachen, 1995.

Fault detection and quality assessment in textiles by means of neural nets S. Sette

Fault detection and quality assessment 73

Department of Textiles, Universiteit Gent, Ghent, Belgium, and

L. Boullart Department of Control Engineering and Automation, Universiteit Gent, Ghent, Belgium Introduction The importance of quality and fault detection in textile research cannot be underestimated. Both have considerable impact on the end-product, application possibilities, price, customer satisfaction. They also suffer from the same problem: human subjectivity. Today, most industrial textile production processes still use human experts to detect (and classify) faults or to make a classification of the quality of the end product. As human judgement is influenced by eyesight, concentration and personal preferences this is certainly not an objective and cost-effective method. In this paper we suggest a more objective approach to quality assessment and fault detection by using two different types of neural networks: (1) neural network using the Backpropagation Rule; and (2) a Kohonen network. We will apply those techniques on the following case studies: • assessment of set marks; and • assessment of carpet wear. Neural networks Definition Neural networks are models for computational systems, either in hardware or in software, which imitate the behaviour of biological neurons (the human brain) by using a large number of structurally interconnected artificial neurons. A biological neuron (Figure 1) consists of: • a nucleus; • several input axons connected to the nucleus by so-called synapses; • an output axon. The authors wish to thank Dr L. Vangheluwe, Dr L. Van Langenhove, W. Van Steenlandt and P. Bernard for providing the raw data, comments and discussions.

International Journal of Clothing Science and Technology, Vol. 8 No. 1/2, 1996, pp. 73-83. © MCB University Press, 0955-6222

Output axon

IJCST 8,1/2

Synapses

Dentrites Nucleus

74 Input axons Figure 1. The biological neuron

A neuron passes information from its inputs to the output (leading to other neuron(s)) obeying a certain transfer function. This function consists of two consecutive stages: (1) adding up the information from the input axons, whereby each input will be attenuated (enforced/weakened) by the synapse strength (a biochemical binding); (2) deciding if and how it will be transferred to the output axon. An artificial neuron (Figure 2) is a good mimic of the biological neuron, and maps the biological parts to a mathematical model: (1) The nucleus becomes a processing element. (2) The synapses become input weights. (3) Adding up the N inputs becomes a linear mathematical operation: Ij =

N –1

∑

wij xi

i =0

where wij is the weight coefficient between input xi and node j; and Ij is the resulting weighted sum; xN–1 xi

Figure 2. The artificial neuron

x0

y

wN–1j Σ

wij w0j

IJ x

yJ

(4) The “decision step” is made by the following non-linear operation: yj = f(Ij – θ ) where θ = threshold value and the function f ( ) can either be • a hard limiter; • a threshold function; or • a (continuous) sigmoid function (see Figure 3). Although neural networks show an intrinsic non-linear behaviour, by using the last sigmoid function, an attempt is made to make such systems more suitable for analytical study.

f(I)

+1

+1

I

f(I)

+1

I

75

f(I) I

–1 Hard limiter

Fault detection and quality assessment

Figure 3. Transfer functions Threshold

Sigmoid

Using neural networks Neural networks (NNs) consist of an agglomerate of neurons interconnected in some specific architectural way (rows, layers, planes, see Figure 4). NNs are learning systems, i.e. they are trained by real-life examples, whereby the weighting factors are adapted following a certain strategy until they converge to a more or less stable steady state. After learning the system may enter the recall stage, whereby unknown exemplars are presented at the input,

Output layer

Intermediate layer

Input layer

Figure 4. A typical multi-layered neural network

IJCST 8,1/2

76

leading by a simple computation (i.e. applying the NN functions at each node in sequence) to an output value. Although the training phase may be very highly demanding in computing power and execution time (because it is simulating in fact a highly parallel system on a sequential computer), the recall phase itself is very straightforward and fast. This characteristic makes NNs very powerful and attractive. From the point of view of artificial intelligence, NNs present some peculiarities: • The learning capabilities, as indicated. • The knowledge is distributed inside the whole system (i.e. inside the weights); this leads to a fault tolerant behaviour, because one faulty neuron cannot cause the overall operation to collapse. • They have strong associative properties: the unknown input exemplar is in fact associatively matched against the learning examples (reflected in the weights); thereby they have strong pattern matching capabilities. • They have excellent generalization properties: even with noisy or incomplete inputs they can behave rather well. Learning There are several ways NNs can go through the learning phase. Very generally speaking, it is essential to understand that there are two general strategies to have NNs trained: (1) All weights in the system are adapted at each learning step: e.g. an output of the system with a training example produces some output which is compared to a known output; the resulting error is propagated by slightly adapting all weighting coefficients of the system. (2) There is a competition between the neurons for learning, and only one or more “winners” see their strength (weights) increased. This operation lets the “fittest” neuron survive. Each neuron or group of neurons in such a system may become the strongest (the winner) for a particular set of input patterns, reflecting a representative duster for a “class” of input patterns (features). Furthermore, a distinction can be made between supervised and unsupervised learning: • In supervised learning, there is an almighty teacher who, at each iteration, compares the actual output of the NN with the known “should be” output, as given by each example. He/she uses this result to supervise the learning process. • In unsupervised (or self-organizing) learning, there is no evaluation of some output value, and the learning is spontaneously driven by the learning algorithm.

The backpropagation network is an example of an architecture where all weights are adapted at each learning cycle (see (1)) combined with supervised learning. The Kohonen Network is an NN based on the competition rule for adapting weights (see (2)) combined with unsupervised learning. It is outside the scope of this paper to go into detail about the algorithms used in both neural networks. For more information about the aforementioned NNs network types we recommend the following: • a good introduction and overview is given in[1]; • the Kohonen architecture is explained in[2]; • implementation details about the Kohonen Network used in this paper in[3]; • implementation details about the backpropagation network in[4]; and • some other research on Kohonen maps by one of the authors in[5] and [6]. Implementation of neural networks for quality assessment and fault detection by means of neural networks Set marks Problem description. One of the important fabric defects in weaving is the set mark. The set mark is characterized by a deviation in the interlacing structure of the fabric. It can be seen as a line across the fabric with a higher or lower intensity depending on the change in distance between successive weft threads. In most cases set marks are caused by loom stops, resulting in relaxation of the yarn and different (lower) velocity of the loom at subsequent start up. Existing procedures to avoid set marks tends to be unsatisfactory as they require a lot of experimenting with machine parameters and are not reliable[7]. Set marks can be divided in five classes corresponding to severity: (1) no visible set mark; (2) dubious; (3) very slightly visible set mark; (4) slightly visible set mark; (5) set mark. Until now, the evaluation of set marks was done visually by experts. However, deviations between experts of one or two classes are common. Selection of image features. A total of 587 images of set marks were digitized and the following features were extracted for each image: • distance between weft threads near the loom stop (total of seven distances); • mean value for the distance between weft threads; • standard deviation of the distance between weft threads; • yarn count of the weft yarn; • filament or staple yarn.

Fault detection and quality assessment 77

IJCST 8,1/2

A learnfile was constructed using 500 samples picked at random. The remaining 87 samples were used as test file.

78

Carpet wear Problem description. One of the most important parameters of a carpet is the change of appearance during wear[8]. Wear is simulated by applying an intensive mechanical action to the carpet. Subsequently, the carpet’s wear behaviour is evaluated (on a scale from 1: maximum wear to 5: no wear) by visual comparison with a set of reference samples in standard conditions. This method has important disadvantages: •

it is not objective and requires a certain expertise; in most of the industry laboratories, there is lack of experienced people;

•

it is subject to discussion;

•

it is slow, as at least five people are involved;

•

a limited number of reference sample sets have been established for the evaluation of an almost infinite number of carpet qualities.

Selection of image features for ISO aspect classification. Ten different coloured samples of the same cutpile carpet with the following production characteristics were obtained: •

material: polypropylene;

•

mass: total 1,730.8g/m2; effective 523.4g/m2;

•

volume mass: 0.09g/cm3;

•

thickness: total 8.83mm; effective 5.83mm;

•

gauge: 3.2mm;

•

stitches: 40/dm.

Each sample was submitted to mechanical wear tests by a Vetterman drum at 0, 1,000, 2,000, 3,000, 5,000 and 22,000 cycles, obtaining five different wear levels. Of each sample a digital image was taken. The following image parameters were extracted and used as input features for the NN for determining the ISO aspect classification of the carpet: (1) average value of the Fourier Spectrum; and (2) average value of the Radial Fourier Spectrum. Furthermore, we added as a third input feature; the number of Vetterman drum cycles. A learnfile was constructed selecting all carpet colours with corresponding input features at random. Owing to the small number of samples no testfile was constructed.

Results Set marks Table I gives the percentage classified with an error ∆x using the Kohonen Network and the Backpropagation Network. ∆x = |Ce – Cn|, where Ce is the Classification made by the human expert (from 1 to 5) and Cn is the classification made by the Kohonen Network (from 1 to 5) or the Backpropagation Network. Table II gives values calculated for the distance matrix[3]. The distance matrix is derived from the resulting Kohonen map and gives an indication about the difference between classes. A small value between two classes indicates almost no difference, while a large value indicates clearly different classes (see Appendix). Table III gives the linear deviation[3] values for each class. The linear deviation is also derived from the results of the Kohonen map and is an indication of the difference between the input vectors of a certain class (see Appendix). The following conclusions can be drawn from these results: • Table I shows us that the Kohonen Network classifies 59 per cent correctly and 27-32 per cent with one class difference (i.e. 86-91 per cent is accurate within one class). The Backpropagation Network classifies 53 per cent correctly and 41 per cent with one class difference (94 per cent

Kohonen learnfile Kohonen testfile Backpropagation learnfile Backpropagation testfile

0

1

∆x 2

3

4

59 59 53 53

27 32 41 41

10 6 4 6

1 2 2 –

3 1 – –

Class

1

2

3

4

5

1 2 3 4 5

0

70 0

1,132 1,150 0

1,476 1,492 363 0

1,923 1,930 1,096 868 0

Class 1 2 3 4 5

Fault detection and quality assessment 79

Table I. Percentage classification versus error ∆x

Table II. Distance matrix values (set marks)

Linear deviation 626 556 1,403 1,342 862

Table III. Linear deviation values (set marks)

IJCST 8,1/2 •

80

•

is accurate within one class). The maximum error for the backpropagation is only two classes (three for the learnfile), while the Kohonen Network has a maximum error of four classes. It is interesting to note that based on the distance matrix there is almost no difference between class one and class two (see Table II). As the determination of the surface map corresponding to a class is based on the evaluation of the experts, this indicates a confusion between those classes. The definition of class one and class two is very close: no set mark/dubious. This makes up for a bad criterion, which is also seen directly in the experts’ evaluations: about half of the cases evaluated by expert one as class one is classified as class two by expert two. In other words the Kohonen map gives an indication of a class difference not clearly defined by the experts. It was also noticed that the linear deviations (Table III) corresponding with classes three and four were considerably larger than those of the other classes. This could be a consequence of the tendency of the experts to average out their evaluation when in doubt.

Carpet wear As the number of samples for the carpet wear experiment was small and no test file was constructed, we should be careful when generalizing the results of this experiment. Table IV gives the results in percentage classified in reference to an error ∆x (see definition above). Table V gives the distance matrix while Table VI gives the values for the linear deviation. As there are nine classes and only 60 samples the results should be considered carefully. We can conclude from these results that about 57 per cent was classified correctly by the Kohonen network and 30 per cent with a deviation of only half a class. The backpropagation classified 55 per cent correctly and 36 per cent with a deviation of half a class. Maximum deviation for both networks is one class. Although the results from Table V and Table VI can only be interpreted very carefully and should be confirmed by further experiments on this topic, the following tendencies are seen: • Classes 3, 3.5 and 4 are very close to one another (Table V). This indicates that the experts have a problem in making a distinction between those classes. This is also the range which is the most important for carpet

Table IV. Per cent classification versus error ∆x

Kohonen learnfile Backpropagation learnfile

0

Error ∆x 0.5

1.0

57 55

30 36

13 9

Class

1

1.5

2

2.5

3

3.5

4

4.5

5

1 1.5 2 2.5 3 3.5 4 4.5 5

0

4.5 0

19.5 15.1 0

27.2 22.7 7.8 0

30.6 26.2 11.6 4.2 0

31.1 26.8 12.3 5.4 1.5 0

31.1 26.8 12.8 6.8 3.7 2.3 0

29.9 25.6 12.6 8.2 6.2 5.0 3.0 0

25.8 21.8 11.8 10.8 11.1 10.7 9.2 6.5 0

Class 1 1.5 2 2.5 3 3.5 4 4.5 5

81 Table V. Distance matrix values (carpet wear)

Linear deviation 0.0 5.4 6.3 3.2 1.8 2.0 1.7 1.6 0.0

•

Fault detection and quality assessment

wear classification, as half a class difference in this range can have large consequences for the final classification (and use) of the carpet. Linear deviation (Table VI) generally increases with lower classes (except for class one with only one sample). In other words, the difference in opinion of the experts, classifying an unknown carpet sample, increases as the sample is further removed from the original (class five) sample.

Conclusions The classification in both cases by means of a Kohonen map and backpropagation shows good results. About 90 per cent of the evaluations made by both systems are acceptable. The Backpropagation Networks tend to classify somewhat better and also have a lower maximum deviation. However, the Kohonen map gives us additional information about the “evaluation” of the experts. In the case of set marks we could conclude that the difference between some classes was ill-defined, and that there was a tendency among the experts to classify doubtful cases in the middle range. In the case of carpet wear assessment we could conclude (with the necessary reservation) that there is also a difficult range to classify for the experts and that they tend to diverge in opinion when classifying samples of increasing wear. This quality of the Kohonen map can be attributed to the fact that the system is self-organizing and

Table VI. Linear division values (carpet wear)

IJCST 8,1/2

82

as a consequence not dependent on the evaluations of the teacher (expert). This is in contrast to the Backpropagation network, which is supervised and gives a kind of interpolation of the classification by the experts. Future work in this field will concentrate on the classification of carpets produced by the main European carpet companies. Future research will be conducted within the framework of a CRAFT project of the European Commission (CR-1070-91). CRAFT stands for Co-operative Research Action for Technology and aims to strengthen the European Industry by joint research with universities and research centres.

References 1. Lippman, R.P., “An introduction to computing with neural nets”, IEEE Acoustics Speech and Signal Processing Magazine, April 1987, pp. 4-22. 2. Kohonen, T., “An introduction to neural computing”, Neural Networks, Vol. 1, 1988, pp. 3-16. 3. Sette, S., Boullart, L. and Kiekens, P., “Self-organizing neural nets: a new approach to quality in textiles”, accepted 15 August 1994 for publication in Textile Research Journal. 4. Vangheluwe, L., Sette, S. and Pynckels, F., “Assessment of set marks by means of neural nets”, Textile Research Journal, Vol. 63 No. 4, April 1993. 5. Vercauteren, L., Sieben, G., Boullart, L., Praet, M., Otte, G., Vingerhoeds, R., Calliauw, L. and Roels, H., “The classification of brain tumours by a topological map”, Proceedings of the International Neural Network Conference-90, Paris, 1990. 6. Vercauteren, L., Vingerhoeds, R. and Boullart, L., “Intelligent dimensional data reduction by a topological map; the interpretation and use of an insurance database”, Proceedings of the International Conference on Parallel Processing in Neural Networks and Computers-90, Düsseldorf, 1990. 7. Weinsdörfer, H., “Internationale Textil Maschine Ausstellung 92; Webereivorwerk und Weberei”, Chemiefasern Textilindustrie, Vol. 42 No. 94, 1992, pp. 110-8. 8. Carnaby, G.A. and Wood, E.J., “The physics of carpets”, Journal of the Textile Institute, Vol. 80 No. 1, 1989, pp. 71-89. Appendix Distance matrix and linear deviation with Kohonen Networks After the learning phase, the learning samples are regrouped for each class and used as input vectors for the Kohonen Network. Each sample generates an output in the two dimensional map. Within a class and for each output node the result is averaged. This gives, for each class, an average output on the M2 nodes which can be visualized as a surface. During the recall phase the “surface” output of a new (unknown) input vector is compared to the average “surfaces” of each class. Thereby the linear deviation Dk for the unknown input vector from an average “surface”, corresponding with class k, is calculated as follows: Dk =

∑ S xy – AS xyk ,

x,y

where 1 ≤ x, y ≤ M , S xy

= value of the node with co-ordinates ( x , y ) for new imput vector

k AS xy

= average value of the node with co-ordinates ( x , y ) corresponding with class k .

Dk gives an indication about the difference between the input vector and a class k. An unknown feature vector is classified based on the lowest Dk value (where k designates the corresponding class). A distance matrix between classes (i.e. distances between the corresponding average surface maps) can be calculated. The elements of the matrix DMij are given by DM ij =

∑ AS ixy – AS xyj

1 ≤ i, j ≤ 5.

x,y

The distance matrix gives an indication about the difference between classes according to the neural network. A low value between two classes indicates almost no distinction while a large value indicates clearly different classes.

Fault detection and quality assessment 83

IJCST 8,3

Three models for garment simulation Haruki Imaoka

10

Nara Women’s University, Nara, Japan Introduction We are confronted with a situation whereby various works on garment simulation are carried out but there is no evaluation of them. One of the reasons for this confused situation is that there are many kinds of techniques to solve the complex simulation problem. Another reason is that there are mainly two kinds of disciplines in which the works are completed, textile engineering and computer graphics. The aim of the former group is garment construction and the aim of the latter group is animation. In consequence, the degree of approximation is sometimes different. To clarify this situation, the complex simulation is divided into three kinds of modules, namely a garment model, a human body model and an environment model. Furthermore, each model is discussed from a structural point of view, that is the conceptual-mathematical-posed problem structure, or CMP structure for short. Barzel[1] proposed the CMP structure of a physically-based model and expressed the meaning as follows: What is the model or technique trying to do? (Conceptual model) What are the underlying equations? (Mathematical model) What are the knowns and unknowns? (Posed problem) What are the solution techniques? (Implementation).

It is very effective strategy to relieve the confused situation, for sometimes confusion occurs by mixing either the level of a question or the universe of discourse.

International Journal of Clothing Science and Technology, Vol. 8 No. 3, 1996, pp. 10-21. © MCB University Press, 0955-6222

Background Breen et al.[2] proposed the drape simulation using interactive particles. Their technique is discussed later, but the review part of the paper is considered as the most recent review of the related works. Historically speaking, in the field of computer graphics, a representation of a cloth object[3], dynamic behaviour of cloth and interaction with a rigid body[4], and dynamic behaviour of a garment and a synthetic actor[5] are well-known works. The last work is considered as the first dynamic garment simulation and the important models as the modules for garment simulation are mostly listed. They are the garment, the actor and the environment such as wind, a floor, a trapeze, etc. On the other hand, in the field of textile engineering, there is a long history of the research on cloth drape. The recommendable review is found in the paper by Amirbayat and Hearle[6]. Mathematical characterization of the anisotropy of sheet properties[7] and simulation technique by the finite element method[8] are

the first works of drape simulation. After that, some trials have been carried out Three models for in the context of drape simulation[2]. In contrast to the computer graphics field, garment the static simulation is major, and Okabe et al.[9] attempted to simulate garments simulation put on a mannequin. This work may be considered as the first 3-D apparel CAD system. This system contains static garment simulation, and it is improved to be applicable to the multi posture of a human body[10]. Similarly to the dynamical 11 garment simulation, two important models, i.e. a garment model and a human body model are considered as the modules of the simulation. A major point to consider is that “sewing operation and dressing operation” are very important in achieving the proper simulation of a great variety of garments. There is another type of attractive simulation, namely draping simulation[1113]. As a conceptual model, draping simulation treats a draping process to create or design a garment and, from a mathematical point of view, its governing equation is obtained geometrically. As for garment simulation, conceptually it treats a test-wearing process to evaluate a garment, and mathematically its governing equation is derived from an equation of motion or a mechanical equation of equilibrium. In other words, garment simulation is a 2-D to 3-D problem and draping simulation is a 3-D to 2-D problem. Although they are closely connected, we discuss only garment simulation in this paper. In the following sections, we discuss the three models and the interaction among them in detail. Three models Figure 1 shows an overview of the three models which are necessary to achieve garment simulation. According to this Figure, each model is first independently discussed, and the difficulty underlying in each CMP structure and implementation is picked up. The interaction among the models is discussed in the next section. Garment model A garment model is, of course, the most important model. Conceptually speaking, our aim is to simulate garment behaviour, especially its 3-D shapes. Garments are classified into two global categories, i.e. inner clothing and outer clothing. The inner clothing means various kinds of foundations and lingerie. The outer clothing is a set of various items such as a skirt, blouse, suit, etc. We consider Japanese traditional clothing, “the kimono” as an exceptional item of outer clothing, because the shape of it is determined mainly by the friction between “the kimono” and “the obi”, which is a kind of belt made of cloth. Here our interest is limited to normal outer clothing. It is constructed of several pieces and “the sewing operation” is highly important. The difference between garment simulation and cloth simulation is clearly defined by the existence or not of the sewing operation. Each piece is considered as a thin flexible body and its flat shape is defined by a paper pattern. Usually the apparel CAD system treats the geometry of paper patterns. As for the mechanical characteristics stressed in the word “flexible”,

IJCST 8,3

Sewing C Flexible body Garment Self-collision

12

Skirt Trousers Suit Blouse .........

Piece 1 Piece 2 .........

Dressing collision

Fabric M Cotton Silk Polyester P ..........

Equations of motion Mechanical properties

Tree-hierarchy Human

C Man Woman Child Baby .........

Head Torso Legs .........

Rigid body

M

Hierarchical configuration

P

Kinematics for action/posture

External force Environment

Figure 1. An overview of three models for garment simulation

Gravity Wind (air) ......... Floor Chair Bicycle ........

Things being modelled

Interaction between things

CMP model

there are two kinds of fabrics, i.e. textile fabric and knitted fabric. Their mechanical properties such as tensile rigidity and bending rigidity are very different. Many researchers think the most simple textile fabric may be a plain woven one. Although there are a wide variety of garments, the paper patterns, the sewing operation, and the mechanical properties are three main factors which affect the garments’ shape. Mathematically speaking, a paper pattern is the geometrical shape of a garment in an unstrained condition. The sewing operation is the topological aspect of a garment after sewing. Mechanical properties mean the coefficients of a governing equation. The governing equation is the equation of motion in general. If both inertia term and damping term are ignored, the governing equation changes to a mechanical equilibrium equation. This is the difference between a dynamic simulation and a static one. As for the problems posed, the unknowns are easy to understand. It is of course the 3-D form of a garment. But we must be aware that there may be many solutions even if we try static simulation. When we try the dynamic simulation under windy conditions, the following behaviour may be chaotic. In

the list of knowns, there are the paper patterns, the initial 3-D position of a Three models for garment, the sewing information, the mechanical properties and some rigid garment bodies such as the human body, the floor, a chair, etc. The difficulty arising here simulation is how to determine the proper initial 3-D position and the mechanical properties. The problem of how to determine the initial position is very important and we must pay special attention to the appropriate initial shape of 13 a garment around a human body. The technique is called “dressing or fitting”. There are two types of dressing techniques, namely “geometrical dressing”[9] and “mechanical dressing”[5] , and they are discussed later. The second problem is the most severe and deeply connected to the governing equation. Many researchers proposed many kinds of coefficients. Cloth is clearly considered as a noncontinuum system. However, many researchers approximate it as a continuum system, because the system is easily described by partial differential equations and the discretized approximation such as the finite difference method (FDM), and the finite element method (FEM). FDM and FEM are familiar and the solver of finally derived ordinary differential equations is also familiar. The interacting particles system[2] proposed by Breen et al. is the only exception. The particles system can be regarded as one of the representation techniques of FDM, but their motivation of the usage of the particles system is more positive and their claim is that the particles system is itself essentially cloth. In my opinion, both a direct noncontinuum system like the particles system and continuum approximation are now attractive. In the future, the averaged properties of micro-organization will be interpreted as a macrocontinuum system. When we adopt the continuum approximation, Amirbayat and Hearle’s two principles[6] must be considered. The first principle is that the elastic parameters in planar extension or shear (trellis is more appropriate in my opinion), and in out-of plane bending and twisting are independent of one another. The second principle is that both membrane deformation and bending deformation occur simultaneously. The mechanical properties of cloth are divided into elastic, plastic and damping properties. Which parameter is major is determined by the engineering sense. In the minimum list for elastic mechanical properties, there may be weight, tensile rigidities of warp and weft directions, trellising rigidity, Poisson’s ratio, especially for knitted fabric, bending rigidities of warp and weft directions, and twisting rigidity. Each rigidity is nonlinear with regard to the problem of large strain. The final word for cloth modelling is that it is a large displacement and large strain problem. As for implementations of both static simulation and dynamic simulation, discretized formulation and numerical solvers are selected according to the balance of weights between some requirements such as accuracy, computational costs, and whether or not the procedure can be used effectively in general-purpose analysis. First, we discuss how to discretize the governing equations. FDM and FEM are two famous methods used to discretize the equations. The difference between them appears to be whether or not dummy elements are used. FDM needs some dummy elements and the number of the variables which describe the shape is low. On the other hand, FEM needs no

IJCST 8,3

14

dummy elements but some additional variables are needed to describe the shape. The finite-difference energy method, (FDEM)[14], has intermediate characteristics between FDM and FEM. At the implementation stage, the sewing operation must be considered when the paper pattern is divided into triangular or quadrangular meshes. During this step, additional work, namely “consistent division of lines to be sewn” is necessary. As for the numerical solver, both dynamic simulation and static simulation are different. During both simulations, severe difficulty arises because of the special values of mechanical properties in cloth objects and the tensile property is quite stiff. This means an ill conditioned Hessian matrix will appear in the static analysis, and a stiff system will appear in the dynamic analysis. To avoid this difficulty, some relaxation methods can be used, but in that case, some important behaviour of cloth, such as wrinkles and folds, may disappear. In the dynamic analysis, implicit and stable methods may be suitable. If we attempt the static simulation, one more consideration is required. Sometimes energy minimization is equivalent to solving the nonlinear simultaneous equations, but if cloth were falling freely through gravity, then special attention that the Hessian matrix is singular must be considered. This means, in static analysis, it is not always a boundary-valued problem such as the simulation of the drapemeter. Human body model Perhaps the most simple human body model is a mannequin which is represented only by its surface and is a frozen, rigid body. Alternately we may want a more advanced model which can move like a robot. In the future, more soft bodies will be needed, especially to treat the inner clothing, such as foundations. Here the model is limited to a rigid body and it is considered the special environment of a garment. Conceptually speaking, a garment cannot enter inside the body. As for movable or multiposture models, a hierarchical configuration is useful to control the motion, because every human being fortunately has the same skeleton structure. Mathematically speaking, the local co-ordinate system for each small body is combined according to the tree hierarchy. It is a structure such that a hand is a smaller part of an arm, and therefore we can know the location of the body in the global co-ordinate system. Next, we must describe the surface around the skeleton. There are mainly two types of description methods regarding the surface of a human body, namely an explicit method and an implicit method. Polygonal expression and a more smooth expression such as a spline patch are explicit ones, and a blobby model[15] called a meta-ball is an implicit one. Henceforth we focus on the blobby model. A metaball is defined by the scaler field of density. If we use many meta-balls, then the density is added up and this operation is called fusion. The surface of this model is defined by a contour surface of constant density. Using the model we can easily create a smooth surface, but we must avoid unnecessary fusion. Though it is not an efficient model for rendering, it is very efficient in solving the contact problem between a garment and a human body[16].

Environment model Three models for Garments may be affected by some environmental aspects. Since we focus on the garment mechanical behaviour of a garment, the external force is important. First of all, simulation gravity must be considered. If we attempt dynamic simulation, the existence of air cannot be ignored. Both gravity and air resistance are typically external forces which appear in the governing equation. There are other things in the 15 environment, such as the floor, a chair, etc. They are considered as rigid or flexible bodies which limit the existence of a garment. A human body is always considered as a necessary environment for a garment. Mathematically speaking, this type of environment may be interpreted as a geometrical constraint condition. Since the governing equation is usually a force-oriented equation, we must change the interpretation of the condition to a kind of mechanical condition. At this stage, some difficulty may appear, and is discussed later. Interaction among three models Here we discuss the interaction among the above three models, and focus on only three major topics: dressing; external force; and collision. Dressing The word “dressing” means how to determine the initial position of a garment around a human body. This problem must be artificial, because it is determined by the thinking of the wearer. A young person may perhaps put the clothing on inside out. A garment simulation system must have the ability to simulate each situation. There are two types of techniques for dressing, namely geometrical dressing and mechanical dressing. The geometrical method is a sequential method of sewing and dressing. At first, topological sewing, in which the corresponding two points in 2-D are combined and become one point in 3-D, is achieved. Second an initial position is geometrically calculated. The mechanical method is a simultaneous method of sewing and dressing. In this method sewing is implemented by a spring between two sewing points. External force Here gravity and air resistance are discussed. With regard to gravity, there is no difficulty, if we do not consider the garment wet by sweat or rain. Unlike gravity, however, there is greater difficulty in treating air resistance. The mathematical description of air is as a topic in the field of fluid dynamics. Its governing equation is the Navier-Stokes equation. Since the equation is very difficult to solve, a simpler method is used. Collision and self-collision As mentioned before, the role of the human body is as the constraint condition for the movable area of a garment. In static analysis, the interaction between a garment and a human body is regarded as a contact problem. In dynamic analysis, the interaction is regarded as a collision problem[17]. In both analyses, two functions are required, i.e. “monitor function” and “switching function”. We

IJCST 8,3

16

must consider at least two different kinds of systems, which are the “in-contact situation” and the “out-of-contact situation”. The monitor is always watching whether the system is in contact or out of contact. The switching function has the role of switching the governing equation. The analysis of collision is a little bit more difficult, because collision is an instantaneous phenomena. Mathematically speaking, collision occurs at very high frequency mode, compared with the usual garment movement. This means the ordinal differential equations system is rigid. For this reason, some relaxation methods or some other similar convenience are needed. The coefficient of restitution must be determined by an experiment and must pay special attention to the employment of numerical solvers. There is a more difficult problem called “self-collision.” We must not allow the situation in which the part of a garment crosses another part of it. The answer to this problem is difficult, because it is a combinatorial problem. The monitor must work harder and harder. Discussion Before discussing the above statements, we will summarize another topic. After the complex calculation, the garment is painted by a renderer. This step is a kind of finishing process and very important. Texture is one of the important characteristics of a garment. Nowadays we can achieve the texture mapping technique[18] easily, but more cloth like reflection models will be needed. To construct a garment model, we must consider the paper pattern, the sewing operation and the mechanical properties of cloth. The mechanical properties are most important, but there may be as yet no final answer. Textile engineers must deal with this problem. Of course there may be several answers according to the levels of simulation. The difficulty of cloth modelling comes from the nonlinearity. Nonlinearity, in this case means materially nonlinear, large displacement and large strain and changes in boundary conditions. As for large displacement and large strain, it is more difficult than a large displacement and small strain problem. As for materially nonlinear, the first consideration is whether the cloth material is elastic material or inelastic material. This is closely connected to the selection of a pair of stress and strain models. If the material is regarded as elastic, second Piola-Kirchhoff stress and Green-Lagrange strain is recommended. If the material is regarded as inelastic, Jaumann stress rate and velocity strain is recommended[19]. This relation is deeply connected to the selection of static analysis and dynamic analysis. Because inelastic property means that the result depends on the path of the movement, static analysis has little meaning. As for the changes of boundary condition, they are essential nonlinearity in our garment simulation, for contact or collision they are essential. Thus garment simulation is a collection of nonlinearities. With regard to the implementation of cloth material, two types of discretization are needed for space domain and time domain. FEM, FDM and FDEM are well-known methods of space domain discretization. Using these methods, the actual continuous system is reduced to an appropriate discrete system. FDM is the direct method to derive the discrete system from the

governing differential equations. On the other hand, FEM and FDEM are the Three models for variational methods. In the FDEM scheme, the derivatives in the function of the garment continuous system are approximated by finite differences. In the FEM scheme, simulation the shape is approximated by some piecewise well-known functions. Regarding the time domain discretization, there are many methods and they are classified into two categories, namely an explicit integration method and an implicit 17 integration method. As a consequence, there are many kinds of combinations of solvers. How can we evaluate them? Perhaps accuracy and computational costs are two major items of evaluation; they are in a trade-off relationship. The accuracy means the degree of agreement between the calculated shape and the experimentally-observed shape. It is a difficult problem to compare the two shapes, because we cannot clearly determine the distance between them. Though there are many difficulties, it is necessary to have some standard problems with well defined evaluations on a worldwide scale. Next, we discuss the human body model. The model must have the ability to describe the individual person, especially in the field of textile engineering. It will be called an “indentification problem” of a human body model, and the problem is deeply connected to the 3-D measuring technology. The most important role or aim of garment simulation is to simulate the test-wearing process for each person without producing a real garment. Garment simulation is not a toy but a revolutionary technique to produce the garment. The artificial garment in the computer is not a real garment, but it is a complete, fully informed sketch. We can imagine a new world, where people may have their own personal diskette in which information about the shape of their own body is included, and they can easily access the virtual garment shop and therefore can simulate the garment just as if they were standing in front of the mirror in a real shop. Before ending this discussion, we want to stress that the role of garment simulation is not only in predicting the shape but also predicting some kind of scientific values. They are, for example, distortion, contact pressure, and the Gaussian curvature, and are useful in creating a more desired garment. Just like a thermal camera, we can express them by colour contours. Researchers in the field of garment construction may be highly interested in the scientific values. Though they may be very important, we can calculate them with the simplicity of Columbus’s egg. Conclusion Garment simulation may be one of the most difficult problems in the textile engineering field. Today’s situation is better than 15 years ago when we started the research, because we can say that “Though it may be difficult, it is possible.” The first generation work was to show that it is possible, the role of the second generation is to make more advanced systems. The aim of this paper is to dispel the confused situation which is that there are many works but we cannot know which one is better than the others. The conclusion is not so precise, because there are many possibilities to adopt one of the combination of conceptual model, mathematical model, posed problem and implementation.

IJCST 8,3

18

Plate 1. Three models necessary to achieve garment simulation

Plate 2. Multi-posture body simulation

Our examples are shown in Plates 1 and 2. The simulation is static, but a Three models for multiposture body is available. Since the material is regarded as elastic, second garment Piola-Kirchhoff stress and Green-Lagrange strain are used, and data from the simulation Kawabata’s mechanical tester are simplified so as to be adapted to the stressstrain model[20]. As for implementation, FDEM is adopted[21]. To calculate energy minimization, an original descent method is used[9]. To demonstrate the 19 method, an example program is contained in the Appendix. It is stressed that no evaluation of total energy is needed. For dressing, the geometrical method is used[10,22,23]. The human body model is a blobby model which is improved to avoid unnecessary fusion[16]. To avoid it, we distinctively use two operations of density sum, ordinary sum, i.e. plus and logical sum, i.e. maximum. The stronger features of the simulation system have been summarized as follows. It is easy to treat the anisotropy of materials, it is applicable to a wide variety of garments and bodies in various postures. The garment pressure can be predicted and expressed[24]. Furthermore, we will be able to enjoy the expression of the Gaussian curvature in the near future. The weaker features of the system have been summarized as follows: we cannot simulate the dynamic behaviour of garments; the identification problem of the human body model has not yet been solved; frictions between a garment and a human body are not taken into consideration. We do not use the solver of the self-contact problem now. As for the selfcontact problem, we can solve the problem and can demonstrate the performance but do not use the solver mainly because the calculation cost is very high. This review is not complete, for there may be a huge number of neglected works. Sincere apologies are given to those who have been omitted. At the end of this short review, I would like to say that there are many words to describe the word “garment”, for example clothing, clothes, dress, costume, garment, attire, habiliments and apparel. This implies that there is a long history of clothing and people have long been enjoying wearing it. It is now time to create a new century advance of garment simulation. References 1. Barzel, R., Physically-based Modeling for Computer Graphics, Academic Press, New York, NY, 1992, p. 58. 2. Breen, D.E., House, D.H. and Wozny, M.J., “Predicting the drape of woven cloth using interacting particles”, Proceedings of SIGGRAPH’94. Computer Graphics, 1994, pp. 365-72. 3. Weil, J., “The synthesis of cloth objects”, Proceedings of SIGGRAPH’86. Computer Graphics, Vol. 20 No. 4, 1986, pp. 49-54. 4. Terzopoulos, D., Platt, J., Barr, A. and Fleischer, K., “Elastically deformable models”, Proceedings of SIGGRAPH ’87. Computer Graphics, Vol. 21 No. 4, 1987, pp. 205-14. 5. Carignan, M., Yang, Y., Magnenat-Thalmann, N. and Thalmann, D., “Dressing animated synthetic actors with complex deformable clothes”, Proceedings of SIGGRAPH’92. Computer Graphics, Vol. 26 No. 2, 1992, pp. 99-104. 6. Amirbayat, J. and Hearle, J.W.S., “The complex buckling of flexible sheet materials – part 1. Theoretical approach”, International Journal of Mechanical Science, Vol. 28 No. 6, 1986, pp. 339-58.

IJCST 8,3

20

7. Shanahan, W.J., Lloyd, D.W. and Hearle, J.W.S., “Characterizing the elastic behavior of textile fabrics in complex deformations”, Textile Research Journal, Vol. 48, 1978, pp. 495-505. 8. Lloyd, D.W., “The analysis of complex fabric deformations”, in Hearle, J.W.S., Thwaites, J.J. and Amirbayat, J. (Eds), Mechanics of Flexible Fiber Assemblies, NATO ASI Series, 1980, pp. 311-42. 9. Okabe, H., Imaoka, H., Tomiha, T. and Niwaya, H., “Three dimensional apparel CAD system”, Proceedings of SIGGRAPH’92. Computer Graphics, Vol. 26 No. 2, 1992, pp. 105-10. 10. Matsuda, R. and Imaoka, H., “A graphic method to simulate garment fitting on a human body model in various posture” (in Japanese), Sen-i Gakkaishi, Vol. 51 No. 5, 1995, pp. 225-33. 11. Heisey, F.L. and Haller, K.D., “Fitting woven fabric to surfaces in three dimensions”, Journal of the Textile Institute, Vol. 79 No. 2, 1988, pp. 250-63. 12. Van West, B.P., Pipes, R.B. and Keefe, M., “A simulation of the draping of bidirectional fabrics over arbitrary surfaces”, Journal of the Textile Institute, Vol. 81 No. 4, 1990, pp. 448-60. 13. Hinds, B.K., McCartney, J. and Woods, G., “Pattern development for 3-D surface”, Computer-aided Design, Vol. 23 No. 8, 1991, pp. 583-92. 14. Bushnell, D., Almroth, B.O. and Brogan, F., “Finite-difference energy method for nonlinear shell analysis”, International Journal of Computers & Structures, Vol. 1, 1971, pp. 361-87. 15. Muraki, S., “Volumetric shape description of range data using blobby model”, Proceedings of SIGGRAPH’91. Computer Graphics, Vol. 25 No. 4, 1991, pp. 227-35. 16. Matsuda, R. and Imaoka, H., “Modeling of human body by density balls for garment design” (in Japanese), Sen-i Gakkaishi, Vol. 50 No. 5, 1994, pp. 221-8. 17. Moor, M. and Wilhelms, J., “Collision detection and response for computer animation”, Proceedings of SIGGRAPH’88. Computer Graphics, Vol. 22 No. 4, 1988, pp. 289-98. 18. Blinn, J.F. and Newell, M.E., “Texture reflection in computer generated images”, Communications of the ACM, Vol. 19 No. 10, 1976, pp. 542-7. 19. Bathe, K.J., Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1982, p. 302. 20. Imaoka, H., Okabe, H., Akami, H., et al., “Analysis of deformations in textile fabrics” (in Japanese), Sen-i Gakkaishi, Vol. 44 No. 5, 1988, pp. 217-28. 21. Imaoka, H., Okabe, H., Akami, H., et al., “Prediction of three-dimensional shapes of garments from two-dimensional paper patterns” (in Japanese), Sen-i Gakkaishi, Vol. 45 No. 10, 1989, pp. 420-26. 22. Okabe, H., Imaoka, H., Shibuya, A., et al., “Transformation from paper pattern to spatial structure of dress by computer-simulation of sewing and dressing” (in Japanese), Sen-i Gakkaishi, Vol. 44 No. 3, 1988, pp. 129-36. 23. Okabe, H., Imaoka, H. and Akami, H., “Paper patterns of dress for 3-dimensional CAD/CAM and their automatical division into finite elements” (in Japanese), Sen-i Gakkaishi, Vol. 42 No. 4, 1986, pp. 231-9. 24. Niwaya, H., Imaoka, H. and Shibuya, A., “Estimation of garment pressure distribution and its expression” (in Japanese), Sen-i Gakkaishi, Vol. 52 No. 2, 1996 (submitted). Appendix CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C ENERGY MINIMIZATION BY OKABE AND IMAOKA C EXAMPLE: ROSENBROCK TEST FUNCTION C E=100.*(x(2)–x(1)**2)**2+(1.–x(1))**2 C INITIAL POSITION X(1)=–1.2, X(2)=1.0

CC----------VARIABLES C X: STATE VARIABLES C DX: GRADIENT AT TIME T, BDX: GRADIENT AT TIME T-1 C ACC: STEP SIZE>0, D: DESCENT DIRECTION=SGN(DX) C ITIME: ITERATION TIMES CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DIMENSION X(2),DX(2),BDX(2),ACC(2) CC----------INITIALIZATION X(1)=–1.2 X(2)=1.0 DO 100 I=1,2 DX(I)=0. BDX(I)=0. ACC(I)=1. 100 CONTINUE CC----------ITERATION, ALF=1.4 AND BET=0.7 ARE MAGIC NUMBERS ALF=1.4 BET=0.7 C WRITE(6,*)' HOW MANY ITERATE?' READ(5,*) ITIME CC---------->>>>>START OF ITERATION LOOP DO 1000 J=1,ITIME C' ' ' ' ' ' ' ' ' ' ' ' ' ' CALCULATE THE GRADIENT DX(1)=–400.*(X(2)–X(1)**2)*X(1)–2.*(1.–X(1)) DX(2)=200.*(X(2)–X(1)**2) C' ' ' ' ' ' ' ' ' ' ' ' ' ' CALCULATE THE NEW STEP SIZE OF EACH VARIABLE DO 1100 I=1,2 ADMB=ABS(DX(I)–BDX(I)) ADB=ABS(DX(I))+ABS(BDX(I)) IF(ADB.EQ.0.)THEN STPP=1. ELSE STPP=ADMB/ADB ENDIF STPF=ALF–(ALF–BET)*STPP ACC(I)=ACC)I)*STPF 1100 CONTINUE C' ' ' ' ' ' ' ' ' ' ' ' ' ' MOVE THE STATE VARIABLES DO 1200 I=1,2 IF(DX(I).GE.0.)THEN D=1. ELSE D=–1. ENDIF X(I)=X(I)–D*ACC(I) BDX(I)=DX(I) DX(I)=0. 1200 CONTINUE 1000 CONTINUE CC---------->>>>> END OF ITERATION LOOP CC----------------------- OUTPUT WRITE(6,*) IIII,X(1),X(20 STOP END

Three models for garment simulation 21

IJCST 8,3

22

Modelling fabric deformation as a nonlinear dynamical system using Bäcklund Transformations Jacqueline R. Postle and Ron Postle Department of Textile Technology, University of New South Wales, Sydney, Australia

International Journal of Clothing Science and Technology, Vol. 8 No. 3, 1996, pp. 22-42. © MCB University Press, 0955-6222

Introduction In the past two decades, we have witnessed spectacular developments in computer speed and power which are now readily accessible in all research laboratories. Thus it has become feasible to obtain numerical mathematical solutions having negligibly small errors for many long standing problems in fabric mechanics. Several problems of fabric buckling and folding have been solved numerically and also fabric cantilever problems have been treated. Numerical solutions for the micromechanics of yarn interactions within woven fabrics have been considered. A consistent problem associated with numerical treatment of the nonlinear differential equations encountered in fabric deformation and mechanics relates to the occurrence of numerical instabilities. The computational difficulties that these instabilities cause lead to very long computation times. Many numerical solutions to fabric mechanical problems must be obtained by iterative methods especially those involving interfibre friction or fibre viscoelastic effects within the fabric. These iterative methods also often involve considerable computer time and therefore are only feasible for a limited range of problems having very specific boundary conditions. Nonlinear differential equations of the same mathematical form as those differential equations encountered in mathematical models of low stress fabric deformation and recovery, occur in dynamical systems in many branches of physics and engineering. In the mathematical literature, this family of differential equations is now known to be integrable. The analytical solutions of some of these nonlinear partial differential equations are by no means easy to obtain however. Therefore, the aim is to use rigorous mathematical principles in order to obtain analytical solutions for nonlinear partial differential equations of the same form as those encountered in fabric deformation problems. Once analytical solutions are obtained for these equations, problems of fabric deformation can be reformulated analytically and solutions obtained for all material properties and for all boundary conditions. Furthermore we can realistically consider for the first time problems of fabric dynamics such as the

dynamic draping behaviour of textile materials and the evolution of fabric Modelling fabric buckling during apparel manufacture. deformation Differential geometry of fabric surfaces In differential geometry, a surface is considered as a series of twisted curves which generate into a three-dimensional shape. This theory is applicable to the surface of the material in fabric buckling, folding and drape. The differential geometry parameters can incorporate the mechanical properties of a material by relating these mechanical properties to the changes in curvature as a surface is transformed into another surface. The shape of a textile material can be defined as a two-dimensional surface which exists in three-dimensional Euclidean space. The differential goeometry is required to define a surface as a series of twisted curves evolving in space. Orthogonal trajectories of these curves on the surface of the material are the geodesic curves (known as the parallels and meridians). The curvatures of these curves at a point on the surface are the principal curvatures. When one surface is transformed into another surface, the geodesic curves are changed. Two surfaces, S and S1 are applicable (or isometric) if, around every point on the first surface S there is a portion of that surface which can be bent so that it coincides with a corresponding portion of the other surface, S 1 , without stretching or duplication. A deformation of one surface to another can be mathematically modelled using the concept of a homotopy. A deformation of a surface S to another surface S 1 can be considered as a continuous function h(u, v, t) of three variables, taking values in three-dimensional space, such that (i) h(u, v, 0) is the point with co-ordinates (u, v) on the surface S; (ii) h(u, v, T ) is the point with co-ordinates (u, v) on the surface S1. For a fixed value of t between 0 and T, the values of h(u, v, t) should be thought of as describing the intermediate surface at time t. For a fixed (u, v) and varying time t, the points h(u, v, t) describe the path of a particular point as the surface changes. The deformation is said to be isometric if the geodesic distances on the intermediate surfaces do not vary with time[1]. If the surface, S, can be rolled over the plane and all points on S can be brought into coincidence with the plane, then the surface S is applicable to the plane. When a fibrous material is deformed into three-dimensional configurations, the deformations need not be restricted to isometric (or applicable) transformations of the material surface. Stretching and duplication of portions of the material are possible. This could be achieved by imposing extra conditions on the homotopies described above. Spherical (or Gaussian) representation of a surface It is useful to make a spherical representation of a three-dimensional surface S. The radii of the unit sphere are drawn parallel to the positive directions of the

23

IJCST 8,3

24

Figure 1. Spherical (or Gaussian) representation of a surface. The unit sphere is rolled on the inside (in the positive direction of the normals) of the surface and the points on the surface are projected on to the surface of the sphere

normals to S. The ends of the radii are the spherical images of the corresponding points on S. As a point M moves along a curve on S, its image m describes a curve on the sphere as shown in Figure 1. This map of the surface on to the sphere is called the spherical or Gaussian representation of the surface. Using the spherical representation of surfaces, the curvature of a surface can be defined in the same way as the curvature of a curve. At any one point on a surface, the curvature does not need to be the same in all directions. Gauss[2] has found that it is useful to define the curvature of a point on a surface as the product of the greatest and least curvatures of all the curves which make up the surface at that point. This product is called the Gaussian curvature.

1 0.5 0 –0.5 –1 –1

4

–1 –0.5

0.5 0 –0.5 –1 –1 –0.5 0 1 0

2 0 –2 0.5

–4

0.5 1

The lines of curvature of a surface are represented on the sphere by an orthogonal system. The tangents to an asymptotic line and to its spherical representation at corresponding points are perpendicular to one another. Figure 2 represents three confocal quadrics where the lines on the ellipsoid are lines of curvature, and the lines on the hyperboloid of one sheet are parametric or asymptotic lines. Gaussian curvature Consider a small parallelogram on the surface with vertices (u, v), (u + du, v), (u, v + dv) and (u + du, v + dv). The vertices of the corresponding parallelogram on the sphere have the same curvilinear co-ordinates. The areas are Hdudv on S and ± Hdudv on the sphere (the positive and negative sign being chosen for positive and negative curvature respectively in the neighbourhood of the point (u, v)). The limiting value of the ratio of the spherical and surface areas as the

Modelling fabric deformation

25 Figure 2. Three confocal quadrics with lines or curvature on the ellipsoid and asymptotic lines on the hyperboloid of one sheet

vertices on the surface S approach the point (u, v) is the Gaussian curvature K[3]. An alternative way of describing the Gaussian curvature is as follows. Suppose that U is a point on the surface. For every plane Π through U which is perpendicular to the tangent plane at U, the intersection of the surface with Π is a plane curve Γ. The curvature of Γ can be calculated. The normal curvature in the direction of Π is the number whose magnitude is the curvature of Γ, and whose sign depends on whether Γ is bending away from the tangent plane in the positive or negative normal direction. Let k1 and k2 denote respectively the largest and smallest normal curvatures at U. Then the Gaussian curvature of the surface at U is equal to K = k1k2. If the Gaussian curvature K at point U is positive (K(U ) > 0), then the principal curvatures k1(U ) and k2(U ) have the same sign. Thus the surface is bending away from its tangent plane in all tangent directions at U as shown in Figure 3. An example of this would be all the points on the surface of an ellipsoid defined by ( x – x0 ) 2 a2

+

( y – yo ) 2 b2

+

( z – z0 ) 2 c2

= 1.

If the Gaussian curvature K at point U is negative (K(U ) < 0), then the principal curvatures k1(U ) and k2(U ) have opposite signs. Thus the surface is saddleshaped near U as shown in Figure 4. An example of this surface is the hyperbolic paraboloid x2 a

2

–

y2 b

2

=

z . c

IJCST 8,3

If the Gaussian curvature is zero (K(U ) = 0), then there are two possibilities: (1) Only one principal curvature is zero, say k1(U ) ≠ 0 and k2(U ) = 0

26

which describes a cylinder. Thus the surface is trough-shaped near U as shown in Figure 5. (2) Both principal curvatures are zero k1(U ) = k2(U ) = 0.

k1 (U ) < 0 k2 (U ) < 0 P e2 Figure 3. Surface of positive Gaussian curvature K(U ) > 0 bends away from its tangent plane in all tangent directions at the point U

Figure 4. Surface of negative Gaussian curvature K(U ) < 0 is saddleshaped near the point U

Figure 5. Surface with zero Gaussian curvature K(U ) = 0 where only one of the principal curvatures is zero at the point U. This surface is trough-shaped near U

e1

M

e2

M

P e1

k1 (U ) < 0 k2 (U ) > 0

M

P e2

e2

k1 (U ) > 0 k2 (U ) = 0

In this case, U is a planar point on the surface. An example of this is the central Modelling fabric point of a monkey saddle, where three hills and valleys meet as shown in Figure deformation 6, and is defined by z = x( x +

3 y) ( x –

y ).

27

Figure 6. A monkey saddle is a surface with zero Gaussian curvature K(U ) = 0 where both principal radii are zero. Three hills and valleys meet at the central point U which is a planar point

P

A good example of the cases of different Gaussian curvature is given by the torus of revolution T as shown in Figure 7. At points on the outer half of T, the torus bends away from its tangent plane. Therefore, K > 0 on the outer half of T. But near each point on the inner half, T is saddle-shaped and cuts through the torus. Hence, K < 0 on the inner half of T. Near each point on the circles (top and bottom) which separate the inner and outer halves of T, the torus is troughshaped. Hence K = 0 at points on these two circles.

4

1 0.5 0 –0.5 –1

2 0

–4 –2

–2

0 2

–4 4

Figure 7. Torus of revolution T with the outer half bending away from its tangent plane (K > 0) and the inner half saddle-shaped (K < 0). T is trough-shaped (K = 0) on the two circles separating the inner and outer halves of T

IJCST 8,3

28

In this section, we have introduced the spherical representation of a surface. The Gaussian curvature is defined as the product of the principal curvatures. The following section describes the surfaces of constant Gaussian curvature. Surfaces of constant Gaussian curvature are categorized into flat, spherical and pseudospherical surfaces. In order to construct mechanical models of textile material deformation, the principal curvatures must be functions of the material properties. It follows that when the surface of the textile material is transformed into another surface, the geodesic curves which are functions of the principal curvatures change, according to the specifications of the material properties. The three-dimensional surface of a material can therefore be defined in terms of these curvatures. The fabric mechanical properties, such as bending, shear and extension, can be incorporated into the curvature parameters affecting how one fabric surface is deformed or transformed into another. Surfaces of constant Gaussian curvature The theory of surfaces of constant Gaussian curvature is the link with the fundamental theory of the special algebraic structure for all integrable nonlinear evolution equations. Surfaces of constant Gaussian curvature are categorized into flat surfaces, spherical surfaces and pseudospherical surfaces. The theory of transforming one pseudospherical surface into another is introduced in “The fabric nonlinear dynamical system” (The fabric non-linear dynamic system), as “Bäcklund Transformations of surfaces”. The sine-Gordon equation which is a generalization of the fabric mechanics equations is solved using the direct method of Bäcklund Transformations in “The sine-Gordon equation”. When the Gaussian curvature is identically zero, the surface is developable, i.e. the surface can be generated by a series of lines. A surface S is called flat if the Gaussian curvature is zero K = 0. Two applicable surfaces have the same total curvature at corresponding points. Consequently, every surface applicable to the plane is the tangent surface of a twisted curve. The nondevelopable surfaces are called spherical for positive Gaussian curvature and pseudospherical for negative Gaussian curvature. The classical examples of surfaces of constant Gaussian curvature are given by surfaces of revolution where the point with surface co-ordinates (u, v) sits in three-dimensional space at the point (h1(u) cos v, h1(u) sin v, h2(u)). Here h1 and h2 are functions such that (

dh1 du

)2 + (

dh2 du

)2 = 1.

For a surface of this form, the Gaussian curvature at a point U with surface coordinates (u, v) is given by (see [4, p. 66])

d 2 h1 2 K (U ) = – du . h1 Thus, the surface will have constant Gaussian curvature K if h1 satisfies the elementary differential equation

d 2 h1

+ Kh1 = 0. du 2 If we can find a solution h1 to this equation which satisfies

(1)

2

 dh  1   ≤ 1,  du 

(2 )

then we can construct a surface of revolution with Gaussian curvature K by setting 2

h2 (u ) =

u

∫0 ±

 dh (t )  1 –  1  dt .  dt 

The form of the solution of equation (1) depends on the sign of K. If K = 0 then the only solutions are those of the form h1 (u) = au + b where a and b are real constants. Condition (2) implies that |a| ≤ 1. Choosing a = 0 gives the result that the surface has parametric description, (b cos v, b sin v, u), which is merely a circular cylinder. Setting a = 1 gives h2 = 0 and hence the surface has parametric description ((au + b) cos v, (au + b) sin v, 0), which is part of the xy-plane. Spherical surfaces To construct a surface of positive constant Gaussian curvature, let K = α2. The solutions of Equation (1) in this case are of the form h1 (u) = c1 cos αu + c2 sin αu, where c1 and c2 are constants. In order to construct a particular example, let α = 1 and c2 = 0. Condition (2) translates into the condition that c21 sin2u ≤ 1. In the special case that c1 = 1, we get (by a suitable choice of sign) h2 (u ) =

u

∫0

1 – sin2t dt =

u

∫0

cos t dt = sin(u ).

This gives a surface with parametric description (cos u cos v, cos u sin v, sin u) which is just the standard “latitude-longitude” representation of the unit sphere (Figure 8). It is this example which explains why surfaces of positive constant Gaussian curvature are called spherical surfaces.

Modelling fabric deformation

29

IJCST 8,3

1 0.5 0 –0.5 –1

30

1 0.5 0 –0.5

Figure 8. The sphere is a surface of constant positive Gaussian curvature

–1 –1 –0.5 0 0.5 1

Pseudospherical surfaces To construct a pseudospherical surface, i.e. a surface of negative constant Gaussian curvature, it is necessary to solve equation (1) for K = α2 < 0. In this case the solutions are of the form h1(u) = c1eαu + c2e–αu. with the condition that α2(c1eu + c2e–u)2 ≤ 1. Again, particular examples can easily be found by fixing values of α, c1 and c2. In the examples below we have set α = 1. The case when c1 = c2 produces the surface shown in Figure 9 – a type of horizontally fluted column. This pseudospherical surface is said to be of hyperbolic type. Choosing c 1 = –c 2 gives the hourglass type shapes of Figure 10. Such a pseudospherical surface is said to be of elliptic type. The final example in this section is called the pseudosphere. This surface corresponds to the solution for c 1 = 0 and c 2 = 1. In this case the z-axis is asymptotic to the surface. Indeed the length of the segment of the tangent from a point on the surface to the z-axis is always equal to 1. This is the defining condition of a type of curve known as tractrix. Thus the pseudosphere is the surface of revolution of tractrix. The pseudosphere, shown in Figure 11, is a pseudospherical surface of parabolic type. This result leads to the question of how to (mathematically) generalize surfaces of constant negative Gaussian curvature. In the next section we introduce Bäcklund Transformations (developed by Bäcklund in the 1880s) which

Modelling fabric deformation

31

Figure 9. Pseudospherical surface (or surface of constant negative Gaussian curvature) of hyperbolic type

Figure 10. Pseudospherical surface (or surface of constant negative Gaussian curvature) of elliptic type

transform one pseudospherical surface into another by solving a nonlinear partial differential equation. The fabric nonlinear dynamical system Bäcklund Transformations of surfaces There are several rigorous mathematical methods now available for the solution of nonlinear partial differential equations. These methods include Bäcklund Transformations[5], Hirota’s Method[6] and the Inverse Scattering Method[7]. Preliminary studies were carried out in order to decide which of these methods would be most appropriate for fabric deformation problems. Bäcklund Transformations were chosen in view of the fact that this method is capable of

IJCST 8,3

32

Figure 11. Pseudospherical surface (or surface of constant negative Gaussian curvature) of parabolic type

solving the nonlinear differential equations used in the present work and is less complicated mathematically than the other methods. Bäcklund Transformations are related to transformations of surfaces of constant negative Gaussian curvature[8]. They transform one pseudospherical surface into another surface of the same Gaussian curvature. On these two surfaces the lines of curvature correspond. The line of corresponding points is tangent at these points to the surface and has a constant length. The tangent planes at corresponding points meet at a constant angle. The definition of a Bäcklund Transformation Let ω be the supplementary angle between intersecting geodesic lines so that our co-ordinates are polar geodesic as shown in Figure 12. The parameters α and β represent the asymptotic lines. When the transforms of a given pseudospherical surface are known, the Gauss equation becomes O'''

Figure 12. Description of the polar geodesic parameters used to transform one pseudospherical surface into another

O''

M ω

O

O'

∂ 2w

= sin ω cos ω

(3 a )

∂α∂β which is now known as the sine-Gordon equation. If Ω = φ(α, β) is a solution, then Ω1 = φ(αm, β/m) is also a solution, where m is any constant. Therefore, from one pseudospherical surface, an infinite number of other pseudospherical surfaces can be obtained by solving equation (3a). Only the fundamental quantities of the new surfaces are found by solving equation (3a). The determination of the co-ordinates requires the solution of a Riccati equation[9] which may be different from the one for the given surface. The Riccati equation of a surface mathematically describes the curvature and torsion of a geodesic curve and the evolution of this curve into another dimension required to construct the surface. Enneper[10] first studied surfaces where the lines of curvature on a pseudospherical surface are planar. These are known as surfaces of Enneper of constant curvature and have been catalogued extensively using Bäcklund Transformations. We now relate the theory of Bäcklund Transformations to nonlinear partial differential equations. The generally accepted definition of a Bäcklund Transformation was given by Hanno Rund[11]. Definition Let u(x, t) and v(x, t) satisfy the partial differential equations P(u) = 0

(4a)

and Q(v) = 0

(4b)

respectively, where P and Q are nonlinear operators. A pair of relations ∂u ∂v ∂u ∂v R1 (u , v , , , , , …; x, t ) = 0, ∂x ∂x ∂t ∂t ∂u ∂v ∂u ∂v R 2 (u , v , , , , , …; x, t ) = 0, ∂x ∂x ∂t ∂t between the two functions u and v is called a Bäcklund Transformation if these relations ensure that v satisfies equation (4b) whenever u satisfies equation (4a) and vice versa. If u and v satisfy the same equation (that is, P = Q) then {R1, R2} is an auto-Bäcklund Transformation. Example of Bäcklund Transformations The nonlinear partial differential equation originally posed by Laplace has been used to describe the stability of the solar system, the electric field around a charge of electricity and the steady distribution of heat in a casserole under the grill. The Laplace equation can be written as

Modelling fabric deformation

33

IJCST 8,3

34

∂ 2u

+

∂ 2u

+

∂ 2u

= 0. ∂x 2 ∂y 2 ∂z 2 An auto-Bäcklund Transformation for the Laplace equation is defined by the pair of equations ∂u ∂v ∂v ∂v = and = – ∂x ∂y ∂y ∂x and the Cauchy-Riemann relations are

∂ 2u ∂x 2

+

∂ 2u ∂y 2

= 0 and

∂ 2u ∂x 2

+

∂ 2v ∂y 2

= 0.

If we take the simple solution v(x, y) = xy to the Laplace equation, then ∂u ∂u = x and = – y. ∂x ∂y In order that these two equations be satisfied, we must have 1 2 u( x , y ) = (x – y2 ) 2 which is another solution of the Laplace equation. Soliton theory and applications The dynamic properties of a fabric are crucial for its performance during manufacture and end-use. When a garment is worn, the way it moves against air resistance is analogous to waves travelling through a fluid. To extend the static nonlinear models of fabric deformation to dynamic models, it is necessary to generalize the nonlinear differential equations into a nonlinear dynamical system. This new system allows one type of deformation to evolve into or interact with another type of deformation. In the last few decades, two great discoveries have revolutionized the field of nonlinear dynamical systems – the strange attracter in chaos theory and the solitary wave in soliton theory. Soliton theory involves constructing analytical solutions for nonlinear evolution equations and, in recent years, has developed the concept of integrability. A nonlinear evolution equation is integrable if its solutions are not chaotic for any input value. In other words, a nonlinear partial differential equation is integrable if it has soliton or solitary wave solutions. It has since been proved that integrable nonlinear partial differential equations include a wide variety of useful and universal equations which are central to many areas of mathematical physics and whose solutions are important to the general understanding of nonlinear wave phenomena. The practical importance of integrability in physical applications has been stressed by Newell[12]:

If one is given a hatful of equations and asked to pick one at random from this hat, it is very unlikely that it would be completely integrable. Yet in the hatful of equations that physics provides as asymptotic solvability conditions, there would appear to be a disproportionate share of ones with soliton properties. Can this be simply coincidence?

The solitary wave The first documented observation of the solitary wave was made in 1834 by the Scottish scientist and engineer John Scott Russell. While observing the movement of a canal barge on the Edinburgh-Glasgow canal, Scott Russell noticed a novel type of water wave which he called a solitary wave[13]. This solitary wave motion is a two-dimensional disturbance of a portion of the fluid which travels through the fluid in time in a third dimension as shown in Figure 13. A fibrous material is analogous to a fluid in terms of surface deformation. As in the case of fluid dynamics, a two-dimensional wave in a fibrous material travels in time through fibre to fibre contact into the third dimension of the surface of the material. An example of this phenomenon is a yarn within a fabric being buckled into a two-dimensional bell-shaped wave and then evolving yarn by yarn through the third dimension of the surface of the fabric forming a three-dimensional drape configuration. The words “solitary wave” were coined by Scott Russell himself mainly because this type of wave motion stands alone and apart from the other types of oscillatory wave motion. A solitary wave is typically a bell-shaped, plane wave pulse which translates in one direction in space without changing its

2 1.5 1 0.5 0

Modelling fabric deformation

35

4 0.8

3 0.6 2 0.4 1

0.2 0 0

Figure 13. The solitary wave originally observed by Scott Russell. Note that there is no change in height, width or speed with time

IJCST 8,3

36

shape, that is, a wave of permanent profile or permanent type. Any bell-shaped function u(x – ct) is a solitary wave translating in time t with speed c along x. The nonlinear partial differential equations mechanically modelling fabric deformation belong to the Klein-Gordon family of equations whose solutions can be written as analytical expressions of interacting solitary waves. Therefore, fabric deformation can be modelled using fabric mechanics as a nonlinear dynamical system. In the following section, solutions of the sineGordon equation (3a) are constructed using Bäcklund Transformations. The sine-Gordon equation The nonlinear partial differential equations to be solved analytically in the field of fabric deformation and dynamics can be represented as members of the Klein-Gordon family of differential equations. This family of equations is encountered consistently in nonlinear dynamical systems in all branches of physics and engineering[14]. Equations derived previously which belong to the Klein-Gordon family of differential equations include: Fabric buckling[15], d 2ψ

P

sinψ ; B ds 2 Fabric cantilever[16], d 2ψ

=–

w

s cos ψ ; B ds 2 Fabric structure/micromechanics[17],

∂ 2ψ ∂s 2

=–

=

P B

sinψ –

Q B

cosψ ,

where ψ is the wave function, P and Q are forces external and internal in the fabric respectively, B and w are fabric properties of bending rigidity and weight respectively. The sine-Gordon (SG) equation first arose in the 1880s in relation to the generalization of surfaces of constant negative Gaussian curvature. Forty years later, Klein and Gordon derived a relativistic equation for a charged particle in an electromagnetic field, using the recently discovered ideas of quantum theory. Their Klein-Gordon equation reduces to 1 ∂ 2ψ c 2 ∂t 2

2

 mc  –∇ ψ +  ψ = 0  h  2

( 5a )

for the special case of a free particle of mass m in three dimensions where c is the velocity of light and h is Planck’s constant. This later led to the mathematical generalization[18]

1 ∂ 2ψ c 2 ∂t 2

– ∇ 2ψ + V '(ψ ) = 0

(5 b )

for some differentiable potential function V. If V ' is a nonlinear function, this is called a nonlinear Klein-Gordon equation. The above equation (5b) is invariant under the Lorentz Transformation. In other words, the properties of the solutions of equation (5b) are the same even if the variables are transformed according to the Lorentz Transformation. In particular, if V '(ψ)=sinψ and we restrict the equation to one spatial dimension, then we obtain the sine-Gordon (a pun on Klein-Gordon) equation 1 ∂ 2ψ c 2 ∂t 2

–

∂ 2ψ ∂x 2

+ sinψ = 0

(3b)

which is the same as equation (3a) in “laboratory” co-ordinates. Furthermore, if we use “characteristic” co-ordinates α = 1⁄2(x – ct) and β = 1⁄2(x + ct),

∂ 2ψ ∂α∂β

= sinψ .

( 3c )

The sine-Gordon equation (3c) has also been applied to mechanical models, magnetic-flux propagation in a large Josephson junction for superconductors [19], Bloch-wall motion in domain wall dynamics in magnetic crystals, propagation of ultra-short optical pulses in fibre optics and unitary theory of elementary particles[14]. Solving the sine-Gordon equation The sine-Gordon equation (3) was not considered solvable until the development of Bäcklund Transformations in soliton theory[20]). The sine-Gordon equation is now known to be an integrable differential equation, meaning that analytical solutions can be found which do not become chaotic for any range of the variables u and v. Analytical solutions can be constructed theoretically and written as algebraic/trigonometric expressions. Thus no computer power is needed and the problems of numerical instability, convergence of solutions and error analysis are avoided. Solutions of integrable nonlinear evolution equations are called soliton solutions and hence the partial differential equations are known as soliton equations. Lamb[21] reintroduced a classical Bäcklund Transformation of the sineGordon (SG) equation (3c) that leaves the SG equation invariant by considering the pair of relations  u – v (u + v ) = a sin   2 ∂x  2  1 ∂

( 6a )

Modelling fabric deformation

37

IJCST 8,3

1 ∂ 2 ∂t

38

(u – v ) =

 u + v sin   , a  2  1

( 6 b)

where u(x, t) and v(x, t) are solutions of the SG equation (3c). The concept of Bäcklund Transformations is presented pictorially in Figure 14 which shows a surface σi being transformed through a parameter ai into another surface σj. By cross-differentiating equations (6.4a) and (6.4b), we obtain  u – v a ∂ 1 ∂2 (u + v ) = (u – v ) cos   2 ∂x∂t 2 ∂t  2   u + v 1 ∂2 1 ∂ (u – v ) = (u + v ) cos  , 2 ∂t∂x 2a ∂x  2  where a(≠ 0) is an arbitrary constant. Using trigonometric identities, these two equations can be written as  u + v  u − v 1 ∂2 (u + v ) = sin   cos   2 ∂x∂t  2   2   u – v  u + v 1 ∂2 (u – v ) = sin   cos  . 2 ∂t∂x  2   2  Adding and subtracting these two equations respectively yields

∂ 2u = sin u ∂x∂t ∂ 2v = sin v ∂x∂t

( 7a ) ( 7 b)

Now both equations (7a) and (7b) satisfy the sine-Gordon equation (3c) which implies that equations (6a) and (6b) are auto-Bäcklund Transformations for the SG equation (3c). Figure 14. Pictorial diagram for the Bäcklund Transformation described mathematically by equations (6a) and (6b)

σi

ak

σj

The solitary wave solution Equation (3c) has the zero solution u(x, t) = 0 for all x, and t. If we choose v = 0, then the Bäcklund Transformation described by equations (6a,b) becomes  u  u ∂u ∂u 2 = 2a sin   and = sin   . ∂x ∂t a  2  2

39

Integrating these two equations, 2ax =

∫2

du 1 = 2 ln|tan u|+ f (t ) u 4 sin   2  

and 2t 1 du = ∫2 = 2 ln|tan u|+ g ( x ), a 4 sin u   2  

(8 a )

(8 b )

where f and g are arbitrary functions. For consistency, we must have tan 41 u = 1 C eax+x where C is an arbitrary constant. Putting C = eµ gives the solution u(x, t) = 4 arctan (eax+x + µ), 1

Modelling fabric deformation

(9)

where µ is the phase. Thus, by choosing the zero solution v = 0, Bäcklund Transformations are used to transform this trivial solution into a wave solution. Equation (9) is the solitary-wave solution of the sine-Gordon equation (3c). Figure 15 plots this solitary wave solution. The solution for a > 0 is called a kink and the case a < 0 is described as an antikink, the names being derived from quantum mechanics applications. Thus we have used the theory of Bäcklund Transformations to transform a trivial solution into a series of analytical solitary wave solutions representing the actual fabric deformation behaviour. By considering a deformed fabric as a two-dimensional surface, analytical solutions of fabric deformation are algebraically constructed from the sine-Gordon equation. These analytical expressions describing the curvature parameters of a surface represent actual solutions of the fabric nonlinear dynamical system. The extended Klein-Gordon equation In the previous sections of this paper, all the differential equations used to analyse fabric dynamics have been contained in the Klein-Gordon family of equations. In order to extend this theory to include a larger range of physical situations, we need to introduce physical concepts such as the dispersion of the waves through the medium.

IJCST 8,3

4

40

1

2

0.5

0 – 10

0 –8 –6

– 0.5 –4 –2 –1

0

(a)

6 4 Figure 15. The solitary wave solution (9) for the sineGordon equation (3c) for the case of: (a) α > 0 describing a kink and (b) α < 0 describing an antikink. Because of symmetry, half the bellshaped solitary wave is shown in each (figure a and b)

2 1 0 –10

0.5 –8 0

–6 –4

– 0.5 –2 0

–1

(b)

The sine-Gordon equation (3) has been generalized[22] to include an external force term and a dissipation term. This new equation, referred to as the extended Klein-Gordon system, is expressed as

∂ 2ψ

–

∂ 2ψ

– V ′(ψ ) = G

∂ψ

( 10 )

∂t ∂x 2 ∂t 2 where V is any differentiable function as in the Klein-Gordon equation (5), and G is the dissipation coefficient. The nonlinear partial differential equation (10) is integrable and does possess analytical solutions for all ranges of the dependent variables x and t, provided that the integrability condition

∂ 2ψ ∂ 2ψ = ∂x∂t ∂t∂x is satisfied. The next step in this work would be to generalize the fabric drape, buckling or folding equation for more complicated applied external forces caused by different boundary conditions on the material. The dissipation of the buckling deformations as they evolve yarn by yarn through the fabric also needs to be incorporated by including the loss of energy due to fabric internal friction and fibre viscoelasticity. Thus using equation (10), it should be possible to formulate a whole range of dynamic problems in fabric drape, folding, buckling and wrinkling for which the textile material or garment is subjected to complex forces and moments by including the dissipative effects of interfibre friction and fibre viscoelasticity within the fabric. References 1. Guillemin, V. and Pollack, A., Differential Topology, Prentice-Hall, Englewood Cliffs, NJ, 1974. 2. Gauss, K.E. (1828), Disquisitiones generales Circa superficies Curvas, Göttingen (English translation 1902: General Investigation of Curved Surfaces, by J.C. Morehead and A.M. Hutebeitel, Princeton, NJ). 3. O’Neil, B., Elementary Differential Geometry, Academic Press, New York, NY and London, 1966. 4. Klingenberg, W., A Course in Differential Geometry, Springer-Verlag, New York, NY, 1978. 5. Lamb, G.L. Jr, “Bäcklund Transformations for Certain Nonlinear Evolution Equations”, Journal of Mathematical Physics, Vol. 15, 1974, p. 2157. 6. Hirota, A., “Exact solution of the sine-Gordon equation for multiple collisions of solitons”, Journal of the Physics Society of Japan, Vol. 33, 1972, p. 1459. 7. Ablowitz, M.J. and Segur, H., Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, PA, 1981. 8. Bäcklund, “Theory and applications of the sine-Gordon equation”, Revista del Nuovo Cimento, Vol. 1 No. 2, 1883, p. 227. 9. Eisenhart, L.P., A Treatise on the Differential Geometry of Curves and Surfaces, Ginn, Boston, MA (also Dover, New York), 1909. 10. Enneper, A., “Über Asymptolische Linien”, Nachrichten des Koniglichen, Gesellschaft des Wissenschaften Göttingen, 1870, p. 493.

Modelling fabric deformation

41

IJCST 8,3

42

11. Rund, H., “Variational problems and Bäcklund Transformations associated with the sineGordon and Korteweg-deVries equations and their extensions, in Bäcklund Transformations”, Lecture Notes in Mathematics, Vol. 515, Springer-Verlag, New York, NY, p. 199. 12. Newell, A.C., “The history of the soliton”, Transactions of the ASME Section E, Journal of Applied Mechanics, Vol. 50, 1983, p. 1127. 13. Scott Russell, J., Report on Waves, Report, Fourteenth Meeting of the British Association for the Advancement of Science, John Murray, London, 1844, p. 311. 14. Barone, A., Esposito, F., Magee, C.J. and Scott, A.C., “Theory and applications of the sineGordon equation”, Revista del Nuovo Cimento, Vol. 1 No. 2, 1971, p. 227. 15. Grosberg, P. and Swani, N.M., “The buckling of woven fabrics”, Textile Research Journal, Vol. 36 No. 4, 1966, p. 332. 16. Peirce, F.T., “The handle of cloth as a measurable quantity”, Journal of the Textile Institute, Vol. 21, 1930, p. T377. 17. Peirce, F.T., “The geometry of cloth structure”, Journal of the Textile Institute, Vol. 55, 1937, p. T541. 18. Drazin, P.G. and Johnson, R.S., Solitons: An Introduction, Cambridge University Press, Cambridge, 1989. 19. Scott, A.C., “Propagation of magnetic flux on a long Josephson tunnel junction”, Il Nuovo Cimento, Vol. LXIX B No. 2, 1970, p. 241. 20. Lamb, G.L. Jr, “Propagation of ultrashort optical pulses”, Physics Letters, Vol. 25, 1967, p. 181. 21. Lamb, G.L. Jr, “Analytical description of ultrashort optical pulse propagation in a resonant medium”, Review Modern Physics, Vol. 43 No. 2, 1971, p. 99. 22. Tateno, H., “Behavior of dynamic solition solutions in nonintegrable extended KleinGordon systems by means of a state plane techniques”, Journal of Mathematical Physics, Vol. 29, 1987, p. 365. Further reading Abbott, G.M., Grosberg, P. and Leaf, G.A.V., “The hysteresis during bending of woven fabrics”, Textile Research Journal, Vol. 41 No. 4, 1971, p. 345. Grosberg, P., “The mechanical properties of woven fabrics”, Textile Research Journal, Vol. 36 No. 3, 1966, p. 205. Olofsson, B., “A general model of a fabric as a geometric-mechanical structure”, Journal of the Textile Institute, Vol. 55, 1964, p. T541. Shanahan, W.J., Lloyd, D.W. and Hearle, J.W.S., “Characterizing the elastic behavior of textile fabrics in complex deformations”, Textile Research Journal, Vol. 48, 1978, p. 495.

An approach to the theoretical mechanics of static drape

Theoretical mechanics of static drape

David W. Lloyd Department of Industrial Technology, University of Bradford, Bradford, UK

43

F. Mete Department of Textile Industries, University of Leeds, Leeds, UK

K. Hussain Department of Industrial Technology, University of Bradford, Bradford, UK Introduction This paper outlines an approach to the theoretical mechanics of the static drape of textile fabrics. The aim behind the approach is to develop a computationally convenient implementation of the theoretical mechanics of fabrics treated as two-dimensional continua, where as little approximation as possible is introduced into the physics of the model and where the approximation necessary to arrive at a solution is introduced through the numerical analysis techniques used to obtain solutions of the equations. Other philosophical approaches are possible, including making all approximations in the physics of drape and solving the resulting equations analytically. The approach described in this work was chosen because it offered the possibility of developing a programme package capable of solving a wide range of practical static drape problems, and because this would in turn be capable of extension to the more general problem of dynamic drape. The approach can be summarized simply. It is assumed that a fabric can be represented as a two-dimensional continuum and that this, in turn, can be represented by a surface embedded in Euclidean 3-space. The shape of this surface can then be described for both the deformed and undeformed states by the differential geometry of the surface, and the strain measures can be deduced from the differences in the differential geometry for the two states. Constitutive equations can then be used to describe the material properties of the fabric and to link the strain measures to the forces and moments applied to the fabric. Equations describing compatibility and the equilibrium of forces and moments then complete the model. Two previous researchers provide much of the inspiration for this approach. Womersley[1] was the first, to the best of the authors’ knowledge, to represent a fabric using the differential geometry of a surface, although he was unable to develop the model to the point where it would have been capable of yielding useful solutions. Konopasek[2] developed a computer implementation of elastica theory which provided an exemplar for the approach adopted here. In particular, he developed a computationally convenient expression of the

International Journal of Clothing Science and Technology, Vol. 8 No. 3, 1996, pp. 43-58. © MCB University Press, 0955-6222

IJCST 8,3

44

equations of computational elastica theory which he then incorporated into a conceptually simple computer package for the routine solution of practical problems. An elastica can be regarded as the one-dimensional analogue of a surface (or vice versa), with essentially the same subsets of equations (though no compatibility equations are needed in the one-dimensional case). Indeed, the equations of the surface can be reduced to the equations of the elastica for particular special cases[3]. Konopasek’s approach of seeking scalar differential equations capable of easy numerical solution (at the expense of increasing the number of equations) and the basic structure of Konopasek’s computational package were adopted for the more complex problem of drape. The origins of the partial differential equations obtained in this work to describe drape have been given elsewhere[3]. The equations can be stated in a compact form, using tensor notation; however, tensor notation is not appropriate for computational implementation, which requires calculations at the level of individual components. The partial differential equations can be expressed in component form, though the result is a set of over 40, first order scalar partial differential equations. Outline of theoretical model Space considerations prevent a full derivation of all the equations being given here. The approach will be given in summary using suitably compact notation, with examples of the derived scalar equations where appropriate. Differential geometry It is assumed that the fabric can be represented by a surface in space that is continuous and has the same mechanical properties as the fabric. A surface is, by definition, two-dimensional, so it does not have thickness; this will affect the way that some elements of the model are expressed. Since the surface is twodimensional, it requires two co-ordinates to describe it. There is no obvious choice of co-ordinate system and most systems have disadvantages. It is convenient, at this stage, to select a general, non-orthogonal, curvilinear coordinate system, ζ1, ζ2 that is convected (or intrinsic) in that it deforms with the surface. An adapted frame field may be constructed on each of the co-ordinates, i.e. vector fields may be established consisting of unit vectors tangent to the surface and the co-ordinate lines, tangent to the surface and normal to the coordinate lines, and normal– to both the surface and the co-ordinate lines. These – – vectors are given by, α1, β1, γ 1, on ζ1 in Figure 1. It is possible to calculate the length of an element ds in the surface[4]: ds2 = dx i dx i = gαβ dζ α dζ β where the summation convention is adopted and Roman indices take the values 1, 2, 3 and Greek indices the values 1 and 2. The term gαβ is called the first fundamental form or metric tensor of the surface and is given by: ∂x i ∂x i gαβ = . ∂ζ α ∂ζ β

ζ2

α2 β

Theoretical mechanics of static drape

1

γ1

45 α1 ζ1

p x3

x2

x1

The principal axes of the material will be orthogonal; for simplicity, it will be assumed from now on that the co-ordinates ζ1, ζ2 coincide with the principal axes of the material. The unit normal vector field U can be constructed – consisting of all the vectors β 1; at a point on the surface given by the position – vector p it is possible to define a shape operator as: dU S p ( v ) = – ∇ vU = ds where S p is the shape operator, ∇v is the directional derivative of U in the direction v–. This is given by dU/ds where w(s) is a curve such that w(0) = –p and dw(0)/ds = –v and if s is arc-length v– is a unit vector. – are unit vectors tangent to the surface at p– with w – in an arbitrary If u– and w – – – are direction, Sp(u) • w is the second fundamental form of the surface. If u– and w – unit tangent vectors to the co-ordinate lines, the normal replaced with the α – i curvatures k(α ) and twist t(α–i) of the surface are obtained. The surface is fully determined up to a rigid body motion if the first and second fundamental forms are specified for the surface. The normal curvatures and twist are related through three equations, the connection equations, that connect them to the – three unit vectors α–, β , γ– on each co-ordinate line, their derivatives with respect to arc-length and the geodesic curvatures of the co-ordinate lines. The meaning of the normal curvatures, geodesic curvatures and twist are discussed more fully elsewhere[3].

Figure 1. Co-ordinates on the surface

IJCST 8,3

46

Deformation measures A number of strain measures are possible, however, one choice appears to be more “natural” than others. Suppose the deformed surface is defined by the coordinates Z i and the undeformed surface by ζi, the change in length of an element in the surface is given by: dS2 – ds2 = 2Eαβ dζα dζβ = 2eαβ dZαdZ β where S is arc-length on the deformed surface and Eαβ and eαβ are the Green and Almansi strain tensors. Since Z = ζ for convected co-ordinates, the difference between the two strain tensors disappears: 1 Eαβ = eαβ = Gαβ – gαβ 2 where Gαβ is the metric tensor for the deformed surface. The appropriateness of this choice of strain measure for fabric modelling has been demonstrated by Norton[5], in his explanation of the origin of the “collapsing shear” measured by fabric shear tests. In a similar way, it is possible to define curvature deformation measures from the difference in second fundamental forms: p(α–1) = K(α–1) – k(α–1) p(α–2) = K(α–2) – k(α–2) q(α–1) = T(α–1) – t(α–1).

(

)

Equilibrium equations The equations of force equilibrium are formed by equating to zero the resultant and resultant moment of all the forces applied to a portion of the surface. The moment equilibrium equations are formed in a similar way by equating to zero the resultant moment of all the forces and moments applied to the portion of the surface. Denoting by S the tangential shear force, T the normal force, N the transverse shear force, G the bending moment and H the twisting moment, the forces and moments per unit length along normal sections along the co-ordinate – – – – lines may be calculated. These will be denoted by R α, Q α and R β, Q β for the ζ1 – 2 and ζ co-ordinate lines respectively. If P is the applied force per unit area acting N1

S'2

T1

T'2

S1 —2

β

N'2 S'1

N2

1

—1 Figure 2. Forces acting on an element of the surface

S2 T2

T'1 N'1

G'2

H1

Theoretical mechanics of static drape

H'2

G1 β

α2 1

47

G'1 α

1

Figure 3. Moments acting on an element of the surface

G2 H2

Qβ

H'1 Rβ

R +δ R

c

α

α

α

Q +δ Q Q

α

d a R

β

α

β

β

R +δ R

β

Q +δ Q

b

on the element of the surface, the following vector equations of equilibrium are obtained[6]: –

∂  ∂  gαα R α  – g ββ R β  +     ∂β ∂α

 2 g g – g αβ  P = 0  αα ββ  

∂  ∂  gαα Q α  – g ββ Q β  – gαα g ββ R α × a –2     ∂β ∂α  2 – gαα g ββ R β × a –1 +  gαα g ββ – gαβ  Q = 0.  

–

and where the gij are the components of the metric tensor or first fundamental form. Constitutive equations The strain measures are connected to the applied forces by the constitutive equations that express the mechanical properties of the material. Retaining the same orthogonal co-ordinate system for clarity, the constitutive equations may

Figure 4. Force and moment resultants

IJCST 8,3

48

be expressed in a simple matrix form[7]. The theoretical framework for the formation of these equations in textile applications has been discussed in detail elsewhere[7]. In the most general case the consitutive equations take the form:  T1   A11     T2    S12    =  G1   G    2   H 12  

A12 A22

A13 A23 A33

B14 B24 B34 D44

B15 B25 B35 D45 D55

B16   B26  B36   D46  D56   D66 

 ε1     ε2  ϖ    κ1  κ   2 κ 12 

where, as before, T1 and T2 are the tensile stress resultants acting along the ζ1 and ζ2 co-ordinate lines respectively, S12 is the shear stress resultant, G1 and G2 are the bending stress couples, and H12 is the twisting or torsional stress couple. The Aij are the in-plane rigidities, the Dij are the bending rigidities, and the Bij are the coupling rigidities that connect the in-plane and out-of-plane deformation modes as a property of the material. It is commonly assumed[7] that textile fabrics are orthotropic with the Bij equal to zero. It has also been shown[8] that the twisting modulus is small enough to be neglected for most practical purposes. The remaining moduli are all capable of being measured routinely in reproducible tests[7]; for the purposes of this paper it will be assumed that appropriate values for material properties will be available for simulating the drape of a given fabric. Compatibility equations Although a surface is specified up to a rigid body motion if the first and second fundamental forms are given as functions of ζ 1 and ζ 2 , specifying the coefficients of the first and second fundamental forms as arbitrary functions of ζ1 and ζ2 does not necessarily define a surface. It is necessary to ensure the continuity of the third derivatives of the vector field consisting of the position vectors, p–, to the surface. This is expressed in the Gauss theorema egregium: ∂ Γijn ∂ Γikn – + Γikl Γijn – Γijl Γikn = kik k jn _ kik kkn ∂ζ j ∂ζ k where i, j, k, n = 1, 2 and the index l is summed, and the Codazzi-Mainardi equations: ∂ k12 ∂ k11 l l – + Γ12 kl 1 – Γ11 kl 2 = 0 1 2 ∂ζ ∂ζ ∂ k22 ∂ k21 l l – + Γ22 kl 1 – Γ21 kl 2 = 0. 1 2 ∂ζ ∂ζ

The Γikl are the Christoffel symbols of the second kind. The Christoffel symbols of the first kind, Γikm, are given by: Γikm =

1  ∂g im ∂gmk ∂g ki  + –   2  ∂ζ k ∂ζ i ∂ζ m 

where the Christoffel symbols of first and second kinds are related by:

Theoretical mechanics of static drape 49

Γikl = g lm Γikm and where g lm = (l/g) g lm , the contravariant metric tensor, g = |g ij | and kik = kij gkj. Numerical solution The equations given above are not in a computationally convenient form, nor are they amenable to analytical solution. Konopasek[2] adopted an approach for the elastica of expressing the governing equations in a computationally convenient scalar form, at the cost of increasing the number of equations. The resulting first-order ordinary differential equations were integrated using the Runge-Kutta-Merson method in a general, standard subroutine. The inital value-boundary value problem arising in simulations of practical problems was solved iteratively using the Newton-Raphson method, also in a standard subroutine. Other standard subroutines were included to carry out routine, unchanging tasks, the user only being required to supply a main program to control any incremental loading and to supply initial guesses to unknown boundary conditions, a subroutine to define the problem through setting boundary conditions, and a function to define the initial shape of the elastica. Konopasek’s philosophy was adopted in the development of a method to solve the governing equations of the surface. One of the motivations for this choice was the close relationship between the two sets of equations, indeed, the equations of the surface can be reduced to those of the elastica given an appropriate choice of problem[3]. This also suggests that the first simulations should be of problems that can be modelled using elastica theory, to enable the simulations of surfaces to be compared directly to known, correct solutions. The general structure adopted by Konopasek and here is shown in Figure 5. Main program controls incremental solution, sets initial guesses

Solve initial value-boundary value problem

Initial shape

Constitutive equations

Set initial values Calculate boundary values

Numerical integration

Figure 5. Structure of numerical solution procedure

IJCST 8,3

The simplest problem to use as a test of the method is the cantilever bending test or bending length test. Solutions for this problem go back to Pierce[9], and it has the advantage of being a surface that can be spanned by an orthogonal coordinate system. Scalar equations were obtained for this orthogonal case as a special case of the general co-ordinates[6]; these are given below:

50

On ζ1 Direction cosine equations: ∂ux = r1 vx – q1 wx ∂α ∂u y = r1 v y – q1 w y ∂α ∂u z = r1 v z – q1 w z ∂α ∂vx = p1 wx – r1 ux ∂α ∂v y = p1 w y – r1 u y ∂α ∂v z = p1 w z – r1 u z ∂α ∂wx = q1 ux – p1 vx ∂α ∂w y = q1 u y – p1 v y ∂α ∂w z = q1 u z – p1 v z ∂α Curvature equations ∂p1 = – q1 r1 ∂α ∂q1 1 = (τp1r1 – F2 p2r2 – N 1 ) ∂α F1

∂r1 = – p1 q1 ∂α ∂p2 = – q1 r2 ∂α ∂q 2 = – r1 p2 ∂α

(1) (2 ) (3 ) (4) (5 ) (6 ) (7 ) (8 ) (9 )

(10 ) (11) (12 ) (13 ) (14 )

∂r2 = – p1 q 2 ∂α Internal force equations: ∂T1 = r1S1 + r2T2 – q1 N1 – q 2 N 2 – fu ∂α ∂S1 = p1 N 1 + p2 N 2 – r1T1 + r2 S 2 – fv ∂α ∂N1 = q1T1 + q 2 S 2 – p1S1 – p2T2 – fw ∂α Co-ordinate equations:   ∂x T T = ux  1 + 1 – 2 ν 2  ∂α E1 E2  

(15 )

(16 )

51 (17 ) (18 )

(19 )

  T T = u y 1 + 1 – 2 ν 2  ∂α E1 E2  

(20 )

  T T = u z 1 + 1 – 2 ν 2  ∂α E1 E2  

(21)

∂y ∂z

On ζ2 Direction cosine equations: ∂ux = r2 vx – q 2 wx ∂β

∂u y ∂β ∂u z ∂β ∂vx ∂β ∂v y ∂β ∂v z ∂β ∂wx ∂β

Theoretical mechanics of static drape

(22 )

= r2 v y – q 2 w y

(23 )

= r2 v z – q 2 w z

(24 )

= p2 wx – r2 ux

(25 )

= p2 w y – r2 u y

(26 )

= p2 w z – r2 u z

(27 )

= q 2 ux – p2 vx

(28 )

IJCST 8,3

52

∂w y = q 2 u y – p2 v y ∂β ∂w z = q 2 u z – p2 v z ∂β Curvature equations: ∂p1 = – q2 r1 ∂β ∂q1 = – r2 p1 ∂β ∂r1 = – p2 q1 ∂β 1 ∂p2 = F1 q1 r1 – τq2 r2 + N 2 ∂β F2 ∂q2 = – p2 r2 ∂β ∂r2 = – p2 q2 ∂β

(

(29 ) (30 )

( 31) ( 32 ) ( 33 )

)

( 34 ) ( 35 ) ( 36 )

Internal force equations:

∂T2 = p1 N1 + p2 N2 – r1 T1 + r2 S2 – fv ∂β ∂S2 = – r1 S1 – r2 T2 + q1 N1 + q2 N 2 + fu ∂β ∂N2 = q1 T1 – q2 S2 – p1 S1 – p2 T2 – fw ∂β

(37 ) (38 ) (39 )

Co-ordinate equations:

∂x ∂β ∂y ∂β ∂z ∂β

 T T  S2 = vx  1 + 2 – 1 ν 1  + ux E2 E1  G   T T  S2 = vy 1 + 2 – 1 ν1  + u y E2 E1  G   S2 T T  = vz 1 + 2 – 1 ν1  + u z G E2 E1  

( 40 ) ( 41) ( 42 )

where, in a partial change of notation to avoid confusion with the earlier equations, α, β are co-ordinates along ζ1 ζ2 respectively, ux, uy, … etc. are direction cosines of the moving axes of the trihedra u, v, w on α, β (ζ1 ζ2) referred to the global fixed axes of x, y, z; are rotation elements (curvature components) of α-curve p1, q1 and r1 with respect to the moving axes u, v, w; are rotation elements of β-curve with respect to the moving p2, q2 and r2 axes u, v, w; are principal flexural (bending) rigidities of the fabric; F1 and F2 τ is the twisting (torsional) rigidity of the fabric; are tensile rigidities in the principal directions; E1 and E2 ν1 and ν2 are the corresponding Poisson ratios for extension; G is the shear rigidity; T1, S1 and N1 are the u, v, w components of the internal force acting to the α-curve; T2, S2 and N2 are the u, v, w components of the internal force acting to the β-curve; are the u, v, w components of the external distributed force fz fu, fv and fw per unit area; x, y and z are the global co-ordinates of a point on the surface. If numerical solution of the equations of drape is to be used in routine simulations as part of the computer aided design of garments, it will be necessary for the simulations to be carried out on desk-top computers and, in particular, on PCs. This requires the numerical integration to be achieved in practically short times. It is not clear, a priori, what will be the most appropriate numerical technique. Consultation with specialists in numerical analysis suggested that the first technique to be tried should, briefly, be a scheme of integrating in “strips”, treating one variable as constant and reducing the first order partial differential equations to ordinary differential equations. This method was implemented for the cantilever bending test simulation[6], with the results described below. Space precludes the detail of the numerical results being given, instead the values of essential parameters will be given. Figure 6 shows a simple plot of the co-ordinates of the results of modelling a fabric strip of unit width hanging under its own weight, using 40 × 40 integration intervals. The length overhanging is the bending length, 2.0, and the fabric hangs down to the same angle given by other methods, 41.5°. However, consideration of Figure 7, where a fabric width of 2.0 has been used, shows that the solution is not completely consistent across the width of the fabric. The problem arises with the simplified numerical integration technique used, which is unable, even for this simple problem, to control the boundary conditions properly in the subsidiary direction. Clearly a more sophisticated numerical technique is needed that can integrate first-order partial differential equations. This is likely to incur a penalty in computation time.

Theoretical mechanics of static drape 53

IJCST 8,3

54

Figure 6. Cantilever bending test simulation plotted from the numerical computations, where the angle θ is 41.498˚, the width of the fabric is 1.0 and the overhanging length is the bending length, 2.0, where θ is the angle between the horizontal and a line connecting the two ends of the fabric strip

Graphical display The aim of almost all the research on drape over the last two decades has been to develop the means to produce graphical simulations of garments on the computer screen, to assist the garment designer and to assist the process of marketing and selecting garments. To be of real use, such graphical simulations must be realistic, not just in the sense of looking sensible, but in the narrower sense of being a close representation of the physical reality. By “close” in this context is meant a deformed state that is one of the most probable of the possible deformed states of that particular garment; as the equations of drape are complex and non-linear, the solutions (both physical and mathematical) will be sensitive to small changes in initial conditions, so exact agreement between particular computational solutions and physical states is unlikely. There are three elements in producing such close representations, the mathematical model, the numerical solution technique, and the graphical methods. The mathematical model has been shown to agree with a known previous solution, though further work will be needed in this regard. The initial, simple numerical solution technique has been shown to be deficient in one regard and more sophisticated methods are being studied. The simple plots in Figures 6 and 7 are plainly inadequate for CAD purposes. For simulating garments procedures will be needed that fit surfaces to the co-ordinate data and allow pattern-wrapping, illumination, and other effects to be incorporated. These procedures should not alter the nature of the drape calculated from the model. Consider the surface fitted to the cantilever bending test simulation in Figure 8. The free end of the fabric bends in a way that is not indicated in the simpler plot of Figure 6 or in the numerical results. This bend is an artefact of the

Z axis

X axis

Y axis

surface-fitting routine in the PC-based commercial graphics package used to plot Figure 8. Although the effect is clear in this simple model, it would be difficult to detect in a simulation of a complex garment under dynamic conditions. A detailed discussion of this issue is beyond the scope of this paper. Although the issue will have arisen in engineering CAD, the problem is likely to be more severe in garment CAD, as the surfaces will be much more complicated with many more free edges.

Z axis

Y axis X axis

Theoretical mechanics of static drape 55

Figure 7. Cantilever bending test simulation plotted from the numerical computations, where the angle θ is 41.498˚, the width of the fabric is 2.0 and the overhanging length is the bending length, 2.0. Note the shape of the fabric across the width

Z axis

Y axis X axis

Figure 8. Surface fitted to the solution of Figure 6

IJCST 8,3

56

Extensions to the theory The model of drape summarized above covers only the case of static drape. Garments such as skirts and dresses depend on their dynamic drape for their aesthetic appeal. Consequently, it is necessary to address how the static model might be extended to cover the general dynamic case. It is possible to write down a general equation of motion for a fabric that summarizes the problem. Matrix notation is used here to indicate that the equation represents a larger set of equations; it is analogous to a finite element method expression of the problem, but is intended only to signify the presence of a number of variables rather than a particular discretization of the problem. Consider the equation of motion: [ M ]{d˙˙} + [ D ]{d˙ } + [ S ]{d } = { F } where [M] [D] [S] {F} {d}

are mass terms, are damping terms, are fabric stiffness terms, are applied loads, are displacements and a dot indicates differentiation with respect to time. The terms in the equation represent, therefore, the effects of inertia, damping, and the mechanical response of the fabric under the applied loads. The static model already outlined represents the two terms to the right of the equation, so a dynamic model would require the development of the two leftmost terms. The inertia terms should be straightforward, in that the mass of each differential element of the surface could be specified and the acceleration vectors could be calculated within a time increment. It is less obvious how damping terms could be represented, as two effects are likely to be important, internal damping within the fabric, which might be measured experimentally, and aerodynamic effects as a result of interactions between the fabric elements and the surrounding air. Aerodynamic effects are likely to be complex and of the same order as the effects of fabric stiffness, to judge from the way that flags behave in quite modest airflows. Numerically, the only modification that would be required to the scheme outlined for solving problems of static drape would be to solve the static problem repeatedly within a scheme of time increments. The static problem would be extended by the inclusion of the additional terms contributed by inertia and damping; these would be calculated using time derivatives of the calculated displacements and would enter the calculations in the manner of additional loads on a differential element. It is likely that an additional iterative scheme within each time increment will be needed; this may make the aim of simulating dynamic drape on PC-based computers difficult to achieve in the short term.

Discussion A mathematical model of static drape has been outlined, based on the differential geometry of surfaces. The basic assumption is that it is possible to represent a fabric by a two-dimensional continuum, and that the structure of the fabric is irrelevant except in as much as it determines the material properties assigned to the continuum. This neglects the effect of thickness, but this is already a common assumption that is implicit in the design of many of the tests to measure fabric properties. Including fabric thickness in the model would not allow resorting to three-dimensional theory, as the mechanism of bending in a structured material, such as a fabric, will be different to a continuous solid. The model has been designed to offer computational convenience; that is, the overall aim was to produce a set of equations that could be included in a computational implementation that would allow the routine solution of a broad range of general problems in static drape, without computational problems coming between the user and the problem. The philosophical model for this approach was the Bending Curve Program Package produced by Konopasek for the routine solution of elastica problems. This aim has not been fully achieved as yet; the work has progressed to the point where numerical analysis methods are being investigated so that the most appropriate method can be chosen. An example solution, the simple cantilever bending test, has been given. This problem has been solved previously by other methods, so well-found solutions are available. This allows the developing model to be tested. There are three components of the overall solution process which can give rise to errors in the solution obtained to a problem, errors in the mathematical model, errors introduced by the numerical methods, and errors introduced by the method used to display the results. It is clear that errors have not been completely eliminated from the second and third components used in this work, but that the mathematical model and the overall approach have the potential to achieve the aim of providing a convenient, routine solution procedure for general drape problems. References 1. Womersley, J.R., “The application of differential geometry to the study of the deformation of cloth under stress”, Journal of the Textile Institute, Vol. 28, 1937, pp. T97-T112. 2. Konopasek, M., “Classical elastica theory and its generalizations”, “Computational aspects of large deflection analysis of slender bodies”, and “Textile applications of slender body mechanics”, in Hearle, J.W.S., Thwaites, J.J. and Amirbayat, J. (Eds), Mechanics of Flexible Fibre Assemblies, Proceedings of NATO Advanced Study Institute, Kilini, Greece, 1979, NATO ASI Series E: Applied Sciences No. 38, Sijthoff & Noordhoff, Alphen aan den Rÿn, 1980. 3. Lloyd, D.W., “An integrated approach to the mechanical modelling of one, two and threedimensional textile structures”, in Carnaby, G.A., Wood, E.J. and Story, L.F. (Eds), The Application of Mathematics and Physics in the Wool Industry, Wool Research Organisation of New Zealand Special Publications, Vol. 6, Christchurch, pp. 21-42. 4. O’Neill, B., Elementary Differential Geometry, Academic Press, San Diego, CA, 1966.

Theoretical mechanics of static drape 57

IJCST 8,3

58

5. Norton, A.H., “Fabric deformation: a variational problem on a subspace of a Riemannian manifold”, PhD thesis, University of New South Wales, 1987. 6. Mete, F., “Simulation of fabric drape for computer aided design”, PhD thesis, University of Leeds, Leeds, 1996. 7. Shanahan, W.J., Lloyd, D.W. and Hearle, J.W.S., “Characterizing the elastic behaviour of textile fabrics in complex deformations”, Textile Research Journal, Vol. 48 No. 9, 1978, pp. 495-505. 8. Mori, T. and Lloyd, D.W., “Measuring the twisting rigidity of woven fabrics”, Textile Research Journal, Vol. 64 No. 7, 1994, pp. 397-405. 9. Peirce, F.T., “The handle of cloth as a measurable quantity”, Journal of the Textile Institute, Vol. 21, 1930, pp. T377-T416.

A simple finite element model for cloth drape simulation

A simple finite element model

J. Ascough Department of Mechanical Engineering, Loughborough University of Technology, Loughborough, UK and

59

H.E. Bez and A.M. Bricis Department of Computer Studies, Loughborough University of Technology, Loughborough, UK Background The fashion industry is highly competitive and the increasing use of computers in garment design reflects the desirability of reducing the time taken from the fashion designer’s initial drawing to the large scale manufacture of a garment. It is currently possible for the fashion designer to create two-dimensional drawings of garments with relatively inexpensive PC software, but prototype garments must be made before the final form can be established. The ability to visualize the drape of a garment around the human form at the initial design stage would eliminate much of the time currently taken in making prototype garments. In addition, images produced by the drape software could be used both for demonstrating the garment to the client and for the production of patterns from which the garment is made up. The concept of a customer selecting a garment for purchase from a television or computer screen image showing the garment draped over his or her own body model is not too futuristic and has already been suggested as a future marketing method. Simulations of fashion shows are already available. These catwalk images are produced either by animating designers’ artwork[1] or by using physical models. Magnenat-Thalmann and Thalmann[2] and Carignan et al.[3] discuss the animation problem in the context of the physical models currently available. In the present study the primary objective is to simulate the behaviour of a simple cloth garment as it falls into contact with a human body model from an initial position. The simulation must be sufficiently realistic for the garment designers’ needs and be carried out quickly enough for the designer to work, if The current project has been supported by Coats Viyella plc and the EPSRC under a Case studentship held by Anne Bricis. Dr Ronnier Luo, now of Derby University, was instrumental in specifying and co-ordinating the project proposal. Professor Peter Jones of the Department of Human Science kindly made available LASS body data for the project and Dr R.H. Gong of the University of Manchester Institute of Science and Technology (UMIST) kindly supplied measured properties for material samples supplied by Coats Viyella plc. The authors wish to thank the EPSRC, Coats Viyella plc, Professor Jones, Dr Gong and Dr Luo for their assistance, support and co-operation.

International Journal of Clothing Science and Technology, Vol. 8 No. 3, 1996, pp. 59-74. © MCB University Press, 0955-6222

IJCST 8,3

60

not interactively, then with a simulation taking minutes rather than hours to complete. A variety of approaches have been made to simulate the draping of fabric, Breen et al.[4], for example, predict particle behaviour using an energy method, each particle representing a thread crossing. Terzopoulos and Fleischer[5] solve the differential equations for the problem, based on the theory of elasticity, using a finite difference discretization. The finite element method has been used in the prediction of structural instability and post-buckling behaviour for many years[6]. In view of the timestepping algorithms required, practical problems require relatively long computer processing times. The finite element method is, however, finding increasing use in modelling fabric drape. Fabric material properties and the nonlinear techniques employed are the main topics of discussion in cloth drape finite element analyses. The variety of models employed reflects the views of the individual authors. Lloyd[7] discusses the application of the finite element method to modelling of fabric properties and Shanahan et al.[8] discuss the problem of characterizing the behaviour of fabrics as continuous sheet, based on the engineering theory of plates and shells. Finite element models for cloth drape make use of a variety of element types from simple rods to complex shell elements, with standard well-established techniques to handle the problem non-linearity. Behre[9], for example, uses an isotropic thin plate model, Imaoka et al.[10], and Okabe et al.[11] use a variety of elements and techniques for modelling cloth drape and Collier et al.[12] use a shell element in a geometrically non-linear model. Eischen and Kim[13] and Eischen and McDevitt[14] discuss the use of large deformation shell theory, contact surfaces and adaptive meshes in simulating fabric draping, while Grosberg and Swani[15] include non-linear bending in their model. It is accepted that woven material can be adequately modelled, at least for CAD applications where the visual effect is as important as the accuracy of solutions, as a two-dimensional thin sheet[8]. In the present study, in order to reduce computational times to a minimum, the simplest element capable of modelling cloth, the beam element, is used. The element stiffnesses are based on the gross properties of the material and cover areas of fabric several orders of magnitude larger than the individual fibres. The dynamic analysis is carried out using Newmark’s method[16] to model the changes in geometry during the series of time steps as the cloth falls from the initial position into progressive contact with the body form and then finally to rest in the draped position. Finite element analysis The current drape problem is idealized into the problem of a finite element mesh representing the garment pattern falling freely from an initial position into the final configuration governed by its drape around the body form. The model uses simple beam elements with mass and stiffness properties corresponding to a cloth width equivalent to the element pitch. Used in a

suitable mesh this element can represent iso- or orthotropic cloth properties in both the direct and shear senses. The analysis of problems involving large displacements can be achieved by means of the addition of a geometric or initial stress matrix to the elastic stiffness matrix to form the element characteristic matrix. The finite element equations [K ] {U } = {P}

(1)

where [K ] is the assembled stiffness matrix for the problem, {U } the vector of unknown variables and the{P} the vector of forcing terms, therefore become [KE + KG(P)] {U } = {P}

(2)

where KE are the elastic stiffness terms and KG(P), the geometric stiffness terms. Initially, until the mesh lies at an appreciable angle to the horizontal, the garment model has little stiffness in the vertical direction. The problem must therefore be treated as dynamic, at least during this low-stiffness regime. Later, stiffness dominates the model behaviour and dynamic effects become less significant. Newmark’s method is used here to allow a time-stepping approach to the problem, with the advantage that the mesh geometry can be updated at each step. Constant time steps are used, but varying the size of the time step would more closely reflect the real behaviour of the cloth and also save on computational time. Initially the displacements depend mainly on the inertia of the cloth when the time steps need to be small. In the intermediate stages both inertia and stiffness are important, but in the final stage only the cloth stiffness is important and time steps can then be large. The equation of motion for the problem is [M ] ü + [C ] u + [KE + KG (P)] u = {P}

(3)

where [M ] and [C ] are the mass and damping matrices, ü, u˙ and u the nodal accelerations, velocities and displacements, respectively, and {P} is the vector of nodal forces due to gravity. Element stiffness matrices The stiffness matrices are developed below for the element shown in Figure 1 for bending in the x-y plane. The derivation of the element stiffness matrix for bending in the normal, x-z, plane is similar and the addition of the coefficients for bending in these two planes, together with a torsional stiffness term for each node, forms the complete characteristic matrix for the cloth element. Given the nodel displacements and rotations in the x-y plane {u1 v1 θ1 u2 v2 θ2} with the corresponding forces and moments {P1 Q1 M1 P2 Q2 M2} (Figure 2), the general displacements are related to the nodal values by the shape functions, so that

A simple finite element model

61

IJCST 8,3

(1 – ξ ) 6(ξ – ξ 2 )η (–1 + 4ξ – 3ξ 2 ) Lη u  ξ 6(–ξ – ξ 2 )η  =    0 (1 – 3ξ 2 + 2ξ 2 ) (ξ – 2ξ 2 + ξ 3 ) L 0 (3ξ 2 – 2ξ 3 )  v  

62

2ξ – 3ξ 2 ) Lη  (–ξ 2 + ξ 3 ) L 

u   1  v1    θ1    u2  v   2 θ 2 

(4 )

where ξ = x/L and η = y/L Noting that there are similar relationships for the x-z plane, consideration of the strain energy in the beam, U, and application of Castigliano’s Theorem,

∂U ∂∆ i

= Pi

( 5)

where ∆i are the displacements and Pi the corresponding forces, leads to the elastic and geometric stiffness matrices for the element

y β1

v1

x

z

β2

v2 α2

u1 Figure 1. Simple beam element – displacements and rotations

α1

w1

θ1

w2

u2

L

Q1 Figure 2. Simple beam element – forces and moments

θ2

Q2

P1

P2 M1

M2

 AL2   I   0  0   0    0  EI  0 [ KE ] = 2  L3  – AL  I   0  0   0    0   0

0

0

0

0

0

12

0

0

0

6L

0

12

–6 L

0

0

0 JL2

0

2I ( 1 + v 2 )

2

–

AL2

0

0

I 0

–12

0

0

0

0 –12

0

0

0

0

0 –6 L

6L

0

0

0

0

–6 L

0

4L

0

0

6L

0

0

0

4 L2

0

0

0

0

0

0 AL2

–12 0

0 –12

0

0

0 6L

–6 L 0

–

0 0 JL2

0 0

0 0  6 0  5  0 0    0 0   0 0   L 0 – F 10 [ KG ] =  0 L 0 0 – 6  5   0 0   0 0   0 0   L 0  10

12 0

0 12

0 0 JL2

0

0

0

0

0

0 2 L2

0 0

0 –6 L

6L 0

2L 0

0

0

0

0

0

0

0 L

0 0

0 6 – 5

0

0

10 6

0

5 0

L

0

10 2 L2

0

0

2I ( 1 + v 2 )

0

–6 L 0

2

0 0 JL2

0

0 6L

0

0

2I ( 1 + v 2 ) 0 0

0

0

0

0

0

0

–

6

L

5

10

0

15 L 10 0

2L

0

0

0

0

0

0

6

0

5 0

0

0

0

0

L

15 0 L – 10 0

0 – 0 0

L 10 0 6

0

0

0

0

0

0

0

0

0

0

5 0

0

10 – L2

L

0

10 0

6

0

5 0

0

0

0

L 10

2 L2

0

15 – L2

0

0

0

30 0

– L2 30

2 L2

30 –

0

15 0

0

30

0

–

– L2

2

0

 0    0 6L  –6 L 0   0 0    2 L2 0   0 2 L2  (6 )  0 0    0 –6 L  6L 0   0 0    2 4L 0   0 4 L2  0

0

I 0 0

2I ( 1 + v 2 )

0

0

L

0

10 – L2 30

0 –

L 10

0

2 L2 15

0

0

0   L  10   0     0    0   – L2   30  (7 ) 0   –L   10   0    0    0    2 L2  15 

where E and ν are the Young’s modulus and Poisson’s ratio for the material, I and J are the beam second and polar moments of area and F is the axial force on the beam. The second matrix reflects the effect of the axial force on the stiffness of the element. A tensile force will increase the stiffness while a compressive force reduces this. The condition where the sum of the elastic and

A simple finite element model

63

IJCST 8,3

64

geometric stillnesses becomes small due to the application of a compressive axial force leads to folding of the material. The length of the element, L, varies throughout the analysis. The orientation of the element at the end of each time step is updated using a transformation matrix, so that the element stiffness matrix in local co-ordinates is transformed into the current global co-ordinates by the equation [ K ′] = [T ]T [ K ] [T ] (8 ) where [K' ] is the element stiffness matrix in global co-ordinates [K], the element stiffness matrix in local co-ordinates and [T], the transformation matrix, based on trigonometric functions of the angles between the beam axis and the global co-ordinates. cos( x ' x ) = cos α = l x l ly lz   x  cos( y' x ) = cos β = mx , etc. and [T] =  mx m y m z  (9)    nx n y n z    cos( z ' x ) = cos γ = nx Dynamic analysis Writing the equation of motion, equation (3), as  ∂ 2u n + 1   ∂ 2u n  ∂u n + 1 ∂u n M +C + Ku n + 1 θ +  M +C + Ku n  (1 − θ )     ∂t ∂t ∂t 2 ∂t 2     n +1 = θP + (1 – θ )P n where θ is a coefficient, usually taken as 0.5. Application of Newmark’s method [ 16] leads to the recurrence equation

y' y x

β α γ Figure 3. Local and global co-ordinates

z'

z x'

(10)

 1   1   M + C + θ∆tK u n + 1 =  M + C + (1 – θ )∆tK u n  θ∆t  θ∆t  n ∂u 1 + M + θ ∆t P n + 1 + (1 – θ ) ∆t P n . θ ∂t

A simple finite element model (11)

Interaction with body model In order to model the cloth drape realistically a model of a human form obtained using the Loughborough Anthropometric Shadow Scanner system (LASS)[17] is digitized and introduced into the model as a set of geometric coordinates. Interaction of the cloth with the body form is achieved through a transformation into a cylinder. Interaction issues, e.g. collision determination, can then be addressed in the transformed space where the calculations are trivial. The major part of the computation is thus transferred to the evaluation of the transformation function – which must therefore be as simple as possible and efficiently evaluated[18]. The LASS system is able to produce sets of measured data slices at a number of heights from a human subject. Figure 4 shows a quadrilateral mesh constructed by joining identically numbered points on adjacent data slices vertically. As the fabric drapes on the body model it is necessary to determine the point at which contact is made. Checks for a collision detection of material elements with the body model are made following each time step of the draping simulation. If an element of cloth enters the body volume then a collision response is invoked to move it out again. The mapping method simplifies the response calculation too, by performing it in the space of the cylinder where surface contact points are easier to determine., These calculations require repeated use of the cylinder transformation function F and its inverse (Figure 5). A convenient way to construct the mapping function F is by transfinite interpolation. A suitable mapping, in polar co-ordinates, may be derived in the form    z – z   z – z  r r 0 1 F ( r ,θ , z ) =  ,θ , z 1 +  , θ , z 0  ( 12 )        z – z  A θ + B  z – z  A θ + B    0  1 0  1 1 1  0 0 where A 0 , A 1 , B 0 and B 1 are constants determined from the body sector dimensions. Following collision detection, a geometric technique is applied to estimate the point at which the node of an element makes initial contact with the body model. A reduced time step interval may then be computed and the simulation rerun from the point prior to the collision detection. This process may be repeated until contact rather than penetration of cloth element with the body

65

IJCST 8,3

66

Figure 4. Meshed body model

z1

z1

φ1

φ1

Transformation F

F(p)

z0

Figure 5. Topological mapping on to a cylinder sector

φ0

Test point p

Irregular convex body sector

z0

φ0

Corresponding skewed cylinder sector and transformed test point

repeated until contact rather than penetration of cloth element with the body model occurs. Results The finite element program was run on a Hewlett-Packard 700 series computer, while the graphical output was produced on a Silicon Graphics Indy system[19]. The model shown in Plates 1-4 consisted of 700 elements and took approximately 1 hour 45 minutes to model 100 time steps. More complex models of 1000 elements took in excess of four hours to run. The material properties used are listed in Table I and are measured values taken from material samples of 100 per cent cotton. A variety of mesh densities were used to subjectively determine the optimum density to produce a realistic drape appearance. The density used in the model Plates 1-5 represents the lower limit for an acceptable appearance. Figure 6 shows a coarse finite element mesh representing the cloth pattern for a simple skirt. Plates 1-3 show the various positions of the simple skirt model as it falls freely under gravity and then drapes around the body form. In order to Mass distribution

2.58.10–1 kg/m2

Thickness

7.81.10–4 m

Flexural rigidity /m width (warp)

1.99.10–5 Nm2/m

Flexural rigidity /m width (weft)

1.59.10–5 Nm2/m

Source: [20]

A simple finite element model

67

Table I. Material properties

y x

Figure 6. Finite element mesh

IJCST 8,3

68

Plate 1. Initial position of garment

Plate 2a. Intermediate position of garment

A simple finite element model

69

Plate 2b. Intermediate position of garment

Plate 3. Final (draped) position of garment

IJCST 8,3

70

Plate 4. Simulation of bodyhugging garment

Plate 5. Final position of sheet

A simple finite element model

71

Plate 6. Photograph of sheet

demonstrate the versatility of the finite element code, it was also used to investigate the ability of the model to represent the clinging of a garment as it is stretched over the body form (Plate 4) and the draping of a piece of material over the corner of a table. Plate 5 shows the material draped over the corner of a table and Plate 6 is a photograph of the real situation. The figures are based on straight lines joining mesh nodes and uses only the nodal co-ordinates. The finite element solution gives the curvature of the beam elements in addition to the nodal coordinates and inclusion of this together with curve-fitting the nodal positions would enhance the images considerably. Discussion The results show that the current model produces adequately realistic images of garment drape and the appearance of the garment shown in Plates 1-4 was found to be acceptable to an experienced fashion designer for initial design purposes. This would probably be unacceptable for marketing a garment, however, where presentation to the customer is a very important factor. The immediate concern to the fashion industry, however, would be the length of time taken to analyse the drape of a garment and hence produce the visual display for the designer. The objective of the present study is to demonstrate the feasibility of modelling drape, within the constraint of using a simple finite element model to minimize computational times. Since the appearance of the draped garment, rather than the numerical accuracy of the results is the criterion here, comparison of measured drape with computed values was not attempted. It

IJCST 8,3

72

might be argued that, in any case, refinement of the finite element mesh would be expected to be the main factor in achieving numerical accuracy and, presumably, visually realistic models. This argument neglects the possibility that materials other than the simple cotton considered here might exhibit subtle visual effects not obtainable with a simple beam element mesh. The beam element model, at best, can only physically represent an “open net” material. It may well be fortuitous that, for cotton, the results are visually acceptable. Other types of element have been used to model cloth [9-12], particularly shell elements which can exhibit shear, bending and twisting more accurately than a mesh of simple beams. The penalty of increased computational times, over those already incurred as a result of using the current solution algorithm, however, precludes the use of elements more sophisticated than the simple beam. There is therefore an urgent requirement to test the current model against real drape problems in a range of materials sufficiently comprehensive to cover all those currently used in the fashion industry. If it can be shown that the simple beam element is adequate to model these materials then there is considerable computational advantage in using this and there would be no point in using a more sophisticated element. Currently the time taken for a complete solution at the current level of mesh refinement, although acceptable for an engineering problem, would be excessive for the industry. Any increase in mesh refinement required for improving the appearance of the draped garment and the requirement for modelling more complex garments would make the time taken to produce the display impracticable. There is some scope, however, for improving the solution algorithm to reduce the computational time taken. For example, the timestepping method adopted here, Newmark’s method, is implicit in that a solution of all the finite element equations is required at each step. The adoption of an explicit scheme, where the equations are uncoupled and therefore solved individually promises much shorter solution times, but with the disadvantage that time step lengths become critical for acceptable solutions. Optimizing the size of the time step to ensure the greatest accuracy for each aspect of the simulation is feasible and would also save computational effort. It is envisaged that the model will ultimately be developed for the simulation of cloth drape in situations where the underlying body form is moving, as in the fashion show catwalk situation. This will only be feasible if reductions in computing time can be achieved. In order to simulate this situation realistically the response of the garment due to the model’s movements on the catwalk would also need to be modelled. These movements are partly dynamic and partly aerodynamic. Work has already been carried out into the effect of moving a cloth model through the air[2,21]. If garment aerodynamic and friction data can be readily obtained, these could be incorporated into the model as axial and transverse forces on the beam element. Enhancements such as these, along with the ability to model the release of contacting nodes when necessary, would

provide a system capable of modelling comprehensively the real behaviour of a garment. Conclusions The feasibility of using the simple beam element in a non-linear, dynamic finite element analysis to model garment drape sufficiently realistically for the fashion designer’s needs has been demonstrated. In view of the constraints on computational times, the use of the more complex shell elements is not envisaged. The results confirm the validity of using Newmark’s time stepping approach and the interaction algorithm. Considerable improvements are required in computing time, however, to permit enhancements to be made to the model appearance and to include moving body forms, cloth friction and aerodynamic forces. References 1. Gray, S., “The computerised catwalk”, Textile Horizons International, June 1993, pp. 32-6. 2. Magnenat-Thalmann, N. and Thalmann, D., “Complex models for animating synthetic actors”, IEEE Computer Graphics and Applications, Vol. 11 No. 5, September 1991, pp. 32-44. 3. Carignan, M., Yang, Y., Magnenat-Thalmann, N. and Thalmann, D., “Dressing animated synthetic actors with complex deformable clothes”, Computer Graphics, Proceedings of SIGGRAPH, Vol. 26 No. 2, 1992, pp. 99-104. 4. Breen, D.E., House, D.H. and Wozny, M.J., “A particle-based model for simulating the draping behaviour of woven cloth”, Textile Research Journal, Vol. 64 No. 11, November 1994, pp. 663-85. 5. Terzopoulos, D. and Fleischer, K., “Deformable models”, Visual Computer, Vol. 4, 1988, pp. 306-31. 6. Przemieniecki, J.S., Theory of Matrix Structural Analysis, McGraw-Hill, New York, NY, 1968. 7. Lloyd, D.W., “Complex fabric deformations, buckling and drape”, Mechanics of Flexible Fibre Assemblies, NATO (ASI), Sijthoff and Noordhof, Alphen aan den Rijn, 1980, p. 311. 8. Shanahan, W.J., Lloyd, D.W. and Hearle, J.W.S., “Characterising the elastic behaviour of textile fabrics in complex deformations”, Textile Research Journal, Vol. 48, 1978, pp. 496-505. 9. Behre, B., “Mechanical properties of textile fabrics”, Textile Research Journal, Vol. 31, 1961, pp. 87-93. 10. Imaoka, H., Okabe, H. and Akini, H., “Structure analysis of the draped material”, Bulletin of Research Institute for Polymers and Textiles, 1984-89, pp. 73-80. 11. Okabe, H., Imaoka, H., Tomiha, T. and Niwaya, H., “Three-dimensional apparel CAD system”, Computer Graphics, Proceedings of SIGGRAPH, Vol. 26 No. 2, 1992, pp. 105-10. 12. Collier, J.R., Collier, B.J., O’Toole, G. and Sargand, S.M., “Drape prediction by means of finite element analysis”, Journal of the Textile Institute, Vol. 81 No. 1, 1991, pp. 96-107. 13. Eischen, J.W. and Kim, J.H., “Fabric mechanics analysis using large deformation shell theory”, Proceedings of the 3rd Annual Academic Research Conference, Atlanta, GA, February 1992. 14. Eischen, J.W. and McDevitt, T.W., “Simulation of fabric drapings and manipulation with arbitrary contact surfaces and adaptive meshing”, Proceedings of 4th Annual Academic Apparel Research Conference, Raleigh, NC, February 1993.

A simple finite element model

73

IJCST 8,3

74

15. Grosberg, P. and Swani, N.M., “The mechanical properties of woven fabrics, part III: the buckling of woven fabrics”, Textile Research Journal, Vol. 36 No. 4, 1966, pp. 332-8. 16. Newmark, N.M., “A method for computation of structural dynamics”, Journal of the Engineering Mechanical Division, ASCE, Vol. 85 No. EM3, 1959, pp. 67-94. 17. Jones, P.R.M., West, G.M., Harris, D.H. and Read, J.B., “The Loughborough anthropometric shadow scanner”, Endeavour, Vol. 13 No. 4, 1989, pp. 162-8. 18. Bez, H.E., Bricis, A.M. and Ascough, J., “A collision detection method with applications in CAD systems for the apparel industry”, Computer Aided Design (in press). 19. Bricis, A.M., “Three dimensional simulation of cloth drape”, PhD thesis, Loughborough University of Technology, 1995. 20. Gong, R.H., Private communication, 1990. 21. Ling, L., Damodaran, M. and Gay, R.K.L., “A quasi-steady force motion for animating cloth motion”, IFIP Transactions B-Applications in Technology, Vol. 9, 1993, pp. 357-63.

Towards simulating cloth dynamics using interacting particles Donald H. House and Richard W. DeVaul

Towards simulating cloth dynamics 75

Visualization Laboratory, Texas A&M University, Texas, USA and

David E. Breen European Computer-Industry Research Centre, Munich, Germany Introduction A number of techniques have been developed for predicting the drape of woven cloth in its final equilibrium configuration, producing results that range from the technical to the artistic. These draping models have followed two main directions. Historically, there have been a number of continuum models that treat cloth as a more-or-less homogeneous elastic medium, with draping solutions often calculated via finite-element techniques[1-4]. More recently, a particle model[5] was developed that attempts to directly capture the underlying fine-grained mechanical structure of cloth in a set of energy equations defined at yarn crossings. Plate 1 was produced as a test-case for this model. Draping solutions from this model are calculated via an ensemble energy-minimization technique, employing modified gradient following. Both the continuum and particle approaches share the engineer’s desire that they predict actual behaviour of real materials. For example Plate 2, reproduced from [6], shows a comparison of actual versus simulated drape of two different types of fabric, computed via the particle model. It is also generally demanded that these models accurately determine such classical engineering quantities as stress and strain in the material or in its constituent components[7,8]. A number of other techniques have been developed for simulating the dynamics of cloth[9]. These models have tended to differ from the draping models in several ways. First, they have been motivated by the desire to portray the behaviour of cloth in motion, often for purposes of animation and entertainment. Despite the engineer’s desire for accuracy, these models were developed with the notion that reasonable approximate behaviour is fine, as long as the model can be calculated quickly. Most of them are based on using elastic meshes, producing results that sometimes appear too stretchy or rubbery to someone who has made a careful study of cloth behaviour. Also, these models are not capable of the complex buckles and folds of draped cloth. Nevertheless, they do produce effective animated sequences, and have been Figure 1 was produced by Gene Greger and David Breen. This work was partially supported by DLA contract No. DLA900-87-D-0016, NSF grant No. CDR-8818826, and by the Visualization Laboratory at Texas A&M University.

International Journal of Clothing Science and Technology, Vol. 8 No. 3, 1996, pp. 75-94. © MCB University Press, 0955-6222

IJCST 8,3

76

Plate 1. Draping cloth objects. The complex draping configurations of the cloths over the chair and table were obtained using the particle cloth model Reprinted with permission from [6]

Plate 2. Actual (left) vs simulated (right) cotton and wool drapes. Energy functions in the particle cloth model can be tuned to reproduce the draping behaviour of specific cloth types

perfected to the point where they have been applied to clothing for animated Towards characters[10]. simulating cloth In this article we preview attempts that are currently being made to bridge dynamics the gap between the models that produce accurate draping behaviour and the models that seek to reproduce dynamic behaviour. We begin by giving a brief synopsis of our particle-based draping model. This is followed by a description 77 of how we have used constraint methods to turn this model into one that purports to describe both cloth dynamics and draped equilibria. Finally, we outline our experimental methodology for calculating the constrained dynamics of this new model in a way that is computationaly tractable, and may make the model of real use in engineering, design, and animation. A particle-based draping model Since our particle-based approach to modelling drape does not follow traditional continuum methods, it may be unfamiliar to readers. To understand the extensions to the model that are proposed in this paper, it will first be necessary to understand the underlying methodology. Therefore, we include the following brief summary of the structure of this model. For further information, we refer the reader to the extensive particle system bibliography found in [11], to the detailed review of cloth modelling work found in [12], and to other papers on the particle-based drape model[5,13]. We model cloth as a collection of particles that conceptually represents the crossing points of warp and weft yarns in a plain weave. Important mechanical interactions that determine the behaviour of woven fabric are discretized and lumped at these crossing points. We represent the various yarn-level structural constraints with energy functions that capture simple geometric relationships between particles. These energy functions account for the four basic mechanical interactions of yarn collision, yarn stretching, out-of-plane bending, and trellising that are shown graphically in Figure 1. The potential energy for i is given by U i = U repel i + U stretch i + U bend i + U trellis i + U grav i . (1) In this equation, Urepeli is an artificial energy of repulsion, that effectively keeps every other particle at a minimum distance, providing some measure of yarn collision detection, helping prevent self intersection of the cloth. U stretchi captures energy of tensile strain between each particle and its four-connected neighbours. Ubendi is the energy due to yarns bending out of the local plane of the cloth, and Utrellisi is the energy due to bending around a yarn crossing in the plane. Ugravi is the potential energy due to gravity. Repelling and stretching are functions only of interparticle distance r ij (Figure 1(1a), Collision and stretching), whereas bending and trellising are functions of various angular relationships between segments joining particles (Figures 1(2a), Bending, and 1(3a), Trellising). Ugravi is proportional to the height of the particle. Trellising occurs when yarns are held fast at a crossing and bend to create an “S-curve” in

IJCST 8,3

Rij + Sij i

rij

θi1

j

σ (a) (b) (1) Collision and stretching

78

rij

θi2

θi3

Bij

(a)

(b)

π Θ ij

(2) Bending

φ ij Tij

i Figure 1. Cloth model energy functions. Relationship between particle displacements and the stretching, bending and trellising energy functions in the particle cloth model

i

π /2 φ ij

(a)

(b) (3) Trellising

Note: Reprinted with permission from [6]

the local plane of the cloth, and is related to shearing in a continuous sheet of material. We assume that the yarns in the fabric do not stretch significantly when a cloth is simply draping under its own weight. Therefore, the combined stretching and repelling energy function R + S shown in Figure 1, Collision and stretching, b, is not empirical, and is meant only to provide collision prevention and a steep energy well that acts to tightly constrain each particle to a nominal distance σ from each of its 4-connected neighbours. We have had good success with the functions C [(σ – r )5 / r ]  ij ij R (rij ) =  0 0

rij ≤ σ rij > σ ,

(2 )

and 0 rij ≤ σ  S (rij ) =  5 C0 [(( rij – σ ) / σ ) ] rij > σ ,

(3 )

where C0 is a scale parameter. The function Urepeli prevents collision and self intersection, so it is calculated by summing over all particles, as given by U repel i =

∑ R (rij ).

j ≠i

(4 )

In practice, our simulation algorithm maintains a spatial enumeration, so that Towards the summation need only be done over near neighbours. An energy well is simulating cloth produced by directly coupling each particle with the stretching function S only dynamics to its 4-connected neighbours, as given by (5 ) U stretch i = ∑ S (rij ), j ∈N i

where Ni is the set of particle i’s four-connected neighbours. The particle energy due to gravity is simply defined as U grav i = mi ghi ,

79 (6 )

where mi and hi are the mass and height of particle i, and g is gravitational acceleration. The mass is of the small patch of cloth represented by the particle. In contrast to stretching, we assume that bending and trellising are the significant contributors to the overall drape of cloth, when it is simply draping under its own weight. We define a unit of the bending energy B shown in Figure 1, Bending, b, as a function of the angle formed by three particles along a weft or warp “thread line”, as shown in Figure 1, Bending, a. The complete bending energy is U bend i =

∑

j ∈M i

B (θ ij ),

(7 )

where Mi is the set of six angles θij formed by the segments connecting particle i and its eight nearest horizontal and vertical neighbours. This definition is used so that the derivative of bending energy reflects the total change in bending energy due to the change in position of particle i. The redundancy in this formulation is taken care of later by proper scaling. The phenomenon of trellising is diagrammed in Figure 1, Trellising, a, and a corresponding unit of the trellising energy T is shown in Figure 1, Trellising, b. Two segments are formed by connecting the two pairs of neighbouring particles surrounding a central particle. An equilibrium crossing angle of 90º is assumed, but one could model slippage by allowing this angle to change, over the course of a simulation, as a function of load. The trellis angle φ is then defined as the angle formed as one of the line segments moves away from this equilibrium. The complete function for our energy of trellising is U trellis i =

∑

j ∈K i

T (φ ij ),

(8 )

where Ki is the set of four trellising angles φij formed around the four-connected neighbours of particle i. As with bending, this redundant formulation was chosen so that change in total energy with change in the particle’s position is completely accounted for locally. The simulation of the model is implemented as a three-phase process operating over a series of small discrete time steps[14]. The first phase for a single time step calculates the dynamics of each particle as if it were falling

IJCST 8,3

80

freely under gravity in a viscous medium, and accounts for collisions between particles and surrounding geometry. The second phase performs an energyminimization to enforce interparticle constraints. A stochastic element of the energy minimization algorithm serves both to avoid local minima and to perturb the particle grid, producing a more natural asymmetric final configuration. The third phase corrects the velocity of each particle to account for particle motion during the second phase. The energy functions indicated in the curves in Figure 1 are similar in shape to those that we first used to verify the theoretical model. These initial functions were simply convenient ones that we knew would smoothly interpolate reasonable boundary conditions. In order to tie the model directly to the draping behaviour of actual cloth, we developed a method for deriving the model’s energy equations from empirical mechanical data produced by the Kawabata evaluation system[15]. This allowed us to calculate drapes such as those shown in Plate 2, that begin to accurately predict the drape characteristics of distinct fabric types. This work is detailed in [6,16]. Our strategy was to use the Kawabata bending and shear plots, such as those for 100 per cent cotton and 100 per cent wool shown in Figure 2, to derive bending and trellising energy functions that were accurate for a particular type of cloth. The dynamic model On the surface, the conversion of the particle draping model to a dynamic model appears straightforward – one simply needs to apply the chain rule appropriately to differentiate the energy functions with respect to each of the three co-ordinate directions, to produce a set of non-linear spring forces that are functions of particle displacements. However, this approach has serious computational tractability problems. Owing to the very great difference between the stiffness of the yarns in the longitudinal direction compared with their stiffness when bending in or out of the plane of the cloth, the resulting differential equations are numerically very poorly formed – they are quite stiff. Compromising on longitudinal stiffness, of course, would produce a cloth model with undue stretching – making it more like a rubber sheet than cloth. This is precisely the problem that many of the earlier continuum dynamic models of cloth had. To avoid this problem, we are conducting experiments with a model that represents the distances between adjacent particles (i.e. yarn crossings) by constraints that keep the interparticle distances fixed. Rather than using springs, as depicted in Figure 3a, to produce forces to correct constraint violations, constraint forces are applied directly and immediately, as depicted in Figure 3b, to counteract both external and internal forces tending to violate the constraints. Since constraint forces are calculated to counteract other forces, rather than to correct displacement errors, their effect is instantaneously distributed throughout the entire constrained system.

0.4

–3

–2

Warp

0.3

Towards simulating cloth dynamics

Weft

10

0.2 Weft

0.1

–3 0

15

Shear

Fs, gf/cm

M, gf-cm/cm

Bending

1

–0.1

2 3 K, 1/cm

5 Warp

–8

–6

–4

–2 0

2

–5

–0.2

81

4 6 8 Φ, degrees

–10

–0.3 –15

–0.4 (a) 100 per cent cotton 0.4 0.3 0.2

Weft

–2

–1 –0.1

10 Warp

5

0.1 Warp

0 –3

15

Shear Fs, gf/cm

M, gf-cm/cm

Bending

1

2 3 K, 1/cm

Weft –8

–6

–4

0

–2 –5

2

4 6 8 Φ, degrees

–0.2 –10

–0.3

–15

–0.4 (b) 100 per cent wool Note: Reprinted with permission from [6]

Constrained dynamics In any dynamic simulation, the reaction of the state of the system to applied forces and torques is described by a set of differential equations involving the current state, and the applied forces and torques. In a particle-system simulation things are somewhat simplified, since there can be no torques. However, in a constrained particle-system, in addition to equations describing the dynamics of the system, a set of algebraic equations specifying constraint conditions is also specified. These provide conditions that must always be met by the system. For example, if we have two particles with positions xo and xl ,

Figure 2. Kawabata bending and shear plots. Plots from the Kawabata testing system, plotting applied load on the vertical axis versus geometric deformation on the horizontal axis

IJCST 8,3

82

and the configuration of the system requires that these particles maintain a fixed distance σ from each other, the constraint equation C0(x0 , x1) = || x1 – x0 ||2 – σ2, might be included. As long as C0 = 0 the distance constraint between x0 and x1 is satisfied. A computational scheme for specifying and simulating such a constrained dynamical system is given in tutorial form by Witkin in [17]. A more in-depth discussion, with applications, is given in [18]. We briefly summarize the approach here. A typical unconstrained dynamical particle system can be represented by the equation Mx ¨ = FE + FI.

(9)

relating accelerations in the system to its diagonal mass matrix M, externally applied forces FE, and internally generated forces FI. The internally generated forces are given by FI = F(x, x), ˙

(10)

where F is a function capturing the system’s (possibly time varying) internal dynamics.

A

A F applied

A

F react

A

Fc

F react

B

F applied

B

B

Fc

B

Fc C

C

C

Fc

C

Fc D

D

Iteration 0 (a) Spring chain

Figure 3. Chains modelled numerically by spring forces and constraint forces

Iteration 1

D

Fc

Iteration 0

D Iteration 1

(b) Constraint chain

(a) A force applied to one end of a numerically modelled dynamic chain connected by springs is transmitted via displacements over several time steps. In the first iteration after a force is applied to A, no restoring force exists to keep distance A-B from increasing. On the next iteration, the length change produces a restoring force which is applied to particles A and B and which also results in length B-C increasing, etc.; (b) In the constraint chain, a force applied to particle A instantaneously produces constraint forces that are transmitted along the entire chain, maintaining each length constraint exactly. No additional energy is added because constraint forces can do no work

A system with dynamic constraints is one in which certain relationships Towards between elements of the state must be maintained, although it may be simulating cloth inconvenient or inefficient to include any explicit mechanism in the dynamics of dynamics the system that assures this. Examples of such a system might be a cart constrained to ride on a track, or a bouncing ball constrained never to pass through the floor. 83 One way to maintain such constraints is to add a third set of forces FC to the system, whose sole purpose is to guarantee that the constraints are maintained. This yields an equation of the form Mx ¨ = FA + FI+ FC.

(11)

On the surface it appears that solving equation (11) numerically is no different from solving equation (9). However, the presence of the constraint force term implies the existence of accelerations based on an algebraic relationship between applied forces and current state that is absent in equation (9). It is now necessary to determine an appropriate set of constraint forces FC at each time step. Suppose that we represent the constraints by a set of constraint functions C(x) with the stipulation that C = 0. Assume that the initial state of the system is such that (1) all of the constraints are met, and (2) that none of the constraint · equations are changing (C = 0). Then, we can ensure that all constraints continue to be met if we can guarantee that constraint accelerations are held to zero over the entire course of the simulation, or ˙˙ = 0. C (12) If J is the jacobian matrix J = ∂C/∂x, then by the chain rule ˙˙ = J˙x˙ + Jx ˙˙ . C

(13)

But, by equation (11) ˙˙ = M –1 ( FA + FI + FC ). x Thus, by equations (13) and (12) we have JM –1F = – J˙x˙ – J M –1 ( F + F ).

(14) . Since the constraints must never be violated, system velocity x must have no component in the direction of the gradient of the constraints, thus Jx˙ = 0. (15) C

A

I

Since by the principle of virtual work it is impossible that the constraint forces should do any work, we must have (16) FC ⋅ x˙ = 0. These two conditions can only be satisfied when the constraint forces are scalar multiples of the columns of the jacobian, i.e. each constraint force is parallel to the gradient of its corresponding constraint function. Thus we have

IJCST 8,3

84

FC = J T λ ,

(17)

where λ is a vector of Lagrange multipliers. This result together with Equation (14) gives JM –1 J T λ = – Jx⋅ – JM –1 ( FA + FI ).

(18)

The matrix JM –1JT is a square matrix with number of rows equal to the number of constraints in the system. Typically, this matrix is sparse. Often it is illconditioned, but solutions for λ in equation (18) are usually easy to find using the bi-conjugate gradient approach[19]. Once the vector λ is determined, equation (17) gives the constraint forces directly. A caveat has to be introduced here about the constraint equations. Each row of the jacobian matrix J is the gradient of one of the constraint functions, and equation (18) is intended to keep all of the constraints satisfied. Therefore, it is very important that constraint functions be chosen whose gradients are nonzero when the constraints are satisfied. In more intuitive terms, the gradients of the constraint functions determine the directions and magnitudes of the constraint forces that need to be applied. If this gradient goes to zero when the constraint is met, it is impossible to determine a force to keep the constraint met. One final adjustment to equation (18) is necessary for good practical performance. The algorithm works by keeping the constraint acceleration at zero, but there is no direct control on the constraint values themselves. Even under the best conditions, numerical drift will gradually cause the constraints to become violated. Worse, there are certain conditions for which there may be no solution to equation (18). In this case, the bi-conjugate gradient approach yields a solution with minimum mean-squared error. This behaviour is desirable, but does lead to constraint violations which the algorithm never corrects. To provide a continuous correction for small constraint violations, Witkin[17] recommends that small corrections to the λ vector be added proportional to the constraint and constraint velocity vectors. This yields the final result ˙. (19) JM –1 J T λ = – J˙x˙ – JM –1 ( F + F ) – k C – k C A

I

s

d

Appropriate values for the scaling constants k s and k d must be chosen experimentally. The problem with the constrained dynamics approach in the cloth simulation application is speed. If L is the number of constraints, the underlying constrained dynamics algorithm requires solving a sparse system of L linear equations with L unknowns. If the number of states and the number of constraints are of the same order, then solving this linear system using the biconjugate gradient approach is an O(L 2) operation[18,20]. Figure 4 shows clearly that the number of fixed length constraints in an N × M cloth mesh is

Towards simulating cloth dynamics

N columns N=3 1

2

3 1

3

85 2

M – 1 constraints per column M–1=3

M rows M=4

2 3 1 4 1 2 N – 1 constraints per row N–1=2

2NM – N – M, or approximately twice the number of cloth particles. For even a relatively coarse mesh, such as the 51 × 51 mesh used in [6,16] this results in thousands of fixed length constraints that must be maintained. While systems on the order of 50 constraints can be run at near-interactive speeds[21] on a desktop workstation, a system of 5,000 constraints would take proportionally 10,000 times as long to compute, the difference between one-tenth of a second per iteration and 17 minutes. Grid subdivision A classic approach to algorithm speed-up is the divide and conquer method. To improve computation speed it often makes sense to try to divide the problem up into a set of smaller problems. For example, if a problem has complexity O(N 2 ), and it is divided into two equal size parts, each part will take about a quarter of the time of the original problem, so that the total solution will take about a half of the time. This, of course, assumes that there is no computational overhead in “knitting” the two sub-part solutions back together. Thus, a simple approach to reducing computational overhead in the constrained cloth model would be to divide the constraint mesh into sub-meshes which are solved separately. This idea is diagrammed in Figure 5. It has the advantage of reducing the larger problem into (in this case) four smaller problems, labelled A, B, C and D in the figure, each of which is one-fourth the size of the original and requires one-sixteenth the computation time. If the computations in the system could be fully divided up in this way, the resulting computation would take one-quarter of the computation required to solve the system as a whole.

Figure 4. Interparticle length constraints vs number of particles. There are M (N – 1) constraints in M rows of N particles. Likewise, there are N (M – 1) constraints in the N columns, for a total of 2N M – N – M constraints

IJCST 8,3

86

Figure 5. Subdividing a grid of particles into quadrants. A rectangular mesh divided into smaller rectangular quadrants designated A, B, C and D. These quadrants correspond to four separate constraint groups

Figure 6. Simple subdivision isolates force effects to quadrants. A force applied in quadrant A is handled appropriately within the quadrant, but results in length constraint violations at the boundaries with B and C. This stretching is illustrated in the difference in length between L1, the original length of a boundary constraint, and L2, the new stretched length

However, it is not this simple. The price that would have to be paid for subdividing the problem in this way would be that forces, which were previously instantaneously transmitted through the entire system, would now be instantaneously transmitted only through the subsystems. Figure 6 shows how this would affect the computation. A constraint force applied somewhere in quadrant A is handled correctly inside that quadrant, but is only communicated to quadrants B and C through displacement. If this type of stretching at the boundaries between subsystems were acceptable, then the problem would be solved. However, this is not the case with cloth simulation, where the resulting stretching would produce unwanted and unrealistic artefacts. Worse, this stretching is more than a simple problem of aesthetics or accuracy. The constraint force which displaces the particles on the A-B quadrant boundary makes perfect sense from the point of view of quadrant A,

A

B

C

D

L2 L1 F

A

B

C

D

but to quadrant B this is a “stealth force” which is neither an applied force nor Towards an internal force and it does not figure into B’s constraint force calculation. The simulating cloth result is a displacement, which is correct from A’s point of view, but not a force dynamics transmission. On the next simulation time step, B will find that the A-B boundary constraints have been mysteriously violated. What happens next depends on the weights ks and kd that were chosen for the 87 “spring and damper” constraint correction terms added to equation (19) to absorb numerical drift. If this term is not stiff enough, correction will be inadequate, leading to increasing constraint violations and eventual linearsolver failure. If this term is stiff enough to apply a meaningful restorative force, this becomes a significant “stealth force” from quadrant A’s point of view, shifting the problem back on to quadrant A. Often this “stealth force” tug-ofwar resolves itself by the kind of “buckling” at the boundary of the quadrants that is shown in Figure 7.

F

F

F

F

F A

B

C

D

A hierarchical approach What is needed is an improvement over the original simple approach that retains the computational speedup resulting from subdividing the problem, but which also integrates the solutions to the subproblems in a way that ensures an accurate solution to the overall problem. One way of accomplishing this would be to somehow translate a constraint subsystem into something very much like a single constraint, which could then be plugged into a constraint force calculation at a higher level. If we partition the vector C of N constraint functions into subvectors Cs, each with Ns constraint functions, then a single group constraint function CΣ = || Cs ||2

Figure 7. Effect of uniform force along one edge. A force applied uniformly to the left side of the mesh is handled appropriately in quadrants A and C but is not transmitted to quadrants B and D. The resulting “tug of war” between boundary constraints is resolved by pushing the boundary particles up and out of the plane of the mesh

IJCST 8,3

could be defined as the squared-magnitude of each of these subvectors. CΣ would be zero if and only if all of the constraints are satisfied, which is one of the necessary properties of a constraint function. Unfortunately, since ∇CΣ = 2 || Cs || ∇Cs

88

this formulation results in a zero gradient when all constraints are satisfied. We have previously noted that this is an undesirable property for a constraint function. To solve the zero gradient problem, the grouped constraint function could be reformulated as CΣ =

Ns

∑|C si |,

( 20 )

i =1

the sum of the absolute values of each constraint in the group, which can be defined to have the gradient ∇C Σ =

∇C ,  si

Csi ≥ 0

i =1  – ∇C s i

, C si < 0.

Ns

∑

This gradient has the property of being non-zero everywhere, though it is discontinuous at zero. The advantage of this formulation is that a single linear equation replaces a system of Ns linear equations. The disadvantage of this approach is a loss of dimensionality. Whenever we replace a group of constraints by a single constraint Cs, we calculate only a single lagrange multiplier λs which scales the constraint forces for the entire constraint group, in contrast to the Ns lagrange multipliers which independently scaled the gradients for each individual constraint. Under many circumstances this formulation will either fail to maintain all constraints or it will not be possible to calculate constraint forces that do not violate the principle of virtual work, as given by equation (16). Nevertheless, the notion that constraints can be combined into groups is an attractive one and worth pursuing further, since the computation time pay-off promises to be quite large. To address the loss of dimensionality, the grouped constraint function given by equation (20) could be modified to allow a scale factor ρi for each of the constituent constraints Csi, giving CΣ =

Ns

∑|ρi Cs |.

i =1

i

(21)

The inclusion of these scale factors allows the gradient of each constraint to be scaled before it is summed. If these values are well chosen, the summed constraint gradient will be appropriate for the system of constraints, i.e. some linear scaling of this gradient will produce a correct constraint force which

maintains all constraints and does not violate the principle of virtual work. But Towards how do we find these scaling values? simulating cloth The correct scaling constants ρ i to use in equation 21 are exactly the dynamics Lagrange multipliers we would obtain by solving the original constraint force calculation of equation (19), over only the constraints and particles involved in the subgroup. This can be verified by observing that if each constraint in the 89 system were scaled by the corresponding lagrange multiplier, the sum of the gradients of the scaled constraints would be the constraint force. This formulation has the drawback that any subgroup that has no internal or applied forces, or only forces applied perpendicular to the gradients of the constraints, will yield λ values of zero. This is only a problem for constraint force transmission because, as shown in Figure 8, no constraint forces would result from these circumstances anyway. Also, this is typically a problem for only one simulation time step, since any constraint violations occurring because of the error at one step will result in internal forces at the next time step, and the constraint system will then be able to correctly transmit forces across groups.

Fapplied Gradient 1 (a)

Fapplied Gradient 2

Gradient 1 (b)

Gradient 2

Fconstrained

(a) A particle is constrained to lie at a fixed distance between two nails. If the nails and particle are colinear, and a force is applied perpendicular to this line, no constraint force will result. This is because the constraint force is a linear scaling of a gradient, and in this case the projection of the applied force on to either gradient is zero; (b) The particle and the nails are no longer exactly colinear. As a result, the projection of the applied force on to the two gradients is non-zero, and a constraint force can be applied to exactly counter the applied force

If constraints that are likely to transmit forces are intentionally grouped together then the constraint force transmission problem virtually disappears for reasonable geometric configurations. For the cloth model, there is a natural grouping of constraints along a single yarn (i.e. along each grid row and column), as shown in Figure 9a. This grouping will be effective except for extremely warped configurations, as in Figure 9b, which may defeat the original geometric rational for grouping constraints. However, these configurations will be rare for the cloth model, since the spring torques due to bending and trellising shown in Figure 10 will work to maintain a good force transmission geometry. For large meshes it will be desirable to subdivide rows or columns further to decrease group size and processing time.

Figure 8. Applied forces vs constraint forces

IJCST 8,3

Original configuration

Warped configuration

1

D C

2

A

90

B

C

D

A

B 2

3

3 4

4 (a)

Figure 9. Grouping constraints along warp and weft directions

1

(b)

(a) Grouping constraints along the warp or weft (row or column) directions makes sense because constraint forces are transmitted along a linked chain to the degree to which the links are parallel. Thus a force on link A should immediately result in a force on link D; (b) If the geometric configuration becomes too warped, the original rationale for grouping constraints will be defeated. Under these circumstances it might make computational sense (but not physical sense) to regroup the constraints as A-B-2-1 and D-C-3-4

T spring

T spring Figure 10. Bending and trellising torques maintain reasonable yarn alignments

T spring

The bending and trellising springs produce torques that work to maintain a quasilinear arrangement of particles in a single row or column. These forces help maintain “sane” configurations for constraint grouping

The hierarchical constrained dynamics algorithm for the particle cloth model will work as follows: • group all constraints into a single group at the top of the hierarchy. If we assume a square grid of N yarn crossings (particles), then we will have O(N ) constraints; • subdivide constraints into one group for each warp yarn and one group for each weft yarn to form the second level of the hierarchy; • subdivide each yarn into subgroups, and these subgroups into further subgroups until a predetermined small group size is obtained. If on each division we create a fixed number of new subgroups then the total number of subgroups will be O(log N );

at the lowest subgroup, use equation (19) to calculate lagrange Towards multipliers for each constraint in the subgroup. Since each subgroup is simulating cloth of a predetermined maximum size, this takes a constant amount if time dynamics per subgroup, but the number of subgroups will be O(N ); • repeat, working up to the top subgroup, the calculation of lagrange multipliers for each of the combined constraints of equation (21), using 91 the lagrange multipliers determined at the next lower level as scaling constants ρ. The computation time at each level is O(N ); • calculate the constraint forces at the top of the hierarchy by multiplying the single lagrange multiplier at this level by the gradient of the single constraint at this level. There will be exactly one constraint force calculated for each original constraint, so the time is again O(N ); At each level in the hierarchy, the computational effort will be O(N ), and there are O(log N ) levels, so the total computation time will be O(N log N ). •

Discussion We have implemented and tested the hierarchical constrained dynamics algorithm for very coarse cloth meshes of up to 11 × 11 yarns. The implementation does not yet include the bending and trellising forces that would be exerted in real cloth, and the only forces modelled in the system dynamics are inertial, viscous and frictional. Interparticle distances are maintained by the hierarchical constraint dynamics approach outlined above. We also use constraint dynamics to solve the collision-detection and nonintersection problem between surrounding geometry and the cloth model. No effort has been made to include avoidance of cloth self-intersection. At this point, the model is more like one of a very loose chain-mail than of real cloth. Nevertheless, by the elimination of all but the bare essentials from the model we have been able to run a large number of fast tests to allow us to perfect the simulation approach. Figure 11 shows one time step in a simulation of the cloth patch falling over some simple geometry consisting of two spheres and a cube. The entire sequence of the cloth falling over the geometry, and then eventually sliding off to fall free, is computed and displayed in under a minute on a Silicon Graphics R4000 Indigo Elan. The algorithm, as currently implemented, does not take full advantage of the speed-ups that are possible. There is no attempt to efficiently exploit sparseness. Also, in the hierarchical algorithm it is logical to subdivide the problem to a fine enough level that the biconjugate gradient solver, which is appropriate for large linear systems, is no longer needed. For the small fixedsize problems to be solved in the hierarchical algorithm, it would be much more efficient to use a direct algebraic solution. However, even though none of these efficiencies have been exploited in the current implementation, we have run side-by-side comparisons with the conventional constrained dynamics algorithm and noted significant improvements in performance. Improvements are most apparent for larger problems.

IJCST 8,3

92

Future work will involve expanding the cloth model by adding bending and trellising forces, tuned to match Kawabata test data, and reimplementing the hierarchical algorithm with fixed size direct algebraic linear system solvers. We are planning to conduct large-scale tests with varing constraint group sizes and to compare performance and accuracy with the non-hierarchical constrained dynamics system. We will be seeking to show that: (1) the constrained dynamic approach will allow accurate calculations of cloth dynamics; (2) that the hierarchical approach to solving the constrained dynamics problem will allow the solution to be computed rapidly enough that it can be considered as a viable tool for interactive modelling; and (3) that the physical accuracy of the particle-based drape model can be maintained in the new fast dynamic model. When the completed model is perfected, we will begin experiments with constructing clothing and explore uses of the model in dressing animated characters.

Figure 11. An intermediate step in a test simulation using hierarchical constrained dynamics. An 11 × 11 simulated cloth mesh falling over simple geometric elements. Forces maintaining interparticle distances and preventing clothgeometry interpenetration are all calculated by the hierarchical constraint dynamics algorithm

Conclusion The concept of constrained dynamics simulation has a very natural application to cloth simulation using the interacting particle dynamic model. We feel that the new hierarchical algorithm for constrained dynamics described here is

particularly appropriate for simulating the type of mechanical system Towards represented by cloth. This is because the geometry of force-transmission can be simulating cloth ordered along warp and weft yarns so that good guesses can be made as to how dynamics to subdivide the system into force-transmitting constraint groups. Initial tests confirm this supposition. Further validation of the approach awaits complete implementation and testing to make the necessary accuracy versus speed 93 comparisons with more conventional approaches. Notes and references 1. Collier, J.R., Collier, B.J., O’Toole, G. and Sargand, S.M., “Drape prediction by means of finite-element analysis”, Journal of the Textile Institute, Vol. 82 No. 1, 1991, pp. 96-107. 2. Eischen, J.W., Kim, Y.G., Clapp, T.G. and Ghosh, T.K., “Computer simulation of the large motions of fabric structures”, Proceedings of the 15th SECTAM Conference, College of Engineering at Georgia Institute of Technology, Atlanta, GA, 1990, pp. 119-26. 3. Lloyd, D.W., “The analysis of complex fabric deformations”, in Hearle, J.W.S., Thwaites, J.J. and Amirbayat, J. (Eds), Mechanics of Flexible Fibre Assemblies, Sijthoff & Noordhoff, Alphen aan den Rijn, 1980, pp. 311-42. 4. Shanahan, W.J., Lloyd, D.W. and Hearle, J.W.S., “Characterizing the elastic behavior of textile fabrics in complex deformation”, Textile Research Journal, Vol. 48, 1978, pp. 495-505. 5. Breen, D.E., House, D.H. and Getto, P.H., “A physically-based particle model of woven cloth”, The Visual Computer, Vol. 8 No. 5-6, June 1992, pp. 264-77. 6. Breen, D.E., House, D.H. and Wozny, M.J., “Predicting the drape of woven cloth using interacting particles”, Proceedings of SIGGRAPH Computer Graphics, Annual conference series, ACM Press, New York, NY, 1994. 7. Cusick, G.E., “The resistance of fabrics to shearing forces”, Journal of the Textile Institute, Vol. 52 No. 9, September 1961, pp. T395-T406. 8. Green, A.E. and Zerna, W., Theoretical Elasticity, Oxford University Press, London, 1968. 9. Terzopoulos, D. and Fleischer, K., “Deformable models”, The Visual Computer, Vol. 4, 1988, pp. 306-31. 10. Carignan, M., Yang, Y., Magnenat-Thalmann, N. and Thalmann, D., “Dressing animated synthetic actors with complex deformable clothes”, Proceedings of SIGGRAPH, Computer Graphics, Vol. 26 No. 2, 1992, ACM Press, New York, NY, pp. 99-104. 11. Breen, D.E., Tonnesen, D. and Gates, B. (Eds), Particle Systems Bibliography, Rensselaer Design Research Center Technical Report TR-92029, Rensselaer Polytechnic Institute, December 1992. 12. Breen, D.E., A Survey of Cloth Modeling Research, Rensselaer Design Research Center Technical Report TR-92030, Rensselaer Polytechnic Institute, July 1993. 13. Breen, D.E., A Particle-based Model for Simulating the Draping Behavior of Woven Cloth, PhD thesis, Rensselaer Design Research Center Technical Report TR-93011, Rensselaer Polytechnic Institute, June 1993. 14. House, D.H., Breen, D.E. and Getto, P.H., “On the dynamic simulation of physically-based particle-system models”, Third Eurographics Workshop on Animation and Simulation Proceedings, Cambridge, September 1992, Eurographics Society. 15. Kawabata, S., The Standardization and Analysis of Hand Evaluation, The Textile Machinery Society of Japan, Osaka, 1980. 16. Breen, D.E., House, D.H. and Wozny, M.J., “A particle-based model for simulating the draping behavior of woven cloth”, Textile Research Journal, Vol. 64 No. 11, 1994, pp. 663-85. 17. Witkin, A., “Constrained dynamics”, SIGGRAPH 95 Course Notes (Course 34 Physically Based Modeling), 1995, pp. F1-F12.

IJCST 8,3

94

18. Witkin, A., Gleicher, M. and Welch, W., “Interactive dynamics”, Computer Graphics (Proceedings of the Symposium on 3-D Interactive Graphics), Vol. 24 No. 2, 1990, pp. 11-21. 19. Press, W., Teukolsky, S., Vetterling, W. and Flannery, B., Numerical Recipes in C, The Art of Scientific Computing, 2nd ed., Cambridge University Press, Cambridge, 1992. 20. The notation O[ f ( N )] is commonly used in algorithm analysis to denote an algorithm whose computational time demand per component increases as the function f of the number of computational elements N. This is usually an asymptotic relation that holds strictly only as N approaches infinity. However it is generally a useful measure in determining how an algorithm’s performance can be expected to degrade as the number of computational elements increases. 21. Strictly speaking, interactive speed is considered to be at the TV frame-rate of 30 complete solutions per second. However, rates as low as two or more solutions per second are still useful for many interactive tasks.

Modelling the dynamic drape of garments on synthetic humans in a virtual fashion show

Modelling the dynamic drape of garments 95

George K. Stylios, T.R. Wan and N.J. Powell Department of Industrial Technologies, University of Bradford, Bradford, UK The concept of living without frontiers: the global retailer At the turn of the twentieth century there is little doubt about the influence that technology has over our lives. In the manufacturing sense, technology solves a number of problems related to design, production and the despatching of products, providing the consumer with either low cost, and large varieties of, enhanced, sophisticated or unique products, depending on the direction and philosophy of the company and its marketing strategy. As we are learning to co-exist with technology so are our industries, and it is not who will use the technology to combat competition in the world markets of the future that is crucial, but rather who will develop new technologies to stay competitive. Ironically, one of the first processes to be mechanized during the industrial revolution was clothing manufacture. Is this going to prove to be the last process to be fully technologically developed? There are, of course, sectors of this industry which have made important steps forward over the last ten years or so but, by and large, sectors such as garment making, for example, remain unchanged. The new philosophy of the twenty-first century will be “living without frontiers” with regard to society and, as far as companies are concerned, “competing globally”. Textile garment manufacturing and retailing has to be global, and companies will need to have as great a flexibility as possible to satisfy any possible market requirement. Research and development will provide the required techno-infrastructure for the “global retailer”, which will force restructuring of the industry and provide new possibilities in consumer buying methods and in product attributes. This introduction reflects the authors’ perception of global retailing and manufacturing, which will be established using the next generation of intelligent textile and garment manufacturing systems. Some of these systems This project was conducted at the Centre of Objective Measurement and Innovation Technologies, which is supported by the RETEX 2 project. The visualization tool has kindly been provided by ALIAS Inc.

International Journal of Clothing Science and Technology, Vol. 8 No. 3, 1996, pp. 95-112. © MCB University Press, 0955-6222

IJCST 8,3

96

have already been developed, others are in stages of development and some have not yet been developed. Virtual clothes for synthetic humans As our lives take their course, there are certain attributes, phenomena, developments if you like, which we cannot control or which are out of our control as a consequence of the techno-evolutionary process. In this process, we will argue that techno-evolution is now impossible to stop. There are many schools of thought as to whether we will command or serve technology and, as technology is already changing our lives, whether it will dictate the way in which we live. Will our free time be scarce or will technology enable us to maximize constructively our time in recreational activities, hobbies, and the like for ourselves and our families? Will we become more or less sophisticated, realizing that we must use our valuable time as constructively as possible? Although our generation may think that we will not live to witness these answers in our own lifetime, let us not forget the common practice which we follow nowadays in our lives. Some of us do not have the time to shop in the usual way, or feel more comfortable shopping at “out of town” superstores which can provide any consumer product under one roof. We tend to shop outside the traditional shopping hours, as there is a strong tendency towards weekend shopping. Catalogue shopping is flourishing, and so is home shopping, enabling fresh produce to be delivered on our doorsteps. The banking system is being shaken to its foundations. Many of us question the need to visit the bank to deal with the increasingly complex demands of our financial and economic requirements. Indeed, only the backbone of banks will remain in the twentyfirst century as home banking becomes increasingly widespread. Electronic home office systems, where employees can work from home and home education, where degrees are taught electronically from home, are already being offered and are being further developed. Corporate strategists are already urging companies to develop electronic retailing or “buying by wire”, and there are large companies which have committed themselves to this. The textile, clothing and retailing chain lends itself perhaps more than any other industry to looking at its research and development in order to enable it to develop in this way. To facilitate this, research areas have to be developed within every ring of the chain and also fundamental ways of keeping the chain together. Let us consider a futuristic scenario of providing techno-intelligence for buying a garment. The time has come when, in the comfort of our own homes, we can decide to buy our clothing. The flowchart diagram in Figure 1 highlights the online link between the socalled global retailer, our home and the textile industry. It is possible that we could have the despatch of a semi-tailored garment within two or three days. The reality is that even the garment virtual wear trial may not be far away. Consequently, the next generation of textile and garment manufacturing and automated retailing systems will need to predict the true 3-D behaviour of fabric and garment design and wear.

PIN number Barcode Password

Personal detail databank Shape measurement Bank account Structure/colour/texture

Television/computer/ telecom

Fabric development

Global retailer

Modelling the dynamic drape of garments

Garment virtual wear trial Garment development

97

Home Concepts Textile genetic Automated retailing engineering Global retailers (genetic fingerprinting) Home buying Global manufacturing Satellite companies Intelligent Intelligent Artificial clothes textile garment Synthetic humans manufacture manufacture Virtual environments Industry Intelligent looms Intelligent sewing machines Objective measurement technologies Textile genetic engineering Textile aesthetics Tailored clothes Despatch (72 hours?)

It is generally accepted that one of the most important requirements for the development of a 3-D garment CAD system, is how to obtain the real shape of the garment in 3-D space from the original 2-D design patterns. To do this effectively the deformable behaviour of textile materials would play a very important role in this area. Researchers have studied various methods to achieve this, however, unlike other engineering areas, the successes of such modern methods are very limited in textile engineering. Commercial CAD systems for clothing are still not able to meet those requirements. The major task is to find a precise and efficient approach to determine the real 3-D deformed shape of a cloth according to real fabric properties and to deal with complex 3-D design patterns. Those solutions should be efficient in terms of computer processing time, and easy to use for practical industrial applications. In this paper, we present a physical-based approach using the deformable bar-node and the lumped-parameter concept[1,2] to model the complex deformation of fabrics. Our model is based on a physical analogue to deep shell systems. The governing differential equations of motion and deformation of cloth are derived from the discretization of the system energy over all rigid bardeformable nodes on the surface of the cloth. A critical overview for this work has already been published in an earlier paper[3]. General assumptions and considerations for fabric modelling It was realized that fabric materials display a macrostructure[4]. The meaning of macrostructure can be explained by comparison with normal continuum

Figure 1. A flowchart diagram of the next generation of textile and garment manufacture and retailing

IJCST 8,3

98

materials, such as steel and rubber, the fabric materials appear very much coarser in the view of constructure and mechanical properties. Furthermore, even at very small strains, fabric materials show viscoelasticity and frictional slippage, and the relationships between different strains are very complex, and conventional assumptions cannot be applied. Our fabric model assumes that fabric material is a continuum shell on the condition that the basic elements of the cloth for stress-strain analysis are large enough compared with its macrostructure unit. Fortunately, this requirement is normally met by defining the element size, at least, 100 times larger than its constructure unit. In our approach, locations of the points in the cloth are defined by an orthogonal curvilinear surface co-ordinate system a1, a2 and a3 and the origin of this system is at a local point in the cloth. Also, these locations can be defined by the Cartesian co-ordinate system (x, y, z) as shown in Figure 2. α2

z α3

P0

dr

P1

α1

r r + dr

Figure 2. Location of points in fabric

x y

This treatment is convenient since a local orthogonal curvilinear system coincides with the normal fabric constructure of warp-weft yarns system and also can be easily applied with real measures of fabric mechanical properties. The relationships between the two co-ordinate systems can be generally given by x = f 1 (α1 , α2 , α3 ), y = f2 (α1 , α2 , α3 ), z = f 3 (α1 , α2 , α3 ).

( 1)

The position vector r of a point Po in a fabric can be determined by r(α1 , α2 , α3 ) = f 1 (α1 , α2 , α3 ) ⋅e 1 + f 2 (α1 , α2 , α3 ) ⋅e 2 + f 3 (α1 , α2 , α3 ) ⋅e 3 (2 ) where e 1, e 2 and e 3 are the unit vectors along directions of x, y and z axes respectively. Our approach is developed based on physical concepts through a discretized potential energy formulation. In principle, the formulation of the governing equations of this model can be briefly illustrated as follows: The surface of cloth can be divided as a series of node-bar elements according to the mesh layout

employed, where the elements can be equal or unique sizes. Here, for simplification, we limit our partition to orthogonal linear co-ordinates which coincide with the lines of the principle curvature of the surface. The deformable node-bar elements are defined as consisting of one deformable node with a number of rigid bars, as shown in Figure 3. As can be seen in this figure, the patch of cloth is divided into a grid. In this way, the patch is divided as a series of elements, which can be equal or unequal sizes. W

Modelling the dynamic drape of garments 99

3

V

2 0

4

U 1

Figure 3. Configuration of a nodebar element in fabric

We treat each patch element as the unit of a deformable node with a number of rigid bars. The deformation of each node-bar element can be described by u and v displacements, along the first two surface co-ordinates α1, α2 within the tangent plane, and w displacement along the third surface co-ordinate α3 (the normal direction). The material properties of the continuum in all elements can be lumped together at these deformable nodes by integrating all the energies within those elements. Note that we chose the perpendicular lines of principle curvature as coordinates α1, α2, and the normal to the surface as the third co-ordinate α3, thus we have three-dimensional strain and stress components. Assuming that the fabric surface is homogeneous, isotropic and linearly elastic on which Hooke’s law can be applied, we have[5] 0 = {E }⋅ ε

(3 )

In the expression above, σ is the stress vector and defined by

[

0 = σ 11 σ 22 σ 33 σ 12 σ 13 σ 23

]

Τ

(4 )

where σ11, σ22, σ33 are the components of the normal stress along the directions of α1, α2, α3, respectively and σ12, σ13, σ23 are the components of the shear

IJCST 8,3

stress within the tangential planes of (α1, α2), (α1, α3) and (α2, α3) respectively. (Note that for complete stress components, σ12 = σ21, σ13 = σ31, σ23 = σ32). ε is the strain vector and defined by

[

ε = ε 11 ε 22 ε 33 ε 12 ε 13 ε 23

100

]

Τ

( 5)

where ε11, ε22, ε33 are the normal strains along the directions of α1, α2, α3 respectively and ε 12 , ε 13 , ε 23 are the components shear stress within the tangential planes of (α1, α2), (α1, α3) and (α1, α2) respectively. {E} is the relation matrix for an isotropic material and defined by 2G + λ λ λ 0 0 0   λ 2G + λ 0 0 0  λ  λ λ 2G + λ 0 0 0  {E } =   G 0 0 0 0  0  0 0 0 0 G 0   0 0 0 0 G   0 where λ =

(6 )

µE

, µ is the Poisson ratio, E is the tensile modulus and Gij (1 + µ)(1 – 2µ) is the shear modulus. It is generally known that the cloth is anisotropic and nonlinear and the deformations are history-dependent. In order to incorporate anisotropic material properties, we expand the strain-stress relationship above as follows 2G + λ λ2  1 1  λ 2G 2 + λ2 1   λ λ2 1 {E } =   0 0   0 0   0 0 

λ3

0

0

λ3

0

0

2G 3 + λ3

0

0

0

G 12

0

0

0

G 13

0

0

0

0  0  0  . 0  0  G 23 

(7 )

We assume that all components in {E} are independent from each other. It can be seen that this treatment will not only be able to incorporate the real material properties of fabric but would also be convenient for using real measurements of fabric parameters. G1, G2 and G3 are the tensile moduli along α1, α2 and α3 respectively, λ1, λ2 and λ3 are the corresponding Poisson ratios, and G12 is the shear modulus within the cloth surface and G13 and G23 are the shear moduli within the plane of α1 and α3, and the plane of α2 and α3 respectively, which can be evaluated by measuring the bending properties in both planes.

Energy expressions and modelling of fabric deformation The general strain-displacement relationships in the surface co-ordinates described above are given[5], which can be written as follows: The normal strains are

∂Ai  u j  ∂  ui    +   , i = 1, 2 , 3. Ai j = 1∂α j  Aj  ∂α i  Ai  The shear strains are Aj ∂  u j  A ∂  ui  ε ij = i ⋅ + ⋅   , i , j = 1, 2 , 3 ; i ≠ j   Aj ∂α j  Ai  Ai ∂α i  Aj  where ∂r ∂r A2i = ⋅ , i = 1, 2 , 3. ∂α i ∂α i ε ii =

1

Modelling the dynamic drape of garments

3

∑

(8 )

(9 )

Consider the local area of fabric, since we limit our shell co-ordinate system to coincide with the lines of principle curvature of the surface and the normal direction, the deformation of each node-bar element can be described as the u and v displacements, which are along the first two curvilinear co-ordinates within the tangent plane, and the w displacement along the normal direction. It is therefore reasonable to assume that, for local stress-strain analysis, the fundamental form parameters A 1 ≈ A 2 ≈ A 3 ≈ 1. The strain-displacement relationships can therefore be simplified. It must be emphasized here that according to the above discussion, it would only be appropriate to treat the fabric as being of continuum material if the basic fabric element sizes chosen for modelling are large, compared with the microstructure of the fabric. However, this requirement is normally met by the selection of size of basic cloth elements as mentioned early. The cloth motion equations can be derived from the energy functions of the system as follows: Consider the deformation distribution within one basic fabric element. The question is how to find the strain energy density function or strain energy distribution. We assume that the virtual energy density of strain will change continuously and smoothly within the basic fabric element. This indicates that the energy density function, which is related to stresses σij and strains εij, is continuous. We also assume that they have continuous derivatives everywhere within the basic element and that the resultant effect on the whole shape of fabric, especially at locations of each node, will be identical to the effect of using lumped node-bar element treatment. Under the above assumptions, we treat the shape of fabric as being a continuum shell. Now, we are ready to examine one infinitesimal element, as shown in Figure 4. The strain energy stored in an infinitesimal element within one basic fabric element that is acted by stress σij is

101

IJCST 8,3

Node i

An infinitesimal element

102

Figure 4. An infinitesimal element in a basic fabric element

dU =

1

σ Τ εdV .

(10 ) 2 The strain energy density is therefore 1 χ 1 = σ Τε . (11) 2 The kinetic energy density is 1 χ 2 = ρ (u˙ 2 + v˙ 2 + w˙ 2 ) (12 ) 2 where ρ is mass density and the dot indicates a time derivative. The energy density introduced by external forces is χ 3 = q1u + q2v + q3w (13) where q1, q2 and q3 are forces per unit volume along the directions of u, v and w respectively. The energy density introduced by any applied boundary forces is χ4 = N1u + N2v + N3w (14) where N 1 , N 2 and N 3 are the resultants of the boundary forces along the directions of u, v and w respectively. Hence, the total energy density is L = χ1 + χ 2 + χ 3 + χ 4 . (15 ) It can be seen that we actually define an energy field. Using Euler-Lagrange equations[6], the cloth motion can be determined by 3 ∂ ∂L ∂L ∂  ∂L  = ∑ –  ( 16 )  ( i = 1, 2 , 3 ) ∂ψ i k = 1∂X k ∂ ( ∂ψ i / ∂u k ) ∂t  ∂ψ˙ i 

where ψi are general functions of energy component, representing ui (i = 1, 2, 3). Using matrix notation ψ and X gives (17) ψ = [u v w]T and X = [α1 α2 α3 t]T (18) where t is the time variable. The detailed derivation of all terms in the fabric motion equations may be obtained in our internal report[7]. Our model is also conveniently capable of including viscoelastic properties of fabrics. In order to precisely represent the behaviour of cloth, we have to add viscoelastic terms in the energy equation. For example, we use the linear Kelvin model[8] for describing material viscoelastic properties. The stress-strain relationships as described in equation (3), now become σ = { E }ε + { B }ε⋅ (19 ) where  β11  β 21 β {β } =  31  0  0   0

β12 β 22 β 32 0 0 0

β13 β 23 β 33 0 0 0

0 0 0 β12 0 0

0 0 0 0 β13 0

0   0  0   0  0   β 23 

(20 )

where components βij are damping terms, which may be estimated by various methods. Modelling, implementation and visualization of synthetic humans In order to predict the shape and movement of a garment as it is being worn, knowledge of the underlying shape and motion of the person wearing the garment is essential. This information is required by the cloth model as a constraint to the cloth, in order to stop it penetrating the skin of the synthetic actor. During walking and other activities, the position of all the surfaces that make up the human figure are constantly shifting. Consequently, the motion of the figure is required by the model to update the positions of the skin surfaces. In the current research the data of a female model was described by over 50,000 polygons (Plate 1). An alternative source for this data would be to capture the data directly from the measurement of a real person. To this end, a concurrent research project in our group, which uses video capture technology, is in progress. This female data, described above, provides only the data concerning the static shape of a person; it then requires animating with walking motion. In

Modelling the dynamic drape of garments 103

IJCST 8,3

104

Plate 1. A model of a synthetic human lady

order to achieve this, a skeleton model with animation was developed during the current work. The skeleton (Plate 2) model consists of a hierarchical structure of joints. The joint at the top of the hip forms the root of the structure and the head, hands and feet form the leaves. The locations of each of the skeleton’s joints can be controlled by a set of paths, or motion curves over a series of time steps. The motion curves are generated in a local co-ordinate system relative to and determined by the position and orientation of the joint above it in the hierarchy of joints (from top level to bottom level) as shown in Figure 5. Once the skeleton model is developed, the body surface could be attached to the animated skeleton to form an animated female figure. Plate 3 (a-f) demonstrates a number of stills of a walking female in a virtual environment, which are taken from a completed animated sequence. Modelling, implementation and visualization of artificial clothes The simulation of whole drape process is divided into a sequence of small time steps. At each time step, the initial locations of each point in the fabric are firstly identified and all the forces, such as gravity, boundary forces and collision

Modelling the dynamic drape of garments 105

Plate 2. A skeleton model

Hip

Back

Neck

Left shoulder

Right shoulder

Left hip

Right hip

Left upper arm

Right upper arm

Left upper leg

Right upper leg

Left lower arm

Right lower arm

Left lower leg

Right lower leg

Left hand

Right hand

Left foot

Right foot

Head Figure 5. Hierarchical skeleton structure

IJCST 8,3

106

a

b

c

d

e

f

Plate 3. Walking female in a virtual environment

forces between the cloth and synthetic humans, are calculated, so that we can find all the energy terms in the equations of the cloth model. Then energy minimization is applied to find the new locations of each point in the cloth. In this paper, we demonstrate two sets of drape simulations as follows. Measurement and prediction of static and dynamic drape of fibrous materials With the development of new lightweight fabrics for garments, a new attribute that consumers are describing is the moving gracefulness of these garments visà-vis their dynamic drape. This is particularly apparent in the new lightweight polyester type of Shingosen fabrics developed primarily by the Japanese synthetic fibre industry.

In the Research Centre of Excellence, COMIT, we have developed a new generation of drape meter[9], one that measures the drape of any fabric both statically and dynamically, in true 3-D by using a CCD camera as a vision sensor. This system, called the Marilyn Monroe Meter (M3) has been used to measure real fabric drape behaviour, and is being used to verify our drape prediction model. The prediction system is based on our simulation model and is aimed to be used as a tool in predicting and engineering the static and dynamic drape behaviour of fabrics. Drape prediction is made by the use of fabric properties. If the aesthetic static and dynamic drape simulation, as given on the computer screen in true 3-D, is not satisfactory, the properties can be manipulated to engineer or re-engineer (textile genetic engineering concept) the acceptable drape attribute. This can be done automatically, but this is outside the scope of this paper. For this work we have used two different fabrics. The properties of both fabrics were measured and photographs of their drape were provided (Plates 4 and 5). Drape predictions (using 720 deformable node bar elements) were also initiated using our simulation model and Plates 6 and 7 show good agreement with the real static and dynamic drape. Both fabrics were made from cotton polyester blends and they had the same tensile properties but different bending properties (fabric A had approximately twice the bending magnitude of fabric B). Garment drape simulation and visualization Real garments made from cotton/polyester and polyester lightweight fabrics have been modelled with 1440 (20 × 72) deformable node bar elements and have been used in dressing the model of our synthetic human in a virtual fashion show. The 2-D garment patterns are joined together to form the complete garment surface in 3-D wire forms. The final drape stage is mainly determined by material properties and body shape data. For convenience the starting point of garment drape can be defined arbitrarily; the initial state is the top of the skirt (constructed by a set of elliptical curves) and the initial state of the lower part of the skirt (a flat circular piece of cloth). The only constraints initially are the forces applied to the edges of each panel. Consequently, the slope of the garment will be deformed and draped over the body of the synthetic lady model in accordance with the laws of physics. The constraints used at this stage are the forces owing to gravity and the forces from collisions[10], which are applied to each deformable node. The rendered instances of the simulation are shown in Plates 8a to 8f. The computation of one whole draping simulation takes one hour of CPU on the Iris Indigo 2 workstation (excluding image rendering). Compared with other proposed models, our model is more efficient and less computer intensive. Plates 9, 10 and 11 show three instances of draping simulations, in which modelling of different fabrics, garment designs and body sizes are being represented.

Modelling the dynamic drape of garments 107

IJCST 8,3

108

Plate 4. Photographed drape of Fabric A

Plate 5. Photographed drape of Fabric B

Modelling the dynamic drape of garments 109

Plate 6. Rendered image of drape simulation, (Fabric A)

Plate 7. Rendered image of drape simulation, (Fabric B)

IJCST 8,3

110

a

b

c

d

e

f

Plate 8. Early stage in the draping simulation

Discussion and conclusion The deformable node-bar model based on a physical analogue to a deep shell system has been developed, and is capable of dealing with the complex deformation of fabric in garments. The major advantages of this model over other models are that its configuration is based on the surface co-ordinate system, so it is convenient for modelling complex fabric by directly using fabric “engineering” mechanical parameters. In addition, this model appears to be more efficient and capable of incorporating the visco-elastic properties of flexible materials. The model has been verified with the simulation of a real drape system and the modelling of a lady with synthetic skin in a computerized

Modelling the dynamic drape of garments 111

Plate 9. Simulation of a long skirt constructed from a stiff fabric

Plate 10. A rendered image of draping simulation (final stage). A short skirt constructed from a soft fabric

virtual fashion show in the context of global retailing. The consequences of this work in cinema, TV, advertising and in graphics and animation are also important but outside the scope of this paper.

IJCST 8,3

112

Plate 11. Simulation of a skirt worn by a synthetic lady with larger hips

References 1. Mohraz, B. and Schnobrich, W.C., “The analysis of shallow shell structures by a discrete element system”, Civil Engineering Studies, SRS 304, University of Illinois, March 1966. 2. Schnobrich, W.C. and Pecknold, D.A., “The lumped-parameter or bar-node model approach to thin shell analysis”, in Perrone, F. and Schnobrich, R. (Eds), Numerical and Computer Methods in Structural Mechanics, Academic Press, New York and London, 1973, pp. 377402. 3. Stylios, G., Wan, T.R. and Powell, N.J., “Modelling the dynamic drape of fabrics on synthetic humans, using a physical, lumped-parameter model”, International Journal of Clothing Science and Technology, Vol. 7 No. 5, 1995, pp. 10-25. 4. Shanahan, W.J., Lloyd, D.W. and Hearle, J.W.S., “Characterizing the elastic behaviors of textile fabrics in complex deformation”, Textile Research Journal, Vol. 48, 1978, pp. 495-505. 5. Werner, S., “Vibrations of shells and plates”, 2nd ed., Marcel Dekker Inc., New York, NY, 1993. 6. Moiseiwitsch, B.L., Variational Principles, John Wiley & Sons Ltd., London, 1966. 7. Stylios, G. and Wan, T.R., “A physical-based cloth model for garment design and manufacture”, Internal report, COMIT, Bradford University, Bradford, 1995. 8. Cook, R.D., Concepts and Applications of Finite Element Analysis, 2nd ed., John Wiley & Sons Ltd, Canada, 1981. 9. Stylios, G. and Zhu, R., “The definition of fabric drapability as an aesthetic property investigating static and dynamic drape of limp materials”, submitted for publication. 10. Carignan, M., Yang, Y., Magnenat-Thalmann, N. and Thalmann, D., “Dressing animated synthetic actors with complex deformable clothes”, Proceedings of SIGGRAPH, Computer Graphics, Vol. 26, 1972, pp. 99-104.

Investigation of fabric deformations under different loading conditions Milanka D. Nikolic and Tatjana V. Mihailovic University of Belgrade, Belgrade, Yugoslavia Introduction Fabrics are materials of complex structure whose behaviour under action of tensile force differs from the behaviour of homogeneous materials. Because of that, the well-known theory of elasticity[1,2] cannot be completely applied in explanation of fabrics’ behaviour. Deviations from the theory of elasticity have appeared to occupy the attention of numerous investigators for a long time. These phenomena can be observed keeping in mind the type of material, raw materials, geometric and constructive parameters as well as the conditions in which material is exposed under action of tensile force (the size of force, time, velocity of acting, etc.)[3-8]. Thereto it is possible to observe the reaction of material under conditions to which it is exposed during investigation of the influence of tensile force. Thus, results obtained can be used to predict the behaviour of material under certain wearing conditions. In other words, it is possible more precisely to determine the narrowest purpose of fabrics according to demands of quality and stability of form. In this paper the influence of tensile force size on a total deformation as well as the deformation components – elastic, viscoelastic and plastic – was quantifiably investigated. The experiment The experiment was conducted on wool clothing fabrics[9] made under constant technological conditions in three variants of weaves. The fineness of warp and weft yarns was in the limits of (25 × 2)tex + 18 per cent. Weave density was in the limits of 177dm–1 ± 7 per cent for warp yarns and in limits of 178 dm –1 ± 11 per cent for weft yarns. Basic structural parameters of investigated fabrics are given in Figure 1. The samples were exposed to the action of tensile force of various intensities (5, 10, 15, 20, 25, 30, 35 per cent of breaking force) in warp and in weft direction for a constant period of time (15 minutes) on a standard fabric loading machine – dynamometer (Textest, Switzerland). After this time had expired, the relaxation of fabrics was examined by measuring the recovery of sample lengths from the moment of unloading to 24 hours, more exactly 48 hours, even seven days. Taking into consideration that gained values did not change after 24 hours, this time (24 hours) was chosen as the time limit value in this experiment. On the basis of elongation-time diagrams, the values of elastic

Investigation of fabric deformations 9 Received October 1995 Revised and accepted March 1996

International Journal of Clothing Science and Technology, Vol. 8 No. 4, 1996, pp. 9-16. © MCB University Press, 0955-6222

IJCST 8,4

Fabric structure No.

10

Figure 1. Basic structural parameters of investigated fabrics

Fineness (tex)

Density (dm –1)

Crimp (%)

Warp

Weft

Warp

Weft

Warp

Weft

1

23 x 2

24.5 x 2

183

179

4.92

4.47

2

23 x 2

24.5 x 2

189

196

4.77

5.11

3

23 x 2

23 x 2

179

183

5.52

4

23 x 2

24 x 2

176

172

5

27.5 x 2

27.5 x 2

165

6

27 x 2

23 x 2

7

49

8

Mass [g/m2]

Breaking force (N) Warp

Weft

183

358

327

193

327

386

5.24

183

341

322

6.46

5.59

175

339

327

163

6.53

8.18

199

382

364

170

184

4.59

8.48

193

389

343

23 x 2

171

181

5.67

5.42

180

284

344

23 x 2

55

170

170

5.79

6.22

170

314

266

9

23 x 2

25.5 x 2

173

171

6.32

9.18

178

322

322

10

27 x 2

23.5 x 2

165

181

5.88

9.54

194

335

345

11

29 x 2

27.5 x 2

165

165

7.37

7.57

197

363

368

12

23 x 2

23.5 x 2

183

192

5.62

6.59

194

322

363

13

23.5 x 2

23.5 x 2

181

193

5.57

6.66

190

345

354

14

23.5 x 2

24.5 x 2

180

175

5.87

6.73

180

322

324

15

21.5 x 2

23 x 2

171

160

5.96

7.94

169

323

283

16

23 x 2

23.5 x 2

171

172

5.81

5.90

179

292

322

17

27 x 2

21 x 2

166

181

5.36

6.89

188

362

351

18

27.5 x 2

28.5 x 2

166

166

6.07

7.54

197

343

363

deformation (instantaneous recovery), viscoelastic deformation (time up to 24 hours) and plastic deformation (difference between the length of treated sample after 24 hours and starting length) were determined. All measured values of elongation changes during the investigated period were converted into percentage of total elongation. One of the obtained diagrams is shown in Figure 2 for fabric number 11 (Figure 1) in warp direction after the cessation of tensile force of 35 per cent of breaking force. The amount of force which causes only elastic deformation was determined from the force-elongation diagram in determining the breaking force from the limit point of the linear part of curve (like parameter LT according to KESsystem[10,11]). Results and discussion On the basis of 126 elongation-time diagrams (18 samples – seven loads), the sizes of all three deformation components of woollen fabrics at chosen loads were determined. The results obtained are shown on triangular graphs (Figure 3) from which the sizes of all three kinds of deformation for each fabric and each tensile force are read according to the simple key. Order of load magnitude which causes only elastic deformation is shown in Figure 4. From Figure 3 it is clear that, for the values of load up to 15 per cent of breaking force (Figure 3 a,b,c) no matter what kind of weave as well

Investigation of fabric deformations

Elongation, mm 120

115

11

Elastic

110

105

Viscoelastic

Plastic

100

95 0

2

4

6 8

Loading time (min)

10

2

4

6 8

100

2

4

6 8

1,000

2

Relaxation time (min)

as the differences of structure parameters for investigated fabrics are, the component of plastic deformation does not exist in the total deformation. The interval range of elastic deformation is from 50-90 per cent for the smallest load value to 48-75 per cent for loads which are 15 per cent of breaking force. Irreversible (plastic) deformation is noticed for loads which are 20 per cent of breaking force (Figure 3d) for 89.9 per cent of investigated fabrics and this value is not over 5 per cent, which indicates that there is still a high degree of reversible deformation (total 95 per cent). With further increasing of load up to 25 per cent of breaking force (Figure 3e), 94.44 per cent of fabrics (with the exception of fabric number 7, Figure 1) show all three deformation components, but with still very important participation of reversible deformations (90-98 per cent). A load which is 30 per cent of breaking force (Figure 3f) causes all three deformation components for all investigated fabrics, but with maximal value of plastic deformation of 11 per cent and mean value of plastic deformation of 9 per cent. At the most drastic conditions of loads, which is 35 per cent of breaking force (Figure 3g), the zone of elastic and viscoelastic deformation becomes narrower, but the zone of plastic deformation component (10 per cent) increases with maximal value of 14.5 per cent. On the basis of maximal and minimal values of elastic and viscoelastic deformation for each of the applied loads, the diagram in Figure 5 is constructed. This diagram gives information about the range of deformation

Figure 2. An example of relaxation curve of woven fabric

0 0 10 ma tio n( 40 %) 30 20

for

50

de

20

80

70

60

tic las

60

oe Vis c

0 10 ma tio n( 40 %) 30 20

for

50

de

10

Vis co ela stic 70 de 60 for ma 50 tio n( 40 %) 30 20 80 90 10 0

0 10

Vis co ela stic 70 de 60 for ma 50 tio n( 40 %) 30 20 80 90

30

)

10 ) (% 20 on 30 40

ati

rm

50

(%

70

60

efo

cd

70

sti

Pla

80

on

40

80

90

ati

tic

0

0

10

rm

50

las

10 %) 20 n( tio 30 40

0

60

efo

cd

70

sti

Pla

80

10

0

0

10

0

90

10

0

a rm

10 %) 20 n( 30

10 0

efo

50

tio

90

oe

cd

60

a rm

40

0

Vis c

sti

70

efo

50

10 20 30 40 50 60 70 80 90 100 Elastic deformation (%)

(d)

90

P la

cd

60

0

10

10 20 30 40 50 60 70 80 90 100 Elastic deformation (%)

0

0 10 (% ) 30 20

tio n

40

ma for

50

de 70

40

10 20 30 40 50 60 70 80 90 100 Elastic deformation (%)

10

0

0

10

0

10

10

90

60

stic ela 80

Vis co

10 (% ) 30 20

tio n ma for

50

de 70

60

stic ela

%) 20 n( tio 30 ma 40 50

) (% 20 on ati 30 rm 40 efo cd 50 sti 60 70

for

60

de

80

80

Pla

70

tic

Vis co

90

s Pla

80

0

0

10

(f)

90

90

10 20 30 40 50 60 70 80 90 100 Elastic deformation (%)

0

(e)

0

10

0

0

Figure 3. Deformation components of investigated fabrics in warp direction at various intensities of load

80

sti

70

10 20 30 40 50 60 70 80 90 100 Elastic deformation (%)

(c)

90

P la

80

0

0

90

(b)

10

0

12

(a)

10

IJCST 8,4

0

10 20 30 40 50 60 70 80 90 100 Elastic deformation (%)

(Continued)

0 10

90 P la

80

) (% 20 on ati 30 rm 40 efo cd 50 sti 60 70

Vis co ela stic 70 de 60 for ma 50 tio n( 40 %) 30 20

0

80

Investigation of fabric deformations

10

(g)

Key Plain weave Twill weave Cross twill weave

13

0

10 0

90

10

0

Figure 3.

10 20 30 40 50 60 70 80 90 100 Elastic deformation (%)

Force Load

Percentage from breaking force

Percentage from breaking force

Warp

Weft

1.5 – 4.5

1.5 – 4.0

Mean value of load range

3.0

2.8

Modal value of load

2.5

3.4

F•

E• Elongation Graphic presentation of determination of the force which causes elastic deformation Range of load

component values (elastic Ee, viscoelastic Ev and plastic Ep ) for each load. The point of appearance of the viscoelastic deformation component for load which is 2.5 per cent of breaking force is also noticed from this diagram. Increasing the value of the load reduces the dispersion of elastic and viscoelastic deformation values (the zone is getting narrower), but the zone of plastic deformation increases from 15 to 35 per cent of breaking force. All these investigations and analyses were also performed for weft direction. Figure 6 presents the mean values of fabric deformation components in warp and weft directions, depending on load size.

Figure 4. Magnitude of load which causes only elastic deformation

IJCST 8,4

14

Elastic deformation (%)

Viscoelastic deformation (%)

100

0

95

5

90

10

85

15

80

20

Eemax Evmin

75 Ee

25 30

Ep

Ev

70

Ev

Ep

65

35 Evmax

Eemin

40 Ep

Ee

Ee

60

Ev Ep

55

45

50

50 0

5

10

15

20

25

30

35

Load, % of breaking force

Figure 5. Maximal and minimal values of deformation components of investigated fabrics in warp direction

Key Upper limit of elastic deformation zone Lower limit of elastic deformation zone Upper limit of viscoelastic deformation zone Lower limit of viscoelastic deformation zone Ee Range of elastic deformation Ev Range of viscoelastic deformation Ep Range of plastic deformation

With regard to the mean values of deformation components, viscoelastic deformation in warp direction appears at lower load values (2.5 per cent of breaking force) while in weft direction at higher values (3.4 per cent of breaking force). For loads of up to 15 per cent of the breaking force it can be stated that elastic and viscoelastic components are identical in both directions. Insignificant differences are noticed at higher loads, but with identical size of plastic deformation component interval. Conclusion Imposed investigations, aimed at discovering the behaviour of clothing fabrics in various conditions of uniaxial load, show that regardless of various starting parameters of experimental materials in this test, it can be concluded that:

Elastic deformation (%)

Viscoelastic deformation (%)

100

0

95

5

90

10

85

15

Viscoelastic deformation

80

20

75

25

70 Ep

Ee

15

30

Ev

65

Investigation of fabric deformations

35

Plastic deformation

60

40 Elastic deformation

55

45

50

50 0

5

10

15

20

25

30

35

Load, % of breaking force Key In warp direction In weft direction

(1) for small load values up to 2.5 per cent of breaking force (warp direction) and 3.4 per cent of breaking force (weft direction), fabrics only have elastic/quickly reversible deformation; (2) fabrics only have reversible deformations (elastic and viscoelastic) for loads up to 15 per cent of breaking force; (3) all three deformation components appear for loads over 15 per cent of breaking force; (4) increases the load increases the interval of plastic deformation up to a mean value of 10 per cent, but the participation of reversible components is very high (90 per cent); (5) regardless of is it warp or weft direction, differences are insignificant and they stand out for small load values. On the basis of these conclusions it is possible to state that for investigated wool clothing fabrics in a chosen experiment, the same mechanisms of behaviour are valid regardless of their mutual differences in warp and weft fineness, warp and weft density and the type of weave.

Figure 6. The zone of mean values of deformation components of investigated fabrics in both directions

IJCST 8,4

Note 1. 2. 3. 4.

16

5. 6.

7. 8. 9. 10. 11.

and references Sears, F.W., Mechanics, Wave Motion and Heat, Addison-Wesley, Reading, MA, 1959. Sivukhin, D.V., General Course of Physics, Science, Moscow, 1979. Hearle, J.W.S., Grosberg, P. and Backer, S., Structural Mechanics of Fibers, Yarns, and Fabrics, Vol. 1, Wiley-Interscience, New York, NY, 1969. Latzke, P.-M., “Testing the elongation and elasticity of stretch fabrics”, Mell iand Textilberichte, No. 2, 1983, p. 117. Savast’yanova, A.G., Dronova, I.-V. and Krajnova, E.G., “Testing the wearing properties of flax and flax-blend woven fabrics”, Express Information, No. 16, 1987, p. 11. Primachenko, B.M. and Prokhorova, I.A., “Influence of the structural parameters on rigidity of cotton woven fabrics during their stretching”, Technology of Textile Industry, No. 2, 1987, p. 106. Dhingra, R.C., de Jong, S. and Postle, R., “The low-stress mechanical properties of wool and wool-blend woven fabrics”, Textile Research Journal, No. 12, 1981, p. 759. Scardino, F.L. and Ko, F.K., “Triaxial woven fabrics. Part 1: behaviour under tensile, shear and burst deformation”, Textile Research Journal, No. 2, 1981, p. 80. Fabrics were produced in Serbia in Paracin textile factory Branko Krsmanovic. Mahar, T.J., Dhingra, R.C. and Postle, R., “Measuring and interpreting low-stress fabric mechanical and surface properties”, Textile Research Journal, No. 6, 1987, p. 357. Matsudaira, M. and Kawabata, S., “A study of the mechanical properties of woven silk fabrics Part I. Mechanical properties and handle characterizing woven silk fabrics”, Journal of the Textile Institute, No. 3, 1988, p. 458.

Simulation of flow lines in clothing manufacture Part 1: model construction G. Fozzard De Montfort University, Leicester, UK,

J. Spragg

Simulation of flow lines

17 Received July 1995 Revised and accepted December 1995

The Robotics Institute, Carnegie Mellon University, Pittsburgh, USA, and

D. Tyler Manchester Metropolitan University, Manchester, UK Introduction A simulation model of the progressive bundle system has been constructed, incorporating operator performance variations and learning effects, machine failure and repair, operator absenteeism, quality failure and knowledge-based supervisory control. Part 1 summarizes these achievements. Complex system models are not easy to validate and a four-stage approach has been used to demonstrate conformance with real-world systems: qualification, face validity, modular validation and time-series system behaviour. Applications of the model are discussed and the results of experiments with a line starting work on a new style are presented. Part 2 considers these issues of validation and provides examples of applications. Production context There is considerable pressure on the clothing industry in the western world to remain competitive in the face of global competition. In addition, market forces and a trend of decreasing contract sizes have resulted in numerous practical difficulties in the control of traditional flow-line methods of manufacture. Faced with these problems there are broadly two lines of action available to the industry: radical changes in the system of production, or improvement of the existing systems[1,2]. Changes coming from automation are limited at present and this situation is likely to continue. The problems of automatically assembling garment pieces are substantial, and the automation of materials handling alone has not produced systems that are more flexible. Radical changes in the organization of Funding for this research was provided by the ACME Directorate of SERC, Grant Reference GR/D 74246. The authors would like to thank their industrial collaborators for providing access to factory data.

International Journal of Clothing Science and Technology, Vol. 8 No. 4, 1996, pp. 17-27. © MCB University Press, 0955-6222

IJCST 8,4

18

skilled labour are occurring[2] but it is clear that the requirement successfully to control systems involving skilled manual labour will continue for the foreseeable future. Computer simulation is now well established as a powerful problem-solving tool within machine-dominated manufacturing industry. Its credibility here is to be expected as simulation has its roots in the hard systems engineering approach to problem solving in which the problem and the objectives are well defined. This is more difficult to achieve when modelling human systems, as the modeller must develop a credible abstraction of the human components and face numerous challenges during model qualification and validation. The potential rewards from simulation are great in terms of the improved control exerted over the widely practised progressive bundle system or the newer innovations in team working. The four aims of the research reported here were to: (1) develop a suitable abstraction of the production elements of clothing manufacture; (2) evaluate alternative methods of including control strategies in the model; (3) look critically at the credibility issues involved when simulation is taken into this type of “human” domain; (4) demonstrate the potential for simulation in the clothing industry. The first two aims are addressed in Part 1; aims 3 and 4 are considered in part 2. Model building All models are the result of abstraction and simplification. A theory of modelling and simulation[3] suggests that such abstraction should try to preserve the usefulness of the model within its domain of intended application while minimizing the general level of detail within the model (and hence development cost). Zeigler[3] introduces terms that will be used in subsequent discussion: the “base model” is a hypothetical complete model of the real system that is valid under all experimental conditions; the “lumped model” refers to real models that only represent some part(s) of the base model. Process times One of the major elements of the flow-line model in this research is the mechanism for deriving operation process times. The assumption of a static process time (defined either as a constant or by the parameters of a standard distribution), used in engineering applications and in published clothing-related models[4-7], can be regarded as an over-simplification of behaviour in industrial progressive bundle lines. The time required to complete a task has been found to depend on the task, the operator and the practise opportunity, and an approach to incorporating these operator learning effects into simulation models has been explained elsewhere[8]. A further problem is introduced in that the actions of the line supervisor to balance capacity at each operation result in

operators being moved between operations. In these circumstances, a change of operation certainly affects the process time. In order to develop a model of clothing production, the effects of individual operators and individual operations on process times must be ascertained. A conceptual division between operator and job factors is an example of the abstraction of reality which occurs in formulating the lumped model. As an input variable to the model, the work content (measured using standard minutes) should ideally provide a contribution to the process time that is entirely independent of the operator. By defining tasks in terms of their work content, the same basic model can be configured to describe many different production lines. To avoid the problems associated with time study in unstable production environments[9], work content values determined using predetermined motion-time systems have been used in this research wherever comparisons between real-world and simulated data were made. There can never be a single testable account of any mechanism purporting to explain performance variation because each human actor in such a system is free to attribute his/her own world view to the events taking place[10]. In addition, it is clear that there are a large number of factors which could affect performance due to the complexity of human behaviour. In the conceptual model these unknown factors are replaced by stochastic variables. Performance is sampled from a parametrized distribution that is nonstationary and can represent performance changes during the start-up of a style. Distribution parameters are provided from a family of nine deterministic performance curves[8]. During the simulation of production, the appropriate curve is selected from classification of operators and operations. The distribution parameters are retrieved to locate the performance distribution, and then a random sample of operator performance is taken. The process time can then be calculated by dividing the the standard minute value by the performance and multiplying the result by 100. Machine breakdown and repair Sewing machines are an essential component in clothing manufacture. In the domain of a model the machine may be considered just to constrain the movement of operators within the line, allowing a simplification whereby machines are not explicitly modelled. However, more comprehensive models must consider machines as resources which have characteristics both of the kind of work they can do and the problem of failure. In these models, machine types should be appropriate for a particular operation and, at the line design stage, it is necessary to consider the availability of machines of the correct type. From the supervisor’s perspective, the level of spare machinery is a factor which affects the management of machine breakdown and operator absenteeism. The effect of machine failure on the production line is complex: catastrophic failures result in total loss of production and require the attention of a mechanic. Operators receive make-up pay during the down time and the breakdown is appropriately identified in production records. Degradation failures and partial

Simulation of flow lines

19

IJCST 8,4

20

failures also occur which may not be immediately reported to the mechanic. These failures are manifested in the observed process times as the operator attempts to use the machine that is performing sub-optimally. A typical example of this type of failure is a persistent thread-snapping problem. For the purposes of the model only reported failures are explicitly modelled. Process time variability must contain an element of hidden breakdown from partial failures. In any case partial failure is confounded in the observed operator performances from which process times are derived. Down time due to failure has the potential to have a serious adverse effect on production. Models of breakdown and repair usually consider down time as a function of the number of machines, the number of mechanics and the repair time. This level of detail is required in the simulation model if the model, for example, is to be used to determine mechanic staffing levels. The standard treatment of breakdown[11] uses the concepts of reliability and failure rate. In the conceptual model, machine failure is represented by a parametrized distribution for mean time between failures (MTBF) which was determined through analysis of breakdown data. An abstraction from the base model considers the cause of breakdown to be an entity, the release of which constitutes the entry into machine breakdown. Time until next breakdown is a descriptive variable of this entity and is sampled from the MTBF distribution. Machine repair is a human activity and as such was considered too complex to model through deterministic component interaction. In the model presented here, repair time is a random variable that follows a log normal distribution and is based on the analysis of factory-based data. Absenteeism Absenteeism is one aspect of a garment production system that is clearly influenced by a large number of human factors. General texts relate absenteeism to a wide range of factors such as demographic, social and health phenomena[12]. The underlying processes behind absenteeism are unfortunately confounded in the available data held by some clothing factories. The frequency of absence demands that data over a long period of time are required to form an adequate sample and factory data must be used. Factory records of absence are, typically, entries in an absence book in which the days “off sick” of each operator are identified. Incorporating absence therefore involves a simplification of the base model by representing the complex factor interaction behind absence with stochastic variables within the model in a similar manner to machine breakdown. An abstraction from the base model considers the cause of absence to be an entity with a descriptive variable “mean time between absence”. The release of this entity in the model causes a given operator to enter a period of absence. Absence spell length is sampled from a second distribution. The fact that absences are generated over a long time frame means that data must be obtained from existing factory records. The three factories studied were manufacturing knitwear, underwear and lingerie. Of these, one (the

underwear factory) maintained no absence records at all. From the other two factories it was possible to obtain information on absence interarrival and absence spell length for each operator over a period of one year. The numbers of operators at each factory are shown in Table I.

Factory Lingerie Knitwear

Number of operators

Percentage having at least one absence during year

120 280

93 72

Simulation of flow lines

21

Table I. Absence spell data

For absence interarrival modelling, the data were analysed initially for the underlying distributional form. Consideration was given to homogeneity of the samples and an assumption was made that the data obtained within a single factory were homogeneous. For all operators, observed interarrivals were calculated from the time between two absence spells. Operators were then pooled within each factory and the data provided the interarrival distributions shown in Figures 1 and 2. These distributions contained selection bias to those operators who had been absent during the collection period and were used for visual analysis only to hypothesize an underlying form. From visual analysis of Figure 1, it is noted that both interarrival distributions are positively skewed, and that the absence rate may be higher for the lingerie factory. On the basis of this visual analysis, it was decided to simplify the data by adopting the negative exponential distribution as a data model. This is a single parameter distribution that is commonly used to model chance failure in Relative frequency (%) 0.6 0.5 0.4 0.3 0.2 0.1 0

1-20 –40 –60 –80 –100 –120 –140 –160 –180 –200 Days between absence

Figure 1. Absence interarrival time for a lingerie factory

IJCST 8,4

Relative frequency (%) 0.6 0.5

22

0.4 0.3 0.2

Figure 2. Absence interarrival time for a knitwear factory

0.1 0

1-20 –40 –60 –80 –100 –120 –140 –160 –180 –200 Days between absence

machines when failure rate is assumed to be constant[11]. The negative exponential distribution has an infinite right tail and could generate interarrivals beyond the range observed in the factory. However, the distribution is continuous and a transformation to the nearest whole day was adopted in the simulation model. A null hypothesis that the absence rates at each factory were not significantly different was rejected, and absence rate could not be assumed to be fixed in the simulation model. The simulation was then developed to allow absence rate to be specified for any particular factory, the parameter being derived from the standard absence rate (failure rate) equation so that the absence rate is corrected for operators not absent during the analysis period. A similar analysis of absence spell-length was undertaken and revealed marked similarity between the spell-length distributions (Figures 3 and 4). From either histogram in Figures 3 and 4, it can be seen that approximately 60 per cent of all absences are single-day absences. In addition, there is a marked peak at five days in both plots preceded by a trough at four days. It is considered that this latter finding is a manifestation of human behaviour: five working days may correspond to the whole week being taken off by the operator. It was considered unwise to hypothesize a standard distributional form for absence spell length. The distribution is discrete, with a small number of halfday absences, followed by 60 per cent whole-day absences. From examination of Figures 3 and 4 it can be seen that spells of more than 20 days contributed about 2 per cent of all absences. A discrete empirical probability distribution was used for absence spell length, defining the probability of all absences up to 20 days. The benefit of the empirical distribution was its ability to recreate the observed “peculiarities” that appeared to be common. Its only disadvantage was that insufficient data were available to define the right tail of the distribution, and 20-day absence spells would be the maximum generated by the model.

Relative frequency (%) 0.8

Simulation of flow lines

0.7 0.6

23

0.5 0.4 0.3 0.2 0.1 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Absence spell length (days)

Figure 3. Absence spell length for a lingerie factory

Relative frequency (%) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20+ Absence spell length (days)

A null hypothesis that the histogram spell-length distributions were not significantly different was tested by calculating expected cell frequencies at factory 3 (knitwear) from the empirical distribution from factory 1 (lingerie). χ2 was 23.512 against a critical value of 24.996 (15 DF, p = 0.05). The test failed to

Figure 4. Absence spell length for a knitwear factory

IJCST 8,4

24

reject the null hypothesis. On the basis of this finding an empirical absence spell-length distribution was developed by pooling data from both factories. Quality The incidence of faulty work may be modelled by random variables and integrated with factory-based statistical quality-control programmes. The model permits fault rates to be specified for each operation, and also enables the detection rate at “Final examination” to be predetermined. The rework route for faulty garments is specified by the user. While these facilities are present in the model, comparisons with factory sources of data have not been made because of constraints on data collection and project time. Supervisory control The production supervisor has considerable interaction with the clothing production line. A review of the role of the supervisor by Chuter[13] indicates responsibility for line balancing, organizing working methods, meeting production targets, work scheduling, quality control and many other personnel duties. During the development of the lumped model it became apparent that the role of the supervisor could not be omitted if all of the project aims were to be satisfied. The major performance indicators of production, cost per standard minute and line efficiency all illustrated unacceptable deviation from reality in an unsupervised model. However, the modelling of clothing production supervision is non-trivial. The problem is analogous to that of production scheduling, concerning which Rodammer and Preston White[14] concluded that no single modelling paradigm appears satisfactory. Whitaker[15] did attempt to model the supervisor. In his model of the progressive bundle system he stated that the procedure for implementing line balancing was “one of the most complex areas of the simulation”. Rebalancing was triggered if it was foreseen that any buffer stock would become zero during the next hourly period of production. He claimed success, but revealed little about how it was validated. Schroer’s[4] model of a unit production system is unsupervised, with throughput controlled by the operation with the slowest production rate. Rosser et al.[6] were concerned primarily with material flows and the reported problems of computer memory saturation are a direct consequence of the absence of supervision. Oliver et al.[16] make no reference to supervisory issues in their simulation of the bundle system. One alternative to adopting a modelling paradigm for representing human control is actually to use human supervisors in the control of the simulated system. This is a common method adopted in visual interactive simulation or VIS[17]. It is generally accepted that VIS does provide a powerful means of communicating the content and operation of a model to non-experts, because it utilizes animated computer graphics. However, the development of the visual interactive model is also non-trivial since the modes of interaction have to be considered. In addition, the presence of the “man-in-the-loop” having to respond to accelerated time cues creates problems for experimentation. Therefore, although control via the user (from

the keyboard) is appropriate for some types of experiment, it is not considered to be universally appropriate, as it cannot provide the high volumes of data required for statistical data analysis. Consequently, in addition to the VIS development route, it was decided to explore the possibility of a multiparadigm model of clothing production. A second aspect of the research project was an exploration of a knowledge-based approach to clothing production supervision. The supervisory “module” could be used to drive the simulated production line in a batch mode of operation to provide high volumes of data, and had the potential to be used in a standalone capacity as a training aid or as a monitor of real-world data. The combination of these areas of work presented a unique opportunity to use data from a surrogate real world in the development of an expert system. Validation of this system could then be attacked with far more rigour than is usually possible. Software development considered the definition of interactions between the discrete event simulation and external control software and the communications between them. The requirements for the supervisory component of the generic model were dictated by the limitations of discrete event/stochastic modelling languages, like SIMAN, at simulating cognitive behaviour. An embedded intelligent system which could simulate supervisory behaviour in real time, at fast inference speeds and in tandem with the existing generic progressive bundle model, was required. Unstructured interviews were carried out with an industrial line supervisor to identify the feasibility of the project. Conceptual analysis followed to gain familiarization with industrial practice. Once the feasibility and need for the system was established, a solution analysis was undertaken to identify a suitable software architecture in which to represent supervisory behaviour. This involved a period of knowledge elicitation interviews with a line supervisor. Structured interviews utilizing domain “props” to simulate the supervisor’s environment identified specific supervisory rules and reasoning strategies which could be modelled using a software architecture based on aspects of expert system and planning system. The knowledge engineering sessions culminated in a formal model of supervisory behaviour. This formal model of supervisory behaviour attempts to represent a human supervisor’s ability to understand complex manufacturing systems and perform a variety of reasoning tasks about those systems. Human supervision is generally performed with only minimal use of quantitative information, and often with incomplete or conflicting information. Supervisory reasoning about manufacturing systems is dependent on understanding the kinds of changes that can occur, the causes of those changes and their effects on the system. A formalization of supervisory behaviour must therefore take account of a number of human capabilities: (1) Humans understand fundamental concepts and can apply those concepts to different situations. A line supervisor understands the organizational necessity of producing to target. (2) Humans are able to establish the cause of changes and centre their reasoning about the effects of these changes. A line supervisor

Simulation of flow lines

25

IJCST 8,4

26

understands the relationship between operator absenteeism and line balance, and the sequence of events that connects one with the other. (3) Humans are able to reason about changes over time. Furthermore, humans understand the sequence of events through time. A line supervisor knows that a neckband cannot be attached to a garment until both the garment and the neckband are made. (4) Humans are capable of spatial reasoning. A line supervisor knows that an operator cannot be moved on to a machine which is already being used by another operator. These human skills are supplemented by domain-specific expertise. For example, the initial balance of a line is obtained by matching the work content of the operations to the skill and performance of the operators. In practice, the operators’ skills and performances rarely fit the work content of the operations and potential bottlenecks become inherent in the line’s design. The supervisor must identify these operations where the performances of the assigned operators fall short of the performances required to produce to target and give them appropriate help with the occasional transfer of another operator. Moreover, even if it were possible to achieve a perfect line balance, it would be impossible to maintain it over time due to line perturbations caused by machine breakdowns and operator absenteeism. The supervisor must exercise balance control. Balance control is necessary because of the sectionalization of the line which leads to different operations being performed at different rates. To provide protection against variations in output over discrete periods of time, an agreed amount of work-in-progress is allowed to act as a buffer between the sectionalized operations. These buffers tend to rise and fall depending on whether the operations performed first are accomplished at a higher or lower rate than the operations which follow. A supervisory goal is to make the flow of work through each operation as similar as possible. The success of this behaviour will be reflected in the measures of line efficiency and productive performance. Balance control is achieved by satisfying the goals of operator transfer according to the supervisor’s interpretation and prediction of line performance. Further details of the control aspects of this work are in Spragg et al.[18]. Conclusions for part 1 The research presented here is concerned with the development of models for the simulation of flow lines in clothing manufacture. While recognized guidelines for simulation studies have been generally adhered to, there are a number of specific new challenges that the work has addressed to ensure that the model has high credibility to industry experts: • The modelling of process times was a key issue. It is the authors’ view that the abstraction into operation and operation attributes is useful and contributes to the ability of the model to portray the dynamics of the start-up phase of manufacture.

•

•

Other major stochastic variables (machine breakdown, repair, absenteeism) are modelled according to distributions that have been empirically qualified and the parameters used are based on long-term factory studies. The role of the production line supervisor is recognized as a significant factor, but complex to model. The issues have been avoided in most reports of previous research. The methodology reported here has utilized real human experts together with visual interactive simulation to analyse the required control logic. This research has specifically addressed how supervisory control can be modelled in an appropriate paradigm and integrated with a more typical discrete event simulation model.

References 1. Fozzard, G.J.W., “Simulation of clothing manufacture”, PhD thesis, Department of Clothing Design and Technology, Manchester Metropolitan University, Manchester, 1989. 2. Tyler, D., “Managing for production flexibility in the clothing industry”, Textile Outlook International, September 1989, pp. 63-84. 3. Zeigler, B., Theory of Modelling and Simulation, Robert and Krieger, Malabar, FL, 1976. 4. Schroer, B.J., “Using simulation before implementing a unit production system”, Bobbin, Vol. 32 No. 3, 1990, pp. 110-16. 5. Schroer, B.J., Wang, J. and Ziemke, M.C., “A look at TSS through simulation”, Bobbin, Vol. 32 No. 11, 1991, pp. 114-19. 6. Rosser, P.S., Sommerfeld, J.T. and Tincher, W.C., “Discrete-event simulation of trouser manufacturing”, International Journal of Clothing Science and Technology, Vol. 3 No. 2, 1991, pp. 18-31. 7. Leung, S.Y.S. and Tyler, D.J., “Buffering operator variability in the clothing factory: a simulation study”, Journal of China Textile University, Vol. 12 (Supp.), 1995, pp. 85-94. 8. Tyler, D.J. and Fozzard, G.J.W., “Simulation incorporating characteristics of manual skill”, Proceedings of the 3rd International Conference, Simulation in Manufacturing, Turin, 1987, pp. 95-106. 9. Tyler, D.J., “Company time standards and the role of PMTS in the clothing industry”, Management Services, Vol. 32 No. 5, 1988, pp. 6-11. 10. Checkland, P.B., Systems Thinking Systems Practice, John Wiley & Sons, New York, NY, 1981. 11. Caplen, R.H., A Practical Approach to Reliability, Business Books, London, 1972. 12. Matthewman, J., Controlling Absenteeism, Junction Books, London, 1983. 13. Chuter, A.J., An Introduction to Clothing Production Management, BSP Professional Books, Oxford, 1988. 14. Rodammer, F.A. and Preston White, K., “A recent survey of production scheduling”, IEEE Transactions on Systems Management and Cybernetics, Vol. 18 No. 6, 1988, pp. 841-51. 15. Whitaker, D., “A study of a production line in the garment industry”, Clothing Institute Journal, Vol. XXI, 1973, pp. 113-20. 16. Oliver, B.A., Kincade, D.H. and Albrecht, D., “Comparison of apparel production systems: a simulation”, Clothing and Textiles Research Journal, Vol. 12 No. 4, 1994, pp. 45-50. 17. Hurrion, R.D., “Visual interactive modelling”, European Journal of Operational Research, Vol. 23, 1978, pp. 281-7. 18. Spragg, J., Tyler, D. and Fozzard, G., “FLEAS: flow line environment for automated supervision of simulated clothing manufacture” (forthcoming).

Simulation of flow lines

27

IJCST 8,4

28 Received March 1995 Accepted March 1996

International Journal of Clothing Science and Technology, Vol. 8 No. 4, 1996, pp. 28-43. © MCB University Press, 0955-6222

An analytical scheme for the change of the apparel design process towards quick response Cipriano Forza and Andrea Vinelli Istituto di Ingegneria Gestionale, Vicenza, Italy Introduction Increasingly fierce competition is pushing industrial companies towards the reduction of delivery times and costs while at the same time maintaining high product quality and variety. In order to meet this competitive pressure, the operative logic of the entire sector has been subjected to profound changes with the aim of achieving an “immediate response” system. The operative strategy which shapes these changes is known as quick response (QR) and when this term is interpreted in its broadest sense its primary purpose is the reduction of all the time spans that occur from the design of the cloth to the purchasing of the garments by the final customers. In QR strategy, the compression of time is seen as a necessary condition, on the one hand, and a means, on the other, of the improvement of company performance in terms of efficiency and the level of service offered. This improvement can be translated into an increase in company competitiveness and, for the final consumer, it can even have the effect of producing a reduction in price. QR can therefore be shown to be a critical factor in the process of improvement of competitiveness in the sector because, by making the entire chain directly dependent on market expectations, it ensures that a better service is provided and that there is a reduction in stocks, due to the long through times present in all the phases of the chain, and also eliminates the clearance sales caused by forecasting errors. Modelling of the phenomenon has been lacking up to now but, above all, there seems to be a lack, on the one hand, of QR models available to companies in order to evaluate QR applicability to contexts that may not be those of the early applications and, on the other hand, precise indications of an operative managerial type of the changes necessary in order to realize QR. The authors of this present paper wish to offer a contribution to this field. Given the innovative nature of the problems analysed, with particular reference to the lack of widespread and consolidated company applications, the research methodology used is based on the first-hand knowledge, on the consideration and experience of privileged operators in the sector and of managers of leading companies belonging to the various links in the chain. Indeed, the observations made in this paper are a result of meetings and appraisals that have occurred in the course of the last two years with the managers of Benetton, Coin, Levi’s and Marzotto.

In the study, several considerations will be proposed that, with reference to the entire textile-apparel sector, show the significance and strategic importance of QR and the organizational, managerial and technological conditions necessary for its realization in terms only of the design activities and the interrelations between these and production activities. In addition, a descriptive and interpretative model will be presented that examines the temporal sequences of the activities and decisions along the textile-apparel chain in relation to the typology of the product. This scheme of reference, which has been discussed and verified with the managers of the companies, will constitute a chance to examine the opportunities for improvement and also to identify the obstacles that interfere with the realization of QR in design. A first examination of a class of clothing products (the hanging garment spring-summer collections) carried out by means of the proposed model demonstrates the possibility of compressing the long response times, typical of the chain, in order to achieve QR. In the analysis, the design activities at the level of the entire chain and the interaction of these with production that necessarily require restructuring using the QR approach will be identified. In the study the prospects for intervention will be presented, considering the technologies and the organizational changes most significant in the redesign of company processes for QR. These general indications reflect specific applications which have already been realized or are in an implementation phase. The success of QR initiatives implies, in fact, interventions and systemic changes on levers both of a technological or organizational kind, which are specific to the reality of each individual company, and on factors purely external to the company, such as the evolution of relationships with the partners in the chain or, in more general terms, the evolution of the conditions of the productive context. The strategy of quick response As the name implies, the main aim of QR can be considered the reduction of the inefficiencies of the textile-apparel chain and the increasing of final customer satisfaction through the compression of response times by the various actors in the chain. Blackburn[1] considers QR an extension of the principles of just in time (JIT) over the whole value-chain system, through active integration of all the actors, from the producer of fabrics to the final distributor. Ferrozzi et al.[2] define QR as an operative strategy for the co-ordination of the textile apparel companies with the manufacturing industries, in order to achieve the flexibility necessary to be able to respond faster to market oscillations. QR aims at modifying the current organizational system of the chain, speeding up the physical and information flow in both directions along all the phases of the value-operative chain system. The traditional modality of communication between the actors in the chain, based on sectorial trade fairs and on the sequence of supply orders – in terms of quantity and price – is replaced by a punctual, accurate and bi-directional information flow from and between all the actors in the chain[3]. Each link in this system shares

An analytical scheme for change 29

IJCST 8,4

30

information on sales, orders and stock with the other links and, in this way, JIT principles are extended to the entire value-operative chain, substituting stock with information and reducing the Forrester effect of amplification of the oscillations in final demand[4]. In order to reduce stock levels and risk along the chain, thus guaranteeing better service to the final customer, it is necessary to think through the question of dislocation of warehouses and the possibility of reducing component variety by making changes in the design and planning phase. It can be noted, in fact, that product variety increases exponentially, passing from the yarn manufacturer to the fabric manufacturer and then to the tailoring stage, but then diminishes drastically at the distributors and at the point of sale. In this way, the production commitment of the first phases becomes partly invalidated and does not materialize in the improvement of service to the customer at the sales outlet, since the final consumer, although correctly segmented, “sees” only a very small part of the entire production realized at the sales point. Figure 1 is a graphic representation of the structural situation of the chain.

Variety

Figure 1. Product variety in the various phases of the textile-apparel chain

Fibre

Yarn

Fabrics

Garments

Assortment Consumer at point alternatives of sale

In order to respond closely to the needs of the final consumer, it is not sufficient to reduce the lead time to the distributor. Greater customer satisfaction is obtained by meeting and predicting their different needs in all periods of the year. Following the same logic, the two traditional collections, spring/summer and autumn/winter, which are still typical in many firms, are no longer sufficient, and in fact a larger number of collections is needed for the same target. This need is already present on the market, and many firms are increasing the number of collections, either of their own accord or on the explicit request of the large-scale distributors. This clearly involves, on the one hand, an

increase in their design capacities in terms of the reduction of design time and costs, which can be obtained through interventions of a technological or organizational-management nature and, on the other, increased collaboration between the various actors in the chain. The long wait for the new fabrics Production stage chart in the textile-apparel industry To analyse the changes in the decisions and activities of the textile-apparel chain from a QR point of view, it is useful to refer to the production stage chart (PSC)[5]. In this diagram, the activities of design, production, ordering and dispatch are clearly correlated with the exact moment at which decisions must be taken about the activities involved and about the periods in which such activities occur. Figure 2 presents the PSC typical of hanging garments (i.e. coats, jackets, overcoats, etc. or rather everything that is stored through “hanging”) with reference to the spring/summer season. The PSC of the hanging garment has been deliberately chosen for consideration because this product seems to present greater problems in the realization of QR. It is worth noting also that the second season typical of the sector (i.e. autumn/winter) presents some differences from the one illustrated. The times and phases are, moreover, conventionally assumed. The PSC represented in Figure 2 is now used in company practice independently of the type of clothing involved. It follows that for all the garments a period of about four to 12 months lapses between the moment of

An analytical scheme for change 31

Production and delivery of yarn for design and realization of fabric sample collection

2 Yarn

Ordering of yarn for the design and realization of apparel sample collection Circulation of fabric sample 3 Production and delivery of fabrics for the design 5 and realization of apparel sample collection

1 Fabric

Definition and realization of sample collections, ordering of necessary materials

4 Apparel

6

“In the dark” fabric ordering

7

Ordering of items

Distribution

October

September

July

August

May

June

April

March

January

February

December

October

November

September

July

August

May

June

April

March

January

February

December

October

November

September

Sales to the public of previous spring/summer collection

Figure 2. Production stage chart in the textile-apparel chain for the spring/ summer season

IJCST 8,4

32

fabric design and the presentation of the sample collection to the distributors. It should also be emphasized how, according to this PSC, when the distributor defines the purchasing order, the previous spring/summer season has not yet ended and, therefore, information on the trends is still rather limited. The PSC of Figure 2 can be analysed with reference to the example of the spring/summer season 1996. Following this, the individual activities and their interrelations will be identified and briefly described. The dates of the beginning and end of the various activities are, in reality, less defined than what appears in the figure and tend to be less and less so, because of the tendency to increase the number of collections through previews and post-season collections which are aimed at a very clearly defined target and make it possible to serve the potential customer by continually following the evolution of the moment. This tendency, whether derived from market needs or the need to achieve a levelling off of production, means that, in practice, there is not one single PSC for a given season, but a PSC for each collection. These collection PSCs are characterized by having the same sequence relative to the various activities, but shifted in time. For simplicity, reference will be made to the more traditional situation which better illustrates the operative logic of the sector and the activities relative to the realization of the spring/summer season 1996 will be considered. The activities relative to the design of fabrics and apparel and the realization of sample collections To analyse the first activities relative to the spring/summer season 1996, it is necessary to go back to September 1994. It was approximately in that month, in fact, that the fabric manufacturers began the design of the fabric to propose to the garment manufacturers. It should be remembered that not only one product is designed, but a whole product range with certain characteristics (for example, light fabrics, with pastel colours suitable for spring garments). Very often, standard yarns are used for the design of fabrics, and these yarns are not difficult to obtain. Even when the yarn used is not standard there are no serious problems, since this yarn, or yarn of a similar type, can be taken from the designer’s warehouse which, even if it is of limited dimensions, contains a huge variety of yarn. Non-standard yarn can also be ordered in small quantities from the manufacturers, who generally have a very flexible response, both because they have sections dedicated to the rapid production of small quantities of yarn and also because the spinning is in many cases an offshoot of the weaving department. Other modifications of the sample collection can be effected with a minimum design effort, since recourse is made to new variants (or new colours) on articles which are already present in the sample collection. The ordering, production and the delivery of the yarn necessary for the realization of the fabric sample collection generally occurs simultaneously with the design of fabrics, and only in a very few cases does this occur at the end of the design stage. The production of the fabric collection takes place in February/March 1995, for an overall period of approximately a month and a half.

In the second half of March 1995 the fairs take place and, on this occasion, the samples of cloth are delivered to the garment manufacturers. The fairs make it possible for the proposals of the fabric manufacturers to circulate widely, even if this exchange is limited to a short period of time. At about this same period, the garment manufacturers begin the activity of defining the design of their collection. This task includes various activities, which take place in the following order: (1) the analysis of the corresponding previous season; (2) the definition of the general scheme of the models; (3) the manufacturing of the models, through the two parallel activities of detailed definition of the models and the fabrics. The test garments which are thus produced are evaluated in terms of their look, wearability, production cost and possible commercial difficulties. As a result of this, it is often necessary to modify many of the models presented (up to 80-85 per cent). The modified models are retailored and re-evaluated and this is when the garments/models which will make up the sample collection are finalized. Other factors are also taken into consideration in the finalization of the models, and these factors are also determined by creation/design criteria in the strictest sense, but these can nevertheless have a significant impact on the production of the garments, such as, for example, the need to limit the number of garments in relation to production capacity, or the availability on the market of the fabrics and colours in the necessary quantities and with suitable supply conditions. The supply of the fabrics for the production of the collection happens alongside these activities. The new fabric collections are based, as far as colour, fabric weight and design are concerned, on the analysis of the most successful articles of the previous season. Moreover, in order to make the correct choice of fabrics (and for the first fabric-order launch) the suppliers are taken into consideration. This analysis takes account of the various company operative lines, and requires adaptation of the design and industrialization on which the collection will be based. Once the fabrics have arrived, the garment manufacturers will carry out tests in order to ascertain both the technological characteristics of the fabrics and their suitability for industrial production levels, and in order to avoid difficulties of a technical nature during the production cycle. The collections of tailoring companies are in part composed of models to which fabrics defined as “continuative” are matched, the supply of which is not problematic since such fabrics imitate, both in composition and colours, fabrics already presented in previous seasons. For models tailored in innovative fabrics, however, the supply of fabric for the realization of the sample collection is problematic and often the clothing manufacturers launch collections which include models for which the definitive fabric has not been used, but rather a similar fabric. The placing of orders from sample bolts of fabric, necessary for the realization of the sample collection, is therefore of decisive importance, given the brief time span which has to lapse between the placing of orders and

An analytical scheme for change 33

IJCST 8,4

34

the arrival of the fabrics. The quality, timeliness and punctuality of the suppliers in this phase strongly conditions the realization of the sample collection. Tailors start to make orders for sample bolts necessary for producing the sample collection at the fairs, they continue through the design phase and, in some cases, even after the end of the design phase. The sample bolts are requested in a limited way, since it is very difficult for the suppliers to reproduce many different fabrics in very small quantities. The ways in which textile manufacturers meet the requests for sample bolts varies according to the types of yarn which make up the fabrics. The yarns which are not very fungible, or rather those with a higher fashion content, are in fact dealt with strictly on the receipt of orders, and therefore the delivery of fabrics which require this type of yarn can have lead times of as long as 120 days. Nevertheless, many yarns have a continuing character, or rather they are always being used and requested: the fabric manufacturer operates according to forecasting with these yarns. For certain types of continuative yarns the manufacturers work according to “point of reorder” stock methods, and the stock levels can represent 50 per cent of the total goods purchased for a medium-quality producer, while it can represent 20 per cent for a high-quality producer. The yarn lead time also depends on the yarn manufacturer’s level of specialization, because with those yarn manufacturers who are specialized in only a very few types of yarn, the lead times can be very short. From the beginning of June to the first days of July 1995 the garment samples are produced and the sample books of articles and colours that make up the collection of fabrics matched to the models are prepared. The complete success of this phase depends on the resolution of conflicts between the realization of the collection and production for the preceding season that is still in progress, on the timely receipt of fabrics and accessories according to plan, and on how suitable these are for production in terms of quality. Last but not least, the capacity of production to take the stylistic innovations proposed on board, and translate the directions which emerged in the sample study phase into wearability and quality should be mentioned. The interactions of design activities with activities relating to fabric purchasing and the sales campaign Contemporaneously with the production of the collection, the clothing manufacturer also releases some fabric purchase orders. In fact, given that delivery times are inconsistent with those necessary for production, it is unthinkable for them to supply themselves exclusively according to needs, but a large part (quantifiable at about 40 per cent of the total fabric purchased) is acquired on the basis of forecasting. The fabric orders, placed before receiving the orders from the distributors, are called “orders in the dark”. The orders in the dark are based essentially on how sales went the preceding season. Once the garment collection is realized, the sales campaign begins, with the presentation of the collections to the sellers. On this occasion a first verification of the collection is made when the sellers choose between the

models presented to find the ones that are best suited to the characteristics of their own clientele. Next, the representatives of the garment manufacturers begin to visit clients to receive orders for articles of clothing. Order collection lasts three to four months (from the beginning of June to October). It should be noted that the placing of orders for garments by the distributors is completed only a couple of weeks before the end of sales relative to the spring/summer season 1995. A couple of weeks after the arrival of the first orders, the garment manufacturer begins to order fabric according to forecast and sales. This practice is a consequence of the sales campaign, during which the company obtains information concerning sales (e.g. models, conformation, sizes, types of fabric, colours, etc.) which will make it possible to get more and more precise data concerning quantities and types of fabrics to be ordered. The processing of these data can be carried out per model (with subsequent specifications for classes of model, conformation, height, size, etc.) in the attempt to speed up the sample, favouring concentration on models considered to be the most commercial ones. Otherwise, the analysis can be conducted according to price and fabric, emphasizing the price ranges which are more pleasing to the customer as well as the popularity rating of certain typologies of fabric and colour. All this information can be used to make possible alterations to the first dispatch of fabrics and to send out successive ones with an improved degree of reliability. The informational power of these data is greater the more numerous the recorded data on sales and the more homogeneous the geographical zones in terms of preference of fabrics and colours. In the most favourable case, it already becomes possible by the first week of sales to formulate very accurate and reliable forecasts of future demand for fabrics and accessories. Prospective areas for intervention by quick response QR proposes to make the chain more competitive through the speeding up of time to market, the continuous transmission of information from the customers and, beyond that, along all the links in the chain and the construction of value with the improvement of the quality of service to the customer, on the one hand, and the overall decrease of entrepreneurial risk along the chain, on the other. The technological and organizational impact which this has is very high, particularly because of the need for the interconnection of a whole series of conditions, prerequisites and constraints, both internal and external to the company. From the analysis of the PSC of all the activities in the chain, and from the reflections and accounts of first-hand experience collected during encounters with experts in the sector and managers of important leading firms which are representative of various links in the chain of textile manufacturing, two significant areas of intervention seem to emerge[6]: (1) the fabric and garment design/industrialization cycle; (2) the supply, production and sale to final customer cycle.

An analytical scheme for change 35

IJCST 8,4

36

In the present study, only the first of these two macro-areas for intervention will be considered, but it should be remembered that interventions on the two macro-areas are, of course, interrelated. These interventions always presuppose notable organizational changes, even if, in many cases, technology plays a fundamental role. In other words, the availability of new technologies and integration of the links in the textile/apparel chain seem to be strongly interrelated factors which reinforce each other. The technological and organizational impact is not free of obstacles and, if the adoption process is to be successful, it must overcome a “force of attrition” inherent to every process of change. This is a reference to intraorganizational constraints that the company wishing to realize QR must overcome in terms of greater functional integration, and to those interorganizational ones where overcoming a long-standing sectorial culture is necessary. QR in design The interventions in the design macrophase can be essentially linked to three main aims: (1) the reduction of lead time in design; (2) the reduction of the variety of production input, without penalizing the variety available to the final customer; (3) the acquisition of preliminary information on future sales. Objective: reduction of lead time in fabric design. The trend today is towards an increasing number of collections, due both to specific requirements of the largescale distribution companies and to the attempts by manufacturers to achieve continuous satisfaction for potential customers by supplying properly targeted collections. This tendency, which is felt to be even more important by companies operating in foreign markets, paradoxically has a positive effect on the levelling of production during the year but creates new challenges for companies to design new articles in short time spans and at low costs by choosing the most suitable assortments to meet market demand. The “design time” should generally be understood to be the time that lapses between the beginning of fabric design and the realization of the sample collection of the tailoring company. The shorter this time is, the more fabrics and models can reflect the expectations and needs of the final customer. From the analysis of the PSC the rigid sequentiality between fabric design and garment design has become apparent, as well as the knowledge that in practice these phases are “solidified” during the sectorial trade fairs in March. This traditional method of operating means that a fabric which is designed in September/October has to wait for March to be seen by the tailor. This time span is used today to rationalize the demand and the offer of novelty in fabrics so that they can match up. However, in a perspective of an increasing number of garment collections, the fractioning of these collections in the space of a year

and of the reduction of the time which lapses between the ordering and the delivery of the garments, such a time span seems to be excessive. Thus, the proposal of new fabrics and the design of new garment collections must be oriented towards a less cyclical and a more continuative progression. Consequently, new occasions and methods of exchange and interaction between fabric manufacturers and tailoring companies in the design phase should be found. A closer, more flexible and continuous contact between them, which is not rigidly tied to the dates of the fairs, is possible. Experiences of important Italian companies in the sector indicate, in fact, that although the annual turnover is pretty high (about 10-20 per cent), the suppliers – understood in the broad sense, including not only habitual suppliers, but also potential suppliers who are in line with company requirements and needs – is not especially variable in the medium term. In the light of this, design times and costs gain enormous benefits from the support offered by information technology[2,8]. The level reached by these technologies is very high today, and promises further important improvements in the short term. The stylistic creation and elaboration phase is supported by CAD systems, which make it possible to drastically reduce the model invention time by the designers. These systems also allow the designer to modify photographic images (or even three-dimensional ones produced by the telecamera) and work on the models, changing their colour, design and fabric with extraordinary ease, so that thousands of colours can be tried out. It is possible to simulate the dressing of a dummy, with the folds, draping and shadows. These systems reduce the waste of time and money in the production of samples, allowing the designer to check and modify the models without the need for any sewing, just producing paper models automatically. The system has also proved to be an effective sales instrument and those responsible for the selection or commercialization of the goods can see an immediate representation of a finished garment in a variety of colours, models and fabrics together with different combinations of accessories. It is also useful in the preparation of material for catalogues, brochures and advertising. Support is also supplied to the designers in the form of similar interfaces to the traditional ones (for example, the optic pen combined with an electronic board), which does not demand a complete change of mentality and a computerized approach. Recent progress made in the theory of elastic deformation applied to the textile apparel industry means that in the fairly near future (four to five years) it will be possible to have three-dimensional simulation of wearability. Even in the next phase of base cutting creation, computer studies provide excellent support. With the pattern design system the models are generated quickly and with precision, thus considerably reducing the model development cycle. It is possible to create the new model, or to modify the existing one, in the space of a few moments, instead of hours or even whole days. New programmes make it possible to design the models with instruments or rules similar to those used to create them manually, but in such a way that the passage from manual work to automatic work becomes more comprehensible. These systems offer

An analytical scheme for change 37

IJCST 8,4

38

automatic simulation functions to reproduce such things as folds, darts, ruffles, widths and seams. These also make it possible to obtain the measurements of one of the parts of the model (by applying different rules) and to file them for later use. The models created with these systems maintain the consistency of the type of lines and measurement of the model, and a further advantage is gained in that there is greater producibility and an improvement in the use of the material. The next phase is that of the development of cutting and the study of positioning, and there are software packages available which offer a huge variety of options, guided either by menus or by automatic procedures for the development, placing, printing and drawing of the models. The most advanced software interfaces interactive and automatic positioning programmes, thus supplying the possibility of digitalizing, modifying, developing and positioning the models in a time span which is vastly inferior to the time necessary if these operations were carried out manually. The management of the constraints linked to the fabric (top side/reverse side/velvet, etc.) and the pieces of the garment to be placed (rotation, outlining values, etc.) completely eliminates human errors of positioning of the various images. For greater flexibility, it is possible to modify these constraints in the graphic treatment directly and in real time, in an interactive way, and thanks to this interactivity greater economy of raw material is obtained. The updating of the positioning is instant and automatic; all the modifications of a piece of cloth (for example, the addition of a notch or an inner seam, etc.) are carried out systematically in the positionings in which it is inserted. In the most recent versions a wide range of production typologies is included: checked cloth, closed, double, tubular, etc. Even cost forecasting is aided by special production software packages. Software exists on the market that even uses the support of graphics and analyses and simulates manufacturing process costs of a model. These programmes calculate the use of materials and accessories, thus making it possible to obtain the precise industrial cost. To this end, all the information which is the fruit of the individual company’s experience is memorized and exploited. In some cases predetermined standard time methodologies are associated to this information and are incorporated into the calculation. With some of these software packages it is also possible very quickly to construct manufacturing cycles, selecting the style and the different elements of the products to be realized as well as the various operations necessary for production. These software applications can communicate between them to achieve the most advanced applications, thus uniting in one central data bank the information relative to the creation, the development, the materials and the tailoring of the model, thus constituting an integrated information system. This makes it possible to document all the information, from the creation phase to that of production, in relation to the models subdivided by line or collection. This integration makes an effective product data management and a timely

updating of the work sheets possible and, in some cases, it also presents the ability to achieve multimedial telecommunication, leading to a timely coordination of units which are geographically distant. The presence of a central data bank eliminates the need for repetitive insertion of identical information coming from different divisions of the same company. One single stock area allows authorized operators to gain access to display information or data modification, such as information on fabrics, seams, models, sketches, assembly and costs. The information on models can be catalogued by division, season/year, or in order of creation. Thus, even the preparation of technical product sheets is automized, with the recall ability from the central data bank and from other information programmes on fabrics and sketches of models, technical design for tailoring, measurement of the various cuts, description of the materials and accessories with the relative costs and suppliers, data relative to positioning and information of the modifications made to the model. The new technologies and, in particular, the CAD and CAD/CAM, lend support to all the phases in the process of invention, design and industrialization of the garments and fabrics. In order to cite some examples which are already present at significant levels in many companies in the fabric sector, these new technologies are employed for fabric design, automatic creation of fabric samples, the development of print designs, colour analysis and the development of print transparencies, the reception and automatic certification of colours on terminals for the dyeing and finishing processes, the analysis and control of colours online, etc. In the garment trade information technologies are a precious support for the invention of new models, analysis of garment wearability, production of paper models, control and modification of the models without previous cutting, preparation of material for catalogues and advertising, creation of the cutting base, development of cutting and study of positioning, realization of sample garments in greatly reduced time spans, cost forecasting, etc. The integrated management of these technologies makes it possible to create work sheets which are always up to date in relation to the most recent variations, such as the model description sheet, tailoring diagram, packing/ despatch documents, cutting order, measurement sheet, cost table, material description sheet, positioning sheet and, finally, revision history. The new technologies have also shown themselves to be efficient in resolving the problem of the supply of fabrics to be used in the realization of the sample collection. As has already been mentioned, the textile factories encounter considerable difficulties in producing very small lots which are also very varied, and this lengthens the response times considerably. Today, through the use of wax and ink-jet printers, patterns and colours can be reproduced on special paper with surprising results, in that they are able to substitute the “big sample collections” in the preparation of the bundles and samples that make up the textile sample collections. Objective: reduction of the fabric input variety. The reduction in variety in the initial phases of the productive process and, at the same time, the

An analytical scheme for change 39

IJCST 8,4

40

displacement/ maintenance/increase in variety in the final phases of production, can offer significant help in establishing new modalities for sales, production launching and supply, as demonstrated by initiatives of this kind in the automobile and electronics sectors[9,10]. These initiatives suggest that one should operate, during design/planning, on the elements both parties have in common and seek product differentiation in the last phases of the productive cycle. If applied to the textile-apparel industry chain, this would mean producing yarn or fabric according to forecast, and garments on the basis of data on current sales data. The reduction in variety as far as yarn is concerned should be pursued in the fabric design phase and requires a different use of CAD from that used up until now. So far, in fact, CAD has been used for the creative part of fabric design, with particular attention to the resolution of images on fabric. Less attention has been paid to the use of CAD to reduce the types of yarn used or to allow differentiation in the last phases of fabric production. A very close interaction between yarn and fabric designers, moreover, could lead to the attempt to reduce the number of threads, through a suitable choice of fabrics on the part of the garment tailors. It should be noted that several types of fabric exist that respond to the same quality and aesthetic criteria, but currently the range of freedom of fabric choice is not used to increase the standardization of fabric and yarn. If this were done, the variety of productive input and the complexity of the system would be reduced, without penalizing the variety and service offered. Finally, the combination of these initiatives followed up in the design phase allows the achievement of a basic standard that makes it easier to operate on the basis of forecasting. In fact, a reduction in the number of yarns makes knowledge of mix for the purpose of supply less important and, at the same time, increases the information value correlated to sales volume. This practice, if consolidated, would extend and make the trend towards producing yarn according to forecasting easier. This is the reality, already verifiable today for some yarns historically in great demand or for which fashion trends indicate a high probability of use. Objective: acquisition of information. In a context in which one can/must also work on forecasts based on current sales data concerning the final customer, and where immediate response to the needs of the client signifies competitive advantage, any information that makes the future less uncertain has a high value and should be used to advantage. Today, the information concerning the choice of fabrics by tailors is not systematically recorded and is not properly exploited by the fabric manufacturers. It is difficult, for example, to know which fabric, among the many proposed and presented in the fabric sample collection, actually interested the person who picked up the fabric catalogue during the fair and, even if this information is known, it is not particularly significant, because it may not be that person who decides which fabric is to be adopted by the tailoring company.

In particular, the first indications of fabrics that will be used are given by requests for sample bolts or pieces, but these are still considered weak signals and are not sufficiently elaborated. The “true” information is derived instead from orders received for actual production. Translated into time, this means that the garment maker knows what is most in demand only when the advertising sales campaign for the garments has begun. In a QR context, therefore, an increased interaction between textile producers and clothing manufacturers should be sought, as far as the design and choice of fabrics during the design of articles of clothing is concerned. In particular, an actual use on the part of textile producers and yarn manufacturers of information about the fabrics and yarns used (and/or already ordered) for the preparation of samples should be sought. This information should be finalized towards the acquisition of indications on future yarn and fabric production needs as well as towards the rationalization of the fabric offer. As regards this, it should be noted that information concerning the garment manufacturer’s sample collection is more useful to the manufacturers of yarn than to the producers of fabrics, since the various yarns can be reproposed in several different fabrics. For example, the number of models that contain a particular fabric can be deduced from the sample collection of the garment manufacturer. By putting together the information collected from the various garment manufacturers served, information can be gained about the respective consumption of the various fabrics. From the breakdown obtained in the basic specification and the collected information concerning the various fabrics, information is then obtained about the respective consumption of the various yarns. This is a minimal level of information, but it is very useful and reliable for the forecasting phase, since the fabrics which are not used in the garment manufacturers’ sample book will certainly not be requested. On a second level, as far as the yarns are concerned, this information also provides some fairly clear indications concerning the statistical distribution of the yarn in the various garments present in the sample book. A further area for improvement lies in better communication between the fabric manufacturer and the garment manufacturer concerning the fabrics which are being evaluated in the design phase. This information should of course be transmitted before the ordering of the fabrics necessary for the realization of the sample collection, and could make it possible to eliminate some fabrics for which demand is very low; indeed, for the fabric manufacturer, this could mean a reduction in the variety offered without having a negative effect on the level of service offered. In this case, therefore, information technology can provide useful support[11], even if the key element in the production of greater information exchange remains organizational and cultural. Nevertheless, there are already examples of the success in the electronic exchange of information. In particular, reference should be made to the early transmission from and to suppliers of technical information concerning materials, and to the transmission of prints and display images of fabrics to the upstream phases and groups of users.

An analytical scheme for change 41

IJCST 8,4

42

Conclusions The present study has attempted to offer a contribution to the creation of models in the phenomenon known as quick response and, in particular, it has proposed models of a descriptive and interpretative type which examine the temporal sequences of the activities and decisions taken in the textile-apparel chain with reference to design. These models have been used in order to examine the opportunities for improvement in the design activities in the textile-apparel chain with a view to the adoption of quick response, and possible areas for intervention, both from a technological point of view and an organizational and management one, have been presented. Emphasis has been placed on the long time span which in general lapses between the fabric design phase and the evaluation of these fabrics by the tailoring companies. This time interval, which is tied to the fairs as a privileged point of contact, reduces the possibility of following a potential customer’s preferences more closely. It has also been shown how the length of accumulated lead time up to delivery to the distributors generates a system which is in general rather inefficient, and which produces high costs and a limited level of satisfaction for the final customer. By using the models for analysis proposed, the possible interventions along the chain as regards design activities and interaction between these and the production and sales activities have been analysed. The interventions in the design macro-phase can be summarized in the following essential points: • the reduction of design lead time, through the parallelization of fabric and garment design and through the use of information technology; • the reduction of the variety of production input without penalizing the variety perceived by the final consumer; and • the acquisition, during design, of preliminary information on future sales, in order to rationalize the offer and carry out the initial assortment of production input. These last two interventions which have been identified are preparatory to the restructuring of production/distribution activities and in particular to the reduction of fabric supply lead time and garment lead time. These operations require new types of relations between the various actors in the chain, and this is perhaps the most complex type of intervention to be made, since it implies a cultural change in the relations between the actors and its realization will of course be a long-term project. References 1. Blackburn, J.D., Time Based Competition, Irwin, Homewood, IL, 1991. 2. Ferrozzi, C., Hammond, J. and Shapiro, R.D., Logistica & Strategia due, ISEDI, Torino, 1993. 3. Forza, C. and Filippini, R., “The role of information and communication systems in world class manufacturing”, in Hollier, R.H., Boaden, R.J. and New, S.J. (Eds), International Operations: Crossing Borders in Manufacturing and Service, North Holland, Amsterdam, 1992, pp. 175-80.

4. 5. 6. 7.

8. 9.

10. 11.

Stalk, J.G. and Hout, T.M., Competing against Time, Free Press, New York, NY, 1990. Corke, D., Production Control is Management, Arnold, London, 1969. Forza, C. and Vinelli, A., Quick Response, CEDAM, Padova, 1996. Forza, C. and Vinelli, A., “Quick response in the textile-apparel industry and the support of information technologies”, Integrated Manufacturing Systems, Vol. 7 No. 3, 1977 (forthcoming). Aldrich, W., CAD in Clothing and Textiles, BSP Professional Books, London, 1992. De Toni, A. and Zipponi, L., “Operating levels in product and process design”, International Journal of Operations and Production Management, Vol. 11 No. 6, 1991, pp. 38-54. Lucas, D.I., “The impact of information technology on logistics”, International Journal of Physical Distribution & Logistics Management, Vol. 21 No. 5, 1991, pp. 32-9. Clarke, R., “A contingency model of EDI’s impact on industry sectors”, Journal of Strategic Information Systems, Vol. 1 No. 3, 1994, pp. 143-51.

An analytical scheme for change 43

IJCST 8,4

44 Received May 1994 Revised and accepted October 1995

The application of fabric objective measurement in shirt manufacture Kwok-Po Stephen Cheng, Yan-Lai How and Kit-Lun Yick Institute of Textiles and Clothing, Hong Kong Polytechnic University, Hung Hom, Hong Kong Introduction With the increasing pressure of quick response and severe skill shortages in the clothing industry, many clothing manufacturers in Hong Kong have sought a scientific solution to support their production efficiency and product performance[1]. Fabric objective measurement has recently been profitably applied in the tailored clothing industry for predicting fabric tailorability and garment appearance and quality. In the present investigation, the objective measurement of mechanical properties has been extended to shirting materials. Based on the mechanical parameters, some difficulties during the production processes such as spreading, cutting, overfeed operation, handling, pressing, and garment appearance can be predicted and controlled by the manufacturers in order to achieve high-quality and efficient shirt manufacturing. Instrumentation The fabric low-stress mechanical properties can be measured by two sets of instruments – Kawabata evaluation system for fabrics (KES-F) and fabric assurance by simply testing (FAST) system. In a previous work[2], it was identified that both of the instruments, originally designed for suiting materials, could be used for measuring shirting fabrics with accurate evaluation of fabric performance. Some other factors, such as the cost of the system, installation costs, training cost and limitations of time must be considered when selecting a better system for the industrial environment. As the KES-F system is a very sensitive and complex system, it is preferable for research or academic purposes. For industrial application, an inexpensive, robust and simple-to-use system would be preferable[3,4]. In view of the above, it is concluded that the FAST system is to be favoured for the industrial environment as there are no obvious discrepancies between the two systems when measuring shirting materials.

International Journal of Clothing Science and Technology, Vol. 8 No. 4, 1996, pp. 44-64. © MCB University Press, 0955-6222

Experiment In the present work, 60 commercial shirting materials were sourced from a large local shirt manufacturer. The fabric details are listed in Table I. All the fabrics were tested for their mechanical and physical properties by using the FAST system.

P/O

Fabric ID

546 546 1411 3607 3607 3981 3981 5009 5057 5152 5152 5252 5252 5252 5252 5355 5355 5466 5466 5500 5534 5534 5544 5544 5593 5638 5659 5696 5698 5771 5785 5818 5865 5895 5958 6362 6374

SMT-01582 SMT-01605B SMT-01605 SMT-11448EC SMT-11448RE SMT-20204BL SMT-20204BU SMT-20367 SMT-01457 SMT-20363GR SMT-20363WH SMT-01474A SMT-01474B SMT-01474C SMT-01474D SMT-01498 SMT-11431 SMT-01475A SMT-01475B SMT-01480 SMT-0148EC SMT-01484WH SMT-11366 SMT-11371 SA-70594 SMT-015507 SMT-01501 SMT-20382B SMT-20382A SMT-01512 SMT-01514 SMT-11426 SMT-11429 SMT-11436 SMT-11365 SMT-01516 SMT-01535

Fibre (%) 100C 100C 100C 80C, 20W 80C, 20W 100C 100C 100C 100C 55C, 45P 55C, 45P 100C 100C 100C 100C 100C 100C 100C 100C 100C 100C 100C 100C 100C 55C, 45P 100C 100C 100C 100C 55C, 45P 100C 100C 100C 100C 55C, 45P 100C 100C

Density (/cm) Count (s) Thickness Weight Warp Weft Warp Weft Structure (mm) (g/m) 63 63 63 28 28 47 47 47 31 43 43 63 63 63 63 57 57 57 57 63 57 57 63 63 54 31 27 57 57 63 63 51 59 63 43 32 63

24 24 24 26 26 39 39 31 18 28 28 24 24 24 24 30 30 35 35 24 31 31 24 24 28 18 21 30 30 24 24 39 31 24 28 20 24

80/2 80/2 80/2 24 23 50 50 40 16 45 45 80/2 80/2 80/2 80/2 50 50 50 50 80/2 50 50 80/2 80/2 45 16 21 50 50 85/2 80/2 50 50 80/2 45 20 80/2

80/2 80/2 80/2 22 22 50 50 40 20 45 45 80/2 80/2 80/2 80/2 50 50 50 50 80/2 50 50 80/2 80/2 45 16 21 50 50 85/2 80/2 50 50 80/2 45 14 80/2

Oxford Oxford Oxford Twill Twill Twill Twill Gingham Twill Gingham Gingham Oxford Oxford Oxford Oxford Broadcloth Gingham Jacquard Jacquard Oxford Broadcloth Broadcloth Oxford Oxford Poplin Twill Chambray Gingham Gingham Oxford Oxford Twill Twill Oxford Poplin Twill Oxford

0.244 124 0.262 127 0.300 127 0.536 137 0.592 137 0.255 110 0.265 110 0.316 121 0.592 199 0.278 104 0.245 98 0.299 129 0.298 129 0.310 129 0.300 129 0.198 104 0.223 102 0.302 108 0.314 108 0.302 130 0.260 104 0.260 104 0.268 133 0.247 135 0.280 114 0.688 208 0.366 141 0.229 104 0.273 104 0.271 128 0.330 132 0.323 108 0.305 106 0.289 128 0.251 96 0.715 258 0.268 131 (Continued)

The application of FOM in shirt manufacture 45

Table I. Details of the 60 shirting materials

IJCST 8,4

46

Table I.

P/O

Fabric ID

6379 6379 6379 6401 6432 6432 6434 6434 6669 6669 6707 6790 6790 6832 6912 6912 6958 7056 7251 7251 7251 7282 7282

SMT-01421 SMT-01423 SMT-01472 SMT-01538 SMT-11446A SMT-11446B SMT-01545A SMT-01545B SA-70603WH SA-70603BL SMT-01551 SMT-20389A SMT-20389B SA-75366 GR-93051NA GR-93056HO SMT-20368 SMT-01471 SMT-20400A SMT-20400B SMT-20400C SMT-11451A SMT-11451B

Fibre (%) 100C 100C 100C 100C 55W, 45C 55W, 45C 10C 100C 100C 100C 55C, 45P 55C, 45P 55C, 45P 100C 100C 100C 100C 100C 55C, 45P 55C, 45P 55C, 45P 100C 100C

Density (/cm) Count (s) Thickness Weight Warp Weft Warp Weft Structure (mm) (g/m) 63 63 63 39 29 30 22 22 63 63 43 43 43 51 53 53 47 63 43 43 43 52 52

24 24 24 20 29 28 21 21 24 24 28 28 28 28 28 28 31 24 28 28 28 27 27

80/2 80/2 80/2 40 26 25 32/2 32/2 80/2 80/2 42 45 45 40 32 32 40 80/2 45 45 45 33 33

80/2 80/2 80/2 20/2 28 24 32/2 32/2 80/2 80/2 42 45 45 40 32 32 40 80/2 45 45 45 37 37

Oxford 0.268 Oxford 0.254 Oxford 0.294 Oxford 0.484 Twill 0.568 Houndstooth 0.601 Caseman 0.430 Caseman 0.433 Oxford 0.285 Oxford 0.251 Poplin 0.250 Gingham 0.225 Gingham 0.234 Poplin 0.268 Twill 0.474 Twill 0.429 Gingham 0.402 Oxford 0.232 Gingham 0.233 Gingham 0.215 Gingham 0.209 Gingham 0.289 Gingham 0.264

129 132 133 187 139 139 164 164 131 130 104 97 97 124 167 162 130 134 97 97 101 145 138

Notes: P/O = Production order; Fabric ID = Fabric identity; C = Cotton; W = Wool; P = Polyester

The shirting materials selected in this work ranged widely in weight, structure and mechanical properties. For each fabric, six to 12 specimens were tested, and the mean values of each parameter were obtained. The results are shown in Table II. Using the FAST system, the interpretation of data is simplified with the aid of the FAST control chart, as shown in Figure 1. In the control chart, the measured properties are plotted to form a “fingerprint” of each fabric, which indicates whether the tested fabric will be suitable for the intended end use. The prediction of making up performance can be based on the established maximum and minimum limits for each property. If the fingerprint falls outside the limits, it indicates more work needs to be done on this particular property of the fabric.

–0.4 –2.0 –1.6 1.5 0.9 –1.2 –0.7 0.3 –0.3 0.2 0.9 –0.2 –0.7 –0.4 0.0 –1.5 –0.8 –0.1 0.1 –0.7 –0.7 0.6

SMT –01582 SMT–01605B SMT-01605 SMT-11448EC SMT-11448RE SMT-20204BL SMT-20204BU SMT-20367 SMT-01457 SMT-20363GR SMT-20363WH SMT-01474A SMT-01474B SMT-01474C SMT-01474D SMT-01498 SMT-11431 SMT-01475A SMT-01475B SMT-01480 SMT-0148EC SMT-01484WH

546 546 1411 3607 3607 3981 3981 5009 5057 5152 5152 5252 5252 5252 5252 5355 5355 5466 5466 5500 5534 5534

0.9 –0.2 0.1 2.1 1.6 0.9 0.4 0.7 0.5 0.0 0.4 0.4 0.7 0.6 0.4 0.1 0.2 1.3 1.2 1.3 0.4 0.5

RS Warp Weft

Fabric ID

P/O 0.8 1.0 0.7 1.2 0.6 1.0 →2.1 2.7 1.9 2.6 1.5 1.6 1.4 2.4 0.2 –0.2 0.7 1.0 0.4 0.0 0.1 0.2 1.0 1.3 1.0 1.3 1.0 1.3 0.9 1.3 0.5 1.7 1.3 1.1 1.6 2.3 2.1 2.5 0.5 1.1 –0.2 0.9 2.4 1.5

HE Warp Weft 0.16 0.32 0.40 0.21 0.24 0.17 0.16 0.25 1.33 0.16 0.05 0.17 0.26 0.20 0.24 0.21 0.27 0.17 0.22 0.31 0.20 0.18

0.26 0.26 0.29 0.27 0.30 0.23 0.26 0.06 0.31 0.06 0.09 0.27 0.23 0.23 0.23 0.13 0.12 0.19 0.22 0.27 0.08 0.07

F Warp Weft 1.65 2.45 3.40 2.20 2.80 3.20 2.70 3.50 3.80 2.90 →1.10 1.90 2.10 1.90 1.90 3.35 3.70 2.50 2.90 2.55 3.50 3.15

5.10 5.60 4.90 4.30 4.70 5.10 6.10 1.70 3.20 2.30 2.80 5.10 5.00 4.90 4.90 4.30 3.90 4.20 4.80 4.20 2.75 2.15

E100 Warp Weft 10.7 11.1 9.8 5.7 5.5 →4.5 →4.6 5.8 39.2 4.3 7.5 10.8 11.6 11.2 11.6 6.5 5.9 4.9 4.6 10.3 5.0 4.9

3.4 3.3 3.8 4.1 3.9 3.0 2.8 5.2 7.3 3.4 3.9 3.6 3.5 3.2 3.3 3.0 3.2 3.0 3.0 5.2 3.0 3.4

B Warp Weft 37.0 43.0 41.9 →20.1 →20.3 27.3 25.4 103.0 70.0 42.8 54.7 33.1 39.3 39.0 40.3 37.5 36.9 20.3 22.1 33.5 48.5 46.0

G 0.256 0.267 0.30 0.536 0.592 0.255 0.265 0.316 0.592 0.278 0.245 0.299 0.298 0.310 0.300 0.238 0.223 0.302 0.314 0.304 0.262 0.258

T2 0.111 124 0.110 127 0.125 127 0.212 137 0.225 137 0.134 110 0.129 110 0.118 121 0.109 199 0.122 104 0.121 98 0.109 129 0.095 129 0.104 129 0.098 129 0.115 104 0.116 102 0.113 108 0.120 108 0.116 130 0.121 104 0.123 104 (Continued)

0.094 0.091 0.128 0.225 0.266 0.101 0.108 0.155 0.139 0.129 0.115 0.095 0.089 0.099 0.096 0.100 0.087 0.117 0.124 0.108 0.114 0.117

W

STR

ST

The application of FOM in shirt manufacture 47

Table II. FAST test results of the 60 shirting materials

SMT-11366 SMT-11371 SA-70594 SMT–01507 SMT-01501 SMT-20382B SMT-20382A SMT-01512 SMT-01514 SMT-11426 SMT-11429 SMT-11436 SMT-11365 SMT-01516 SMT-01535 SMT-01421 SMT-01423 SMT-01472 SMT-01538 SMT-11446A SMT-11446B SMT-01545A

5544 5544 5593 5638 5659 5696 5698 5771 5785 5818 5865 5895 5958 6362 6374 6379 6379 6379 6401 6432 6432 6434

Table II.

Fabric ID

–0.5 –0.6 0.8 –1.5 –1.7 0.1 0.4 0.3 –0.5 0.5 0.2 –0.3 0.8 →–4.3 –0.3 –0.7 –0.5 –0.8 0.0 1.1 0.8 –0.8

0.1 0.1 0.4 0.1 –0.6 –0.1 0.3 0.5 1.2 0.6 0.7 1.3 0.4 0.1 0.3 0.8 0.2 0.4 0.4 1.1 2.1 0.0

RS Warp Weft 1.0 1.0 1.2 0.8 1.5 1.2 1.2 0.7 2.3 1.2 1.8 1.5 0.0 0.7 1.0 0.5 0.9 0.9 1.2 →1.8 1.2 1.0

0.9 0.8 0.2 0.9 0.6 0.6 0.4 1.5 1.0 2.2 1.7 1.1 0.0 1.5 1.3 0.9 1.2 0.8 1.2 3.8 2.2 0.8

HE Warp Weft 0.24 0.28 0.11 2.03 0.51 0.26 0.16 0.27 0.30 0.17 0.18 0.26 →0.03 3.68 0.27 0.36 0.17 0.18 0.25 →0.09 →0.10 →0.88

0.27 0.16 0.03 0.35 0.36 0.06 0.04 0.23 0.21 0.20 0.16 0.30 0.07 0.52 0.26 0.31 0.28 0.32 0.74 0.49 0.35 0.61

F Warp Weft 2.60 2.70 4.10 2.45 5.95 4.30 2.70 2.00 2.60 2.00 2.20 2.10 →1.00 1.65 2.35 2.60 2.20 2.20 2.70 1.40 1.40 →7.10

B Warp Weft

4.65 9.8 4.1 3.70 9.5 3.3 3.00 4.9 3.3 2.60 →105.6 10.5 5.10 6.7 5.2 2.00 4.5 3.1 1.80 5.4 3.0 5.10 11.8 3.2 4.20 12.0 3.8 3.70 6.3 4.0 3.20 5.8 3.6 4.60 13.0 4.8 2.10 7.5 4.2 2.65 →296.0 18.1 4.20 10.6 4.9 4.40 11.3 5.5 4.90 12.7 4.9 5.20 10.1 5.2 4.40 9.2 15.6 6.90 6.5 4.5 5.40 7.7 4.4 5.60 7.7 6.8

E100 Warp Weft 35.0 50.2 39.3 →129.5 63.0 42.4 45.8 28.7 44.2 27.6 22.3 44.2 74.8 321.0 34.0 41.9 53.0 49.5 109.0 16.4 25.7 54.0

G 0.279 0.247 0.280 0.677 0.377 0.229 0.273 0.271 0.330 0.323 0.305 0.289 0.251 0.698 0.282 0.268 0.254 0.294 0.484 0.568 0.601 0.432

T2 0.103 0.096 0.102 0.184 0.117 0.096 0.136 0.108 0.151 0.171 0.130 0.116 0.125 0.136 0.118 0.100 0.089 0.121 0.162 0.245 0.271 0.137

ST

48

P/O

W

0.116 133 0.107 135 0.100 114 0.125 208 0.128 141 0.129 104 0.113 104 0.081 128 0.109 132 0.138 108 0.161 106 0.132 128 0.114 96 0.089 258 0.117 131 0.101 129 0.103 132 0.095 133 0.166 187 0.183 139 0.198 139 0.133 164 (Continued)

STR

IJCST 8,4

SMT-01545B

SA-70603BL

SA-70603WH

SMT-01551

SMT-20389A

SMT-20389B

SA-75366

GR-93051NA

GR-93056HO

SMT-20368

SMT-01471

SMT-20400A

SMT-20400B

SMT-20400C

SMT-11451A

SMT-11451B

6434

6669

6669

6707

6790

6790

6832

6912

6912

6958

7056

7251

7251

7251

7282

7282

–0.2

0.8

0.7

0.7

0.3

0.1

–0.7

–0.3

–0.6

–0.7

1.0

0.9

–0.6

–1.1

–1.0

–1.8

–1.7

–1.4

–0.3

0.3

0.4

0.4

0.4

1.5

0.5

0.7

0.5

0.4

0.1

0.1

0.4

0.1

RS Warp Weft 0.9

0.2

0.0

0.8

1.3

1.5

1.2

1.5

0.1

0.0

0.4

1.1

0.8

0.7

1.1 1.7

1.8

0.5 –0.1

0.4

0.2

0.7

0.9

2.1

1.4

1.5

0.6

0.5

0.6

1.3

1.0

1.2

HE Warp Weft

0.20 0.18

0.23 0.20

0.07 0.08

0.08 0.08

0.09 0.07

0.17 0.16

0.35 0.44

0.35 0.15

0.27 0.17

0.24 0.09

0.08 0.08

0.07 0.07

0.20 0.08

0.33 0.24

0.21 0.30

0.69 0.52

F Warp Weft

1.50 3.90

1.80 3.70

1.65 2.50

1.75 2.65

2.00 2.45

1.60 3.45

3.60 6.10

2.90 2.20

2.20 2.45

2.80 2.45

1.70 2.65

1.45 2.35

3.60 2.90

2.90 4.25

1.90 5.60

6.40 5.50

E100 Warp Weft

14.8

12.5

4.7

4.6

4.0

10.8

7.8

9.4

12.6

7.3

4.3

4.7

4.6

9.6

11.5

6.7

5.3

6.4

3.1

2.8

3.1

3.6

5.3

6.5

7.6

4.0

2.8

3.1

2.6

4.4

4.2

6.0

B Warp Weft

127.0

115.0

44.0

39.5

39.5

39.0

45.0

51.0

67.0

53.5

37.0

43.5

29.5

33.5

40.5

49.9

G

0.264

0.289

0.225

0.229

0.240

0.251

0.385

0.432

0.474

0.271

0.243

0.237

0.250

0.288

0.251

0.433

T2

0.113 131 0.123 104 0.128 0.129

0.124 124 0.240 167 0.222 162 0.179 130 0.116 134 0.112 0.115

0.102 101 0.108 145 0.136 138

0.114 0.116 0.105 0.113 0.112 0.233 0.177 0.137 0.105 0.106 0.099 0.086 0.124 0.100

97

97

97

97

0.138 164 0.121 130

0.142

W

0.092

STR

ST

Notes: P/O = Production order; Fabric ID = Fabric identity; RS = Relaxation shrinkage (%); B = Bending rigidity (µNm); STR = Released surface thickness (mm); HE = Hygral expansion (%); G = Shear rigidity (N/m); W = Weight (g/m2); F = Formability (mm2 ); T2 = Thickness (mm); E100 = Extensibility at 100 gf/cm (%); ST = Surface thickness (mm); → = described in text

Fabric ID

P/O

The application of FOM in shirt manufacture 49

Table II.

IJCST 8,4

50

Minimum

Units

Maximum

Sizing

Relaxation shrinkage

RS-1 RS-2

Hygral expansion

HE-1 HE-2

Formability

F-1 F-2

Sizing

–2

–1

0

1

2

3

1.5 per cent 2.1 per cent

4

Appearance wool 0

0.4

0.8

1.2

1.6

1.8

Pucker sleeve setting

Sewing 0.36

0.18

0.0

0.62

Overfeed

Extensibility

0.70

1.8

1.6

2.0

1.0

2.4

2.2

2.0

2.2 per cent

2.6

4.3 per cent

3.0

4.0

5.0

10.0

12.0

14.0

8.0

12.0

Cutting handling

Cutting stiff

B-1 B-2

8.0

6.0 0.0

4.0

G

40

20.1 N/m

70

60

50

Minimum

Maximum

Lean

Thickness

4.1 µNm

Shaping moulding 30

20

5.7 µNm

16.0

Spreading, sewing handling

Shear rigidity

Full

0.536 mm

T 0

0.2

0.4

0.6

0.8

1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.0

0.1

0.2

0.3

0.4

0.5

Surface thickness ST

Figure 1. FAST control chart for a wool-blended twill sample (SMT-11448EC)

0.225 mm

Released surface thickness STR

0.212 mm

Light

Weight

0.21 mm2 0.27 mm2

Spreading sewing

E100-1 E100-2

Bending rigidity

2.1 per cent 2.7 per cent

2.2

Heavy

137 g/m2

W 60

80

100

120

140

160

180

200

220

However, it must be emphasized that the limits given by the system are only guidelines for lightweight suiting fabrics. In order to find out the distinctive limits and therefore predict the production performance of shirting fabrics, some analyses were carried out according to the production investigation and the experimental results of these 60 shirting materials. Production investigation Investigation of manufacturing processes was carried out in order to assess the making up performance of the selected fabrics. In this work, processes under investigation included fabric spreading, cutting, sewing and handling. All the fabrics or garments were processed in the usual way and the performance was

judged subjectively by the operators and/or their supervisors. The fabric performance and behaviour were divided into four levels: (1) fabrics which processed with no special difficulty and no special control was required; (2) fabrics which processed with a little difficulty and some control was required; (3) fabrics which processed with poor performance and needed to be handled with special attention; (4) fabrics which processed with serious problems and for which manual assistance was extremely important. The fabrics’ performance of spreading, cutting, sewing, handling, pressing and packaging operations are presented in Tables III-V. The application of FOM to process control From the collected information and analytical work, each property was classified according to its value and the degree of control required in the operations to which it had specific relevance. In the present study, the desirable ranges of mechanical properties for high-quality shirt production are calculated by using 99 per cent confidence intervals which estimate the range on either side of a sample mean. Details of the mechanical properties and their respective limits are described. Extensibility Extensibility is a measure of the fabric’s ability to be stretched during makingup. Both excessive and insufficient extensibility will cause problems for the manufacturer. For lightweight suitings, the minimum limit is 2 per cent in both directions where the maximum limits are 4 per cent in warp and 6 per cent in weft[5]. According to the results of the present work, shirting fabrics with extensibility less than 1.84 per cent tended to cause difficulties during seam overfeeding; for example, fabrics SMT-20363WH (1.1 per cent in warp) and SMT-11365 (1.0 per cent in warp) received scores of 3 and 4 respectively in the sewing operation (Table IV). If the extensibility was greater than 2.53 per cent in warp and/or 4.07 per cent in weft, the fabric could be easily stretched during spreading and sewing unsupported seams. This might also lead to size variation in cut panels as fabrics may shrink or relax after being cut. Therefore, special attention and control have to be exercised by the operative. The higher the value in extensibility, the more difficult in laying up, cutting and sewing; for example, fabric SMT-01545A exhibited very high extensibility (7.1 per cent in warp and 5.6 per cent in weft) and processed with serious problems during spreading and sewing operations (a score of 4), as shown in Tables III and IV.

The application of FOM in shirt manufacture 51

SMT-20367

SMT-01457

SMT-20363GR

SMT-20363WH

SMT-01474A

SMT-01474B

SMT-01474C

SMT-01474D

SMT-01498

SMT-11431

SMT-01475A

SMT-01475B

SMT-01480

5009

5057

5152

5152

5252

5252

5252

5252

5355

5355

5466

5466

5500

2

2

2

3

3

2

2

2

2

1

1

3

1

4

4

1

1

1

1

1

1

1

1

1

1

3

3

3

→ SMT-20204BL 3

→ SMT-20204BU 2

3981

4

→ SMT-11448RE 3

3607

3981

1 4

2

1

1

SMT-01605

2

1

→ SMT-11448EC 2

SMT-01605B

546

Distort

3607

SMT-01582

546

Stretch

1411

Fabric ID

Table III. Spreading and cutting performance of the 60 shirting materials 1

3

3

1

1

1

1

1

1

1

1

1

1

3

3

3

3

1

1

1

1

3

3

1

1

1

1

1

1

2

2

1

3

1

1

2

2

1

1

1

1

1

1

1

1

2

2

2

2

1

1

1

1

1

1

1

1

1

1

1

–

–

–

–

–

2

2

2

2

–

–

2

–

–

–

–

–

–

–

–

Slippery Others

1

3

3

2

2

1

1

1

1

2

3

1

2

4

4

3

3

1

1

1

1

1

1

1

1

1

1

1

1

1

1

3

1

1

1

1

1

1

1

1

Soft to cut Stiff to cut

3

3

3

1

1

2

2

2

2

1

1

1

1

1

1

1

1

3

3

3

1

1

1

1

1

2

2

2

2

1

1

2

2

2

2

2

1

1

1

1

2

1

1

1

1

2

2

2

2

1

1

1

1

1

1

1

1

1

1

1

(Continued)

–

3

3

–

–

–

–

–

–

–

–

2

–

–

–

–

–

–

–

2

Cutting Size Ravel variation Slippery Others

52

P/O

Spreading Pattern Sticky bowing

IJCST 8,4

SMT-01501

SMT-20382B

SMT-20382A

SMT-01512

SMT-01514

SMT-11426

SMT-11429

SMT-11436

5659

5696

5698

5771

5785

5818

5865

5895

SMT-01535

SMT-01421

SMT-01423

SMT-01472

SMT-01538

6362

6374

6379

6379

6379

6401

2

2

2

2

2

1

1

SMT-11365

→SMT-01516

5958

1

1

1

2

1

2

2

4

2

2

2

2

SMT-11371

5544

SA-70594

SMT-11366

5544

3

3

→SMT–01507

SMT-01484WH

5534

5638

SMT-0148EC

5534

Stretch

5593

Fabric ID

P/O

1

1

1

1

1

1

1

1

4

3

1

3

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

2

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

1

2

2

1

3

1

1

2

1

1

1

1

1

1

Spreading Pattern Distort Sticky bowing

1

1

1

1

1

1

1

2

1

1

2

1

1

1

1

1

1

1

1

1

1

2

–

–

–

–

3

–

–

–

–

–

–

–

–

–

2

–

–

–

–

–

Slippery Others

1

1

1

1

1

1

2

1

2

2

1

1

2

2

2

1

3

1

1

2

2

2

1

1

1

1

4

1

1

1

1

1

1

1

1

1

4

1

1

1

1

1

Cutting Soft to cut Stiff to cut

1

3

3

3

3

1

1

3

1

1

2

3

1

1

1

1

1

3

3

1

1

1

1

1

1

1

2

1

1

1

1

1

1

1

2

2

1

1

1

1

2

2

– – 3

1 1 1

– – – –

1 1 1 1

(Continued)

–

1

2

–

1

2

3 –

1

1

3

2

1

2 –

1

–

–

1

–

–

1

1

–

1

1

–

1

Size Ravel variation Slippery Others

The application of FOM in shirt manufacture 53

Table III.

2

4

SMT-11446B

→SMT-01545A

SMT-01545B

SA-70603WH

SA-70603BL

SMT-01551

SMT-20389A

SMT-20389B

SA-75366

GR-93051NA

GR-93056HO

SMT-20368

SMT-01471

SMT-20400A

SMT-20400B

SMT-20400C

SMT-11451A

SMT-11451B

6432

6434

6434

6669

6669

6707

6790

6790

6832

6912

6912

6958

7056

7251

7251

7251

7282

7282

1

1

1

1

1

1

1

1

1

1

1

1

2

2

1

1

1

3

4

Distort

1

1

1

1

1

1

1

2

2

1

1

1

1

1

1

1

1

3

3

1

1

2

1

1

1

3

1

1

1

1

1

1

1

1

3

3

3

3

1

1

1

1

1

2

1

1

1

1

1

1

1

2

2

1

1

1

1

2

2

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

2

2

Slippery Others

1

1

2

2

2

1

3

1

1

2

2

2

3

1

1

2

2

3

3

3

3

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

Soft to cut Stiff to cut

1

1

1

1

1

3

1

1

1

1

1

1

1

3

3

1

1

1

1

1

1

1

1

1

1

2

1

1

1

1

1

1

1

1

2

2

1

1

1

1

1

1

1

2

1

1

1

1

1

1

1

2

2

1

1

1

1

Notes: P/O = Production order; Fabric ID = Fabric identity; 1 = No problem; 2 = Borderline; 3 = Problem; 4 = Serious problem; → = Described in text

1

1

1

1

1

1

3

2

1

2

1

1

3

2

2

4

2

SMT-11446A

6432

Stretch

Fabric ID

Table III. 2

2

–

–

–

–

–

–

–

–

–

–

–

–

–

3

3

–

–

Cutting Size Ravel variation Slippery Others

54

P/O

Spreading Pattern Sticky bowing

IJCST 8,4

1

1

SMT-01582

SMT-01605B

546

546

1

1

1

1

1

1

1

1

1

1

SMT-01474A

SMT-01474B

SMT-01474C

SMT-01474D

SMT-01498

SMT-11431

SMT-01475A

SMT-01475B

SMT-01480

5252

5252

5252

5252

5355

5355

5466

5466

5500

1

1

1

1

1

1

1

1

3 3

2

SMT-20363GR

3

3

SMT-01457

5057

→SMT-20363WH 3

2

2

SMT-20367

5152

1

→ SMT-20204BU 1

3981

5009

5152

1 1

→ SMT-11448RE 1

→ SMT-20204BL 1

3607

3607

3981

1 1

1

SMT-01605

→ SMT-11448EC 1

1411

1 1

Puckering

Fabric ID

P/O

Sleeve setting

1

1

1

1

1

1

1

1

1

1

1

3

3

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

3

3

2

1

1

1

2

2

1

1

1

1

2

2

1

1

1

1

1

1

1

1

3

1

1

1

1

1

1

1

1

1

4

4

1

1

1

1

1

1

1

1

1

1

3

3

4

4

1

1

1

Sewing Form and Stitch and shape Overfeed needle Distort

2

3

3

3

3

2

2

2

2

1

1

3

2

3

3

3

1

2

2

1

2

–

–

–

–

–

–

–

–

–

–

–

–

3

3

3

3

–

–

–

1

3

3

3

3

1

1

1

1

2

3

1

2

4

4

3

3

1

1

1

1

2

2

1

1

1

1

1

1

1

1

1

1

3

3

3

3

1

1

1

Stretch Others Soft Sticky

1

1

1

1

1

1

1

1

1

1

1

3

1

1

1

1

1

1

1

1

– –

1 1

(Continued)

– –

1

–

1 1

– –

–

1 1

–

1

1

– –

1

–

3 1

– –

1 1

– –

1 1

– –

1 1

– –

1 1

Handling Stiff Heavy Others

The application of FOM in shirt manufacture 55

Table IV. Sewing and handling performance of the 60 shirting materials

3

4

1

4

4

SMT-01484WH

SMT-11366

SMT-11371

SA-70594

→SMT–01507

SMT-01501

SMT-20382B

SMT-20382A

SMT-01512

SMT-01514

SMT-11426

SMT-11429

SMT-11436

→SMT-11365

→SMT-01516

SMT-01535

SMT-01421

SMT-01423

SMT-01472

5534

5544

5544

5593

5638

5659

5696

5698

5771

5785

5818

5865

5895

5958

6362

6374

6379

6379

6379

1

1

1

1

1

1

1

1

2

2

1

1

1

2

2

SMT-0148EC

Puckering

5534

Table IV.

Fabric ID

1

1

1

1

4

4

1

1

1

1

1

3

3

2

4

3

1

1

3

3

1

1

1

1

4

3

1

1

1

1

1

2

1

2

4

1

1

1

1

1

1

1

1

1

3

4

1

1

1

1

1

2

2

2

3

3

1

1

2

2

1

1

1

1

3

1

1

1

1

1

1

1

1

1

3

1

1

1

1

1

1

1

1

1

1

1

1

4

3

1

3

1

1

1

1

1

1

1

1

1

Sewing Form and Stitch and shape Overfeed needle Distort

2

2

2

1

1

1

1

1

1

2

1

2

2

4

2

1

2

2

3

3

–

–

–

–

–

–

–

2

2

2

3

–

–

–

–

–

–

–

–

–

1

1

1

1

1

2

1

2

2

1

1

3

3

3

1

3

1

1

3

3

1

1

1

1

1

1

1

3

3

1

1

1

1

1

1

1

1

1

1

1

Stretch Others Soft Sticky

1

1

1

1

4

1

1

1

1

1

1

1

1

1

4

1

1

1

1

1

1

1

1

1

3

1

1

1

1

1

1

1

1

1

3

1

1

1

1

1

(Continued)

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

Handling Stiff Heavy Others

56

P/O

Sleeve setting

IJCST 8,4

Fabric ID

Puckering

Sewing Form and Stitch and shape Overfeed needle Distort Stretch Others Soft Sticky – – – – – – – – – – – – – – – – – – – –

Handling Stiff Heavy Others

6401 SMT-01538 3 3 3 2 1 1 2 – 1 1 2 3 6432 →SMT-11446A 3 3 1 2 1 4 3 – 3 2 1 1 6432 →SMT-11446B 3 3 1 2 1 3 3 – 3 2 1 1 6434 →SMT-01545A 3 3 1 2 1 1 4 2 2 1 1 1 6434 SMT-01545B 3 3 1 2 1 1 4 2 2 1 1 1 6669 SA-70603BL 1 1 1 1 1 1 2 – 1 1 1 1 6669 SA-70603WH 1 1 1 1 1 1 2 – 1 1 1 1 6707 SMT-01551 2 3 1 2 1 2 3 – 3 1 1 1 6790 SMT-20389A 3 3 1 2 1 1 1 – 3 1 1 1 6790 SMT-20389B 3 3 1 2 1 1 1 – 3 1 1 1 6832 SA-75366 2 3 1 1 1 1 1 – 3 1 1 1 6912 GR-93051NA 1 1 2 1 1 1 1 – 1 3 1 1 6912 GR-93056HO 1 1 1 1 1 1 2 – 1 3 1 1 6958 SMT-20368 1 1 1 1 1 1 3 – 2 1 1 1 7056 SMT-01471 1 1 1 1 1 1 1 – 1 1 1 1 7251 SMT-20400A 3 3 1 2 1 1 1 – 3 1 1 1 7251 SMT-20400B 3 3 1 2 1 1 1 – 3 1 1 1 7251 SMT-20400C 3 3 1 2 1 1 1 – 3 1 1 1 7282 SMT-11451A 2 2 3 2 3 1 1 3 1 1 1 1 7282 SMT-11451B 2 2 3 2 3 1 1 3 1 1 1 1 Notes: P/O = Production order; Fabric ID = Fabric identity; 1 = No problem; 2 = Borderline; 3 = Problem; 4 = Serious problem; → = Described in text

P/O

Sleeve setting

The application of FOM in shirt manufacture 57

Table IV.

IJCST 8,4 P/O Fabric ID

58

Table V. Pressing and packaging performance of the 60 shirting materials

Pressing Garment Shine Packaging appearance Temperature relaxed seams Others Puckering Loose Crease Others

546 SMT-01582

1

1

1

–

1

1

1

–

546 SMT-01605B

1

1

1

–

1

1

1

–

1411 SMT-01605

1

1

1

–

1

1

1

–

3607 →SMT-11448EC 2

1

1

–

1

3

1

–

3607 SMT-11448RE

2

1

1

–

1

3

1

–

3981 SMT-20204BL

2

1

3

–

1

2

2

–

3981 SMT-20204BU

2

1

2

–

2

3

2

–

5009 SMT-20367

1

1

1

–

2

1

1

–

5057 SMT-01457

1

1

1

2

2

1

1

–

5152 SMT-20363GR

3

1

3

–

2

1

1

–

5152 SMT-20363WH

3

1

1

–

3

1

1

–

5252 SMT-01474A

1

1

1

–

1

1

1

–

5252 SMT-01474B

1

1

1

–

1

1

1

–

5252 SMT-01474C

1

1

1

–

1

1

1

–

5252 SMT-01474D

1

1

1

–

1

1

1

–

5355 SMT-01498

1

1

1

–

1

1

1

–

5355 SMT-11431

1

1

1

–

1

1

1

–

5466 SMT-01475A

1

1

1

2

1

3

1

3

5466 SMT-01475B

1

1

1

2

1

3

1

3

5500 SMT-01480

1

1

1

3

1

1

3

–

5534 SMT-0148EC

1

1

1

3

2

1

3

–

5534 SMT-01484WH

1

1

1

3

2

1

3

–

5544 SMT-11366

1

1

1

–

1

1

1

–

5544 SMT-11371

1

1

1

–

1

1

1

–

5593 SA-70594

1

1

2

–

3

1

1

–

5638 SMT-015507

1

1

1

2

2

2

1

–

5659 SMT-01501

1

1

1

2

2

2

1

–

5696 SMT-20382B

1

1

1

–

1

1

2

–

5698 SMT-20382A

1

1

1

–

1

1

1

–

5771 SMT-01512

2

1

1

–

1

2

2

–

5785 SMT-01514

1

1

1

–

1

2

1

–

(Continued)

P/O Fabric ID

Pressing Garment Shine Packaging appearance Temperature relaxed seams Others Puckering Loose Crease Others

5818 SMT-11426

1

1

3

–

1

2

1

3

5865 SMT-11429

1

1

3

–

1

2

1

3

5895 SMT-11436

1

1

1

–

1

1

1

–

5958 SMT-11365

3

1

1

–

4

1

1

–

6362 →SMT-01516

1

3

1

3

2

2

1

2

6374 SMT-01535

1

1

1

3

1

1

3

3

6379 SMT-01421

1

1

1

–

1

1

1

–

6379 SMT-01423

1

1

1

–

1

1

1

–

6379 SMT-01472

1

1

1

–

1

1

1

–

6401 SMT-01538

1

1

1

–

2

1

1

–

6432 →SMT-11446A

3

1

1

2

3

3

1

–

6432 SMT-11446B

3

1

1

2

3

3

1

–

6434 SMT-01545A

1

1

1

–

1

1

1

–

6434 SMT-01545B

1

1

1

–

1

1

1

–

6669 SA-70603BL

1

1

1

–

1

1

1

–

6669 SA-70603WH

1

1

1

–

1

1

1

–

6707 SMT-01551

3

1

1

–

2

1

1

–

6790 SMT-20389A

3

1

1

–

3

1

1

–

6790 SMT-20389B

3

1

1

–

3

1

1

–

6832 SA-75366

1

1

1

3

1

3

3

3

6912 GR-93051NA

1

1

3

–

2

2

1

2

6912 GR-93056HO

1

1

1

–

2

3

1

2

6958 SMT-20368

1

1

1

2

2

1

1

–

7056 SMT-01471

1

1

1

2

1

2

3

–

7251 SMT-20400A

3

1

1

–

3

1

1

–

7251 SMT-20400B

3

1

1

–

3

1

1

–

7251 SMT-20400C

3

1

1

–

3

1

1

–

7282 SMT-11451A

1

1

1

2

2

2

1

3

7282 SMT-11451B

1

1

1

2

2

2

1

3

Notes: P/O = Production order; Fabric ID = Fabric identity; 1 = No problem; 2 = Borderline; 3 = Problem; 4 = Serious problem; → = Described in text

The application of FOM in shirt manufacture 59

Table V.

IJCST 8,4

60

Bending rigidity Bending rigidity determines the fabric’s resistance to bending. Fabrics with higher value of bending rigidity have stronger resistance when fabrics are bent by external force such as that encountered during fabric manipulation in spreading and sewing. For lightweight suitings, the minimum limit for bending rigidity was 5 µN.m in both directions[5]. However, the experimental results of the present investigation showed that shirting fabrics with 7.67 µN.m in warp and 4.06 µN.m in weft in bending rigidity were regarded as soft and easy to bend, and the fabrics were difficult to handle and cut. For example, fabrics SMT20204BL (4.5 µ N.m and 3.0 µ N.m in warp and weft bending rigidity respectively) and SMT-20204BU (4.6 µ N.m in warp and 2.8 µ N.m in weft bending rigidity) were judged a score of 4 in both cutting and handling processes (Tables III and IV). On the other hand, fabrics with very high bending rigidity (stiff fabrics), such as fabrics SMT-01516 (296 µN.m in warp) and SMT-01507 (106 µN.m in warp), also led to cutting, sewing and handling problems as they were too stiff to be manipulated and controlled. Hence, the maximum limit of bending rigidity was 12.35 µN.m in warp and/or in weft. Formability Fabric formability can be used to predict the limit of overfeed before buckling. The lower the formability the more likelihood of seam pucker[6,7], because a fabric is unable to accommodate the small compression placed on the fabric by the sewing thread. The maximum and minimum limits of fabric formability will also depend on the sewing thread, needle size and thread tension, as well as the skill of the operators. For shirting fabrics, the minimum limit of fabric formability tended to be a bit lower than that of the lightweight suitings (0.25mm2 in both directions)[5]. Puckering or sleeve-setting problems occurred easily only in fabrics with formability less than 0.18mm2 in both directions. For example, fabric SMT11365 exhibited very low formability in both ways (0.03mm2 in warp and 0.07mm2 in weft) and processed with serious problems in seam puckering and sleeve setting (both received grade 4), as shown in Table IV. Moreover, it was found that warp formability was more important than weft formability in shirting manufacturing. For example, fabrics SMT-11446A (0.09mm2 in warp and 0.49mm2 in weft) and SMT-11446B (0.10mm2 in warp and 0.35 mm2 in weft) both received grade 3 in seam-puckering and sleevesetting problems during the sewing operation, and even their weft formability values were comparatively high (Tables II and IV). As with many other fabric properties, problems can occur if fabric formability is too high (F > 0.46mm2 for shirting materials), as for fabric SMT01545A (0.88mm2 in warp and 0.61mm2 in weft).

Shear rigidity Fabric shearability is one of the major concerns when making-up a garment, as the fabric needs to be stretched and sheared to a certain degree in order to conform to the intended garment shape. If the shear rigidity is too low, then the fabric is easily distorted and can skew or bow during handling, laying up and sewing. If the shear rigidity is too high, the fabric will be difficult to form, mould, or shape at the sleeve head. Based on the FAST control chart, for lightweight wool suitings, the maximum and minimum limits for shear rigidity are 80N/m and 30N/m respectively[5]. According to the present investigation, fabrics having shear rigidity higher than 55.3N/m tended to have shaping and moulding difficulties, for example, fabric SMT-01507 (129N/m in shear rigidity) processed with a serious shaping problem during the sewing operation (received a score of 4), as in Table IV. On the other hand, fabrics SMT-11448EC and SMT-11448RE acquired very low shear rigidity value (20N/m). When their production performance was observed, both fabrics processed with serious problems during spreading, sewing and handling as the fabrics were distorted very easily. Operator and machine adjustments were required in order to produce high-quality and goodappearance shirts. Relaxation shrinkage Relaxation shrinkage is defined as the percentage change in dry dimensions of the fabric measured after relaxation in water at room temperature. Excess fabric relaxation shrinkage may cause sizing problems as the finished garment will be smaller than it was planned. Also, problems are often caused by fabrics which have insufficient (or negative) relaxation shrinkage as the fabric is relaxed in manufacture or when worn. From the experiment results, it was difficult to state any criticism on relaxation shrinkage because the dimensional changes of the selected shirting materials were obscure. It was because no obvious problem was found during the production processes in most of the materials. Only one fabric sample (SMT01516) relaxed substantially in garment length (in the warp direction) when the fabric was pressed, as in Table V. Its fabric relaxation shrinkage value was considerably low (–4.3 per cent in warp) when compared with other fabrics. Hygral expansion Hygral expansion is defined as the percentage change in dimensions of the relaxed fabric from wet to dry. From the FAST control chart, for suiting fabrics, hygral expansion of up to 6 per cent can normally be tolerated[5]. Excessive hygral expansion may result in poor garment appearance because the garment panels increase in dimensions as the moisture content of the fibres increase. In some cases, seam puckering may also occur if different panels receive different expansion.

The application of FOM in shirt manufacture 61

IJCST 8,4

62

Basically, it is believed hygral expansion is only a problem related to wool/wool-blended materials. However, according to the present investigation, around one-sixth of the tested shirting fabrics relaxed after being packaged and gave a loose appearance. The problem was magnified in wool-blended fabrics, such as fabrics SMT-11448EC (2.1 per cent in warp and 2.7 per cent in weft) and SMT-11446A (1.8 per cent in warp and 3.8 per cent in weft). Both fabrics received grade 3 in packaging appearance (Table V). Based on the statistical analysis, it is found that shirting fabrics having hygral expansion higher than 1.53 per cent in warp and/or in weft result in garment appearance problems. Weight Basically, fabric weight has no limits but weight does affect many fabric properties. As a general rule, the lighter the fabric, the more difficult it is to manufacture satisfactory garments[8]. For shirting materials, it was indicated that puckering occurred easily in the fabrics having properties such as light fabric weight with tight structures, such as poplin, gingham and broadcloth. Moreover, polyester blended fabrics appeared to have seam puckering more readily than 100 per cent cotton fabrics as lightweight CVC fabrics exhibited low extensibility and bending rigidity, and therefore low fabric formability. The relationship between the mechanical properties and the level of control required Based on the measured fabric mechanical properties, it was possible to highlight which fabrics would need special care and which would cause serious problems. As a result, specific manufacturing instructions could be prepared in advance to compensate for deficiencies in certain fabric properties. For example, a value of fabric extensibility > 2.4 per cent (in warp) would produce difficulties in spreading and sewing operations. Therefore, operators should avoid tension during spreading operation and/or spread the fabric a bit longer than it requires as the fabric may shrink after being spread. At seam overfeeding, fabric can be pushed slightly by the operator and the presser foot pressure should also be reduced gently to avoid excess fabric extension. On the other hand, a value of fabric formability < 0.15 mm2 (in both directions) would cause risks in sleeve setting and seam puckering. Thus, a smaller size of needle must be used and the sewing thread tension must be reduced. Operators may also guide the top ply of fabric carefully during setting sleeves. The instructions for process control according to each parameter are suggested in Table VI. However, it is important to emphasize that the maximum and minimum limits for each property obtained in this study can only be applied to companies with a similar set-up. This may include the type of spreading machines, sewing machines, needles and the skill of operators, otherwise the limits would need to be adjusted accordingly. In this study, for example, the factory employs automatic spreading machines, various brands of industrial sewing machines equipped

with different kinds of attachments and work aids, size 10-12 sewing needles, skilful operators, etc. However, even by using the same machines, the layout, conditions and production engineering may vary considerably. Also, the skill of operators is difficult to quantify or compare with other companies. Therefore, according to the fabric properties, each company can develop its own control chart with limits suited to its operation and the particular end use of its products. It is also suggested that the limits would need to be fully evaluated and modified regularly by the inclusion of new fabric, new marketing and processing data, etc.

The application of FOM in shirt manufacture 63

Instructions for workers who are concerned with this indication

Range of parameters

Difficulty predicted in

Extensibility < 1.84%

Overfeed operations

Guide fabric carefully Confirm the length of seams being sewn

Extensibility in warp > 2.53% and/or extensibility in weft > 4.07%

Spreading Sewing operations

Avoid excess tension during spreading Spread fabric a bit longer than it requires Push fabric to avoid excess extension Confirm the length of seams

Bending rigidity in warp < 7.67 µ N.m and/or bending rigidity in weft < 4.06 µ N.m

Cutting Handling

Use very sharp cutting knife Reduce cutting speed

Bending rigidity > 12.35µ N.m

Stiff Cutting operations

Reduce number of plies in a lay Guide fabric carefully during cutting Use very sharp cutting knife

Formability < 0.18mm2

Seam puckering Sleeve setting

Reduce needle size Reduce sewing thread tension Guide top fabric ply carefully

Formability > 0.46mm2

Sewing operations

Increase needle size Change thread Reduce sewing thread tension

Shear rigidity < 33.9N/m

Spreading Sewing operations Handling

Take care not to stretch fabric and repeat adjustment for each ply Reduce sewing thread tension Reduce presser foot pressure Reduce machine speed Push fabric to avoid excess distortion

Shear rigidity > 55.3N/m

Shaping and moulding operations

Pull fabric during sewing

Hygral expansion > 1.53%

Garment appearance

Avoid excess steam press

Table VI. Instructions for process control according to each parameter

IJCST 8,4

64

Conclusion The present work has clearly demonstrated that with the adoption of objective measurement of fabric mechanical properties it is possible to predict a shirting fabric’s possible behaviour and performance during garment manufacture. Manufacturers, therefore, are able to distinguish which fabrics will fall within the desirable range of mechanical properties and process them efficiently for high-quality shirt production. In the case of problem fabrics, concise control instructions must be given to operators in advance so as to avoid faulty selection and processing of fabrics. References 1. Harlock, S.C., “Fabric objective measurement: 4, production control in apparel manufacture”, Textile Asia, July 1989, pp. 89-97. 2. Cheng, K.-P.S., How, Y.-L. and Yick, K.-L., “FOM in shirt production”, Textile Asia, December 1993, pp. 47-50. 3. Ly, N.G., Tester, D.H., Buckenham, P., Roczniok, A.F., Adriaansen, A.L., Scaysbrook, F. and De Jong, S., “Simple instruments for quality control by finishers and tailors”, Textile Research Journal, Vol. 61 No. 7, 1991, pp. 402-06. 4. Postle, R., “Fabric objective measurement technology”, International Journal of Clothing Science and Technology, Vol. 2 Nos 3-4, 1990, pp. 7-17. 5. CSIRO Division of Wool Technology, The FAST System for the Objective Measurement of Fabric Properties – Operation, Interpretation and Applications, CSIRO, Sydney, 1989. 6. Biglia, U., Roczniok, A.F., Fassina, C. and Ly, N.G., “The prediction of garment appearance from measured fabric properties”, International Journal of Clothing Science and Technology, Vol. 2 Nos 3-4, 1990, pp. 48-55. 7. Ly, N.G. and De Boo, A.G., “Application of the FAST system to the manufacture of fabrics and garments”, Wool Research Organisation of New Zealand, Vol. 5, 1990, pp. 370-09. 8. Kawabata, S., Masako, N., Ito, K. and Nitta, M., “Application of objective measurement to clothing manufacture”, International Journal of Clothing Science and Technology, Vol. 2 Nos 3-4, 1990, pp. 18-31.

Knowledge-base construction of a garment manufacturing expert system Chang Kyu Park and Dae Hoon Lee Textile Technology Centre, Kaitech, Seoul, Korea, and

Tae Jin Kang

Knowledge-base construction of a garment 11 Received September 1995 Revised and accepted August 1996

Department of Fibre and Polymer Science, Seoul National University, Seoul, Korea Introduction In recent years, in the developed countries, textile industries such as Korean garment manufacturing has produced men’s suits through factory automation (FA) and has been continuously phased for diversifying to multikind and smallquantity production systems as well as introducing high quality production technology of apparel goods. However the lack of accumulated expert knowledge about the scientific apparel technology still remains a large problem. In garment manufacturing, when the fabrics and styles are chosen, the welltrained human experts select suitable auxiliary materials and processing parameters based on their test results and experiences. This process requires substantial time and cost, and the selected materials and processing parameters are not scientific and systematic. It often happens that different selections of materials and machine settings can be chosen by the human experts for the same fabric. The objective of this study is to solve the technical difficulties using the knowledge base so that it can search the optimum processing conditions for high quality garment manufacturing through development of the expert system. It is expected that the developed expert system emulates the decision making of human experts in garment manufacturing. Suitable auxiliary materials and processing parameters will be identified from the system. It will provide to the fabric manufacturer the guidelines of the manufacturing process for high quality garments and will also evaluate the fabrics. Background and reviews An expert system is a computer system with both hardware and software, which mimics the thinking process of human experts in order to solve the complex problems in a given domain. Since it was introduced in DENDRAL to analyse the structure of chemicals at Stanford University in 1965, there have been many applications in various fields, such as MYCYN, XCON and so on. The expert system has some advantages such as an increase in availability and

International Journal of Clothing Science and Technology, Vol. 8 No. 5, 1996, pp. 11-28. © MCB University Press, 0955-6222

IJCST 8,5

12

reliability, reduction of cost and danger, explanation, fast response, unemotional and steady response at all times, permanence, and so on[1]. The importance of artificial intelligence for textiles and garments has been emphasized since the late 1980s. The expert system was explained as one of the artificial intelligence applications which had potential for the textile industry[2,3]. Textile applications using expert systems and the related research laboratories were introduced by Ruettiger[4] and Demers[5], and they explained that the expert system captures and preserves the knowledge, reasoning and experience of highly skilled managers, engineers and technicians. Stylios[6] also pointed out that the expert system had encouraged apparel manufacturers to move closer towards computer integrated manufacturing (CIM), and would become more widely available. In garment manufacturing, the applications of artificial intelligence, such as expert systems, neural networks and neurofuzzy algorithms, have been introduced and emphasized by Stylios et al.[7-11]. Their work covered the automatic system to predict the sewability of fabrics, to solve the seampucker problems, and to optimize the sewing parameters for the high quality garments, based on the measuring systems developed by them. Jayaraman[12] developed two knowledge-based software systems, called the fabric defects analysis system (FDAS) and the sewing defects analysis system (SDAS), for analysing the defects in trouser manufacturing. The expert system was expected to become a standard element in the weaving room of the near future. Cruycke[13] compared the computer expert systems for weaving operations with the performance of human experts. Fan and Hunter[14] developed an expert system for providing guidelines for the engineering of worsted formal wear fabrics. Using the expert system, which consists of eight sections, fabric design including fabric composition, yarn type and twist, finishing procedure and the processing parameters were decided. Also the fabric properties and performance can be predicted. There are some articles related to expert systems for the dyeing and finishing processes. Frei and Walliser[15,16] reported that a developed expert system was both a decision-making instrument and a reference tool for the wool dyer. With the expert system, the dyer can access important chemical and physical data on products used in dyeing. And the optimal selection of dyes and processing parameters can be simplified. Ruettiger[17] examined the textile expert systems for cheese and cone dyeing process optimization, and Gailey[18] reported the colour expert system. The applications of knowledge-based systems in the textile finishing industry were presented. The use of expert systems for decision making in the continuous finishing process has been reported[19-21]. Curiskis and Grant[22] summarized a brief overview of expert systems, the basic components of which are knowledge base, inference engine, dynamic/ global database, user-friendly interface, and knowledge acquisition module. They also introduced the rule-based expert system for fibre identification.

Some articles relating to the expert systems for vision-based image analysis Knowledge-base were introduced[23-25]. The expert system has been used for the inspection of construction of a visual fabric defects with location and nature. Drean[26] reviewed the garment monitoring systems for fibre preparation, fabrication of ribbons and classic spinning, and explained an ideal expert system for the spinning process. Jacobs-Blecha and Riall[27] used the expert system and neural networks for 13 marker making in the apparel design process. Some applications of the expert system to the measurement technique were easily found. Stjepanovic and Jezernik[28] predicted the properties of cotton yarn including strength, mean staple length, colour, maturity and trash content using artificial intelligence. Cotton yarn quality can also be defined by strength, elongation, twist, neps, count variation and other properties. The expert system for evaluating fatigue strength was developed by Dai and Ishikawa[29]. The future prospects for knowledge-based quality management were discussed by Moon[30] and Fischer and Horstmann[31]. Development of the expert system Figure 1 shows the structure of the developed expert system. The expert system in itself consists of the knowledge base, the inference engine and external routines. The knowledge base contains all the relevant, domainspecific, problem-solving knowledge which has been gathered by the knowledge engineer from the various sources available. Knowledge has many different forms such as rules, predicates, frames, associated networks and objects. An inference engine manipulates the knowledge represented in the knowledge base to develop a solution to the problems described by the information in the database. It attempts to find connections between the objects and the solutions. Database or utilities are included in external routines, which are connected with external resources.

Stand alone

Integrated environment

Input

Input

Knowledge base

Expert system

Application program

Expert system

Output

Output

Knowledge base

Inference engine

External routines

External resources

External routines

External resources

Figure 1. Structure of the expert system

IJCST 8,5

14

In an integrated environment, the expert system is included in the application program as a module. The application program, which has a user interface, carries out the data input or output, and communication with the expert system and external resources. For example, the expert system can be joined with the line scheduling and planning, or seam pucker evaluating system. The developed system is operated under Microsoft Windows version 3.1 and is IBM PC 486 compatible. The database was constructed using Microsoft Excel version 5.0 of Hangeul Microsoft Office 4.0. The programming language is Microsoft Visual C++ version 4.0. The development of the expert system in garment manufacture is divided into the following six stages: (1) definition of domain and selection of the tools; (2) development of the prototype: • formulating the application into an organized problem; • collecting the preliminary knowledge; • constructing the knowledge base; • designing the inference engine; (3) construction of the expert system: • refining the prototype for effective implementation; (4) test and evaluation of the expert system; (5) integration and implementation of the expert system; (6) maintenance of the expert system. Stages 1 and 2 were performed in this study. The process of men’s suit manufacture and controllable processing conditions were analysed and searched. Then, the knowledge was acquired and the knowledge base was constructed. The engine was also designed to decide inference strategies. Figure 2 shows the organization for developing the expert system. The role of knowledge engineer is the most important. The knowledge engineer acquired the knowledge from the domain experts and the collected data, and then constructed the expert system using the expert system development tool. Also, the domain experts and assistants tested and evaluated the expert system. Inspection and evaluation Tool programmer

Domain expert

Construction

Figure 2. Organization for developing the expert system

Expert system development tool

Communication

Use Expert system

Knowledge engineer Use

Construction

User Knowledge insertion and test

Assistant

Definition of the application domain Knowledge-base It is very important to select the application domain and to evaluate whether the construction of a domain is adequate or not[32]. A men’s suit manufacturer, mainly using wool garment fabrics, has accumulated know-how of the human experts and the relatively standardized process. The processes of sponging, spreading and cutting, sewing, fusing and pressing and ironing for men’s suits were considered in this 15 study. Garment finishing, pattern making, and marking processes were excluded because of the difficulties in knowledge acquisition and insufficient accumulated know-how of human experts. Selection of the development tool After studying various development tools, the Nexpert Object version 1.0 was chosen as the development tool. The selected Nexpert Object was more effective and has more functions than others. This tool supports the Windows environment, in which graphic user interface (GUI) and client-server, eventdriven and open architecture can be performed. The most attractive feature is that it was coded using “C” language. This means that object-oriented programming (OOP) and cross-compatibility are possible. The various editors and debuggers are included in this tool. Using these utilities, inheritance and knowledge checking functions are supported. Knowledge representation is a hybrid type including a rule- and object-based semantic network and frame. The most important advantages are the reasonable price and the dependency on the platform[33]. Acquisition of the knowledge The knowledge was acquired through the meetings with human experts and using about 400 technical reports and articles which were collected by the Korea Institute of Industry and Technology Information (KINITI) and the British Library Document Supply Centre (BLDSC) search. The case study and the results of experiments were also important for knowledge acquisition. The Kawabata evaluation system (KES)[34] and the fabric assurance by simple testing (FAST)[35] system are adopted to orient the best apparel quality control system and systematize the knowledge for quality control. The knowledge engineer formulated the knowledge and rules from this acquired knowledge. The knowledge classification is shown in Figure 3. The acquired knowledge was divided into four groups: materials, processing, problems and total reviews. In the material properties group, there are four subgroups: appearance, sewability and tailorability, formability, and auxiliary materials. Similarly, in the processing group there are six subgroups including the quality control system. In the problems and defects group, there are five subgroups such as seam pucker, seam quality, dimensional stability, and so on. Design of the object diagram The database and knowledge base were designed using an object diagram, in which the organic relationship between attributes of the materials and

IJCST 8,5

Appearance, silhouette, etc. 1.

Materials properties for garments

Sewability, tailorability, etc. Wearability, formability, etc. Auxiliary materials

16

Quality control system, automation, etc. Spreading/cutting processing conditions Sewing processing conditions 2.

Processing Fusing processing conditions Sponging/pressing/ironing processing conditions General information

Seam pucker Seam quality, seam appearance, etc. 3.

Problems and defects

Dimensional stability Wrinkle, crease, etc.

Figure 3. Classification of the knowledge

General problems

4.

Total reviews

processing parameters was defined. The structure of the semantic network and frame was represented through the object diagram, and then the engine to decide inference strategies was constructed. This diagram was divided into two types – materials and machines subdiagrams – as shown in Figures 4 and 5. The symbol “l” means a higher ranked class and “∆” means a dynamic or static object. They have attributes such as identification, company, composition and so on. These attributes are inherited by the lower-ranked classes or objects according to the inheritability strategy. For example, the woven fabric subclass has structure, density, cover factor and so forth as its attributes. Four main classes, including fabric, yarn, thread and their properties, are included in the materials subdiagram shown in Figure 4. The fabrics class has two subclasses: woven fabric and non-woven fabric. Some attributes of the sample fabric and interlining subclasses are inherited from their higher classes. Each subclass has its dynamic objects: test fabric1 or interlining1. Also, the test fabric1 object has four subobjects. Two of them, the TF1_KES property and the TF1_FAST property, are connected with the KES property and FAST property subclasses of the higher-ranked property class. The interlining1 object has a

Bobbin thread

Bobbin thread 1

has a

BT1 – ya property

Needle thread

Needle thread 1

has a

NT1 – yarn property

Threads

KES property

FAST property

Yarn property

Properties

TF1 – KES property

has a

TF1 – FAST property

has a

Nonwoven property

TF1 – warp yarn property

TF1 – Warp

has a

Test fabric 1

Sample fabric

Woven fabric

has a

Fabrics

TF1 – weft yarn property

TF1 – Weft

Interlining 1

Interlining

Nonwoven fabric

TF1 – Nonwoven property

has a

Class

Key:

Warp

Yarns

Object

Weft

Knowledge-base construction of a garment 17

Figure 4. Object diagram – materials

Sponging m/c

Figure 5. Object diagram – machines

Footpress

has a

Speed Teeth count Teeth type

has a

Feed-dog

has a

Lock stitch m/c

Sewing m/c

Needle

Tension Thickness

has a

Press

Bobbin

Tension

Fusing m/c

Class

Key:

18

Type pressure

Spreading and cutting m/c

Speed Stitch count

Machines

Object

Iron

IJCST 8,5

subobject, I1_non-woven property, which is connected with the non-woven Knowledge-base property subclass. construction of a Some attributes of two subclasses, warp and weft, are inherited from the garment yarns class. In the case of the dynamic subobject named TF1_warp, it is simultaneously shared by the warp subclass and the test fabric1 object of the sample fabric subclass. The TF1_weft subobject is similar to the TF1_warp. 19 Each subobject has its lower-ranked subobject, TF1_warp_yarn property or TF1_weft_yarn property. It is joined to the yarn property subclass included in the properties class. Similarly, the threads class consists of needle thread and bobbin thread subclasses. Each has its dynamic object, needle thread1 or bobbin thread1. Some attributes of the NT1_yarn property subobject are inherited from those of the needle thread1 object and the yarn property subclass. The BT1_yarn property subobject is similar to the NT1_yarn property. Thus, all the materials, including fabrics and sewing threads, have specific properties of the properties class. In the machines subdiagram (Figure 5)), there are six subclasses related to manufacturing processes including sponging, spreading and cutting, sewing, pressing, fusing and ironing. For example, a lockstitch sewing M/C object is inherited from the sewing M/C subclass of the machines class and has four subobjects such as foot presser, feed dog, needle and bobbin. These subobjects represent the accessories of the lockstitch sewing machine. Each has some attributes as its processing parameters. In the case of the foot presser subobject, it has two attributes, type and pressure, as its parameters. Similarly, other machines have subobjects with the controllable parameters. Figures 6 and 7 show the constructed object diagram in a hierarchical network. These are hard copies using window capture at run-time. Figure 6 shows the object overview and Figure 7 shows the partially enlarged screen of the above-mentioned object diagram. The symbol l indicates a class and s indicates an object. The symbol n means an attribute of which bracket, (S), does the data type as string. Design of the rule-based system With the completion of the object diagram, the database and knowledge base have been constructed. The structure of the rules is as follows: Rule: If…hypothesis…then do…else do… The procedure for creating and editing the knowledge base using a rule editor is shown in Figure 8. The rule editor is composed of the tool bar, the name box of rule, the hypothesis and the knowledge base, the “If” box, the “Action” box, and so on. Each condition of the “If” box is connected by the “AND” operator, and can be represented by the Boolean, numeric, string, variable and assignment operators. Condition results can be true, false, not known, and unknown. The meaning of not known is “Asked and no answer was known”, and that of unknown is “Not yet asked”.

IJCST 8,5

20

Figure 6. Object diagram – overview

Figure 7. Object diagram – enlarged view

Hypotheses are Boolean variables and gateways between conditions and Knowledge-base actions. They can be used as variables in conditions of other rules. The “Action” construction of a box has two parts, “then do” and “else do”, of which operations are performed garment according to the Boolean result of a rule. Some operators of the“Action” part are available for executing the expert system. There are some boxes including “Comments”, “Why”, and “Priority number” as the attributes of a rule. These 21 are useful for editing and searching the rules. A rule example is shown in Figure 8. The name of the rule, of which the hypothesis is “Dimensional_stability”, is “R_dimensional_stability”. The dimensional properties of test fabric were defined by HESC-FT 103A method[36] and FAST[35]. The conditions and text files for suitable advices were referred from the guidelines by Kawabata et al.[34] and FAST[35], and the article by Dorkin and Chamberlain[37]. There are five conditions and action parts as follows. If: (1) S2 of fabric by HESC method > 1.0; and (2) S4 of fabric by HESC method > 1.0; and (3) relaxation shrinkage of fabric by FAST > 6.0; and (4) dimensional stability of needle thread – “not so good”; and (5) material of needle thread = “cotton”. Then do: Open the text file (AD_1T.txt) and show the advice. Else do: Open the text file (AD_1F.txt) and show the advice. The list window of rules maintains the created rule easy to read using a textual format. After compiling the rule in the rule editor, the contents of rules can be shown. Figure 9 shows the list of the created rule as Figure 8.

Figure 8. Rule editor

IJCST 8,5

22

Figure 9. List of the rules to be created as in Figure 8

Design of the inference engine An inference is the logical conclusion or implication by reasoning which is the process of drawing inferences from the rules and connections between the objects and rules. The inference engine makes inferences according to the strategies. Based on the knowledge base, the inference engine was designed by setting the strategies using the strategy editor shown in Figure 10. The

Figure 10. Strategy editor

strategy window is divided into several distinct components related to inference Knowledge-base engine processing as follows: construction of a • the inheritability settings; garment • the inheritance search strategy settings; • the inference strategy setting with a separate set of forward action 23 effects; • the system method evaluation settings; • the data validation settings. There are two alteration modes of these strategies, “default” or “current”. The “default” mode indicates the system setting at the outset of processing, and the “current” mode reflects changes to the default strategies which occur as the system evaluates the rules defined. In inheritability, it is decided whether some attributes of classes and objects will be inherited or not. The unmodified global behaviour of the system lets objects inherit attributes and values down from class only. The up/down arrow means that the parents/children of the object or class can inherit up/down from their child/parent. The inheritance strategy component has two sets of check-book which together determine the pathways through the class and object network. When searching for a value, and there are multiple places from which to get the value, the inheritance strategies help to determine where to look. Thus, the system follows certain predetermined pathways in order to propagate attributes and values. The default modes of inference strategies and forward action effect are explained in Tables I and II. Also, rules that do not have direct data links called Strategy Forward confirmed hypotheses Forward rejected hypotheses Forward not known hypotheses Forward through gates Exhaustive evaluation

Default

On

Off

Off

On On

Description Rule of which hypothesis evaluates to “true” propagates the inference process to weakly-linked hypotheses via the context mechanism Rule of which hypothesis evaluates to “false” propagates the inference process to weakly-linked hypotheses via the context mechanism Rule of which hypothesis evaluates to “not known” propagates the inference process to weakly-linked hypotheses via the context mechanism Rule of which data makes the conditions of another rule “True” propagates the inference process to that rule’s hypotheses via the gates mechanism All rules leading to a suggested hypothesis will always be evaluated, even after the value of the hypothesis has already been determined by a previous rule

Table I. Inference strategies

IJCST 8,5

Strategy

Default

Description

Rule global

On

From rule else

Off

Rules of which “then” actions change the value of shared data of another rule’s conditions propagate the inference process to that rule’s hypothesis via the action effects mechanism Rules of which “else” actions change the value of shared data of another rule’s conditions propagate the inference process to that rule’s hypothesis via the action effects mechanism Methods of which “then” actions change the value of shared data of another rule’s conditions propagate the inference process to that rule’s hypothesis via the action effects mechanism Methods of which “else” actions change the value of shared data of another rule’s conditions propagate the inference process to that rule’s hypothesis via the action effects mechanism

24

Table II. Forward action effects strategies

Method global

Rule global (on)

From method else

Off

“strong links” but have been connected with contexts are defined as “weak links”. These links can make the connections between rules according to inference strategies and forward action effect. Inference strategies are performed by the results of hypotheses, and the forward action effect is used when the rule’s actions change the value of shared data of another rule’s conditions. For effective data management, there are two system methods, “order of source” and “if change”, and the user-defined method. Order of source makes users define and prioritize the sources when the system needs to get the value of an object or a class on inferencing. This method of assigning the values into the attributes of object can also be chosen between user’s input and database. “If change” action is performed whenever the value of an object or a class is changed. Using user validation or engine validation, new values provided by the end user or the system are tested against the data validation functions defined. Implementation of the expert system The expert system was developed with the knowledge base and the inference engine. Figure 11 shows the procedure for implementation of the developed expert system. There are two types of data input: from the interactive user’s input using natural language, or from the database. Through the inferencing by the expert system, some advices are shown. In this captured window, a user answered “not so good” using natural language when the expert system asked the user “What is the dimensional stability of your test needle thread?”. Figure 12 shows the output after inferencing. It indicates the result that the system has evaluated the rules true or false. All the six conditions of the first

Knowledge-base construction of a garment 25

Figure 11. Implementation of the expert system

Figure 12. Inference by the expert system

if-clauses were accepted as true by the values automatically obtained from database of HESC and FAST properties and user’s input. Thus the first rule of the hypothesis “dimensional_stability” was evaluated true. However, the second rule named “R_overall_treatment1” was evaluated false because the first condition was rejected by the HESC property. Figure 13 shows an advice text adopted by the expert system. This advice explains the dimensional instability of the test fabric with high relaxation shrinkage and some special instructions. The conditions of processing such as

IJCST 8,5

26

Figure 13. Advice by the expert system

cutting, fusing, steam-pressing and sewing were recommended, for high quality garments, as well as the suitable material of sewing thread (with the reason). Conclusions Using the developed expert system, the good guidelines for the suitable auxiliary materials and controllable parameters of processing conditions were made in garment manufacture. It is necessary to evaluate and expand the system to be more applicable to men’s suit manufacturing in the future. Instead of the human experts, the advanced expert system should solve the more difficult and practical problems in garment manufacturing. The development of the expert system can solve the various problems in garment manufacturing as well as automate the factory with more efficient productivity. This expert system will contribute to improvements in the garment quality in the diversification of the multikind and small quantity production system. This research can bring about standardization of the apparel production process and the management of the raw materials. The application of the expert system can be expanded to other manufacturing industries such as leather, suitcases, shoes, etc. The expert system with CAD/CAM and management information systems (MIS) will make it possible to construct computer integrated manufacturing systems (CIMS) in garment manufacturing. References 1. Waterman, D.A., A Guide to Expert Systems, Addison-Wesley, Reading, MA, 1986. 2. “AI puts an expert in your computer system”, Textile World, Vol. 137 No. 5, May 1987, pp. 48, 50. 3. “Artificial intelligence for the textile industry? Programming”, Textil Praxis International, foreign ed., Vol. 43 No. 2, February 1988, pp. 144-5.

4. Ruettiger, W., “Expert systems – the future instrument of technical management. Part 3. Step-by-step development of a textile expert system”, Textilveredlung, Vol. 23 No. 5, May 1988, pp. 159-62. 5. Demers, A.J., “Artificial intelligence – computerize your expertise”, Textile World, Vol. 139 No. 1, January 1989, pp. 56-8. 6. Stylios, G., “Artificial intelligence and the garment industry with special reference to expert systems”, International Journal of Clothing Science and Technology, Vol. 1 No. 3, 1989, pp. 4-5. 7. Stylios, G., “Expert system for the prediction of fabric sewability and optimization of sewing and fabric conditions in garment manufacture – Stylios sewability system (SSS)”, Knitting International, Vol. 97 No. 1164, December 1990, pp. 98-9. 8. Stylios, G. and Fan, J., “An expert system for the prediction of fabric sewability and optimization of sewing and fabric conditions in garment manufacture (sewability system (SS))”, Textile Objective Measurement and Automation in Garment Manufacture, Ellis Horwood, Chichester, 1991, pp. 139-47. 9. Stylios, G., Fan, J., Sotomi, J.O. and Deacon, R., “A new concept in garment manufacture (the sewability integrated environment incorporating automated objective measurement systems)”, International Journal of Clothing Science and Technology, Vol. 4 No. 5, 1992, pp. 45-8. 10. Stylios, G., “Neural networks in garment manufacture”, International Journal of Clothing Science and Technology, Vol. 5 No. 2, 1993, pp. 5-6. 11. Stylios, G. and Parsons-Moore, R., “Seam pucker prediction using neural computing”, International Journal of Clothing Science and Technology, Vol. 5 No. 5, 1993, pp. 24-7. 12. Jayaraman, S., “Analysis of defects in trouser manufacturing – development of a knowledge-based software system”, Georgia Institute of Technol-Atlanta Series No. Ad-A248 647, 1991, p. 22. 13. Cruycke, B., “Artificial intelligence in modern weaving”, Mell iand Textilberichte (International Textile Reports), German ed., Vol. 69 No. 8, August 1988, pp. 548-53. 14. Fan, J. and Hunter, L., “The development of an expert system for the engineering of worsted formal wear fabrics”, Proceedings of World Textile Congress, The University of Huddersfield, July 1994. 15. Frei, G. and Walliser, R., “Wooly – an expert system for the wool dyer”, Textilveredlung, Vol. 23 No. 6, June 1988, pp. 203-5. 16. Frei, G. and Walliser, R., “Wooly – an expert system for the wool dyer”, Journal of The Society of Dyers and Colourists, Vol. 107 No. 4, April 1991, pp. 147-9. 17. Ruettiger, W., “Expert systems – the future instrument of technical management. Part 3. The optimist textile expert system. Function, limits, and prospects”, Textilveredlung, Vol. 23 No. 6, June 1988, pp. 199-203. 18. Gailey, I., “Expert system for textiles”, International Dyer, Textile Printer, Bleacher and Finisher, Vol. 174 No. 5, May 1989, pp. 31-2. 19. Frei, G. and Poppenwimmer K., “Texperto expert system”, Textilveredlung, Vol. 27 No. 9, September 1992, pp. 276-9. 20. Bauhofer, R., Huet, M., Schacher, L. and Viallier, P., “Artificial intelligence and expert systems for textile finishing”, Textilveredlung, Vol. 27 No. 9, September 1992, pp. 280-84. 21. Lange, A., Nahr, U. and Schurmann, K., “Bafarex expert system”, Textilveredlung, Vol. 27 No. 9, September 1992, pp. 268-75. 22. Curiskis, J.I. and Grant, C.W.C., “Expert systems in textile technology – the fibre experiment”, Textile Institute 1988 Annual World Conference, 1988, pp. 208-17. 23. Shao, C. and Kuze, E., “Fabric defect valuation method by using expert systems”, Journal of The Textile Machinery Society of Japan, Vol. 42 No. 3, 1989, pp. T36-T46.

Knowledge-base construction of a garment 27

IJCST 8,5

28

24. Shimizu, Y., Ishikawa, T., Furukawa, T., Kayama, N., Toba, E. and Kondo, A., “Expert system to inspect fabric defects by pattern recognition”, Sen-I Gakkaishi, Vol. 46 No. 10, 1990, pp. 460-69. 25. Srinivasan, K., Dastoor, P.H., Radhakrishnaiah, P. and Jayaraman, S., “FDAS – a knowledge-based framework for analysis of defects in woven textile structures”, Journal of The Textile Institute, Vol. 83 No. 3, 1992, pp. 431-48. 26. Drean, J.Y., “Toward expert spinning systems”, Industrie Textile, No. 1216, December 1990, pp. 42-6. 27. Jacobs-Blecha, C. and Riall, W., “Feasibility of improving the marker making process”, International Journal of Clothing Science and Technology, Vol. 3 No. 4, 1991, pp. 13-24. 28. Stjepanovic, Z. and Jezernik, A., “Prediction of cotton yarn properties using artificial intelligence”, Computers in Industry, Vol. 17 No. 2/3, November 1991, pp. 217-23. 29. Dai, X. and Ishikawa, H., “Development of expert system for evaluating fatigue strength”, JSME International Journal Series A, Vol. 37 No. 2, 1994, pp. 161-5. 30. Moon, J., “Bringing in the expert”, Journal of The Society of Dyers and Colourists, Vol. 107 No. 9, September 1991, pp. 296-8. 31. Fischer, T. and Horstmann, G., “Knowledge-based data processing for quality management in the textilemill – requirements and system structure”, Its Textile Leader, No. 8, April 1991, pp. 16-36. 32. Prerau, D.S., “Selection of an appropriate domain for an expert system”, The AI Magazine, Summer 1985, pp. 26-30. 33. Smart Element Manual, Neuron Data Inc., USA, 1993. 34. Kawabata, S., Ito, K. and Niwa, M., “Tailoring process control”, Journal of the Textile Institute, Vol. 83 No. 3, 1992, pp. 361-74. 35. Fast Manual, CSIRO Division of Wool Technology, Australia, 1989. 36. HESC, “HESC-FT-103A, the testing method of dimensional instability of fabrics”, Journal of the Textile Machinery Society of Japan, Vol. 32, 1979, pp. 268-83. 37. Dorkin, C.M.C. and Chamberlain, N.H., “Seam pucker – its cause and prevention”, Clothing Institute Technological Report, No. 10, June 1961, pp. 1-38.

The effect of moisture transfer on the compression properties of wool futon padding Sachiko Sukigara Faculty of Education, Niigata University, Niigata-shi, Japan,

Hiroko Yokura

The effect of moisture transfer 29 Received September 1995 Accepted April 1996

Faculty of Education, Shiga University, Otsu-shi, Japan, and

Masako Niwa Faculty of Human Life and Environment, Nara Women’s University, Nara-shi, Japan Introduction Wool futon padding has become popular in Japan[1,2]. The price is relatively low compared to that of down, and the weight of a wool futon is lighter than that of a cotton futon, making it easier to lift. There are several papers on the performance of cotton futon padding[3], but an adequate evaluation test for wool futons has not yet been proposed. The main disadvantage of using a wool futon is the decrease in elasticity during use. The authors have already reported thickness changes in the model futon that a woman used for 51 days[4] and about the repeated compression property of wool futon padding under atmospheric conditions of 20˚C, 65 per cent RH[5]. These studies clearly indicated that the presence of moisture affects both the recovery and non-recovery of wool futon thickness. The purpose of this paper is to investigate how the presence of moisture affects the compression properties and volume of wool futon padding, and to obtain basic ideas on how to improve the performance of wool futon padding. The experiment Three cases of moisture transfer are thought to occur with futon use: (1) A futon absorbs moisture when the person sleeping on it sweats. In high humidity, a futon also absorbs moisture during storage in a house. (2) A futon desorbs moisture when it is dried by body temperature during sleep. It is a Japanese custom to dry a futon in the sun. In this case, a futon desorbs moisture. (3) In this case both moisture absorption and desorption do not occur. The authors gratefully acknowledge the financial support received from the Best Wool Club and IWS in Japan.

International Journal of Clothing Science and Technology, Vol. 8 No. 5, 1996, pp. 29-41. © MCB University Press, 0955-6222

IJCST 8,5

30

These three cases usually occur through daily use of a futon. The experimental procedure was designed to evaluate the three cases listed above. Sample preparation Two types of wool, one cotton and one polyester carded web wadding were supplied to this study as shown in Table I. The samples were dried in an oven at 80 +2˚C for seven hours and then transferred to a room at 20˚C, 65 per cent RH for more than 48 hours prior to the experiments.

Fibre B wool F wool Cotton PET Table I. Samples

Diameter (µ)

Length (mm)

Crimp (per cent)

28.8 30.5 18.1a 9.6b 45.0

46.4 37.4

24.0 46.4

Notes: a a diameter along the long axis of ellipse b a diameter along the short axis of ellipse

Volume change caused by the moisture transport First, the relation between volume change and water content was examined without applying pressure. Water was applied to 3g of dried samples and left in the desiccator at 20˚C, 90 per cent RH for eight hours. The water contents of wool B, wool F and the cotton samples were 49, 59 and 115 per cent respectively. The samples were transferred to an atmosphere of 20˚C, 65 per cent RH, then both the volume and water content of the samples was measured for one week. During these measurements, samples desorbed the moisture and reached equilibrium water content at 20˚C, 65 per cent RH. Pressure volume measurement A sample weighing approximately 3g was placed in a cell with a cross-sectional area of 39.57cm2. This cell was set in a Handy Compression Tester (KATO TECH) at an apparent fibre density of 0.017 g/cm3, which is equivalent to that of commercial futons. Compression and release cycles were carried out at a rate of 1mm/sec. The maximum displacement of the compression plate was 20mm. From this curve, compression energy WC( J/m2) and resilience RC (per cent) were calculated. Compression and release cycles were carried out according to the procedure illustrated in Figure 1 to obtain the curves both after absorption and after desorption. The first compression curve was obtained for the sample

conditioned at the equilibrium moisture regain in 20˚C, 65 per cent RH. Water containing 0.01 per cent Twin 80 was applied to the same sample and left in the desiccator at 20˚C, 90 per cent RH for 24 hours. The moisture regain of this sample was approximately 20 per cent. The sample was taken out of the desiccator and a 2kPa weight was applied for three hours. This pressure of 2kPa was chosen as the average pressure reported when a man weighing 45-65kg lies on a futon[6]. Moisture desorption occurred during this test. 2kPa pressure was applied for three hours to the sample three times as shown in Figure 1. Every time, pressure-volume curves were obtained both before applying the weight and after removing the weight. Compression tests were also carried out for the conditioned sample at 20˚C, 65 per cent RH with 2kPa pressure applied in the same manner, but moisture transport of these samples did not occur (control sample). 2kPa 7 hours 80+ 2°C

48 hours

24 hours

3 hours

20°C 20°C 65 per cent 90 per cent RH RH

1

2kPa

2

24 hours

3 hours

3

31

2kPa 1 week

3 hours

20°C 65 per cent RH

2′

The effect of moisture transfer

3′

4

4′

Note: 1, 2, 2′, 3, 3′ = Pressure-volume measurements

Repeated creep test in atmospheres of various relative humidities. A fibre assembly weighing approximately 2g was placed in a cell with a crosssectional area of 39.57cm2. This cell was set in a creep tester (KATO TECH) in a controlled atmosphere of 20˚C, 60 per cent RH, 90 per cent RH and 15 per cent RH. Then a 2kPa weight was applied for 50 minutes. After removing the weight, the sample was left for 50 minutes. The same test was carried out five times with the same sample. During this experiment, changes in thickness were continuously recorded. Through these experiments, the relative humidity around the sample was controlled, therefore moisture absorption and desorption did not occur. Results Volume change caused by moisture transport Figure 2 shows the relative volume (V/Vo: Vo is volume before applying water ) of a sample plotted against the water content during storage at 20˚C, 65 per cent RH. During storage, the water content of the samples decreased. In the case of wool samples B and F, an increase in volume was observed when the samples absorbed moisture after being taken out of the desiccator. The volume further increased with the decrease in water content. It was found that, for wool fibre assemblies, an increase in volume occurred from both absorption and

Figure 1. Procedure for pressurevolume measurements

IJCST 8,5

V/Vo 1.8 1.6

32

Key Wool B Wool F Cotton

1.4 1.2 1 0.8 0.6

Figure 2. Changes of relative volume against water content for wool B, wool F and cotton samples

0.4 0 20 40 Water content per cent

60

80

100

120

Notes: V:volume, Vo:Conditioned volume at 20˚C, 65 per cent rh before applying water

desorption. This tendency was more obvious in the high crimpy wool fibre (sample F). For cotton samples, the volume decreased when fibres absorbed water when water was applied to the sample, and was almost stable at a moisture regain of 40-120 per cent. The pressure volume property Table II shows the comparison between compression properties obtained under standard conditions and those obtained at a higher water content. For all samples, a decrease in RC was obvious at high water content. Figure 3 shows the ratio of the initial values of WC(1) and RC(1) to those obtained after absorption and desorption for wool samples treated by the

Symbol Table II. Compression properties of both standard and wet conditions

B F Cotton PET

Standard condition (20˚C, 65 per cent RH) WC (J/m2) RC (per cent) 4.57 6.38 8.29 37.15

64.5 51.3 57.8 48.6

Wet condition WC' (J/m2)

RC' (per cent)

Water content (per cent)

2.89 4.72 9.72 43.58

32.6 32.0 26.8 43.5

25.1 24.0 21.5 20.4

The effect of moisture transfer

WC/WC(1) 1.4 1.2 1

33

0.8 0.6 0.4 0.2 0 1

2

2′

3

3′

4

4′

RC/RC(1) 1.2 1 0.8 0.6 Key B (control) B – (allowed to change water content) F (control) F – (allowed to change water content)

0.4 0.2 0 1

2

2′

3

3′

4

4′

procedure illustrated in Figure 1. In these figures, the effect of moisture absorption on WC and RC is shown in the second measurement (see 2 in Figure 3) and desorption in the third measurement (see 3 in Figure 3). The samples having higher water content were more easily compressed than the standard sample, and the relative values of WC and RC were smaller than those of the conditioned sample as shown in stage 2 and 2' in Figure 3. When samples having a water content of approximately 25 per cent were dried in the conditioned room at 20˚C, 65 per cent RH, the futon padding desorbed the moisture and its volume tended to recover to its initial level. The values of the relative RC of wool sample F returned to the level of the standard condition before absorption (see 3 in Figure 3). From this observation, the

Figure 3. Changes of compression characteristics (WC/WC(1), RC/RC(1) for both absorption and desorption of moisture

IJCST 8,5

34

moisture absorption of wool fibre assembly seems to have little effect on the viscoelastic property of fibres. However, the values of WC for the third measurement did not return to the initial level and were smaller than those of the control sample. This phenomenon might be the result of a decrease in the reversible fibre slippage produced by the previous test. Samples were left for one week at 20˚C, 65 per cent RH, after which the third test was carried out. The results were almost the same as those observed in the previous test. For wool sample B, the sample was compressed once in the presence of water and a decrease in compression energy was observed even when the water content of the fibre returned to the value at 20˚C, 65 per cent RH. Creep phenomenon In Figure 4, the thickness of a wool fibre assembly, T(mm), is plotted against the creep and recovery times. In this figure, the thickness change obtained by compression and recovery of the fibre assembly consists of two parts; the immediate deformation (Ei – compression process; or Ei ' – recovery process) and the deformation occurring with the passage of time. It is seen that the immediate deformation accounts for a greater proportion of the total change in thickness. The immediate thickness change. In Figure 5, the ratio of immediate thickness change (Ei, Ei') to the initial thickness ,Ti(0), in three different humidities are shown for wool B, cotton and polyester samples for each compression creep test. The residual strain ∆ Ei/Ti(0) = (Ei – Ei')/Ti(0) Thickness (mm) 70 T1

60

T2

T3

50 T5

T4 T1′

40

T2′

T3′

T4′

T5′

30 Ei

Ei′

20 10 0 0 50 100 150 200 250 300 350 400 450 500 Time (minutes) Figure 4. Thickness change during five creep tests

Key Ei = Immediate thickness change for deformation Ei′ = Immediate thickness change for recovery Note: Wool, 20°C, 65 per cent RH

1

Key Percentage RH 60 60 90 90 15 15

Ei/Ti(0)

0.9 0.8 0.7 0.6

Ei′/Ti(0)

0.5

The effect of moisture transfer 35

0.4 0.3 0.2

Wool B 1

2

3

4

5

1

Key Percentage RH 90 90 15 15 60 60

Ei/Ti(0)

0.9 0.8 0.7

Ei′/Ti(0)

0.6 0.5 0.4 0.3

Cotton 0.2

1

2

3

4

5

1 60 per cent RH

0.9 0.8 0.7

Ei/Ti(0)

0.6 0.5 Ei′/Ti(0)

0.4 0.3

Polyester 0.2

1

2

3

4

5

Figure 5. The ratio of immediate deformation (Ei or Ei') to the initial thickness (Ti(0)) for each creep test

IJCST 8,5

36

decreased with the increase of creep cycles and reached a near equilibrium value for all samples. The effect of relative humidity on the immediate thickness change was obvious in the first creep test. When a fibre assembly was compressed at high relative humidity, a large decrease in volume occurred. It is though that water between fibres accelerated the fibre slippage, thus increasing the fibre density. Thickness change occurring under weight pressure with the passage of time. Figure 6 shows the normalized creep curves obtained at 20˚C, 65 per cent RH for wool B, cotton and polyester samples. T1(0. 1) represents the thickness at 1 minute for the first creep test. It is found that the second creep curve was shifted on a logarithmic time scale to the right and superimposed on the first curve. Similarly, subsequent curves are superimposed on the first curve, producing the master creep curve shown in Figure 7. By using this technique, creep curves of longer creep times can be predicted from a single master creep curve. This technique was applied to the other curves obtained at 15 per cent and 90 per cent RH, but the superposition was not as successful. The slope of the normalized curve, R was obtained (see Figure 8), rather than using surperposition technique. Obtained values R in the first cycle are plotted against water content as shown in Figure 9. R values of for wool and cotton samples increased remarkably at a water content of over 20 per cent. For recovery behaviour, the ratio T/T'(0.1) is defined as, T/T'(0.1)= thickness during recovery/thickness at 0.1 minute after removing the weight. The values for wool and cotton samples at the three relative humidities are plotted in Figure 10. It is seen that the recovery of thickness occurred quickly during the first ten minutes. After that, the thickness recovered slowly and became almost constant, as shown in Figure 10. The recovery of thickness for the wool sample is larger than that of the cotton sample. Discussion When dried wool futon padding absorbs moisture, an increase in volume is observed. This phenomenon results from the deformation of fibres caused by the increase of fibre crimp or the change of crimp shape. During the desorption of moisture, an increase in volume for wool is also observed. It has been reported for cotton futon[7] that when the moisture in the fibre assembly decreases, the fibre assembly expands. This expansion of fibre assembly is mainly caused by the expansion of air inside the cotton fibres rather than between the fibres. In the case of wool fibre assemblies, the increase in the fibre assembly thickness is caused by the expansion of air between fibres. The recovery of futon padding after compression is largely influenced by reversible and irreversible fibre slippage. The irreversible fibre slippage produces a decrease in volume after compression. It is considered that the reversible fibre slippage decreases from compression when moisture is present in the fibre assemblies, thus reflecting the decrease in RC.

T/T1 (0.1) 1

The effect of moisture transfer

0.98 0.96 0.94 0.92

37

0.9 0.88 0.86 0.84 Wool B

0.82 0.8 0.1

1

10

100

1 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 Cotton

0.82 0.8 0.1

1

10

100

1 0.98 0.96 0.94 0.92

Key =1 =2 =3 =4 =5

0.9 0.88 0.86 0.84 0.82

Polyester

0.8 0.1 Time (minutes)

1

10

100

Figure 6. The normalized creep curves obtained at 20˚C, 65 per cent RH

IJCST 8,5

T/T1 (0.1) 1 0.98 0.96 0.94

38

0.92 0.9 0.88 Key

0.86

Polyester Wool B Wool F Cotton

0.84 Figure 7. Master creep curves obtained at 20˚C, 65 per cent RH

0.82 0.8 0.1 1 Time (minutes)

10

1,000

100

10,000

T/T(0.1) 1 0.95

R

0.9 0.85 Key 15 per cent RH 90 per cent RH 60 per cent RH

0.8 0.75

Wool B, first Figure 8. Definition of creep rate, R

0.7 0.1 1 Time (minutes)

10

100

Note: T = Thickness, T(0.1) = thickness at 0.1 minute creep time

In the case of wool sample B, once the sample was compressed at a high water content, the volume did not return to the initial level. These results suggest that if sample B was used for futon padding, the sample would need to be dried at a high temperature to obtain recovery. It has been reported in previous papers[4,5] that fibre crimp was found to be an important parameter in the non-recovery of futon padding. In this study, a

The effect of moisture transfer R (percentage) 3.5

First cycle

39

3 2.5 2 1.5 Key Wool B Wool F Polyester Cotton

1 0.5 0 10 20 30 40 0 Water content (percentage)

50

60

70

crimpy fibre assembly (Wool F) shows more volume change and better recovery by moisture change than an uncrimpy fibre assembly (Wool B). The fibre crimp is also an important parameter for a wool fibre assembly at high water content as well as under standard conditions. Conclusions The moisture inside futon padding has a great influence on the compression and recovery process. This phenomenon differs between samples for absorption and desorption. When futon padding was compressed with the presence of moisture, the fibre slippage was considered to have accelerated compared to the standard condition sample. In repeated creep tests, the residual strain decreased with the increase of creep cycles and tended to reach an equilibrium value for all levels of water content. The effect of moisture on the residual strain was most obvious in the first creep test. The creep curves at 20˚C, 65 per cent RH were superimposed to obtain a single master curve which allowed us to estimate the viscoelastic behaviour of a large number of loadings and thickness changes. Taking the master curve at 20˚C, 65 per cent RH, with the equilibrium values of the residual strain obtained

Figure 9. Plots of creep rate R against water content for wool B, wool F, polyester and cotton samples

IJCST 8,5

T/T′(0.1) 1.4

Key 60 per cent RH 90 per cent RH 15 per cent RH

1.35

40

1.3 1.25 1.2 1.15 1.1 1.05 Wool B 1 10 20 0 Recovery time (minutes)

30

T/T′(0.1) 1.4

40

50

Key 90 per cent RH 60 per cent RH 15 per cent RH

1.35 1.3 1.25 1.2 1.15 1.1 Figure 10. Thickness recovery of wool B and cotton samples in the first creep test under three relative humidities

1.05 Cotton 1 10 20 0 Recovery time (minutes)

30

40

50

from the repeated creep test, the tendency of non-recovery of wool futon over a long period of use can be predicted.

References 1. Maekawa, Y., “Required property for bedding”, Journal of the Japan Research Association for Textile End-uses, Vol. 25, 1984, pp. 20-25. 2. “Investigation of futon”, report by Nara Prefectual Home Science Center, 1992. 3. Tada, C., “The study on the Japanese bed from the viewpoints of health”, Racial Hygiene, Vol. 45 No. 5, 1979, pp. 170-83. 4. Yokura, H., Sukigara, S. and Niwa, M., “Changes in the dimensional and mechanical properties of wool futon padding after repeated compression. Part I: thickness change in model futon during use”, Journal of the Japan Research Association for Textile End-Uses, Vol. 36, 1995, pp. 594-60. 5. Sukigara, S., Yokura, H. and Niwa, M., “Non-recovery of futon padding after repeated compression”, International Journal of Clothing Science and Technology, Vol. 6 Nos. 2-3. 1994, pp. 51-6. 6. Yasuda, T., Tanaka, M., Kamitani, Y. and Tanijiri, S., “The property of wadding”, Journal of the Japan Research Association for Textile End-Uses, Vol. 3, 1962, pp. 310-15. 7. Minamisawa, A. and Takenaka, H., “Studies on the thermal expansion of fibre assemblage (part 3): the expansion in the high vacuum chamber”, Journal of Home Economics of Japan, Vol. 20 No. 1, 1969, pp. 49-53.

The effect of moisture transfer 41

IJCST 8,5

42 Received July 1995 Accepted December 1995

Simulation of flow lines in clothing manufacture. Part 2: credibility issues and experimentation G. Fozzard School of Design and Manufacture, De Montfort University, Leicester, UK,

J. Spragg The Robotics Institute, Carnegie Mellon University, Pittsburgh, USA, and

D. Tyler Department of Clothing Design and Technology, Manchester Metropolitan University, Manchester, UK Introduction Part 1 reported on the construction of a simulation model of the Progressive Bundle System, incorporating operator performance variations and learning effects, machine failure and repair, operator absenteeism, quality failure and knowledge-based supervisory control. In part 2, the issue of validation is addressed. Complex system models are not easy to validate and a four-stage approach has been used to demonstrate conformance with real-world systems: qualification, face validity, modular validation and time-series system behaviour. Applications of the model are discussed and the results of experiments with a line starting work on a new style are presented. Model credibility Background The central issue in any modelling venture is achieving credibility for the model, so that problem owners will have confidence to use the simulation as a problem solving tool. To achieve this end it is essential that problem owners and model developers communicate effectively throughout a project, and that the modeller takes all reasonable steps to demonstrate the worth of the model. This issue is addressed in more detail by Fozzard[1]. Naylor and Finger’s[2] analysis of the “credibility issue” has led to the acceptance of a multi-phase approach. The stages were given the names of qualification, verification and validation by Fishman and Kiviat[3] and have International Journal of Clothing Science and Technology, Vol. 8 No. 5, 1996, pp. 42-50. © MCB University Press, 0955-6222

Funding for this research was provided by the ACME Directorate of SERC, Grant Reference GR/D 74246. We wish to thank our industrial collaborators for providing access to factory data.

since been generally accepted. These stages were adopted in the development of the clothing production line model, and regular communication between factory managers and the modelling team ensured that the model had credibility and the most pertinent model features were present. The work undertaken as an aspect of input data analysis (described in part 1) is an intrinsic element of the qualification exercise. In particular the decisions relating to the adoption of specific particular distributions for process time modelling, absenteeism and machine breakdown were qualified independently. Qualification Qualification of a model is concerned with the underlying postulates and assumptions of a model, and demonstrating that they are reasonable. In the lumped model, for example, it is assumed that materials handling between workplaces does not have to be modelled explicitly, as the handling time is included in the Standard Minute Value for each operation. A full set of assumptions was developed for the model[1] and discussed with the problem owner. Given the limitations on qualifying any postulates in a model of a human activity system[4], no assumption could be presented as a universal truth. In all cases it was found that the assumptions were considered reasonable by production management personnel. Verification Verification is the process of debugging a computer model so that it correctly represents the original conceptual model that the developer intended. Since the sampling of random variables is of central importance to the generation of sound data, verification must include testing of the pseudo random number generators used in the model. In addition, the development of the code in a modular format facilitated verification and a structured walk through of the model elements. Extensive testing of all sampling mechanisms used in the model was performed with particular emphasis on the most critical variables. The modelling of process time variation was tested independently from the operation of the flow line by comparing typical model generated performance variation of a single operator to that of a similar real world operator. As the model relies on categorizing the combination of job and operator to determine underlying performance curve (see part one), it was necessary to identify a similar real operator for comparison. Figure 1 shows model generated performance along with a mean level for intermediate job complexity (2) and operator class B. The mean level is used in the model to determine the mean of a normal distribution from which a random sample of performance (the model generated performance) is drawn. Figure 2 shows a typical real performance variation over the same time frame. Comparison of real and simulated performance time series reveals a broadly similar peak to peak variation in performance and a similar profile in the underlying trend of increasing performance. Note that cross-correlation

Simulation of flow lines. Part 2 43

IJCST 8,5

Performance (per cent) 140 120

44

100 80 60 40 20

Figure 1. Typical model generated performance time series (operator classification B, task complexity 2)

0 0 10 Day of simulation

20

30

40

50

Key Mean level

Sample

Performance (per cent) 140 120 100 80 60 40 20 Figure 2. Typical real performance times series

0 0 10 Day of study

20

30

40

50

between turning points is not expected as each run of the simulation will produce a different set of random performance samples. The comparison indicated that the sampling mechanism for performance generation was reasonable but the credibility of this technique could not be increased further without looking at the behaviour of the complete model.

Simulation of flow lines. Part 2

Validation Validation is the stage of testing that is concerned with model output and its correspondence with data produced from the real system. It is very common to face limitations to validation of a simulation model: • The very fact that the model does not contain all real world elements clearly rejects a null hypothesis that model data and real data are the same before any statistical test is conducted[5]. • Simulation is used when there is a limitation to real world experimentation and data collection. This means that there will be limited real data to compare with the output from the model. • Although objective statistical tests exist to facilitate model validation, their selection is subjective and their results are commonly open to subjective interpretation. • A model of any human activity system can never have absolute validity. If it is valid to the problem owner, then it is an adequate problem solving tool. In these circumstances the modeller must be pragmatic and adopt, on the face of it, purely subjective methods. Indeed, Shannon[6] describes the most important issue in validation to be “Does it make sense?” and believes professional judgement to be far more valuable than any statistical test. Face validity ties in with professional judgement of the model. This is established by asking people who are knowledgeable about the real system if the behaviour of the simulation is reasonable. This technique can be used when the real system may not be defined by reference to the most knowledgeable “expert”. The animation facilities of the model were invaluable here. A number of experts (industrial collaborators) observed the behaviour of the model and declared it to be reasonable in the way production problems were represented and in the way the model responded to changes made. Following this “face” validation of the model, it was considered appropriate to conduct some form of statistical analysis on the predictive power of the model. Here, descriptive statistics were judged to be more valuable than inferential statistics. Statistical tests for objective model validation are described in most texts on simulation[5-7]. In cases where the real system exists, in full or in part, it is likely that the real system will have been observed for a period of time so that time series data are available for each variable of interest.

45

IJCST 8,5

46

Because of limited real data, objective validation is more difficult than comparing the results of two simulation experiments. The transformation process of batching, that can be used to convert auto-correlated simulation time series data to independent and identically distributed data, cannot be applied to the limited one-off real world data sets and thus the standard two-sample tests are precluded. However, as has been pointed out[5], the adoption of this type of test is questionable anyway, and the null hypothesis that the data sets come from the same population should not be asserted. A better technique in validation is to consider the degree of mismatch between model and reality and to argue whether that difference is likely to influence conclusions drawn from the model. For this simulation model the comparison took place at two levels: long-term mismatch in production figures, and the correspondence of time series data. One set of data from the real world system was obtained over 55 days which included a severe disruption of work flow, reaching a climax on day 20. The overall profile allowed the dynamic response of the model to similar disruption to be tested. For the simulation run it was necessary to “replay” the scenario of events (moving operators) to reproduce the real-world changes that took place for line balancing, and also resulted in the disruption noted. Using different random number streams over ten runs the model was, on average, within 5 per cent of the real cumulative production, but was consistently under-estimating the production figures (see Table I). The cumulative production figures indicated that the model was close enough to real production figures to be a valuable estimating tool. Some investigation of the underestimate took place, looking specifically at the mechanism used to decrease performance (and hence production) when an operator changed job. This was found to be an insignificant problem and the

Run no.

Table I. Comparison of cumulative production over 55 days

1 2 3 4 5 6 7 8 9 10

Simulated production (dozens) 9,928 9,792 9,984 9,892 10,008 10,000 9,848 9,944 9,648 10,024

Production real line (dozens)

Absolute difference

Percentage difference (percentage)

10,484 10,484 10,484 10,484 10,484 10,484 10,484 10,484 10,484 10,484

–536 –672 –480 –572 –456 –464 –616 –520 –816 –440

–5.1 –6.4 –4.6 –5.5 –4.4 –4.4 –5.9 –5.0 –7.8 –4.2

underestimate could only be attributed to some approximations in the reply of the control strategy, or the process of generalizing operator performance by one of nine general profiles. Comparison of time series data from the model was done by visual inspection, to locate the amplitude and location of the major turning points in the time series. As the time series generated from the model and the real system were non-stationary, the use of spectral analysis to compare the series[8] was precluded. From Figure 3, it can be seen that there is a good match between the two time series. Although it is not shown here, the correspondence is far better than that obtained from an unsupervised line. The largest discrepancy in the time series occurs at day 25, where production remains at the previous day’s peak in the simulation but has dropped significantly in the real system. This mismatch could be attributed to the particular random number stream used by the simulation. It was felt that the time series comparison indicated that the model was capable of representing the dynamic behaviour of the flow line, in addition to estimating long-term production.

Simulation of flow lines. Part 2 47

Garments produced (dozens) 350 300 250 200 150 100 50 0 0 10 Day of simulation/study

20

30

40

50

Key Simulation

Real line

To summarize the work on achieving model credibility, it is extremely common to face difficulties in validating models simply because models are used when access to real systems is problematic. In this work, wherever possible, model components have been independently tested, in qualification and verification, and the results that were achieved in validation were encouraging. The goal of answering “Does it make sense?” in the affirmative had been achieved.

Figure 3. Interactively supervised run versus real line

IJCST 8,5

48

Results achieved A generalized model has the potential for being used to investigate many production problems. Fozzard[1] has documented single factor analyses of operator absenteeism and machine breakdown, and has discussed further applications after noting the crucial importance of supervisory control. A methodology for using the model interactively to plan flowlines and to determine their dynamics during startup and steady-state is described. Other possible investigations concern the availability of spare machines, the benefits of having multi-skilled operators, and an appraisal of the performance of PBS lines in a climate of frequent style change. The potential for using the simulation for the interactive training of supervisors and line managers has been explored by Tyler et al.[9]. The example given below concerns the startup behaviour of production lines. The model may be used to predict the line efficiencies and total productive performances for a 12-operator progressive bundle line producing a Velour top. Details of the operations are given in Table II.

Operation name

Table II. Garment analysis data for the velour line

1. 2. 3. 4. 5. 6.

Attach sleeve panel (overlock) Insert contrast panel (overlock) Join sleeve and sides (overlock) Make and attach ribs (overlock) Make and attach neckband (overlock) Tab and reinforce underarm (lockstitch)

Standard minute value

Skill requirement

1.0 1.7 0.9 2.0 0.7 0.5 6.8

Medium Medium Medium Medium Medium Medium

Twelve operators working at 100 per cent efficiency are capable of producing 12 × 8 × 60 Standard Minutes in an eight-hour day. These 5,760 Standard Minutes represent 847 garments. The line has balancing losses which result in a lower daily output and, in the startup phase, operators have lower performances associated with learning effects. For the purposes of these experiments, the overlock operatives were assumed to be completely cross-trained on overlocking operations. The lockstitching operator was the only one able to carry out Operation 6. Performance measures were selected which relate to industrial practice. Line efficiency provides a measure of overall productivity, and is calculated by dividing the “Standard Minutes produced” by the “clock minutes worked”, multiplied by 100 to express as a percentage. Productive performance looks specifically at the productive behaviour of operators, excluding all disruptions associated with waiting time and machine failure. It is calculated by dividing the “Standard Minutes produced” by the “productive clock minutes worked”, multiplied by 100. If there are no disruptions, the line efficiency and the productive performance figures will be the same. In the real world, there are

disruptions, and the magnitude of the difference between the two measures is one indication of the effectiveness of the supervisor. Experiment 1 looked at the line under supervisory control, for a 30-day period. Figure 4 shows the results of each simulated day, with data for line efficiency and productive performance. The difference between them is a measure of the effectiveness of the computerized supervisor. Experiment 2 was a repeat of experiment 1, except that supervision is withdrawn on day 15. The results are plotted in Figure 5. During the latter 15

Simulation of flow lines. Part 2 49

Per cent 100 80 60 40 20 0 5 0 Day of simulation

10

15

20

25

30

35

25

30

35

Key Line efficiency

Figure 4. Velour line under supervisor control (experiment 1)

Productive performance

Per cent 100 80 60 40 20 0 5 0 Day of simulation

10

15

20

Key Line efficiency

Productive performance

Figure 5. Velour line showing withdrawal of supervisor control (experiment 2)

IJCST 8,5

50

days, the productive performances are in the 90-100 range, because the learning effects are past. However, the unsupervised line has an efficiency fluctuating around 60 per cent, and the operation with the slowest throughput controls the output of the whole line. This experiment illustrates the importance of modelling the supervisor in any flow-line simulation. The real world of manufacturing has many unique perturbations which mean that predictions of this kind are very difficult to validate. For example, at the same time as flow lines do start up on a new style, they are completing the old style. Transitions of several weeks are common, and this situation is complex to model. Discussion of the issues surrounding flowline startup is in preparation, and applications of simulation models in this area will be addressed in greater detail. Conclusions The research presented here is concerned with the development of models for the simulation of flow lines in clothing manufacture. Large and complex models are difficult to validate and it is necessary to use a variety of related procedures to ensure that the model has high credibility to industry experts. A framework for a multiphase approach to achieving model credibility has been established for a number of years. This research has indicated the degree of emphasis that each phase must take when simulation is taken into this human domain. It has also indicated the specific techniques that can be used to qualify and validate the model. The model is at the stage where it can be developed for industrial use. A version of the model has already been adapted as a training aid for supervisory personnel and line management[9]. The evidence presented by this research illustrates that simulation can provide insight into the operation of flow lines that is otherwise difficult or impossible to obtain. References 1. Fozzard, G.J.W., “Simulation of Clothing Manufacture”, PhD Thesis. Manchester Metropolitan University, Department of Clothing Design and Technology, 1989. 2. Naylor, T.H. and Finger, J.M., “Verification of computer simulation models”, Management Science, Vol. 14 No 2. 1967, pp. B92-B101. 3. Fishman, G.S. and Kiviat, P.J., “The analysis of simulation generated time series”, Management Science, Vol. 13 No. 7, 1967, pp. 525-45. 4. Checkland, P.B., Systems Thinking Systems Practice, John Wiley and Sons Ltd, New York, NY, 1981. 5. Law, A.M. and Kelton, W.D., Simulation Modelling and Analysis, 2nd ed., McGraw-Hill, New York, NY, 1991. 6. Shannon, R.E., Systems Simulation: the Art and Science, Prentice-Hall, Englewood Cliffs, NJ, 1975. 7. Fishman, G.S., Concepts and Methods in Discrete Event Digital Simulation, John Wiley and Sons Ltd, New York, NY, 1973. 8. Fishman, G.S. and Kiviat, P.J., “The statistics of discrete event simulation”, Simulation, Vol. 10 No. 4, 1968, pp. 185-95. 9. Tyler, D.J., Tennent, L.F. and Lowe, T.J., “Simulation as a training medium for industrial supervisors”, Journal of Clothing Technology and Management, Vol. 11 No. 2, 1994, pp. 31-44.

Communications: “engineering” the extensibility and formability of wool fabrics to improve garment appearance

“Engineering” the extensibility and formability 51

A.G. De Boos CSIRO Division of Wool Technology, Australia Geelong Laboratory, Belmont, Victoria, Australia, and

A.F. Roczniok Ryde Laboratory, Ryde, New South Wales, Australia Introduction Techniques for predicting the performance of a woven fabric in garment manufacture from its physical, mechanical and dimensional properties are now used by both fabric and garment makers in a number of countries[1-3]. Garment makers who have adopted objective measurement have been able to anticipate many of the difficulties in garment manufacture that are caused by fabrics with inappropriate properties. Some of these manufacturers[3] now specify appropriate limits on critical fabric properties. The formability and dimensional properties (relaxation shrinkage and hygral expansion) of wool and wool-blend fabrics have been shown to be particularly important in the manufacture of lightweight structured garments. More than 90 per cent of all fabric related problems in the production of lightweight wool suits and jackets can be traced to excessive or inadequate values of these properties. Each of these properties is determined primarily in finishing, particularly by the operations that are designed to control fabric dimensions (such as drying) and by those that permanently set the wool fibres (such as piece dyeing or pressure decatising). When certain fabric properties lie outside the recommended limits, some manufacturing difficulties can be avoided by modifying garment-making techniques[4,5]. However, problems caused by inappropriate dimensional properties or inadequate formability cannot normally be corrected by the garment maker and the fabric must be refinished. In spite of the complexity of finishing, qualitative information is available[6,7] to assist finishers to identify potential problems before the fabric reaches the garment maker and to change the relevant properties (e.g., increase The authors wish to thank Irene Slota and Lucy Sarlej for their assistance with the experimental programme reported in this paper. This work was performed using a grant from IWS whose assistance is gratefully acknowledged.

International Journal of Clothing Science and Technology, Vol. 8 No. 5, 1996, pp. 51-59. © MCB University Press, 0955-6222

IJCST 8,5

52

extensibility or reduce relaxation shrinkage). However, to engineer the properties of a finished fabric from information on the loom-state or partiallyfinished material, the finisher requires quantitative rather than qualitative information on the effects of finishing on fabric properties and the interaction of fabric structure and finishing routes. In this paper, the problems posed for garment makers by inadequate fabric formability and the effects of finishing on this property will be discussed. The feasibility of engineering those properties that determine formability and the options available to the finisher to produce fabric in which formability is adequate will be outlined. The nature of fabric formability The concept of fabric formability was first outlined by Swedish workers in the 1960s[8]. It was recognized that fabrics, like all other sheet materials, buckle when they are compressed by an in-plane load (see Figure 1). The term “formability” was derived to describe the maximum in-plane compression that a fabric will accommodate before it buckles.

Figure 1. In-plane or longitudinal compression of fabric that results in buckling

Originally, fabric formability was defined as the product of the bending rigidity and the in-plane compressibility. However, because of the shape of the load/extension/compression curve for fabrics at low load, the extensibility of the fabric is now used instead of the compressibility to calculate formability. In the FAST system[9], formability is calculated as follows; F = B.R. * EXT(20) - E(5) 14.7 where F = Formability (mm2) BR = Bending rigidity (uNm – from a cantilever bending test) EXt(20) = Extensibility (% – at 20gf/cm) EXt(5) = Extensibility (% – at 5gf/cm)

The use of a difference measurement for extensibility has several advantages. It overcomes problems associated with determining a reproducible dimension at zero load and makes the mounting of the test specimen less critical. In this paper, the term, “formability” is used only as defined above. Unfortunately, the term also has an alternative usage within the garmentmaking industry. Sometimes “formability” is used to describe the ease with which fabrics may be shaped or moulded during garment making. “Moulding” of fabrics and the formation of three-dimensional shapes in garments involves a number of processes. These include the sewing of seams in which one ply is overfed with respect to the other, the stretching and imposition of temporary set on garment panels in pressing and the deliberate shrinking of fabric during pressing. The use of the term “formability” in this context is beyond the scope of this work. The importance of formability in garment appearance Seam pucker The flat appearance of seams is critical for high-quality wool garments. Visible seam pucker, which may be acceptable in non-wool apparel, is normally not tolerated in garments made from wool. Any detectable seam pucker is considered to be indicative of poor sewing technique or of a “problem” fabric. When a seam is sewn, one or both plies are compressed in the plane of the fabric by the tension on, and the space requirement of, the sewing thread. Also, in overfed seams, there is a balance of tension and compression in adjacent fabric layers. Because formability is a measure of the ability of fabric to accommodate in-plane compression without buckling, it is a good indicator of the likelihood of forming a puckered seam. Seams in fabrics with low formability are more likely to pucker unacceptably than those from fabric with high formability. The relationship between formability and pucker in seams, sewn[10] at increasing angles to the warp direction, is shown in Figure 2. Two plain-weave, lightweight wool fabrics were used to compile the data set. Samples were cut 5cm wide and 20cm long, with the long edge at angles of 0°, 15° and 30° to the warp direction. Fabric properties were measured in the direction of the seam using the FAST equipment and formability values along the seam direction were calculated. Two like samples were sewn together with a balanced lockstitch seam (5 stitches per cm) 1cm from one long edge. Two levels of overfeed were used in the seams (0 per cent and 4 per cent). The samples were ranked by a panel of ten judges from worst to least puckered. The score shown in Figure 2 is the rank normalized to fit an arbitrary scale, with larger values indicating less puckering. Puckering was greatly reduced as the formability of fabric increases. The problem of seam pucker is compounded by the need to overfeed one of the fabric plies in some seams, especially those in men’s and women’s jackets. Overfed seams were much more prone to pucker than straight seams (Figure 2). The limit of overfeed that can be accepted by fabrics has also been shown to

“Engineering” the extensibility and formability 53

IJCST 8,5

Ranking (high number–less puckering) 60

50

54

40

30

20

10

Figure 2. Relationship between fabric formability and seam pucker

0 0.2 0.1 0.3 Formability mm2 Key

Zero overfeed

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

4 per cent overfeed

depend on their formability[10]; the limit of overfeed being higher in fabrics with high formability. Sleeve insertion One of the more difficult and skilled operations in the manufacture of men’s and women‘s jackets is the insertion of the sleeve in the arm hole. The time and cost of this particular operation can vary for similar garments made from different fabrics. Faults usually require unpicking and resewing of the seam; a timeconsuming and expensive operation. Considerable amounts of overfeed (as high as 15-20 per cent) can be required to form the seam. The overfeed required will depend on the style of the garment and the techniques used by the individual garment maker. In a trial involving an Australian garment maker and CSIRO, it was established[10] that both the warp and weft formabilities are important in determining the ease with which sleeves are inserted in arm holes. In this trial, it was observed that fabrics that were difficult to sew, or were rated as “needing care”, were characterized by low formability (see Figure 3), in either warp or weft directions or a combination of both. Fabric rated as “easy to sew” generally (but not always) had relatively high warp and weft formabilities. Total garment appearance For reasons that are not entirely understood, the formability of fabrics can also be related to the overall appearance of the manufactured garment. This has

“Engineering” the extensibility and formability

Warp formability 0.45 0.4 0.35

55

0.3 0.25 0.2 0.15 0.1 0.05 0.1 0.2 Weft formability Key

Difficult

Needs care

0.3

0.4

0.5

0.6

(a) Easy

Source: [10]

been demonstrated in at least two studies, one in co-operation with Japanese garment makers[11] and another as part of a long-term study of the use of objective measurement within the Australian textile industry. The reason appears to lie in the importance of seam pucker to the overall appearance of garments. In the Australian trial, two fabrics (a pure wool and a 70/30 wool/polyester blend) were each finished in different ways. The fabric samples were made up into suits by two garment makers and the jackets were rated after wear by a number of judges. The appearance of the seams in the garments improved as the formability of fabrics increased (Figure 4). Correcting inadequate formability Formability depends on both the bending rigidity and the extensibility of fabric. To boost the formability of a fabric, either the bending rigidity or the extensibility, or both properties, must be increased. Because bending rigidity is also an important determinant of the handle of fabric, any attempt to manipulate this property will almost certainly result in changes in the handle of the fabric. Consequently, in most cases, the most acceptable way of increasing formability is by increasing the extensibility of the fabric. Although the extensibility of a fabric depends in part on the weave structure and settings used in weaving, the finishing route has a very large effect on the final properties of the fabric[6]. Control of fabric extensibility is usually considered to be one of the many roles of the finisher.

Figure 3. Relationship between fabric formability and ease of seam insertion

IJCST 8,5

Average rank score for seam appearance 7 6

56

5 4 3 2

Figure 4. Relationship between fabric formability and overall rating of seams in garments manufactured by two garment makers

1 0 0.2 0.4 0.3 0.5 Warp formability (FAST) Key

Manufacturer 1

0.6

0.7

0.8

0.9

1

1.1

Manufacturer 2

Dimensional changes in finishing and fabric extensibility Because wool may be deformed and TEMPORARILY SET in a new shape or dimension, there are two measurements that must be made to characterize the fabric: (1) the “actual” dimensions (width or length per 1000 picks) of the fabric at any stage of finishing. For brevity, these will be called the “unrelaxed” dimensions of the fabric, and (2) the dimensions of the fabric after it has been relaxed, usually in water and reconditioned. For brevity, these will be called the “relaxed” dimensions of the fabric. The difference between these dimensions, expressed as a percentage of the “unrelaxed” dimensions, is the relaxation shrinkage. The changes in the extensibility of wool fabrics that occur in finishing, and ultimately the final extensibility of the fabric, can be related, at least in part, to the changes that occur in these fabric dimensions. During finishing both the “unrelaxed” and the “relaxed” dimensions of the fabric may be altered. The “relaxed” dimensions are altered by operations that permanently set the wool fibres but are relatively unaffected by those processes that impart only temporary set (stenter drying etc). The “unrelaxed” dimensions are affected by stenter drying and virtually all dry finishing operations that impart permanent or temporary set to the fabric.

Models of the behaviour of woven fabrics under tensile loading have suggested that, provided the load applied is small, the extensibility of an individual fabric is closely related to the “unrelaxed” dimensions of the fabric. Consequently changes in extensibility correlate with a simple function of the dimensional changes. To demonstrate that this simple approximation gives a useful description of the behaviour of a fabric, a series of fabrics (described in Table I) were stretched and temporarily set (in steam). The extensibility of the fabric samples was then measured using the FAST system. The results for a pure wool gaberdine fabric (230g/m2) are shown in Figure 5. There was a good (R > 0.95) correlation between the extensibility of the fabric and the dimensional change resulting from the (temporary) setting operation. The correlations were high enough to indicate that, provided the extensibility is Weight(g/m2)

Fabric

Finish

“Engineering” the extensibility and formability 57

Response

A. Gaberdine (100w) 238 Piece-dyed 0.54 B. Plain (100w) 180 Colour-woven 0.25 C. Plain (100w) 250 Colour-woven 0.37 D. Gaberdine (100w) 222 Piece-dyed 0.41 E. Plain (45w/55p) 166 Colour-woven 0.33 Note: Response = change in extensibility (at 100gf/cm) with 1 per cent change in dimensions

Table I. Effect of change in fabric dimensions on extensibility

Extensibility (per cent) 8 7 6 5 4 3 2 1

Relaxation shrinkage (per cent)

10 5 0 -5 -5 0 Dimensional change (per cent) Key

Warp

Fill

5

10

15

Figure 5. Relationship between fabric extensibility (at 100gf/cm), relaxation shrinkage and the dimensional change

IJCST 8,5

58

known prior to a steam-framing operation, the properties of the fabric could have been predicted. This simple operation is a viable option for finishers who wish to engineer fabric properties. Steam frames can be used to adjust the dimensions of wool fabrics and to stabilize the new configuration by steaming and cooling (temporary set the fabric. These machines are used by manufacturers of woven fabric in the woollen industry and for knitgoods. Similar effects can also be achieved by wetting out a fabric and drying it to the required dimensions. The latter approach is already used by finishers to obtain the high levels of relaxation shrinkage necessary to avoid bubbling of garment panels during autoclave pleating of wool fabric. To increase fabric formability, it is necessary to increase extensibility and this, in turn, requires that dimensions of the fabric be reduced in the required direction (warp or weft). All fabrics did not respond in a similar way to the change in dimensions as shown in Table I. For example, a 1 per cent reduction in dimensions produced a 0.5 per cent increase in extensibility of fabric A; a 0.25 per cent increase in fabric B and a 0.4 per cent increase in fabric D. Moreover, the response of fabrics varies at different stages in finishing[12]. These differences create a difficulty for the finisher. It means that, even for this simple temporary setting process, the relationship between extensibility and dimensions must be characterized separately for every fabric. Effects of dimensional change on relaxation shrinkage As stated previously, to increase fabric formability it is necessary to increase extensibility by reducing the dimensions of the fabric in the direction (warp or weft) of concern. If the relaxation shrinkage of the fabric is initially high, fabric dimensions can be reduced in a simple sponging operation or steam framing operation which will, in turn, increase extensibility and thus formability. However, for fabrics that do not have high relaxation shrinkage, unless both the relaxed and the “unrelaxed” dimensions of the fabric are reduced, reducing fabric dimensions will lower the relaxation shrinkage of the fabric to dangerously low levels. In such cases, it is necessary to reduce the relaxed dimension of the fabric either by steam framing and then pressure decatising, or by wet setting the fabric. Conclusions Even with this simple description of the combined effects of fabric structure and finishing on the extensibility and dimensional properties of wool fabrics, the problems for the weaver and finisher in producing lightweight colour-woven fabrics with adequate formability are considerable. The finisher must engineer not only the final dimensions of the fabric but also the “relaxed” dimensions of the fabric. The “relaxed” dimensions of a fabric are determined in setting operations such as crabbing, dyeing and decatising, where there is little opportunity to control the fabric width and length.

On the other hand, the “unrelaxed” dimensions of the fabric can be set using a stenter or steam frame where there is control over both warp and weft dimensions (through width and overfeed settings). However, even if this is the last step in finishing (and further uncontrolled changes in dimensions do not occur in subsequent operations), the finisher is limited in the extent to which relaxation shrinkage, extensibility and ultimately formability can be manipulated. In seeking to increase formability by increasing extensibility, the finisher can reduce relaxation shrinkage to unacceptably low values and may simply replace one problem with another. Although there are certain difficulties yet to be overcome, engineering critical fabric properties will allow the finisher to be confident that a major cause of poor performance of lightweight garments has been eliminated and be confident about meeting the quality standards imposed by the customer. References 1. Duke, R.A. and Duke, S.J., “Measurement of fabric properties in an Australian clothing and retail company”, in Kawabata, S., Postle, R. and Niwa, M. (Eds), Objective Measurement: Application to Product Design and Process Control, Textile Machinery Society of Japan, Osaka, 1986, p. 251. 2. Niwa, M., Nitta, M. and Kawabata, S., “The fieldwork inspection and improvement of tailorability prediction equation”, in Kawabata, S., Postle, R. and Niwa, M. (Eds), Objective Measurement: Application to Product Design and Process Control, Textile Machinery Society of Japan, Osaka, 1986, p. 55. 3. Ito, K. and Kawabata, S., “Conception of automated tailoring controlled by fabric objectivemeasurement data”, in Kawabata, S., Postle, R. and Niwa, M. (Eds), Objective Measurement: Application to Product Design and Process Control, Textile Machinery Society of Japan, Osaka, 1986, p. 175. 4. Amirbayat, J., “An energy approach to the instability problem of overfeed seams”, International Journal of Clothing Science and Technology, Vol. 2 No. 1, 1990, p. 21. 5. Ito, K., “Process control for tailoring based on objective data about fabric properties – progress in the last year”, in Kawabata, S., Postle, R. and Niwa, M. (Eds), Objective Evaluation of Apparel Fabrics, Textile Machinery Society of Japan, Osaka, 1983, p. 89. 6. Karrholm, E., Cednas M. and Nordhammar, P., “An experimental investigation of relationships between construction, finishing and the end properties of wool fabrics”, Proceedings 8th International Wool Textile Research Conference, Paris, Vol. 4, 1965, p. 449. 7. SIROFAST User’s Manual, CSIRO Division of Wool Technology, Australia, 1991. 8. Lindberg, J., Waesterberg, L. and Svenson, R., “Wool fabrics as garment construction materials”, Journal of the Textile Institute, Vol. 51, 1960, T1475. 9. Ly, N.G., Tester, D.H., Buckenham, P., Roczniok, A.F., Adriaansen, A.L., Scaysbrook, F. and De Jong, S., “A simple instrument for quality control by finishers and tailors”, Textile Research Journal, Vol. 61, 1991, p. 402. 10. Tester, D.H. and Roczniok, A.F., “Formability as a predictor of seam pucker in garment making”, IWTO Technical Report, Report No 20, December 1992. 11. Mahar, T.J., Ajiki, I., Dhingra, R.C. and Postle, R., “Fabric mechanical and physical properties relevant to clothing manufacture III shape formation in tailoring”, International Journal of Clothing School Technology, Vol. 1 No. 3, 1989, p. 6. 12. De Boos, A.G. and Slota, I.J., paper to be submitted to Journal of the Textile Institute, 1996.

“Engineering” the extensibility and formability 59