Jiang GaoMing, *Feng XunWei A Simulation Model of Made on a Multibar Raschel Machine

Jiangnan University Abstract *DongHua University, An exact and applicable mathematical model is the basis of computer simulated Multibar ShangHai, People’s Republic of China 200051 lace fabric. In this study, a spline curve is used to simulate the loop structure of Multibarlace E-mail: [email protected] fabric. The number and position of control points are determined for stitch, inlay and fall- plate lapping. Thus, theoretical models are built for each type of lapping, and deformation of stitch brought about by tension is also taken into account. Moreover, the displacement theory and calculation formula are given. VC++.net is used to develop the simulation program. The real Multibar lace effect of the simulation proved that the model is rational and applicable. Key words: warp-, multibar, lace, mathematical model, CAD, simulation.

Features of multibar knitted structure is represented as a certain geo- structure metrical model which defines the relation- ships between structure parameters, then Fabric made on a multibar Raschel ma- the model and the experimental data is chine is a kind of fabric with various pat- corrected. However, another way is to es- terns on the net ground, with different size timate the influential factors for the struc- and shape of holes on the surface. The ture by conducting experiments and then fabric has a ground and pattern structure, find the experiential relationship between so it’s clear to identify whether the pat- the parameters based on the experiments. tern and ground have a different construc- The intention of both ways is to estimate tion and texture. The ground structure of the yarn run-in, output and so on. Most fabric consists of relatively small repeats studies have focussed on warp-knitted with rather simple lapping and normally fabric with fewer guide bars and seldom knitted from thinner yarn, with or without involved the multibar knitted structure. elastic yarn, using two to four guide bars,

such as a “knit-marquisetter”, power net, Figure 1. The structure of multibar lace With experimental verification using a lot fabric. technical net and “honeycomb”. The Pat- of computer programs, the spline curve tern structure is knitted by the complex resented by straight line, which will be lapping of pattern bars. Normally, pat- has proved to be a good mathematic tern bars use inlay to produce the pattern, model to simulate the yarn shape in a adequate for our model. and inlay are held into/onto the loop structure. Therefore, we will use a ground structure. The stitch pattern bars spline curve to describe the backbone In order to simulate multibar lace fabric use a yarn float (named foot) to produce of the stitches. The number and position visually and quickly, we gave the follow- a pattern, and the fabric is featured with of control points are determined for the ing assumptions when we built the model a three-dimensional pattern effect. Fall- features of different structures, including and constructed the displacement theory: plate patterns are also three-dimensional inlay, stitch and fall-plate pattern. The n The three-dimensional loop structure and produced by pattern bars at the front operation speed of computer simulation is simplified as a two-dimensional one; of the fall-plate. Jacquard bars are used is also taken into account. The feet of n The backbone of the stitches are de- to produce a fancy ground structure. Fig- stitches in the fabric are generally rep- scribed by a spline curve, and a straight ure 1 shows lace with a fall-plate pattern and Jacquard ground.

Different multibar machine configura- tions will create a different pattern effect. The Jacquard pattern effect will be more stabile if Jacquard bars are put at the back of the pattern bars.

Modelling the loop structure of multibar fabric Many studies of the loop structure of warp-knitted fabric have been carried out in the last 60 years, and mathematic mod- a) b) els for it were brought forward one after another. In general, there are two ways to build these models: the warp-knitted loop Figure 2. Simulation model of stitches.

58 FIBRES & TEXTILES in Eastern Europe April / June 2008, Vol. 16, No. 2 (67) the number of gauges that the underlap ure 4.b), equal overlapping of open loops goes through. Figure 2.a shows a closed (Figure 4.c) and counter overlapping of loop, and Figure 2.b shows an open loop, open loops (Figure 4.d), respectively. It is respectively. clear that if the overlaps of the fall-plate pattern bar and ground bar are different, A model of inlay the fall-plate lapping is also different. Inlay is mostly used in multibar lace fab- Hence, we determine the number and po- rics. It is a bit simpler and without over- sition of control points with respect to dif- ferent conditions. Four control points are Figure 3. Simulation model of inlay. lap. We use four points P1, P2, P3 and P4 to control its shape, based on its charac- used in Figure 4.c, whereas six are used teristic. The positions of these four points in Figure 4.a and 4.b. Moreover, seven line is used to describe the feet of the can be determined by parameters h , control points are used in Figure 4.d. stitches. 1 h as shown in Figure 3, where h is the For example, seven points determine the n The displacement of the loops only 2 lengthwise distance between neighbour- shape of stitch in the condition of counter occurs in the x-direction and at the ing courses; w is the transverse distance lapping of open loops in Figure 4.d. Con-

root of the stitches. between neighbouring wales; n is the trol points can be adjusted to the optimal n The displacement of some of the guide length of inlay, which is counted by the position by modifying the value of w2, w3 bars can be accumulated. number of gauges that the underlap goes to make the simulation more true. Fig- through. A straight line is used to connect ures 4.b and 4.d, in which the overlap of A model of stitch point P6 of the current course to point P1 the fall-plate pattern bar acts as a counter The ground structure of multibar lace fab- of the next course. to the ground bar, show the conventional ric consists of stitches. Most of the stitch- lapping in most multibar knitted struc- es are of the pillar, varied pillar, or tricot A model of fall-plate lapping tures with fall plate. type. Sometimes, the patten bar also knit The structure of a fall-plate pattern is rel- stitches. We use six points (P1 ~ P6) to atively complex. The stitches have four These three simulation models have describe the backbone of the stitch based different shapes, which are determined been proved to be simple, rational, and on its characteristics (Figure 2). The value by the lapping direction of the fall-plate easier to realise with less calculation. of w1, w1, w3, h1 can be determined by ex- pattern bar, ground bar and the way the The speed of simulation on a computer periment using subsequently a computer stitches are formed. The shape of the fall- is faster, so it tends to be accepted by pat- program. Point P6 of the current course plate stitch is abstracted into a computer tern designers. connects P1 of the next course, where h simulation model, based on the shape of is the lengthwise distance between neigh- the virtual stitches in the fabric. Figure 4 The principle of loop structure bouring courses; w is the transverse dis- shows fall-plate stitch shapes of equal deformation tance between neighbouring wales; n is overlapping of closed loops (Figure 4.a), The loop structure is deformed as a the length of inlay which is counted by counter overlapping of closed loops (Fig- function of yarn tension so that all the

b) a)

c) d)

Figure 4. Simulation model of fall-plate lapping.

FIBRES & TEXTILES in Eastern Europe April / June 2008, Vol. 16, No. 2 (67) 59 Figure 5. Displace- pillar stitches, and we use the yarn layer ment of stitches. concept to display the fabric. The opera- tion speed of the program is faster as a result of the connection of a simple spline curve to the straight line. So our purpose of simulating multibar fabric faster on a computer to view the effect of a fabric before production is validated.

Different yarn count and colour can be selected as the material parameters to display more real multibar fabric. The simulation of lace with a rich Jacquard pattern ground is shown in Figure 6. The texture displayed is more like real fabric. Designers can certainly modify or slight- ly adjust various technical parameters until they are satisfied with the simula- tion effect.

models discussed above are ideal with- placement of a single loop can be calcu- out taking the deformation into account. lated by the following formula 1. n Summary Neighbouring wales may lose connection 1. In this study of a wide range of multi- K ×(UL(j)-UL(j-1)) f(i,t,j)=k in some courses and result in the fabric 1 bar fabrics and analysis of various Dx(j,k)= (1) having holes. The holes will be stretched loop structures with patterns, a simu- and displaced by the tension on the yarns. { 0 f(i,t,j)≠k lation model of multibar fabric was Furthermore, The size of the holes will established by multiple correction and Where: K is the yarn tension factor, be larger. The main deformation of the 1 optimisation. structure is the displacement of the stitch- which is determined by the ground lap- es around. For example, like the ground ping, jacquard lapping, liners, gimps and 2. We built mathematic models for in- structure, pillar stitches will be displaced shade effects; f(i, t, j) is the wale on which lay, stitches and fall-plate lapping. A No. i guide bar No. t yarn on j course with tension on the pattern yarns and computer simulation system based on acts; UL(j) is the length vector of the un- Jacquard yarns. The principle of the dis- these models was developed and the derlap of the current course; UL(j-1) is placement is shown in Figure 5. simulation of multibar lace fabric is the length vector of the underlap of the intuitionistic, fast and exact. previous course. The broken and real lines in Figure 5 present pillar stitches before and after 3. We give a detailed mathematic de- The lapping of every guide bar at j course deformation. Due to the fact that two scription of the deformation principle and k wale causes the total displacement yarns act on the root of the loop of the of multibar knitted structure, and it of final stitches, and the displacements inlay loop, stitch and fall-plate lapping, covers all structures of multibar fab- can be accumulated as formula 2. we think that the displacement mainly ric.

occurs at the root of the loops, and most n dx(j,k) = Σ Dx(j,k) (2) are transverse displacement. In order to i=1

simplify the simulation on a computer, The displacement principle of stitches is References lengthwise displacement and loop size concluded by analysing and studying a change are not taken into account here. lot of multibar knitted structures, and it 1. Xui-lan Chen, Xun-wei Feng. The Deve- Based on the above assumptions, the dis- is perfectly suitable for simulation on a lopment of Research on Warp Knitted Fa- computer. bric Loop Structure [J].Shanghai Textile Science & Technology,1996,24(6):37-40 2. Gao-ming Jiang. Modern Technology and Realisation of simulating Equipment of Warp [M]. Beijing: multibar fabric China Textile & Apparel Press, 2001. 333. The theory discussed above is the basis 3. Raz S. Warp Knitting Production [M]. Her- of our simulation software developed us- delberg: Melliand Textilberichte GmbH ing VC++.NET. The lapping and thread- 1987. 508~514. ing of each guide bar can be achieved in 4. Gao-ming Jiang. Design & Technology of the design procedure. The fabric can be Warp Knitting Products[M]. Beijing: China assumed to be composed of such yarn Textile & Apparel Press, 2002. 73. layers as fall-plate lapping, feet of pillar Figure 6. Simulation of Multi-bar lace fabric Figure 6. Simulation of multibar lace fabric. stitch, inlay, Jacquard yarns, backbone of Received 06.11.2006 Reviewed 10.04.2007

60 FIBRES & TEXTILES in Eastern Europe April / June 2008, Vol. 16, No. 2 (67)