by Dr A. Charalambus, Associate Professor,Technical University Sofia, Bulgaria
In the following, relations are being proved by using an exclusively simple geometrical model. In addition to this, series of graphics are being made which allow fast, simple and effective analysis of the relations between some of the parameters of the knitting process and those of the ready knit fabric. The introduced quantity “relative geometrical prolongation of the thread length in the stitch” plays a significant role in the study. The relations given below allow defining the machine gauge that could help to produce knit fabric with precise density, only by choosing appropriate values for the thread’s sinking depth and acceptable average geometrical prolongation.
Key words: prolongation, stitch, model, geometrical, knitti
Key words: prolongation, stitch, model, geometrical, knitti
The aim of the following report is to theoretically analyze the interrelations between some of the parameters of the knitting process, as well as finding their appropriate values that could ensure best quality of the ready products. With regard to this, what is important is the relation between the thread’s sinking depth (h) (fig.1a) and the achieved subsequent stitch density (courses or wales per 5 centimeters) of the balanced and taken off the machine knit fabric. Also is of interest the influence of the gauge of machine over this relation. Apparently all these indexes contribute to the final dimensions of the ready knit fabric.
The results obtained in this way otherwise could be obtained by means of many experimental researches, which are time-consuming and cost a lot [1],[2].
The approach consists of choosing the appropriate geometrical model and theoretical defining of the relation between the examined parameters. The studies are mainly made of plain single stitch but this approach can also be applied for other patterns.
The initial geometrical thread length, which participates in the loom formation λ kn ( λ knitting ) [3], depends on the thread’s sinking depth (h) as well as the geometrical dimensions of the loom formation elements. When the knit fabric is taken off the knitting machine and is completely balanced, the thread length in the stitch is decreased λsg ( λshrinkage) (fig.1b).
The approach consists of choosing the appropriate geometrical model and theoretical defining of the relation between the examined parameters. The studies are mainly made of plain single stitch but this approach can also be applied for other patterns.
The initial geometrical thread length, which participates in the loom formation λ kn ( λ knitting ) [3], depends on the thread’s sinking depth (h) as well as the geometrical dimensions of the loom formation elements. When the knit fabric is taken off the knitting machine and is completely balanced, the thread length in the stitch is decreased λsg ( λshrinkage) (fig.1b).
Apparently the decrease λsg reflects the total areas shrinkage of the knit fabric itself. On the other hand, during the knitting process the thread is tensioned and after relaxing it recovers. Thus on one hand the length of the loom decreases geometrically, and on the other as a result of relaxing there are no tensile forces.
In consequence of the theoretical analysis it is assumed that thread feeding is such that an additional tension appears. Therefore it is assumed that there is only geometrical difference between the two lengths λ kn and λsg . It is important for the shrinkage of the knitwear after relaxing as well as for its behavior when treated. The following is theoretically analysis of the influence of various characteristics on this difference.
For easy defining the change in the thread length it is termed “relative geometrical prolonging of the thread in the stitch”, which is given by the following equation:
For easy defining the change in the thread length it is termed “relative geometrical prolonging of the thread in the stitch”, which is given by the following equation:
It is also assumed that the structure of the loom at the point when the loops are suspended on the needles corresponds to the simplified model given in fig.1a. It is also assumed that the loop legs are vertical tangents to the sides of the needle (fig.1, position 1) and respectively the needle and connecting (sinker) loop are horizontal tangents. All calculations are done on one level as it is shown on fig. 1 without taking into consideration the thread thickness and the knitwear itself. This simplification of the loop geometry does not ensure precise results for the thread length in the loop (loop length).
However, when comparing the different lengths measured with this model (e.g. λkn and λsg in formula 1) the mistakes are reduced to minimum.
The linear density of the yarn in the model used is not regarded. Basically, in the worked out relations the pitch (needle space) t (mm) (gauge of the machine E) is included, which to some extent reflects this feature having in mind the relation between the machine gauge and the linear density of the thread used.
It follows from fig. la and b that λkn =2h+t (2) and λsg =2B+A (3). It is known [4], that when we have single plain knitting, which is an object of our research
Replacing (4) in (3) we have λsg =3,15B (5) Replacing (3) and (5) in (1) and regarding the fact that course density (course per 5 cm)
The formula (6) and (7) give the geometrical prolonging of the thread length in the stitch in respect to the thread’s sinking depth (h), the pitch (t), the machine gauge (E) and the course density of the ready knitwear. The detailed analysis of these formulas could give us interesting results for the technological features of the knitting process and the basic qualities of the ready knitwear, which have practical significance although being only theoretically proved.
By using (6) and (7) it is analytically searched for the influence of the various features over the “relative geometrical prolongation of the thread length in the stitch” and respectively the shrinkage of the knit fabric when taken off the knitting machine. In table 1, 2 and 3 the value of ε and the different values of knit fabric parameters are given. Table1 shows at constant course density of the knit fabric and different values of the thread’s sinking depth. Graphic 1 clearly shows that when the values of h are higher ε is higher too. If the machine gauge is smaller the influence of the depth of folding over the relative prolongation is less. When having fine gauges machines the relative geometrical prolongation is smaller. The theoretical results, where ε is equal to 0, show that the respective values of the indices could not be real and actually the knitwear could not be produced.
Graphic 1 gives opportunity to defining the machine gauges when, by choosing the appropriate values of the thread’s sinking depth and average acceptable geometrical prolongation, knitwear with course density 20 stitches per 5 cm could be produced. For example, to produce knitwear with density 20 stitches per 5 cm a knitting machine with 7E at h=3,4 mm and relative geometrical prolongation about 24% should be used. Decreasing the value of h at the same machine gauge the relative geometrical prolongation is decreased too. Series of similar to Graphic 1 graphics could be drawn and used according to the fore mentioned way.
Graphic 2 gives the relations between the machine gauge, knitwear course density and relative geometrical prolongation of the thread in the stitch at a constant thread’s sinking depth. For example the value of ε about 23% when having a machine with gauge 10E and h=3mm a knitwear with Pc=24 courses per 5 cm could be produced. The theoretical results, where ε is equal to 0, show that the respective values of the indices could not be real and actually the knitwear could not be produced. Series of similar to this graphic could be drawn when having different h values.
Graphic 3 is examined in the same way as the other two graphics. For a machine with gauge 10E, definite and necessary density the thread’s sinking depth is determined. For example ε =20 % and Pc=22 courses per 5cm the thread’s sinking depth should be 2,89 mm.
The fact that the value of ε determine the stability of the produced knitwear, its shrinkage and treatment, should be taken into consideration. The ε values must be carefully chosen when using the graphics.
The conclusion, which could be drawn, is that the offered approach can easily analyze the existing relations between the different parameters in the knitting process and the parameters of the ready knit fabric.
Literature
1. Mutic, S.R. Dimensional stability, aesthetic and mechanical properties of micro-fiber blended knitted fabrics, National Textile Center Annual Report: September 30, 1993
2. Anand S.C., K.S.M. Brown, L.G. Higgins, P.A. Holmes, M.E. Hall and D. Conrad, Effect of laundering on the dimensional stability and distortion of knitted fabrics, Autex research Journal, vol. 2, № 2, June 2002.
3. Гарбарук В. Н. Проектирование трикотажных машин, Ленинград, 1980. (Garbaruk V. N. Design knitting machines, Leningrad, 1980.)
4. Далидович А. С. Основы теории вязания, Москва, 1970. ((Dalidovic S. Fundamentals of knitting, Moscow, 1970)
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