Arif Kurbak

Two guide bar warp knitted fabrics are used as technical textile applications nowadays. In this, Part III of these series of papers, models for basic two guide bar warp knitted fabrics are created and given based on Parts I and II. Modeling of warp knitted fabrics started in the 1960s with some basic geometrical models and it was continued with using Non Uniform Basis Spline (NURBS) curves and surfaces. There were discontinuities in the loop parts in early created geometrical models and the NURBS models needed some control points from some sources. In this work instead of using NURBS curves, modeling of warp knitted fabric is attempted by using known curves. During creation of the models, curvature equalities are attained as much as possible, loop connection parts are modeled by having two continuously connected parabolas for the Double Tricot fabric and the loop connection parts of the other two bar fabrics are obtained by applying a sinus square curve to the connection part of the Double Tricot fabric. The models created are versatile and they can be changed and used for special cases. Models created are drawn to scale by using the 3DS-Max Computer Graphical Program. At first glance, it is seen that the model shapes are similar to the real fabric structures, which can be observed on photographs of them.

Chain stitches are basics structures to obtain a group of net grounds in warp knitting such as marquisette, curtain-net ground and full-width weft-inserted fabrics. These net grounds are, in turn, used as technical fabrics as well as household goods. Modeling of warp-knitted fabrics started with some basic geometrical models and it was continued using non-uniform basis-spline (NURBS) curves and surfaces. There were discontinuities in the loop parts in the early models and the NURBS models needed some control points from some sources. In this work instead of using NURBS curves, an attempt is made to model warp-knitted fabrics using known curves and continuities in loop parts are attained as much as possible. First of all, open chain stitch is modeled. Closed chain stitch is obtained by changing some parts of open chain stitch model. Models then applied to marquisette, curtain-net ground and full-width weft-inserted warp-knitted fabrics are presented. Models created are drawn to scale by using 3DS-Max computer graphical program. It is seen that the shapes obtained by the models are similar to those which can be observed on real samples.

Warp knitted fabrics are mainly used as household goods, technical textiles, medical textiles, etc. Modeling of these fabrics is necessary for predicting the desired technical or medical functions beforehand. In this context, the present series of papers is devoted to the modeling of basic warp knitted fabrics. In this, Part II of this series, models for single guide bar fabrics are created. There are mainly two types of single bar fabrics, namely closed-lap and open-lap single bar fabrics. Structures are also changed by having different lapping movements up to the five needle spaces. In this work, 1 and 1, 2 and 1, 3 and 1, 4 and 1 closed-lap and 1 and 1, 2 and 1, 3 and 1 open-lap single bar warp knitted fabrics are considered. During modeling, the loop leanings in the course-wise direction are considered, curvature equalities at the loop parts are attained as much as possible, two connected parabolas are taken as the fabric plane model of the loop connection part, loop heads are taken as parametric ellipses in two dimensions and the remaining loop parts are modeled by wrapping parabolic or cubic curves on imaginary cylindrical or conical objects. The models created are versatile and they can be changed and used for special cases. The models created are drawn to scale by using the 3DS-MAX computer graphical program. At first glance, it is seen that the shapes obtained by the models are similar to the ones that can be observed in real samples.

Pierce’s well-known solution to the problem of the load–extension behavior of a circular ring has been used as one of the measurement methods of bending rigidities of textile yarns. This paper provides some additions to Pierce’s solution to make it applicable for a knitted loop head curve. It is found that the load applied to a ring is equal to the bending rigidity multiplied by the difference between the squares of the major and minor curvatures of the extended ring. This equality gives way to apply the circular ring problem for obtaining the load–extension properties of a knitted loop head. It is also shown that, for the loop head curve, the elastica curve can be replaced by an elliptical curve for up to 30% of extension, as it is easier to apply.

In this paper, the load–extension behavior of glass plain knitted fabrics is investigated both experimentally and theoretically. Experiments are carried out by preparing two sets of samples for two directions, namely for the course-wise and wale-wise directions. The load–extension properties are explored by attaching dead weights to the lower ends of the samples. Therefore, while obtaining the load–extension properties in the loading direction, the contraction properties of the samples in the lateral directions are also investigated. By observing the load–extension and load–contraction curves, three stages are distinguished. The first stage can be attributed to the fabric extension or contraction. The second stage can be attributed to the yarn extension or contraction as well as to the changes in the shapes of the samples. The third stage can be attributed to the extension or contraction of the fibers. After obtaining the dimensional properties of a single loop in the knitted fabric, curve fittings are carried out for the three stages. In the rest of the work, a theoretical analysis is carried out to explain the first stage of extension and contraction that was explained above. In the theoretical work, the load–extension or the load–contraction behaviors of the arms of the loops are calculated by using the inflexional elastica theory. The extension behaviors of the loop heads, on the other hand, are calculated by using the extension of the circular ring, which was given in Part I. As a result of the theoretical analysis, some simple equations between the loads applied and the extensions or contractions are obtained. These equations for the extension or contraction rates depend on the initial dimensional properties of the loop, the bending rigidity of the material, frictional restraints and the Poisson ratio. The equations also show that an extension or contraction in the wale-wise direction follows Hooke’s Law, whereas an extension or contraction in the course-wise direction depends on the square root of the applied load. Providing some simple equations about the relation between the load and extension in the loading direction as well as between the load and contraction in the lateral direction are suggested, determining the contractions in the lateral direction in addition to the extensions in the loading direction, which can be used in engineering software in simulating fabric load–extension behaviors under loadings. Finally, the initial and the extended states of the fabric are drawn to scale by using 3DS Max computer software.

Spacer fabrics are very attractive nowadays for use as technical fabrics. Our interest in this study is to give geometrical models for weft-knitted spacer fabrics which can be used in related engineering software. Models of two commonly used weft-knitted spacer fabrics are created here based on Kurbak’s 1998 plain knit model and are drawn to scale using the 3DS-MAX computer graphical program. It is observed that similar shapes to the real fabrics are obtained by the models.

In this work, based on the geometrical model given in Part I, a mechanical model is created for dry relaxed slack plain knitted technical fabrics including the three-dimensional friction effects. The equilibrium of forces and moments applied on a loop are written by using the elasticity theory of thin rods. Through this model, it is shown that a dry relaxed plain knitted fabric can be in a stable state induced by friction. The application of the model was carried out on E-glass technical fabric, which was also used in Part I as its dimensional properties were obtained through the created geometrical model. In the current part, Part II, the mechanical properties of this fabric are obtained and discussed as an exemplary application.

In the current literature, there is a lack of knowledge concerning which parameters are effective on relaxed slack plain-knitted conventional fabrics, although slack fabrics (i.e. fabrics with no occurrence of jamming) are commonly used for technical applications. Thus, the present series of works are conducted as further investigation on relaxed slack plain-knitted fabrics. In the present part, Part I, a geometrical model is created based on Kurbak's 1998 model. The created model is then applied to conventional dry, wet and wash relaxed wool plain-knitted slack fabrics. The model is also applied to E-glass dry relaxed technical plain-knitted slack fabric. The applied models are then drawn to scale by using 3DS-Max computer graphical software. At first glance, the loop shapes obtained through the three-dimensional modeling of E-glass fabrics are observed to be similar to the E-glass fabric loops that were recorded in the photographs of the knitted samples. An investigation on the physical conditions for obtaining such a special loop shape is going to be the subject of the following part, Part II.

A functional rib-knitted cord and the knitting machine for its production were designed having Turkish Patent Institute Applications No: 2011/00438 and No: 2011/00483 respectively. Functions such as mechanical, thermal etc. can be cultivated using the designed cord. Our interest here is to introduce this newly designed cord and to give a geometrical model for this cord. The model is created and drawn to scale by using the 3DS-Max computer graphical program. The model is the general one and can be applied to various applications of the structure of various tightness values; therefore, the direct comparison of the model with any set of experimental findings, depending on the application area of the cord, is left for the future. However, the assumptions about obtaining spirally connected loops of the model are observed to be correct, as the loop shapes are similar when we compare them with the real cord knitted as samples.