Manufacturer of high quality clothing and the need of mechanization and automation of sewing production require the development of technological designs of clothing items of high precision to the specified shape of the parts and products in General reproduced in the garment factories most simple methods in full accordance with the sample models. It is difficult to achieve methods of approximate design, in which the required accuracy of the parts obtained by means of fitting them and making various refinements in the manufacture of re-sample models.
Adaptability and high accuracy of the clothing items can be secured in the determination of their shape and size engineering methods. To apply these methods have to be known form of wear surface that when you are designing the clothing items can be specified in the form of a sample product model (primary model). In this design the primary sample models of products produced by methods of approximate design.
In the future, when experience of designing samples of the models developed improved standard design of products based on anthropological measurements, uniform and standardized individual items of clothing should be established by scientific methods design the primary sample models. With the application of these techniques will be improved and construction of clothing items for mass production.But regardless of this, described in this Chapter, methods for the determination of scan-sampled models can also be used later to control the accuracy of dimensions and shape patterns, designed for manufacturing products in mass production, and to develop design details for the samples of the new models that are significantly different from typical designs products.
To deploy the shells from the tissues using special methods that differ from the methods of descriptive geometry designed for developable surfaces (cylinder, cone, prism, etc.). Methods of descriptive geometry used to approximate the deployment prosverlivayut surfaces (spheres, ellipsoids, etc.), breaking them into small parts, which approximately can be considered developable. For example, the surface of a sphere is divided into 12 parts.For the same surface of the balloon special methods allow a reasonably accurate unfolding of shell fabric in two parts. At the core of these methods is the solution of a problem of differential geometryabout the clothing surface fabric. As a consequence, the study of methods of computation of shells from tissues must begin after mastering the basic concepts chebyshevskii network of geodetic lines, the simplest methods of their determination on curved surfaces, determine the possibility of using chebyshevskii network to determine the expansions of the membranes of the various tissues and others set out below are the General provisions. You almost have to try, as determined by the geodetic lines on the surface and the result is a Chebyshev network is a parallel transfer of its coordinate lines; find out what happens to the fabric when dressing its surface;to get an idea about the deformation of the fabric with the misalignment of her threads and, finally, to see samples of clothing items, molded by changing the angle between the filaments without changing their length.
As discussed below, the theoretical principles and methods of computation of set out on the basis of the elementary concepts of chebyshevskii network, the geodesic lines parallel to the transfer and certain other provisions of the differential geometry.
Set forth in this Chapter, methods of calculation of expansions is not yet used in the garment industry, but their experimental verification on the outer clothing of various kinds, which were conducted over several years, the Department of garment manufacturing of MTILP demonstrates the feasibility of using these methods in the design of clothes of mass production.
Definition chebyshevskii network
The main task of the computation of (patterns) of clothing items is the determination of its rational form, providing dressing the surface of a flat material, the most simple methods with a minimum area of scan and the fewest seams. The theory of the computation of is based on solving a geometric problem about dressing flat fabric curved surfaces. Due to the fact that the fabric is a mesh material, it forms the curve of the curved surface network in which the opposite sides of each quadrilateral (the cells from the filaments) are equal.Clothes made of plaid fabric with small cells, it is easy to see that rectangular cells are changed on the curved areas of the body in parallelograms, but the length of the parties undergoes a noticeable change. The dressing of the surface of the fabric for the first time drew the attention of the academician P. L. Chebyshev, who in his work "On the cutting of garments" in the last century mathematically proved the possibility of determining reamers tapered slim shells of cloth for different surfaces [1].
There are two families of lines intersecting on the surface, differential geometry is called a network [2]. The network that forms on the surface of quadrilaterals with opposite sides equal, is called a Chebyshev network, or chebyshevskii network. The lengths of segments of all lines in each family chebyshevskii network, concluded between the two lines of another family equal. For example (Fig. IV-1).
a₀b₀ = a₁b₁ = a₂b₂ ..., 1 - 2 = a₁a₂ = b₁b₂ ...
From this definition it follows that two intersecting lines chebyshevskii network completely determine the position on the surface of all its lines, because the lines of each family separately arranged in parallel relative to each other (i.e. the distance between the lines of each of the family network on other lines of the family are equal). Therefore, Chebyshev network can be built on any surface by parallel transfer lines of the network. For this you first need to set on the surface of two intersecting baselines of the network.So the build was quite certain, for the baseline network take orthogonal (intersecting at right angles) of the geodesic line.
Geodesic line [3] is the shortest line from all lines connecting two points on the surface. The two original orthogonal geodetic line defined on the surface, can be used in the same way as rectangular coordinate axes on the plane. The smooth surface of a stretched elastic thread is located at the geodesic line. This property is used to determine the geodesic line between two points specified on the surface.Orthogonal geodesic lines on the surface is easier to define by overlaying on it a geodesic of a square, made of narrow strips of thin construction paper or steel tape (for example, one meter tape measure). When a small width of the strips (5 - 6mm) angle allows you to accurately determine the position and length of the orthogonal geodesic lines, surfaces of any shape and size that occur in clothes.If you combine the square with the surface narrow stripes are orthogonal on the shortest (geodesic) lines in the same way as they are on the plane in straight lines, intersecting at right angles. It already strips, the accuracy of determination of geodesic lines on the surface above. The strips should be sufficiently resilient so that when laying on the plane they were located in direct lines. When laying the strips flat square on prosverlivayut surfaces of their geodetic lines run down the middle of the strips.Therefore, the greatest accuracy is obtained when the geodesic line is determined in the middle of the strips through the small holes (Fig. IV-1 b). For highest accuracy it is necessary to repeatedly overlay the strips of the polygon on the surface in order to verify the correctness of applying or measuring the orthogonal geodesic lines.
When you build chebyshevskii network on the surface of printed on it, the original orthogonal geodesics
(Oh, Oh, see Fig. IV-1, a) ask on these lines a series of points (1,2...a, b...) with short intervals between them. From points 1 and a both from centers conducting geodesic arcs of circles of geodesic radius ρ = 01-OA; when crossing
these arcs get the point a. Point a and 2 spend the same radii of geodesic circles arc to get the point a, etc. use a small flat strip with holes at the ends, the so-called surveying compass. One opening of the compass is fixed on the surface of the needle, and the second move the pencil along the arc of a geodesic circle. You can also use an ordinary compass, which on the surface is determined by the chord that is different from the arc at a very small size (third order).Therefore, the error at small length of the sides of the quadrilaterals virtually no effect on the accuracy of the network build.
Thus using the geodesic or normal compass can be constructed by the above method, the Chebyshev net on any surface. Measure the length of all coordinate lines chebyshevskii network, applied to surfaces, they can be moved on a plane in rectangular coordinate axis. The result is a scan chebyshevskii network in the plane bounded by the lines OAB (Fig. IV-1).
If we replace the coordinate lines chebyshevskii network of inextensible strands by combining these yarns with the network lines in the plane, fasten the threads at the points where they cross each other so that it was possible to change the angles between the threads without moving them relative to each other (see Fig. IV-1), we obtain a grid of thread having the shape and dimensions chebyshevskii network in rectangular coordinate axes. If you combine this grid with the surface so that its extreme (the original) thread coincide with the coordinate axes Oh, Oh (see Fig.IV-1 a), and all the other threads were located on the coordinate lines chebyshevskii network is formed on the surface shell mesh. So there is a dressing the surface of the fabric by changing the angle between its threads, without changing their length.
As explained above, the position coordinate lines chebyshevskii network on any surface is determined by parallel shifting of the reference axes of coordinates ox and OU. Therefore, the corresponding alignment of the mesh with the surface you can get without building it all coordinate lines of the network. To do this, first apply on the surface by two orthogonal geodesic line, to combine it with the original thread a piece of netting and fix them. When combined with the smooth surface of the entire grid will receive the location of all of its threads on coordinate lines chebyshevskii network (see Fig. IV-1).If this position is applied to the grid of the line AB that defines the border chebyshevskii network on the surface, and then remove the mesh and to combine it with a plane in rectangular coordinate axes, then obviously get the scan chebyshevskii network for this part of the surface (see Fig. IV-1). Based on this principle a method of determining the expansions of clothing items with the help of an auxiliary mesh, made in the form of rare fabrics plain weave of yarns are not stretchable under a small load.This mesh can serve as an ordinary canvas, which is easy to change the angles between the threads and does not stretch threads for aligning the mesh with the surface. Way to determine scan using an auxiliary grid (the canvas) will use in the future to obtain a scan of items of clothing from various fabrics.
Application chebyshevskii network to scan clothing items
The scan chebyshevskii can be obtained on a shell of tissue of any shape in various weaving weaving warp and weft. To verify this, you need to take a small rectangular piece of fabric cut to the basis, and duck; divide it into several rectangular areas and to make sure that each fabric has its weave weaving: plain, twill or sateen (Fig. IV-2, and sections A, b, C). When you change a rectangular piece of fabric into a parallelogram by warp yarns in the plane changing the angle between the outermost threads of the pieces (Fig. IV-2 b).At the same time will happen the same change in the angle between the outermost strands of each section of the piece and all other threads, regardless of the kind of weave. This is because when you change a rectangular piece of fabric in a parallelogram all the threads of the warp and weft separately located (moved) parallel to the extreme threads of the piece. Similar changes of the cells of the tissue occurs on the surface (Fig. IV-2). In this case, the threads of the fabric are transferred in parallel extreme fibers, maintaining the distance between the points of the weave.Which points of the interwoven strands, has no practical significance if the distance between them is small. Therefore, when the various weaving weaving threads in the form of expansions of the shell fabric can be identified by the coordinate lines chebyshevskii network. Along with this, it is necessary to pay attention that at change of the rectangular cells of the tissue in parallelograms threads are not at right angles to their chains, causing a slight change of the linear sizes of fabric basis and a duck. In addition, when the bending of the fabric there is some straightening of the yarns under tension.However, these changes in linear dimensions of the fabric along the warp and weft are usually insignificant and practically do not render influence on the shape and size of the shells.
In the case of significant changes in the linear dimensions of the fabric when dressing the surface, and also if you need very precise scans need to be amended in the coordinate lines chebyshevskii network. Refine the coordinate lines must be included in the shells of thick materials, since the size of the surface can be removed by inner or outer side of the shell, and the size of the scan is determined by the surface passing the middle of the fabric thickness.Clarification of coordinate lines is also necessary when determining the size of reamer shells of knitted fabric, textile, nonwovens, film and other materials that differ in physical and mechanical properties of tissues.But in all cases the basis for scans of membranes from tissues and other materials can be used scan chebyshevskii network, which, as will be shown later, allow design details of the most rational forms, minimal surface, and ensure the application of the most advanced technology of garment manufacturing.
In the "About cutting clothes" P. L. Chebyshev indicated using an evidence-based method of determining the shape of the scan only tapered slim shells made of fabrics. The work carried out in MTILP, the possibility of fixing the angle of inclination (warp) yarns of the fabric in the shell for wet-heat processing (hot pressing or steaming and drying) and other ways. In addition, the shape of the clothing items (shelves, backs of sleeves, etc.) in addition to fixed tissue sections of the edge or seams when joining parts together.It is also fixing the forms of the parts of the surface of the fabric with frame strips on the shelves and the collar. All this provides a stable shape retention of the parts during wear clothes when forming them by changing the angle between the yarns of the fabric. So chebyshevskii network can be used not only to define the shape of the reamers tapered slim shells of fabrics and skins free fit, which includes clothing.
Applying chebyshevskii network to define the shape of the expansions of the shell fabric, you must consider that changing the angle between the warp and weft can be made within the limits for this corner fabric warp threads (deviation from 90'). The magnitude of this angle is determined by the tensile test tissue samples measuring 10 X 20 cm on a conventional discontinuous machines or on the technical scale with clamping devices [4].
Before the test, the sample is applied to the square, positioning it diagonally down the middle and across the sample (Fig. IV-3). The sample is cut so that the sides of the square was located in the direction of greatest resistance tissue tension, i.e. the basis, and duck, as a coordinate axis when defining the sweep chebyshevskii network. In order for the tensile specimen its sides less deviated from the straight lines, the width of the specimen increases at the ends by 2 - 3 cm on each side.During stretching of the strip sample is measured side of the square and angle of inclination (Δυ, Δu, φ see Fig. IV-Z, and). On the basis of measurements for different angles of inclination of the sides of a square determine the relative elongation of the material (strands of tissue) by the formula εx = (Δυ - Δυ₀)/Δυ₀; EY = (Δu - Δu₀)/Δu₀.
So produce the test of other materials, having samples of the square in the direction of greatest resistance of the material.
When you test different fabrics to determine the permissible deviation of the filaments from the straight angle at low load (1 - 2 kg). This allowed a change (extension) of the filaments is not more than 2 W%, based on the fact that such a deformation of the thread take its original length after wet-heat treatment of tissue and removing it from the load. Therefore, in the design of clothes for the form of scans of the parts is determined by the coordinate lines chebyshevskii network without changing their size.The skew angle of warp and weft in different tissues is usually 15 - 20' that corresponds to the angle between the threads 70 and 75'. The permissible maximum angle of warp yarns for suiting fabrics can be taken: the parts in which the warp thread is secured only wet-heat treatment (for example, by bending the rear halves of the pants) is equal to 10', while the parts with additional fixing of the warp of the fabric seams, edge strip (e.g. shelf) is equal to 15'.
Based on the tests specified manner other materials (knitted fabric, non-woven materials) are tables or graphs of the relative elongation of the material (εx, EY) depending on the inclination angles φ of the sides of a square applied to the sample. The results of these tests are used in specifying the size of the scan chebyshevskii network.
The angle φ will be called network a corner of the material, as it characterizes the change of the angle between the lines of the network applied to the sample under tension in any material (Fig. IV-W, b).
For dressing a surface without folds and assemblies of the material, and in the tissues without the stretching of the filaments it is necessary that the minimum acceptable network the corner of the material was no more than the smallest network of the angle between the coordinate lines chebyshevskii network this surface. This angle is on the surface among the network corners, located near the border of the shell (the angles φ₁, φ₂, see Fig. IV-1). It is determined with a protractor measuring the angles between the threads of the support grid located on the surface, or by calculation, as will be outlined below.
In cases when the minimum acceptable network corner this fabric more than the smallest angle chebyshevskii network network used the shell of several parts connected by seams and Darts. In most cases, the network corner in the clothing items less than 10 - 15'. Due to this dimensional form of a garment can be secured by changing the angle between the filaments without changing their length. This gives the opportunity to partially or completely eliminate the number of seams of the garment.Such seams are the seams located at the edges of the sides and collar, the front seams of sleeves, front tuck through tuck and the side seams of the pads and even the side seams of the pants. The exclusion of these joints while maintaining a predetermined shape of the parts and the appropriate location on them of the fabric pattern improves the quality of the garments, allows to apply the most advanced technology of making clothes that is required for the comprehensive mechanization and automation of sewing production.
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Literature
1. Chebyshev, P. L. collected works, vol V, publishing house of as USSR, 1951.
2. Profitable M. J. Differential geometry, Moscow, 1949.
3. Lusternik L. A. the Shortest lines, State. publishing house of technical-theoretical literature, 1955.
4. Modestova T. A. on the method of determining some indicators of the molding properties of fabrics, journal of applied physics, Technology of light industry, 1960, No. 1.
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