The methods of calculation

 

in the computation of shells of tissue based on the fact that when dressing the surface fabric of her rectangular cells of the filaments are changed in parallelograms. Similar changes occur in small rectangular cells, is applied on knitted fabric, nonwoven fabric, leather, rubber, film of plastics, when these materials wear surface. This is because the rectangle applied to any flat homogeneous material that goes into a parallelogram with a uniform stretching of the material along the diagonal of the rectangle*.

Conducted theoretical studies and tensile test strips of different fabrics, knitted fabrics, nonwovens, leather, rubber, films of plastics shows that inflicted on them after stretching the rectangle changes to a parallelogram [7]. Changing a rectangle to a parallelogram on a range of materials can be obtained in another way, for example by misalignment of the sample, pre-stretched in two mutually perpendicular directions (Fig. IV-28).

In this case, the rectangle goes into a parallelogram without changing the lengths of the sides, i.e. in the same way as it happens with the misalignment of tissue with preservation of the length of its threads. Therefore, when dressing the surface with a cloth or any other material with appropriate tension it can be obtained from shell, having the same inclination angles and dimensions of the cells of the same chebyshevskii network (Fig. IV-29). After deployment of the shell at the plane of the fabric and other material will have different sizes of rectangular cells.Scan shell fabric has the same dimensions of the cells (∆υ, ∆u), and on the surface, since the length of the threads when the dressing surface is preserved (Fig. IV-29 b). For the same shell, but of a different material scan has the size of the cells (∆υ₀, ∆u₀), which differ from their sizes on the surface (Fig. IV-29). The sizes of all cells of the network shell of any material on the surface turn out the same if the material has the same elongation along the axis ox and Oh.As a consequence, denoting by εx - elongation of the material in one direction, and through the EY in the other, have ∆υ₀ = ∆u/(1 + εx), ∆υ₀ = ∆u/(1 + EY).

As the number of cells in each abscissa and ordinate of the sheath from the tissue (x, y, see Fig. IV-29 b) and another material (x, y, see Fig. IV-29) same (n, m), then, multiplying the left and right sides of the first equation by n, and the second to m, we get x = x/(1 + εx), y = y/(1 + EY). (27)

It follows that the coordinates of the sweep sheath of any material ( x, y) are determined by the coordinates of the sweep sheath of tissue (x, y). Thus, to determine the sweep sheath of any material you must first obtain a breakdown of the shells of the fabric and then it is determined by the formulas (27) the coordinates of the sweep for a given material.

When calculating according to the formulas (27) elongation εx, EY can be determined from the stability of shape wear products, the allowable stress of the material, technological and other requirements. Note that the allowed network the corner of the material (φ, see Fig. IV-W, b) must not be greater than the minimum network of the angle between the coordinate lines chebyshevskii network on the surface (φmin), i.e. φ ≤ φmin. This is necessary to ensure that when dressing the surface of the shell prevent the formation of assemblies and folds.

The angle φ corresponding to the specified elongation εx and EY determine the graphs of the deformation of a material, which is made on the basis of test results, as mentioned in the beginning of the Chapter. Minimal network angle chebyshevskii network on the surface is determined by the auxiliary grid on the surface with a protractor.

Parts of the shell can be set to different elongation εx and EY corresponding to the network corners of different plots chebyshevskii network (φmin) on the surface, different operational environments etc. the calculation of the coordinates of the scans at different value of εx, EY produced by the formulas x = xo₁/(1 + εx₁) + xo₂/(1 + εx₂) + ...; y = yo₁/(1 + εy₁) + yo₂/(1 + εy₂) + ..., (28) where xo₁, xo₂, ..., yo₁, yo₂, ... - individual segments coordinate chebyshevskii network for which to set the different values of elongation εx₁, εx₂, ..., εy₁, εy₂, ... By the formulas (28) it is possible to make also the computation of when dressing the surface with minimal deformation of the material.

In this case, the produce dimension network angles on the surface of all the squares of the auxiliary mesh, which is determined by the scan chebyshevskii network. For each network according to the schedule set angle of deformation of the material corresponding value of the lengthening εx₁, εx₂, ...; εy₁, εy₂, ... Segments x xo₁, xo₂, ... and ordinate yo₁, yo₂, ... take the equal sides of the grid squares (K, u), except for the last segment (HP and up), which may be less than the side of the square. Because εx₁, εx₂, ..., εy₁, εy₂, ...usually have a small value compared with the unit-in this case, instead of equation (28) we can apply the approximate formula: x = x/(1 + ECSR), y = y/(1 + EUSR), (29) where ehsr, EUSR - the arithmetic average of the deformation of the material, i.e. ehsr = (εx₁ + εx₂ + ... + EHP)/n; Ausr = (εy₁ + εy₂ + ... + EuP)/n.

For materials, the deformation of which has a linear dependence on network angles, the definition of the average strain ehsr, EUSR on schedule, you can look at the average network corner chebyshevskii network. For example, if the location of the surface network angles chebyshevskii network on individual squares of the auxiliary mesh are 90, 88, 86, 84', the average deformation of the material is determined by the schedule for corner (90 + 88 + 86 + 84)/4 = 87'.In the computation of the average deformation (average network corner) should take into account possible deviations between the mean estimated and the actual deformation of the material due to its heterogeneity, random errors during the test, the misalignment of the parts when cutting and etc. In this regard, it is necessary to provide a slight increase in average strain values, i.e. the reserve in case of possible deviations of the actual from the calculated deformation. The value of this stock is not yet established.But, in any case, it should be more than the value of the maximum deviation of actual performance in the test material taken from averages charting the strain. In clothing, the stock should be greater than in reamers, of shells intended for dressing up any items. This increase in margin deformation in these clothing items allows you to get rid of the need each time to improve the product after movements that cause a change in the surface.

In shells clinging to the surface by stretching the material in one direction only (e.g., jerseys), the coordinates of the scan is determined by formulas that take into account the narrowing of the material (ε₁) in the direction of one axis (Oy): y = y/(1 - EY). (30)

Abscissa is determined as in the previous cases, the formulas (27 - 29). In various embodiments, determining the coordinates of the scan shells of different materials, their area will be the minimum necessary, as well as the area of the original scan, obtained by the coordinate lines chebyshevskii network. To prove this, we Express the square of any component of any material obtained through the scan chebyshevskii network when εx, EY formula F = ∆u₀( u + y₁ + ... yn-1), where u, u,.. - ordinates of the sweep sheath of any material; ∆u₀ is a small interval between the ordinates.

As u = y₀/(1 + EY), u = y₁/(1 + EY) ...; ∆u₀ = ∆u/(1 + εx), F = ∆u/((1 + EY)(1 + εx))(u + y₁ + ... yn-1), where u, u,... - ordinate sweep chebyshevskii network, but ∆u(u + y₁ + ... yn-1) is the area of the original scan ie chebyshevskii network (F). So the square part of any material F = F/((1 - εx)(1 + EY)). (31)

Elongation εx and EY are known, are determined from the physico-mechanical properties of the material, technological, operational, and other requirements. Thanks for the given conditions of the elongation εx and EY can be considered constant parameters. As a result, from formula (31) follows: the detail of any material will have the minimum area ( F) with a minimum of area of the original sweep (F).Therefore, the definition of rational forms parts of membranes of any material is to calculate their coordinates based on the original scan, with the minimum area for dressing the surface. But, as mentioned earlier, the area scan chebyshevskii network is the minimum necessary for dressing the surface (has a relative minimum) when specifying the reference axes of the coordinates on the orthogonal geodesics.Thus, the use of chebyshevskii network for computation of shells of different materials allows to determine the rational form of parts with physical and mechanical properties of materials, operational, technological, aesthetical and other requirements applicable to sewing products.

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* Called homogeneous materials having the same physical and mechanical properties at different points; uniform flat materials have the same tensile deformation throughout square.

 

The computation of parts of knitted garments

 

Consider how, based on the methods of computation of shells of different materials is determined by the shape of parts of garments from knitted fabrics [8]. Knitted fabric has a looped structure and is easily deformed, so regardless of the design of elements it does not restrict movements of the person. This property would seem to simplify the construction of articles of knitwear. However, empirically it is difficult to decide the question of construction of articles of this legkodeformiruemyh material like knit.In addition, the design of elements to ensure minimal consumption of materials, manufacturability of their processing to meet operational requirements. Due to the fact that jerseys fit surface is due to the stretching of the knitted fabric in one direction, the computation of parts is produced according to the formulas (29, 30). x = x/(1 + ehsr) and y = y/(1 - εx₁y).

The value of relative strains εx and ε₁y characterizing forming ability of the material depends on the structure of knitted fabrics. The conducted research of the five most common types of knitted fabrics showed that there is a linear dependence of strain εx and ε₁y from the network angle of the material, i.e. the angle between the sides of the square plotted on a strip sample in the test material [8]. This dependence can be expressed by equations of the straight line ε = ε₁y and aφ = bφ, where a and b are the angular coefficients of the straight lines.

Due to this, the results of experimental data processing to obtain graphs, which can determine εx and ε₁y knitted fabrics of this type for any angle (Fig. IV-30). From this figure it is seen that deformation of the knitted fabric of different types can be divided into two groups with approximately the same value of deformation. So, the first group includes knitted fabrics full jacquard and eraser (εx₁, εx₂, εx₃), and the second group - invoice jacquard and interlock (εx₄, εx₅).Therefore, for the manufacture of products from knitted fabrics of these types is necessary to make the computation of details for the two groups of paintings in particular. In the manufacture of the jerseys from other types of paintings need to determine their schedules physical-mechanical indicators and scanner details. In addition to charts of deformation for design of jerseys you must have mannequins model the external shape of the product.The first sample of this dummy to construct surrounding women's sweater was created at the Department of designing and technology of garments of MTIP (Fig. IV-31). Mannequin developed measurement-based model of female figures according to GOST 9383 - 61 taking into account the aesthetic requirements of women's knitted jackets of the adjacent forms of allowances on linen, and thick cloth.

The reference axis coordinates to calculate the sweep of the shelves and the backs of the jerseys asked: OU - the axes of symmetry of the surface of the dummy from the back and the front, Oh - in the waist on geodesics orthogonal to the axes OU. The line of stitches is applied under the sample model (Fig. IV-31). The original scan is determined by the auxiliary grid in the same way as sweep parts of clothes.Scan the shelves of jerseys, it is advisable to determine without tucks, as they do not provide the desired fit of the shapes that disrupt the structure of the knit and cause an unjustified increase in the consumption of the canvas and the complexity of manufacturing products.

To get scanning of parts with minimal deformation of the knit on the surface, determine the angles between the threads of the net in all squares (5 X 5 cm) that is applied to the mesh before combining it with the surface. In accordance with this scan auxiliary mesh is divided into zones I, II, ... (Fig. IV-32). For each zone, determine the average value of the angles φ, for which the graph of the deformation of the material (see Fig. IV-32) find corresponding values of εx and EY.On the axis OU are asked a series of dots, whose number is determined depending on the shape of the line joints of the sweep and change of the material deformation zones.

On curved sections of sweep number of points to ask more. You must also specify the corner points of the seam lines.

The specified points is measured, the source of the abscissa and ordinate (x, y) and find the coordinates of parts of a knitted fabric according to equations (29, 30). For example, in table. IV-1 shows the calculation of the coordinates of several points of scan the shelves of jumpers from the eraser.

As can be seen from table IV-1, conversion of coordinates of the scan is performed only on x-x due to the fact that deformation ε₁y axis OU insignificant for this form of cloth at the angles φ indicated in the table. In the calculation result received scan of items of knitted fabric (see the dashed lines in Fig. IV-32), which have different sizes and smaller than scanner support grid.

Fabricated samples of jerseys obtained based on the method of computation of, have a nice appearance and provide a figure fitting without wrinkles and folds. At the same time saving of knitted fabrics for the top products is on average 3 - 5% linen - 10%. The computation of parts of jerseys of different models of different paintings can be produced on the finished initial scan, developed for the main types of products, and standard models (sweater, cardigan, jacket, linen).The development of a model of the initial scans should be made on the basis of mannequins created based on anthropological measurements, various allowances and aesthetic requirements. In the presence of a typical source scans mannequins will be used in the development of the original scans of the original models and to test products designed for the typical initial scan.

 

Conditions dressing surface without folds and Assembly material

 

For the manufacture of high quality clothing in full accordance with the sample models the computation of and cutting out, and also their processing, shaping and Assembly must be carried out subject to the conditions, which provide the specified form of the surface and its resistance to wear products. To do this, in the design and manufacture of clothing necessary to carry out the established specifications of acceptance and manufacturing products.In all cases, as mentioned above, the network allowed the angle of the material under strain should not be greater than the minimum angle chebyshevskii network network on the surface (φ ≤ φmin). Failure to do so leads to the formation of folds and assemblies of material on the surface when dressing the finished product. Folds and assemblies can occur, due to the considerable friction between the material and the wear surface of the body. This disadvantage is eliminated by reducing the friction or an appropriate dressing sheath and shift its sites efforts, exceeding the friction force of the material on the surface.

The formation of the assemblies can be in the upper parts tapered slim knitwear where they arise from the movements during wear products. No research on these shortcomings were not carried out. One can only assume that if an incorrect computation of Assembly and folds of the material during wear jerseys to produce more than one at the correct account. We can also assume that the possibility of the formation of the Assembly in the jerseys is more in the computation of average network corner than in the calculation.The fact that in the calculation for the average network corner leaves no reserve in case of change of the worn surface during wear products and are not taken into account possible variations in the properties of the same type of fabric. All this suggests that the rational design of jerseys is necessary to conduct further research. For the appropriate fit of the surface of products made of different materials the importance of the alignment axes of individual parts with the original axes of the surface.While not the exact combination of these axes, the products of a tight fit it is possible to increase or, conversely, the weakening of stretching of the material in some areas. The latter leads to the formation of folds and assemblies on the surface in the finished product. Inaccurate alignment of the axes in products free fit also causes the formation of folds and assemblies of the material. The deviation from the reference axes of the surface can occur due to misalignment of parts while cutting.In this case, the same angle of slant to both axes of the scanner parts, and with them every line a rectangular coordinate network, which was used for the calculation of the sweep. These deviations do not change anything when cutting isotropic materials have the same deformation in different directions.

With the misalignment of parts in an anisotropic material axes are not positioned in the direction of greatest resistance of the material or along the threads of fabric that are the coordinate axes in the calculation of the scan. As a result, when putting on the product threads of the fabric or the line of greatest resistance of the material do not coincide with the orthogonal geodesic lines adopted in the calculation of the axis of reference coordinate on the surface. As a consequence, the form of scans of the parts installed in the calculation, is not quite going to match the dress surface, with the exception of two cases.First, in the case of dressing developable surface, where the coordinate lines chebyshevskii networks do not have deviations from the 90', and, secondly, with bias details on 90'.

The last case refers to an anisotropic fabrics or other materials that have the same deformation on the lines of greatest resistance (εx = EY). Skew the details of the developable surfaces (the first case) practically allowed in limited sizes in accordance with operational requirements, providing in detail the tensile strength and the location of the pattern of the material in a certain direction. For example, when a large misalignment of the front half of the trousers not sufficiently resistant to stretching and drawing of the fabric (strips) do not coincide with the fold (pleat) pants.The second case is theoretically possible misalignment of the parts in clothes made of fabrics only take in the finishing details and podvorotnya where no matter how to cut out a detail: the basis or duck fabric. When cutting straight pieces used for prosverlivayut surfaces, the shape of the scan does not quite match the worn surface due to changes in the elongation of the material along the coordinate lines chebyshevskii network on the surface.Denote by εx₁, εy₁ elongation of an anisotropic material by means of coordinate lines chebyshevskii network on the surface after distortion of a part when cutting. In this case, it is adopted in the calculation of the scan coordinates x = x/(1 + εx), y = y/(1 + EY) will have a different value after the skew of the part when cutting: x = x/(1 + εx₁), y = y/(1 + εy₁).

For an anisotropic non-woven material, this means that the dressing of the surface must occur by a deformation of the material (εx₁, εy₁) than was made in the calculation of the sweep (εx, EY). Therefore, if the calculation for the average network angles of the individual zones of the scan, it may be formed in the shell assemblies where εx₁εy₁ > εxεy.

To avoid this, it is necessary for the computation of average network corners to provide some margin (to increase εx₁εy₁) in the event of misalignment of parts while cutting. When calculating the sweep at the lower corner of the network to increase εx₁εy₁ no need, as their value is usually much larger than in the calculation for the average network corners. In the event of misalignment of parts of the tissue is also possible the formation of assemblies in a tapered slim casings. In addition, the strain of the warp and weft which, when computation of shells of tissue is not provided.The shell fabric casual fit misalignment of parts while cutting causing deviations from the shape of the surface for which the calculation of the sweep. Finally, the misalignment of the parts during cutting affects the magnitude of the deformation of the fabric at the seam lines. To determine the allowed misalignment of parts while cutting tissue does not affect the product quality, it is necessary to conduct special studies. It is not excluded that the adopted technical conditions of the cutting of acceptable deviation, established by experience, not in all cases correspond to their purpose.

Set forth in this Chapter the theoretical principles and methods of computation of the detail of fabrics and other materials help scientifically to solve the issues of construction of clothes and other garments. The specific features of the various types and models of clothes, materials, methods of manufacture and conditions of wearable products will require private methods of computation of parts.

 

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.

5. Suboticki A.V., Lermontov, D. B. Determination of coordinates of the scan shells of fabrics for different surfaces, Izvestiya vuzov, Technology of light industry, 1966, № 4.

6. Suboticki A. V., Melikov, E. H. the Design of shells made of woven materials, journal of applied physics, Technology of light industry, 1961, No. 2.

7. Suboticki A.V. the Method of design of clothing items, Cintalapa, Information, No. 2, 1962.

8. Suboticki A.V., Flerov L. N. Design planopilaris top of knitwear, Textile industry, 1964, No. 11.