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Section 12. Technical science
Artikbaeva Nozima Mumindjanovna, senior lecturer,
Tashkent Institute of Textile and Light Industry, Nutfullaeva Lobar Nurullaevna, senior lecturer,
Bukhara Engineering and Technology Institute, Bakhritdinova Dilrabo Amanbaevna, senior lecturer, Shin Illarion Georgievich, doctor of technical sciences, professor, Tashpulatov Salikh Shukurovich, doctor of technical sciences, professor, Tashkent Institute of Textile and Light Industry, Murodov Tahir Bakhramovich, сandidate of technical sciences, associate professor, Tashkent Institute of Textile and Light Industry E-mail: [email protected]
DEFORMABILITY OF THE PACKAGE OF MULTILAYER COMPOSITE MATERIAL OF THE WORKING PRESS ORGAN FOR WET-HEAT TREATMENT OF SEWING PRODUCTS
Abstract: In this article questions of application of composite materials for manufacturing of pillows of the press equipment for damp heat treatment of garments are considered. More attention was paid to the deformability of the cushion package, which was made of composite material.
Keywords: Fiberglass, deformation, beam, tension, formation, properties, efficiency, cushions, working elements, wet heat treatment.
The responsible stage in the design of machine parts is the justified choice of materials, taking into account the criteria for working capacity, strength, wear resistance, heat resistance, etc. When solving the problem of designing machine parts related to the requirements for reducing metal consumption and weight, energy intensity, construction cost, strength, durability and reliability machines the greatest. Efficiency is achieved when using composite materials. These materials are a two-phase composition of a soft matrix and the high-strength second-phase fibers distributed therein.
The physicomechanical properties of composite materials mainly depend on the properties of the components themselves and their volume combination, as well as the strength of the bond between them. In this case, the composite materials
acquire properties that are not characteristic of the individual components that enter into their composition [1].
Based on the results of preliminary experimental studies on the properties of composite materials, a new technology has been developed for manufacturing a working organ (cushion) of press equipment for wet-heat treatment of parts of garments.
In the manufacture of pillows, a multicomponent (uniaxial, biaxial and triaxial) fibrous fiberglass material and reinforced filler-epoxy resin were used. Thus, it was possible to manufacture press cushions for most of the processed parts and components of the garment. In this case, the quality (accuracy of the reproduction of the three-dimensional form) of the details of the garment and the form-stability will depend on the design and economic parameters of the upper (punch)
and lower (matrix) part of the surfaces of the working organ of the press equipment.
The effectiveness of any technological machine is predetermined by the operability of its working body. Therefore, the study of the thermal and stress-strain state of the working member of the machine under operational loads causing various types of failure, as well as the study of kinematic and dynamic characteristics, represent an important aspect of ensuring equipment reliability.
Let's consider the analytical method of estimating the bending of a package of multilayer composite material, which is used for cushions of press equipment for WHT, the study of the rigidity and resistance to bending of multilayer bags is associated with modeling the bending process under operational loads. The development of analytical methods for calculating parameters that characterize the rigidity of a packet has theoretical and applied values, since it allows predicting the behavior of an object under loading under different initial (input) data.
As a model construction of a package of multilayer composite materials subjected to bending in the molding of garments, the model of a beam lying on a solid elastic base is most closely approximated. This beam is supported along its entire length by an elastic medium resisting the movements caused by the bending of the beam.
The loads acting on the beam are balanced by the reactance of the solid elastic foundation. In this case, the intensity of the reactions of the elastic foundation depends on the mechanical properties of the base, on the deflection of the beam and on the width of the supporting surface of the beam.
In accordance with the hypothesis of E. Winkler [2], the elastic base reaction, represented as a distributed force, is considered proportional to the deflection y:
qR =-ky (1)
where, k - is a coefficient of proportionality, depending on the linear rigidity of the elastic base and having the dimension H/m2.
The Winkler elastic base is usually represented as an infinite set of independent elastically deflecting supports (springs with the same stiffness characteristics) located along the entire supporting surface of the beam (Fig. 2). If the width of the beam is equal to 6, then the proportionality coefficient can be represented in the form
k = bkn
(2)
where, k0 is the coefficient of rigidity of the elastic foundation (bed stiffness coefficient) having the dimension H/m3.
In the general case, when b is a function of z, then k becomes a function of z. Then the elastic base becomes the basis of variable rigidity, which can significantly complicate the problem of the elastic behavior of a beam on a solid founda-
tion. Therefore, we consider the case of a constant value of k or a constant stiffness base along the length of the beam.
The deformation of the package of the multilayer composite material of the matrix of the WHT press equipment takes place under the influence of the forces applied to the punch during the shaping of the fabric during the manufacture of the main parts of the garment. Considering the deformation of one or several layers of the material packet with respect to the underlying layer, it is possible to apply the laws of deformation of the beam bending on an elastic solid foundation.
We use the well-known differential equation of the elastic axis of a beam of constant cross section
EJxy'V = q (3)
where, Jx is the moment of inertia of the section relative to the main central axis perpendicular to the plane of the bending moment; E - modulus of elasticity of the first kind; q is a uniformly distributed load. The shape of the axis of the curved beam is described by a curve of the fourth order.
To calculate the beam on an elastic solid foundation, it is necessary to take into account not only the external distributed load q, but also the distributed reaction forces of the solid elastic foundation qk (l).
Then equation (3) takes the form EJxyIV = q - ky either EJxyIV + ky = q (4)
We introduce the notation k /(EJx) = 4a4 and obtain
(5)
yIV+4a4 7 = q
EJx
Equation (5) is a linear ordinary inhomogeneous differential equation with constant coefficients of the fourth order. The general integral of such an equation, because of its linearity, consists of the general integral of the corresponding homogeneous equation.
yIV + 4a4 y = 0 (6)
And any particular solution (y *) of the inhomogeneous equation (4)
The characteristic equation for (6) has the form
r4 + 4a4 = 0, r4 = -4a4 (7)
Taking into account the roots of the characteristic equation and the particular solution (y *), the general solution of equation (5) can be represented in the form
y = e~az(C sinaz + C2 cosaz) +
2 „ (8) +eaz(C3 sinaz + cosaz) + y*
Ifwe rearrange the terms in (8) and introduce hyperbolic sines and cosines, we have a more preferable form for writing the solution of the equation:
y = C sinaz • shaz + C2 sinaz • chaz + 71 2 (9)
+ C3 cosaz • shaz + C4 cosaz • chaz + y *
where, shaz and chaz respectively, the hyperbolic sine and
cosine.
The package of the multilayer composite is represented in the form of a bar of a rectangular cross-section, loaded in the middle by a concentrated force P. Let us determine the greatest bending moment.
If in any section of the beam to move vertically downward by a distance y within the elastic medium, then on the side of this medium there will appear a pressure equal to (the specific weight of the elastic medium). The intensity of the reaction forces will be
qk =-yby (10)
where, b is the width of the rectangular section of the stack of the multilayer composite. Therefore, and, according to expression
k / (EJx ) = 4a4 we have a = éj-
yb
J
(il)
The proper weight of the beam is balanced by the reaction of the elastic medium, and therefore we set q = 0 in equation (5). Then, under the value of y, the displacement from the equilibrium approximation of the rod, occupied either at P = 0, should be reduced.
Since y*=0, according to the solution of (9) we have obtained:
y = C sin kz ■ shkz + C2 sin kz ■ chkz +
7 1 2 (12)
+ C3 cos kz ■ shkz + C4 cos kz ■ chkz We successively differentiate this expression and find: y = (C2 - C3)a sinaz ■ shaz +
+(C1 - C4)asinaz ■ chaz +
+(C1 + C4)a cos az ■ shaz +
+(C2 + C3 )a cos a z ■ cha z y11 = 2C1a2 cosaz ■ chaz +
+2C2a2 cosaz ■ shaz -
-2C3a2 sinaz ■ chaz -
-2C4a2 sinaz ■ shaz y111 = 2(C2 - C3)a3 cosaz ■ chaz +
+2(C1 - C4)a3 cosaz ■ shaz -
2(C1 + C4)a3 sinaz ■ chaz -
-2(C2 + C3)a3 sinaz ■ shaz
To find the integration constants C1, C2, C3 and C4, we choose the application of the force P from the calculation of zb. For z = 0, by the symmetry conditions, y = 0. The transverse force Q to the right of the mean cross section is equal to - P/2, therefore EJ ////z = 0 for z = l, M = EJ /// = 0 and
' J xy ' ' xy
Q=EJ /// = 0
J xy
Thus, we obtain four equations for determining the constants C, ....C„:
1 4
c2 + c3 =0; c2 -c3= -P/4EJa3 C1 cosalchal + C2 cosalshal -
-C3 sinalchal - C4 sin alshal = 0
C1 (cosalshal - sinalchal) +
+C2 (cos alchal - sin alshal) +
+C3 (-cosal - sin alshal) +
+C4(-cosalshal - sinalchal) = 0
Where do the values come from:
C _ P sh2al + sin2 al
C --3" • ;
8EJ a shalchal + sin al cosal
C2 =-
8EJxa
' ; Co -
8EJa'
C 4 =-
P
ch al + cos al
8EJxa sinalchal + sin al cosal The bending moment in the beam was determined in terms of the second derivative of the function y by the formula MU32 = EJym or
M =
изг
4a
sh 2al + sin2 al
y shalchal + sin al cos al - cos a zsha z - sin a zcha z +
-cos a zchaz -
+-
ch 2al + cos2 al
-sinazshaz )
shalchal + sin al cos al
The maximum bending moment M™ has a value at
z = 0 and will be
„ ,max P sh2al + sin2 al M=---(13)
4a shalchal + sin al cosal With increasing length, the bending moment increases
with a very long length and can be calculated from the formula:
M max = P (14)
U32 .
4a
where, is determined according to the expression (11).
It should be noted that the form of the bending moment diagram depends on the length l. For a short beam length, the entire area of the bending moment diagram is above the z axis and does not change sign. For a longer beam, the bending moment diagrams change sign and part of the diagram is located below the z axis. The maximum bending moment (14) is capable of causing plastic (irreversible) deformations in the extreme zones of the beam if the operating loads (stresses) exceed the yield strength of the beam material:
5>5T
Therefore, taking into account the maximum value of the bending moment, it is possible to write down the condition for carrying out the "bearing capacity" of the beam
hh2
Mmax Mt ]=ÔThf- (15)
o
where, [Mr ] is the permissible bending moment corresponding to the moment at which the normal stresses reach the yield stresses of the materials.
Condition (15) is of great practical importance, since it shows the limiting value of the bending stresses arising in the elastic deformation zone. The transition to the region of plastic deformations with increasing force P leads to an ir-
reversible distortion of the contact surfaces of the working bodies of the press equipment for WHT made of a stack of multilayer composite material. As a result of inelastic changes in the surfaces of the shape-forming profile of the cushions of this equipment, the quality of the molded parts of clothing deteriorates, which is unacceptable when improving the advanced methods of manufacturing garments.
References:
1. Tashpulatov S. Sh. Highly effective resource-saving technology of shaping and WHT clothing details / Monograph. From "Science and Technology", 2010.- 96 p.
2. Philin A. P. Applied mechanics of a solid deformable body. In 3 volumes - Moscow: Nauka, 1978.- T. 2.- P. 231-246.
