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The article is devoted to the study of spreading of the twisted yarn in a spinning cell. The article presents the scheme and principle of operation of the effective design of the yarn-output tube of pneumomechanical spinning machine. To determine the law of motion of a roller installed in a yarn-output tube, the tension of the thread enveloping the surface of the rotating roller was studied, as a result of which the equation of its motion was obtained. As a result of solving the equation, the values of the thread tension on the surface of the rotating roller are obtained. The dependences of the change in the tension of the thread in time are obtained depending on the angle of rotation and the mass of the roller. The recommended design of the yarn-output tube allows increasing the strength characteristics of the pneumomechanical yarn.

One of the important mechanical properties of the yarn is the breaking load, which determines the stability of the spinning process [

Cell pneumomechanical spinning method is most prevalent for the production of high and medium linear yarn from cotton, chemical fibers and their mixtures [

The essence of this method is to transform the tape into a discrete stream of fibers, to form a wedge-shaped fibrous ribbon in the form of an open ring in the spinneret groove of the stream and to form a yarn by twisting it out of the cell using exhaust rollers.

Modernization of pneumatic spinning machines continues to improve the efficiency of pneumatic spinning, improve the quality of yarn and reduce breakage, rational use of energy in the formation of yarn, as described in [

The thread tension and twist distribution under conditions of constant rotation of the cell are numerically simulated, where the influence of various dimensionless spinning parameters on the thread tension and twist distribution is evaluated [

Based on this, the authors of this article studied the movement of yarn in the zone of the spin intensifier of a spinning machine.

In order to reduce the axial force of the yarn at each site of its allotment, the modernization of the corresponding devices continues. Some of them are discussed below.

In the implementation of these processes are used air and mechanical effects. The phenomena occurring during these processes and their patterns were disclosed in the works of A.G. Sevostyanova, I. Ripki, J. Lunenschles et al. [

Recommended yarn-output tube for yarn spinning device, which contains the first and second sections, rigidly interconnected by means of a connecting corner and equipped with a ceramic insert with inclined grooves on the working surface, the first section of tube is connected to the spinning cell [

In order to increase the strength characteristics of the yarn, the design of the yarn-output tube for spinning device has been improved (

In the process of spinning unit operation, the yarn 3 (

resistance from it to the stretched yarn 3 will be smaller, which virtually eliminates additional elongation of the yarn deformation 3. In addition, due to the inclined flute 8 when the roller 6 is rotated, effective torsion of the yarn 3 occurs [

The recommended design of the tube for output the yarn allows an increase in the strength characteristics of the resulting yarn [

To achieve this goal, i.e., to improve the distribution of the torsion in the yarn output through the tube, an analysis was made of the work of the roller, taking into account the tension of the yarn being removed.

The problem of contour-based motion of a thread along the surface of a funnel, which seems to be an arc of a circle, is considered. In this case, the arc moves around a fixed axis with a velocity of v_{e}(t) and each point of the thread has a speed v_{r} relatively to the arc, following [

moment of time have the same modulus speed, then it should be ∂ v r ∂ s = 0

assumed that The relative thread speed is a function for only time t. We enter the natural unit coordinates e 1 and e 2 , directed respectively along the tangent and the contour normal, and write the relative speed of the thread in the form: v = v e e 1 . The total acceleration of an arbitrary point of the thread is represented as the sum of the relative w r and portable w e accelerations.

w = w e + w r

At the same time, the projections of relative and portable accelerations on the connected axes e 1 O e 2 look like [

w r 1 = d v r d t = v ˙ r , w r 2 = v r 2 R , w e 1 = v ˙ e , w e 2 = 0

Here R is the radius of the arc of a circle.

We neglect the weight of the thread, taking into account along the arc of coverage only the friction force τ and the normal reaction q. Considering that for these forces the Amonton-Coulomb law is satisfied, the basic equation of the contour movement along the arc of a circle of a thread is represented as [

∂ ( T − μ v r 2 ) ∂ s e 1 + T − μ v r 2 R e 2 + τ e 1 − q e 2 − μ v ˙ r e 1 − μ v ˙ e e 1 = 0 (1)

where T = T(s, t) is the tension, µ—is the linear mass of the thread. Assuming that the thread moves in the direction of rotation of the circular arc (funnels), we obtain

τ = − k q at v r > v e , τ = k q at v r < v e , − k N < τ < k N at v r = v e (2)

Taking v r > v e , s = R φ Equation (1) in view of (2) we bring to the form

∂ ( T − μ v r 2 ) ∂ φ − k ( T − μ v r 2 ) = μ R ( v ˙ r + v ˙ e ) , N = T − μ v r 2 at 0 < φ < α (3)

where k-is the coefficient of friction between the thread and the surface of the funnel, φ = α—is the arc of coverage, N = Rq is the normal force. The value of the angle φ = 0 corresponds to the point of crowding of the filament to the funnel, φ = α the vanishing point of the filament from the contour. Integrating the first equation from (2) under the condition T(α) = T_{0}, we obtain

T = [ T 0 − μ v r 2 + μ R ( v ˙ r + v ˙ e ) k ] e k ( φ − α ) − μ R ( v ˙ r + v ˙ e ) k + μ v r 2 (4)

N = [ T 0 − μ v r 2 + μ R ( v ˙ r + v ˙ e ) k ] e k ( φ − α ) − μ R ( v ˙ r + v ˙ e ) k (5)

The tension of the thread T and the normal force N by Formulas (4) and (5) will be determined as soon as the speeds v_{r} and v_{в} are known. They are determined from additional physical conditions. Consider the mode of motion of the thread with a constant relative speed i.e. set v_{r} = v_{0} = const In Formulas (4) and (5), we should set v_{r} = v_{0} and v_{r} = 0. In this case, the contour (roller) must satisfy the equation of rotation

J R v ˙ e = k R ∫ 0 α N d φ = R [ T 0 − μ v 0 2 + μ R v ˙ e k ] ( 1 − e − k ∂ ) − μ R 2 v ˙ e α

where J = MR^{2} is the moment of inertia of the roller. The last equation is written as

v ˙ e = T 0 − μ v 0 2 M 1 (6)

where M 1 = M + μ R k [ k α + exp ( − k α ) − 1 ] , M-roller weight

Thus, under the action of the apparent tension of the thread T 0 − μ v 0 2 , the roller makes an equally accelerated motion with acceleration a = T 0 − μ v 0 2 M 1 . This

movement continues until the time t = t_{0}, at which the speed of the roller will be equal to the relative speed, i.e. v_{в} = v_{0} from this condition we find t 0 = a / M 1 .

_{0} and the mass of the roller M.

It is assumed in the calculations: k = 0.3. R = 0.005 m. v_{h} = 100 m/min.

From the graphs presented in _{0} ≈ 10-6-10-5 min) reaches the thread speed.

An analysis of the tension distribution curves along the contact arc shown in

In the study of the spinning in the spinner as described above, the rod of the rolling rolled rope will have a yarn velocity at the moment of theoretical study of the law of the rolled rod in the effective construction of the yarn tractor pneumatic spinning machine. As a result, the rotating roller decreases the tension in the contact area by moving the yarn to ensure a uniform baking across the entire feeding zone and to increase the yarn’s stiffness.

1) The recommended design of the tube for output the yarn of spinning machine, allows an increase in the strength characteristics of the produced yarn.

2) It is established that the roller after contact with a moving thread almost instantly gains the speed of the thread.

3) As a result of the joint movement of the thread with the roller, the tension of the thread at the point of its crowding to the surface decreases with decreasing mass of the roller.

4) Reducing the tension in the zone of contact of the thread with a moving thread allows for a uniform twist along the entire length of the torsion zone.

The authors declare no conflicts of interest regarding the publication of this paper.

Korabayev, S.A., Mardonovich, M.B., Lolashbayevich, M.S. and Xaydarоvich, M.U. (2019) Determination of the Law of Motion of the Yarn in the Spin Intensifier. Engineering, 11, 300-306. https://doi.org/10.4236/eng.2019.115021