Study of dynamics of the turning process in pneumechanical spinning in the presence of false torsion

The paper presents the results of a study of the dynamics of the process of torsion of yarn of pneumomechanical spinning in the presence of false torsion. Dynamic mathematical models of the process of torsion of yarn of pneumomechanical spinning in the presence of false torsion in unsteady modes of starting and stopping the forming-twisting device are constructed. By now, the question of yarn twisting in a transient mode of operation in rotor spinning remains unexplored. We have here made an attempt to fill the indicated gap by constructing mathematical models of a forming-twisting device during torsion. In connection with the above-mentioned problem arises to systematize the accumulated information on new methods of forming yarn and constructions of forming and torque devices, to clarify a number of questions of theory and technology, and also to classify methods of forming yarn. The main direction of development of new methods of yarn formation remains the improvement of the high-speed modes of the working organs and, above all, of the forming and turning devices, which raises a number of important problems of both technological and structural nature.


Introduction
Torsion issues, in particular in transient operation, as one of the most important processes in textile production, have always received a lot of attention and a lot of material.The issues of twisting of yarn and threads in unsteady mode in relation to the conditions for the production of high-volume threads, as well as issues of the dynamics of threads in rotor spinning, have been well studied [1].
In recent years, new works have appeared on the dynamics of forming-twisting device when twisting yarn in a transient mode for new pneumomechanical methods [1], where, in particular, the possibility of obtaining a real twist with a false twist reel in the presence of a sliding clamp is shown.Other questions of the dynamics of the forming-twisting device during torsion in an unsteady mode in relation to the conditions of rotor spinning have not yet been resolved [2].
By now, the question of yarn twisting in a transient mode of operation in rotor spinning remains unexplored.We have here made an attempt to fill the indicated gap by constructing mathematical models of forming-twisting device during torsion [3].
A well-known feature of rotor-spinning yarn, which consists in high twist coefficients compared to ring-spinning yarn, due to the peculiarity of the rotor-spinning yarn structure and the conditions for its formation, greatly aggravates the problem of increasing the power consumed by the forming-twisting device [1].This, in turn, makes the problem of reducing the twist coefficient of rotor spinning yarn topical, the solution of which would give an additional opportunity to achieve an increase in the yarn formation rate in rotor spinning machines without increasing the forming-twisting device rotation frequency with a corresponding decrease in energy consumption.
The increase in operating speeds also makes it relevant to study the dynamics of forming-twisting device during yarn twisting in new methods of yarn production, in particular in rotor spinning in a transient mode during start-up and shutdown [4].

Construction of mathematical models of forming-twisting device during torsion in rotor spinning
We know many studies on the application of false spinning to improve the conditions for the formation of yarn pneumomechanical spinning [5,6].
Figure 1 shows the design diagram of the forming and twisting device for pneumomechanical spinning is shown.We accept the assumptions and designations [7,8]: 1.The frequency of rotation of the organ of false spinning P is a constant value.
2. There is no slipping of yarn relative to the reel.
3. The magnitude of the twist of the yarn is not taken into account, and thus the speed of removal of the yarn is equal to the feed speed.[8] 4. The initial twist of the yarn is equal to the nominal twist of the yarn Kн. 5.The value of twist m, lost in a sliding clamp, at the initial moment of time is equal to zero, there is no torque in the yarn necessary to slip its end since by the beginning of the process.
6.The direction of the nominal twist, as well as the corresponding twisting, it is accepted as positive regardless of whether it is right or left.
7. The rotation frequency of the chamber n and the absolute value of the linear velocity of the outlet and reverse feed of yarn when starting v quantities are constant [9,10].
8. We accept the spin of the yarn in the steady state: in the first section 9.The start time is counted as follows: t = 0 start of the start, at which the yarn begins to move in the opposite direction to ensure the closure, at t = t1 the yarn moves in the opposite direction and the end of the yarn comes into contact with the collection surface, t = t2 -the beginning of the movement of the yarn in the forward direction and the beginning of rotation of the twisting organ of false spinning.When stopped: t = t0 camera power off; t = t3 -termination of contact of the end of the yarn with the prefabricated surface of the chamber; t = t3 -the cessation of movement of the yarn and the spinning organ of false twisting and the completion of the stop.In the period t3<t 4 t  , twist changes occur in all sections in connection with the release of the end of the yarn in the first section.
We assume that, during the time dt, the sections together with caring yarn lose spinning numbers, During the same time, sections II and III receive spinning numbers equal to Since, in the first section, the end of the yarn is already free, the increment in the number of twists in this section is zero.Bearing in mind that the ratio of the increment from the number of twists of the yarn to its length represents the twist increment, we can compose differential equations for the sections of yarn: The equations have solutions in the form of:   (6) The following coefficients are accepted here: ( ) Based on the solutions of the equations, we can write expressions for twisting in sections for the moment the shutdown is completed:

Results and discussion
Now we can proceed to consider the starting mode.
Period 0<t 1 t  . in this period, the movement of the yarn occurs in the opposite direction, so the decision on the sections will be made in the reverse order.Due to the fact that the lengths of sections III and II l3 and l2 are much larger than the yarn feed length in the opposite direction lobr, we neglect the change in the twists of these sections in this period.
The twist of the yarn of the first section also does not change due to the presence of a free end and is equal to zero.Thus, the twist of the yarn in sections is equal to the twists at the end of the break and is: here we accept the coefficients: and it is meant that with the free end We pass to the second start-up period limited by t1<t As we accepted, at the moment t1 the end of the yarn begins to contact with the prefabricated surface and at the same time the movement of the yarn in the opposite direction stops and during the period the yarn is stationary.
Under these conditions, the twist in the third section does not change.The second and first sections during the time dt receive twist numbers equal to ndt ) 1 (

 −
and ndt  respectively.But since  <<1, we can write the equations: By solutions of these equations under the initial conditions: at t=t1 ( ) These solutions allow us to write an expression for twists at t=t2.
( ) Now consider the third, final launch period, determined by t>t2.The moment t2 corresponds to the beginning of the movement of the yarn in the forward direction with the simultaneous beginning of the action of the twisting organ of false spinning.
In connection with the movement of the yarn in the forward direction, the solution of the problem in sections is performed in the direct sequence.
During the time dt, the yarn sections receive spinning numbers, respectively equal to pdt, Under the corresponding initial conditions: at t=t2.

Conclusion
Based on the analysis of the obtained mathematical models, we can determine the maximum value of the twists К2т and К3т and the moments t2т and t3т at which they take place.In addition, we can determine the length of the yarn produced with a twist that differs from the nominal by more than a predetermined small value K  when stopping Y0 and starting Yn.Curves 01, 02, 03 correspond to the change in the twist of the yarn in the sections at stop, and n 1, n 2 , n 3 -at start (Fig. 2. and Fig. 3.).

Figure 1 .3
Figure 1.The design scheme in the presence of false twisting.

Figure 2 .
Figure 2. The dependence of twist on time at stop.

Figure 3 .
Figure 3. Twist versus time during start-up.
During this same time, these sections lose, together with the leaving