DETERMINING THE SPECIFIC VIBRATION FREQUENCY OF A PIECE OF COTTON ON A DRUM WITH A TOOTHED BELT

ABSTRACT

The article presents a formula for analytically determining the natural vibration frequency of a cotton belt suspended from a toothed belt structure of a cotton gin. Based on the numerical solution, the influence of the inclination angle between the saw-toothed belt and the saw-toothed drum on the oscillation frequency was determined. The system parameters are established. The results of analyzing the existing design of the saw-toothed drum for cleaning cotton from large impurities are presented. The possibilities of enhancing the cotton cleaning effect by expanding the range of interaction between the saw-toothed drum teeth and raw cotton have been substantiated. It is recommended to implement this cotton cleaning device in production.

АННОТАЦИЯ

В статье представлена формула для аналитического определения частоты собственных колебаний хлопковой ленты, подвешенной к зубчато-ременной конструкции хлопкоочистительной машины. На основе численного решения определено влияние угла наклона пилообразной ленты с пилообразным барабаном на частоту колебаний. Параметры системы основаны. Представлены результаты анализа существующей конструкции пилообразного барабана для очистки хлопка от крупных примесей. Обоснованы возможности повышения эффекта очистки хлопка за счет расширения диапазона взаимодействия зубьев пилообразного барабана с хлопковым сырьем. Рекомендуется внедрить в производство данное чистящее средство для хлопка.

Keywords: saw drum, toothed tooth, tape, radius, moment of inertia, vibration, frequency, amplitude, force, specific, resonance, cleaning effect.

Ключевые слова: Пильный барабан, коническая передача, ремень, радиус, момент инерции, вибрация, частота, амплитуда, сила, характеристика, резонанс, эффект очистки.

Introduction. In the field of cotton processing, obtaining high-quality cotton fiber is important [1,2]. Currently, in the conditions of widespread use of cluster production, one of the main issues is the creation of new technologies for obtaining high-quality cotton fiber, the development of effective cleaning designs [3]. In this regard, it is important to develop cleaners that have minimal damage to the fiber, high cleaning efficiency, high productivity and resource. In addition, it is necessary to take into account that increasing the number of cleaning operations to clean cotton to a sufficient level reduces quality. Therefore, it is necessary to develop such a cleaning technology and cleaning design that reduces the number of cleaning operations and increases the efficiency of each working unit.

A saw drum design that effectively removes big impurities from cotton has been developed [4,5]. The proposed saw drum significantly increases the contact area of ​​the drum with the cotton pieces by installing curved toothed belts [4].

Methods. Determining the specific vibration frequency of a piece of cotton on a drum with a toothed belt. Figure 1 shows a calculation scheme where a piece of cotton is caught by the teeth of a drum tape. To increase the cleaning efficiency, it is important to create a resonant mode in the vibration of a piece of cotton. In general, the frequency of forced vibration of a piece of cotton in a full rotation of the drum:

Р_m=_bk                                                              (1)

Here, k is the number of bars beneath the saw drum, and ω_b is the saw drum's rotational frequency (angular velocity). However, the forced vibration frequency in the cleaning zone is close to the value of ω.

Based on the calculation scheme (Fig. 1), we denote the length AB of a cotton sliver with a mass of m as l, the radius of the drum as r=OA, and the distance of the fiber seed relative to the axis of the drum as L=OB.

It should be noted that the following forces act on the cotton sliver: gravity, inertia, air resistance, Coriolis force, and centrifugal force.

1-drum, 2-saw tape

Figure 1. Section of the saw drum (a) and calculation scheme representing the movement of the fiber sawdust (b).

We will mainly consider the relative vibrational motion of a piece of cotton relative to a curved tooth with its center of gravity at its tip. In this case, the Coriolis force does not produce a moment about point A. The moment of the force of gravity:

M_g=mgX                                                             (2)

Here, m is the mass of the cotton ball, g is the acceleration due to gravity, and X is the linear displacement of the center of gravity of the cotton ball.

Accordingly, the moment of the centrifugal force relative to point A is determined as follows, taking into account the gear angle [6,7]:

where r is the radius of the drum, l is the length of the cotton strip, φ is the angle of oscillation, j is the angle of inclination of the cotton strip relative to the drum; β is the angle of inclination of the belt tooth.

The moment of inertia of the piece of cotton relative to point A is [8]:

                                                    (4)

Based on the calculation scheme and taking into account the method presented in [7,8]:

We derive a differential equation expressing the natural oscillations of a piece of cotton suspended by a sawtooth belt of a sawing drum relative to point A of the drum, based on the equilibrium condition [6,7], from the moments obtained from all forces:

The specific vibrational frequency of a piece of cotton attached to a toothed belt is:

Results and discussion. In order to determine the patterns of changes in the specific vibration frequency of a piece of cotton caught by the teeth of the drum tape in the recommended cotton cleaner from large impurities, the following numerical values ​​of the parameters were taken into account:

g=9.81m/s²;=(5⁰  10⁰);=(3555)s^-1; r=(0,1780,210)m; l=(1,252,5)10^-2m.

Figure 2 shows graphs of the dependence of the specific vibration frequency of a piece of cotton caught by the teeth of a saw drum on the angular speed of the drum. According to the analysis, if the vibration frequency of the cotton piece attached to the belt tooth increases from 9,2 Hz to 32,3 Hz with an increase in the angular velocity of the drum from 22 s^-1 to 42 s^-1 and β=5⁰, then the natural vibration frequency increases significantly with an increase in the tooth inclination angle. In particular, when the deviation angle is increased to 10⁰, the values ​​of  increase from 14,1 Hz to 40,3 Hz in a non-linear manner. Therefore, in order to increase the cleaning efficiency, it is recommended that the angular speed of the drum be ω>40s^-1 and the gear deviation angle b>7,0⁰.

Figure 2. Graphs of the dependence of the frequency of natural vibration of a piece of cotton caught by the teeth of a saw drum on the angular speed of the drum

Also, Figure 3 shows a graph of the natural vibration frequency of a cotton piece hung on the serrated teeth of a saw-toothed drum belt as a function of its length. According to the analysis of the constructed graphs, when the length of the cotton piece increases from 14 mm to 24 mm and the drum radius is 0,210 m, the natural vibration frequency decreases from 34,5 Hz to 16 Hz with a fine connection, while when the length of the cotton piece is 24 mm, its natural vibration frequency decreases from 29,2 Hz to 13,15 Hz. In general, if the length of the cotton piece is small, the specific vibration frequency will decrease, that is, the cleaning efficiency will also decrease. To ensure high cleaning efficiency, it is advisable to set the drum radius to (0,21÷0,25) m and the cotton piece length l >20 mm.

Figure 3. Graphs of the dependence of the natural frequency of a piece of cotton on the teeth of a bandsaw drum tape as a function of its length

Conclusion. The formula for determining the specific vibration frequency of cotton, which ensures the high efficiency of cleaning cotton from large impurities in a cotton cleaner with a toothed belt saw drum, is obtained, and its parameters are recommended.

References:

1. Джураев А. Динамика рабочих механизмов хлопка перерабатываюших машин //-Ташкент: Фан.1987.-с.188.
2. Джураев Анвар Джураевич, Одилов Хайрулло Рахмонжон Ўгли, & Норбоева Дилфуза Вахобжон Қизи (2024). Эффективная конструксия пилчатого БАРАБАНА очистителя хлопка от крупного сора. Универсум: технические науки, 4 (12 (129)), 55-58. дои: 10.32743/УниТеч.2024.129.12.18898
3. Мирошниченко Г.И. Основы проектирование машин первичной обработки хлопка. М.: Машиностроение, Изд. Легкая промышленность, 1972, 472 стр.
4. Я.Г.Пановко. Основы прикладной теории колебаний и удара. Изд. Машиностроение, Л., 1976, 320 с.
5. Федоров В.С. Технология первичной обработки хлопка. 1937, с.208-209.
6. Авторское свидетельство, №994586. Барабан очистителя волокнистого материала, кл. D01 G9/14. 1981.
7. W.S. Anthony and William D. Mayfield, / Managing Editors, Cotton Ginners Handbook, // "United States Department of Agriculture," Agricultural Handbook p-503.
8. Christopher D. D., Vikki В. M. Martin K. S. Textile industry needs // The Journal of Cotton Science 21:210-219. 2017