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Tashpulatov Dilshod Shalihovich, researcher,
Tashkent Institute of Textile and Light Industry, Djuraey Anvar Djuraevuch, doctor, of Technical Sciences, professor, Tashkent Institute of Textile and Light Industry Plekhanov Alexey Fedorovich, doctor of Technical Sciences, professor, Russian State University named after A. N. Kosygin
E-mail: [email protected]
QUESTIONS OF THE RATIONALE PREPARATION OF THE PARAMETERS OF THE KOLOSNIKOV ON ELASTIC SUPPORTS OF THE FIBER MATERIAL CLEANER
Abstract: in the article the scheme of effective design of the bars on the elastic supports of the fibrous material cleaner is shown. The theoretical basis for calculating the grate parameters on an elastic support with nonlinear stiffness and random perturbation is considered. The results of testo of the recommended design of a cleaner with grates on elastic supports are given.
Keyword: cleaner, fibrous material, grate, elastic support, oscillation, stiffness, dissipation, amplitude, frequency, raw cotton, test, effect.
To reduce the damageability ofcotton fibers and raw cotton seeds, it is advisable to reduce the multiplicity of the interaction of working organs with raw materials in the process of primary processing. At the same time, it is important to increase the efficiency of interaction between cotton and working bodies by improving their design. In this paper, a new design of the grate of cotton cleaner from a large litter is recommended [1].
At the same time, the recommended grate design significantly reduces frictional resistance against the side surfaces with raw cotton. In this case, the elasticity of the supports will in fact be nonlinear. According to the known technique [2], the elastic element can be represented as a conical spring with nonlinear stiffness (see Fig. 1).
Figure 1. The scheme of conical grates on elastic supports and the design scheme
The elastic bushings are also eccentric, have a variable thickness. It should be noted that the eccentricity position may change during operation (there are some circular motions). Therefore, the amount of eccentricity and the difference in diameters of the grate 1 do not exceed (2,0^3,0) 10-3 m with an average diameter of the grate.
According to the calculation scheme (see Fig. 1) we will compose an equation describing the oscillation of the grate.
It is known that the grate operates a random perturbing force from the side of the squeezed raw cotton
Fb = (Fb) ±S(Fb) (1)
It should be noted that the rigidity of the elastic support is non-linear and the restoring force is determined from expression
P = c1X1 + c2xl (2)
QUESTIONS OF THE RATIONALE PREPARATION OF THE PARAMETERS OF THE KOLOSNIKOV ON ELASTIC SUPPORTS OF THE FIBER MATERIAL CLEANER
where, c2, cl - the values of the stiffness coefficients of the elastic support;
- moving the grate in the vertical direction. The oscillations of the grate are described by the following differential equation
mx + cJx +—x3 = F0sinat (3)
where, m - is the reduced mass of the grate; - constant non-linearity coefficient; wt - disturbing force from the raw cotton.
We seek the solution of (3) by the Galerkin method [3] in the form
Xj = x0 sin cot (4)
Substituting expression (4) into the differential equation (3) and taking the integral equal to zero, we have
mx, + c1x1 +—x3 ■
-F0 sin a>t
x1dt = 0
2n
where, ^ - period of fluctuation.
After integrating, we obtain
3 c
—1 x3 + (c1 - ma>2 )x0 - F0 = 0
4 »
In this case, the roots of equation (5), according to the well-known technique [3], will be:
(5)
m
x, =-2rcos—; x2 = 2rcos
1 3 2
n±m 3
where, r = signa ^ffi ; $
a
= arccos—
For specific parameter values, you can select the required amplitude and frequency of the non-linear oscillations of the grate using the recommended method. Consider the well-known method for solving the problem [3].
Equation (3) can be rewritten in the form
c
mx + ma2 x = (ma2 - c 1)x -—x3 + F0 sin cot (6)
V
Using the Duffing method [4], we obtain a solution as a first approximation
x1 = x0 sin cot (7)
Substituting x1 in the first part of equation (6), we obtain the equation for calculating the second approximation:
mx, + mai2x =
(mo2 -ci)x0 -3Clx3 + F, v ' 4 y
(8)
J c, 3 . „
x sin cot +---2 x0 sin 3ct
4 »
We are only interested in periodic oscillations of the grate, then to exclude the secular term, condition
(mm2
(9)
- c 1 )x0 x3 + F0 — 0
4»
Then we can obtain the second approximation, as solu tions of the differential equation:
1 c
mx + mm x = —2x„ sin3mt 4 »
(10)
The solution of the differential equation (10) is
CX 3
x = A sin cot + B cosct--L-^sin3fflt
32® m
The constants of integration are determined from the initial conditions:
where, t = T ; T = — ; x = 0 ; x = 0 4 a
A — x„
Cixn
B — 0
32© m^
Finally, the approximate solution has the form
(11)
C x 3
x = x0 sin cot--^y0—(sin cot - sin3fflt) (12)
32® m^
In this case, the value of X0 is determined from equation (9). Taking into account the initial values of the system parameters, the regularities of the oscillatory motion of the bars on elastic supports with nonlinear rigidity were obtained. Based on the processing of the obtained results, graphical dependences of the swing width of the grate oscillations are constructed with the variation of the average value of the rigidity of the elastic support, the mass of the grate at © = 65c 1 h a = 40c .
Analysis of the data shows that with increasing rigidity of the elastic support Ax becomes more intense. With an increase in the mass of the grate, the influence on the decrease in Ax becomes insignificant. This is explained by the fact that with a large mass of the grate its inertia increases, and the value of Ax tends to a constant value (2.0-2.4 mm). It is at these values of Ax that the cleaning effect becomes tangible, which is confirmed by the results of experiments [5].
Using the proposed method, it is possible to substantiate the necessary parameters of the system, which ensure an increase in the effect of cleaning cotton wool cleaners, from large litter.
Thus, on the basis of theoretical studies, regularities of the grate oscillation are obtained, graphical dependencies of the parameters are constructed, based on their analysis, the best parameters are justified. Experimental studies have justified the effectiveness of using the recommended grate.
References:
1. Juraev A. J., Plekhanov A. F., Bitus E. I., Razumeev E. K., Tashpulatov D. S. Grate fender of fibrous material cleaner Application for the grant of patent № 2017143328 from 12.12.2017 to the Federal Service for Intellectual Property of FIPS.
2. Djuraev A., Daliyev Sh. L. Development of the design and justification of the parameters of the composite flail drum of a cotton cleaner // European Sciences review Scientific journal - No. 7-8.- 2017.- P. 96-100.
3. Panovko Ya. G. Fundamentals ofApplied Theory of Oscillations and Shock, Machine Building, Leningrad,- 1976.- 320 s.
4. Rasulov R. KH. Justification of the parameters of the serrated-grate system of the cotton cleaner - raw from large litter. Author's abstract. diss. ... cand. tech. Sciences, - Tashkent,- 2008.- 28 p.
5. Tashpulatov D. S., Dzhuraev A. J., Plekhanov A. F., Bitus E. I. Optimization of technological parameters of colt-planar drums of cotton cleaners. Journal of Design and Technology, Russia,- Moscow,- No. 62.- 2017.- P. 85-89.
