CC BY
11
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]
KOLOSNIK OSCILLATIONS ON ELASTIC SUPPORTS WITH NONLINEAR RIGIDITY WITH RANDOM RESISTANCE FROM COTTON-RAW MATERNITY
Abstract: The article presents a scheme for the efficient design of the grate on the elastic supports of a fibrous material cleaner. The theoretical basis for calculating the grate parameters on an elastic support with nonlinear stiffness and random perturbation is considered. The results of tests of the recommended design of a cleaner with grates on elastic supports are given.
Keywords: cleaner, fibrous material, grate, elastic support, oscillation, rigidity, dissipation, amplitude, frequency, raw cotton, test, effect.
To reduce the damage of cotton fibers and raw cotton seeds, it is advisable to reduce the multiplicity of the increase in the efficiency of interaction of working organs with cotton in the process of its primary processing. At the same time, it is important to increase the efficiency of interaction between cotton and working bodies by improving their design. We recommend a new design of the grate of cotton cleaner from a large litter [1].
Influence of the grate parameters on the oscillation frequency. For an approximate determination of the deformation value of the grate supports, let us consider the kinetic energy of the raw cotton to be pulled together with the grate in the process of impact, transforming into the potential energy of the deformable support:
mV 2 T = - y
2
n =
J {clx + c2x3 )x
(1)
where: T - kinetic energy of raw cotton and grate; m- total mass of grate and raw cotton; Vy - speed of impact of raw cotton on the grate; c1 — linear component of the elasticity
c 2
stiffness coefficient; c = — - nonlinear component of the V
rigidity coefficient; n - potential energy of a deformable elastic support.
From the accepted interaction condition:
V = — i c1xdx + i—x 3dx y \m0 0V
where, a - is the maximum value of the deformation.
(2)
According to the studies [2-4], with the nonlinear rigidity of the elastic element of a single-mass oscillatory system under conditions from up x = 0 to x = a oscillations,
, n t = 4j- •a a
1-1 j
dÇ
(3)
where, a and n - constant, n —1,2...,; % = X / a, with a restoring force equal to ax2"-1.
In vibrational systems with nonlinear rigidity of the elastic element, there is a definite relationship between the period and the amplitude. For this reason, the term "natural frequency" is also avoided for such systems, since the frequency of free oscillations ceases to be an intrinsic parameter of the system. In this case, the recovering force c 1x + — x3 and therefore in (3) the value takes n the values 1 and 2. Then the period of oscillation of the grate on the elastic support with nonlinear rigidity is determined from the expression:
t = 4y[m
1 d%
(4)
where, ^ - coefficient taking into account the nonlinearity of the elastic characteristic, m2.
In the expression (3) obtained, we integrate the terms in parenthesis, while the second term is computed (integrated) by means of tables of special functions according to [3-5] and we obtain
= 4\fm
, „„ 1 1,8541 6,28 - + '
vci ac22 / v
(5)
2n
+
Section 15. Technical science
For the frequency of free oscillations, taking p2 = 2n /T we have:
Pi =■
0,25a-sJc1c2 / ^
(6)
Vm(2na^lc2 / ^ +1,85y[c~i
An analysis of the derived formula (6) shows that the natural oscillation frequency does not decrease linearly with the increase in the reduced mass of the grate with cotton.
With increasing amplitude of oscillations and stiffness coefficients c and c2, the frequency of natural oscillations changes in a nonlinear relationship.
It is important to ensure the oscillation of the grate in the up to the resonance zone, since the natural frequency of the grate oscillation also varies depending on the values of the reduced mass, the amplitude and also the nonlinear rigid
characteristic of the elastic support. At numerical calculations for initial parameters are accepted: m = 3,8 -4,2kg; c1 = 2,5 -104 H/ m; c2 = 1,2 -10-4H/ m; ix = (0,5 -1,0)m2; a = (1,0 -1,2) • 10-3 m Figure 1 shows the graphical dependences of the change in the relative value of the natural frequency of the grate oscillations from an increase in its reduced mass. Analysis of the graphs shows that the relative value of the natural frequency with increasing the reduced mass of the grate decreases according to a nonlinear regularity. The magnitude of the amplitude (deformation of the elastic support) does not actually affect this regularity, that is, an increase in the amplitude leads to a parallel upward shift in the regularity curve with a difference pk / pH = 0,25 — 0,05 (with increasing a from ot 0,8 -10-3 m to 1,2 -10-3 m).
where, 1-for a = 0,8 -10-3 m ; 2-for a = 1,0 • 10-3 m ; 3-for a = 1,2 • 10-3 m
Figure 1. Graphical dependencies changed relative values the natural frequency of the grate oscillation from an increase in its reduced mass
In the process of cleaning the cotton (or cleaning zone) from a large litter with a saw tooth drum, captured volutes are dragged through the grate bars. In this case, each grate is cyclically interacted with the volatilization of raw cotton. That is, the load on the part of the volutes is a disturbing force of the forced vibrations of polyhedral grates on elastic supports with nonlinear stiffness (variable thickness of the rubber bushing).
From the analysis of experimental data and processing by mathematical statistics it was determined the mathematical expectation of the perturbation force from cotton to grate and its possible variations in both frequency and amplitude.
As a result of the implementation of the mathematical model of the vibrating system of the grate of cotton cleaner from a large litter with variations in parameters, graphic dependencies were obtained.
Therefore, to ensure the necessary vibration amplitudes of polyhedral grates, it is advisable to choose resistance from raw cotton within (25^35) N, which correspond (5,0^7,0) T / h in a cotton cleaning machine UHK.
Based on the results of the full-factor experiment, the optimal values for the parameters of the large-scale cleaning zone were recommended. Comparative tests were conducted in production conditions. During testing, the recommended grate design with polyhedral grates on elastic supports showed high reliability and stability of operation. The results of the tests showed that the cleaning effect increases by an average of10.11%, compared with the existing version of the grate, the mechanical damage of seeds decreases by 1.21%, the free fiber in raw cotton decreases by a factor of 0.23%. This is explained by the fact that when raw cotton is interacted with a vibro-in-sulated multi-faceted grate, raw cotton is additionally shaken.
Conclusions. Vibrating polyhedral grates on elastic supports of the fibrous material cleaner are recommended. On the basis of theoretical studies, regularities of the grate oscillation are obtained, graphic dependences of parameters are
constructed, the best parameters are proved on the basis of their analysis. 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 p.
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.
