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UDC:631.171
STUDY OF THE PROCESS OF LOADING AND LEVELING A HEAP OF ALFALFA
SEEDS ONTO A DRYER CONVEYOR
Razzakov T.Kh.
Ph.D., Associate Professor, Karshi State Technical University,
Alimova Z.Kh.
Ph.D., Professor, Tashkent State Transport University,
Karimova K.G.,
Doctor of Philosophy in Technical Sciences, Associate Professor,
Jizzakh Polytechnic Institute
Abstract:
This article presents in detail the results of a study conducted to determine the optimal
combination of factors selected to determine the minimum coefficient of unevenness of loading
and leveling of quail seed mixtures in conveyor dryers during the loading process into the dryer.
In addition, the expressions for determining the regression coefficient, calculating the Fisher and
Student tests, the results of statistical evaluation of the regression coefficient (vi), and the results
of comparing the absolute value of the regression coefficient and their confidence intervals (∆vi)
are presented.
Key words:
unevenness, magnitude, leveling, pile, dryer, factor, screening experiment, planning,
regression coefficient, criteria, optimal value, interval calibration.
Introduction:
The most important thing when drying the seed heap of forage crops in a
conveyor dryer is the uniformity of the material leveling over the entire area of the
conveyor, since the heap is distributed in a loosened layer of uniform density and thickness. The
creation of such a layer increases the efficiency of drying, reduces drying time, fuel consumption,
energy intensity of the process and increases the productivity of the dryer.
The most important thing when drying the seed heap of forage crops in a conveyor dryer is the
uniformity of the material leveling over the entire area of the conveyor, since the heap is
distributed in a loosened layer of uniform density and thickness. The creation of such a layer
increases the efficiency of drying, reduces drying time, fuel consumption, energy intensity of the
process and increases the productivity of the dryer. Since the energy costs are low when using a
finger working element to level the pile, the unevenness of the material leveling was chosen as
the optimization parameter, which largely determines the value of the economic efficiency
indicator of the proposed loader.
Materials and methods:
A comprehensive study of the technological process of the loader
involves taking into account all factors that affect the course and final results of the process
under study. The main course and final results of the process under study. The main
requirements for the set of factors under study are that they must be controlled and manageable.
After conducting a screening experiment and selecting the most significant factors to bring them
closer to the area of the optimal combination and finding the best conditions for the
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following studies, we used the method of steep ascent along the response surface, based on
movement from a certain point on the surface in the direction of the optimum [1, 2, 3].
To find the optimal combination of the selected factors with a minimum value of the unevenness
of the heap leveling on the conveyor of the dryer, an experiment was conducted, including 8
experiments, constituting a semi-replica of the full factorial experiment of type 23, and a
program of steep ascent along the response surface was also carried out. The experiment was
conducted in triplicate in a randomized order. The planning matrix for such an experiment was
constructed using a well-known method [2,3].
Results and discussions.
Based on the results of the experiment, regression coefficients were
calculated and statistically assessed based on the dependence [3].
;
1
N
У
в
N
и
и
о
=
=
;
1
N
У
x
в
N
и
и
iи
i
=
=
N
У
x
x
в
N
и
и
ij
iи
ij
=
=
1
(
)
;
)
1
(
1
1
2
2
-
-
=
=
=
m
N
У
У
S
N
и
К
i
и
iи
у
;
2
N
S
S
у
вi
=
вi
i
tS
в
±
=
D
±
where
и
У
- average value of the optimization parameter in the experiment;
N
- number of experiments (number of rows in the experiment matrix);
iи
x
,
ij
x
- values of factors in the i-th experiment;
m
- number of repetitions of one experiment (one row of the plan matrix);
iи
У
- values of the optimization criterion in parallel experiments (in the ith line);
вi
S
- squared error of the regression coefficient;
t
- tabular value
t
- criterion for the number of mean freedom,
with which it was determined
2
у
S
;
2
у
S
- variance characterizing the errors of experiments in the design matrix.
в
о
= 12,54;
в
4
= 0,84;
в
5
= +1,52;
в
8
= + 0,82;
в
45
= + 1,50;
в
48
= - 0,38;
в
58
= + 0,18;
2
у
S
= 0,6365;
LF
S
= 0,957;
вi
S
= 0,2827;
i
в
D
= ± 2,12;
0,2817 = 0,5995.
After determining the regression coefficients, their significance was checked. The data for
calculating the significance of the regression coefficients were used from the table, which
presents an algorithm for calculating the adequacy of representing the experimental results by a
first-degree polynomial.
Comparing the absolute values of the regression coefficients (вi) with the absolute value of
their confidence interval (∆вi), we come to the conclusion that not only linear effects, but also
their paired interactions have a significant impact on the optimization criterion..
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To check the adequacy of the presented experimental results, it is necessary to determine the
calculated value of the Fisher criterion using a first-degree polynomial and compare it with the
table value. The calculated value of the Fisher criterion is determined using the formula [1].
,
2
2
у
LF
p
S
S
F
=
where
LF
S
- variance of inadequacy of a mathematical model;
F
p
- Fisher's exact test.
LF
S
was determined by the formula
(
)
,
1
1
2
+
-
-
=
=
K
N
У
У
S
N
и
и
и
LF
where,
У
- theoretical value of the optimization parameter in the i-th experiment;
К - number of factors.
he tabular value of the F-criterion, equal to 5.0, was selected from tables [1] for the number of
degrees of freedom
4
1
1
=
-
-
=
m
N
f
and the number of degrees of freedom of the denominator
16
)
1
(
2
=
-
=
K
N
f
For convenience, all calculations for assessing adequacy are summarized in Appendix 12,
compiled taking into account the recommendations of [1]. Using the data from this appendix, it
is easy to establish that
LF
S
= 0,957, then
p
F
=1,504.
Table value of Fisher's criterion for 5% significance level
05
,
0
F
= 3,0 exceeds the optimal value of
this criterion, therefore the hypothesis about the adequacy of the linear model could be accepted.
However, for such a decision it is necessary to check the second criterion – the null hypothesis
[1,2,8]. For this purpose, the 9th and 10th experiments were additionally set up in the center of
the experiment. The results of calculating the average value of the optimization criterion in these
two experiments turned out to be equal У
0
= 12,51. The null hypothesis is accepted if the
difference
о
о
У
в
-
does not exceed the experimental error [1]. The variance of the experimental
error is equal to
2
у
S
= 0,6365. The significance of this difference is tested using the Student's t-
test.) [1].
(
)
106
,
0
2
=
-
=
у
о
о
расч
S
N
У
в
t
where
о
У
- average value of the optimization criterion for the experiments in the center of the
experiment.
The tabular value of the t-criterion with the number of degrees of freedom of 16 for the 0.05
significance level is 2.12, and the calculated value will be t
р
= 0,106. As a result of comparing
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the value of the t-criterion, we conclude that the difference is unreliable, the hypothesis about the
adequacy of the linear model according to the second criterion could be accepted. However, the
pairwise interaction in 45 turned out to be significant; therefore, the process under study cannot
be described by a linear model. According to [1,4,7], a linear model is not adequate if at least
one of the interaction effects turned out to be significant
Conclusion.
Based on the above, we come to the conclusion that the linear model cannot be
accepted to describe the experimental results, therefore, in further studies to study and describe
the optimum region, the linear approximation is insufficient. It is necessary to use second-order
planning, which allows one to obtain an idea of the response function using second-degree
polynomials. Before describing the process under study with a higher-order model, it is
necessary to first make a steep ascent to the optimum region, for which additional experiments
were conducted, the results of which are presented in the lower part of the matrix. The change in
the material feed rate (factor X5) was chosen as a single step, since in this case the value of the
regression coefficient has the greatest absolute value compared to others. The value of the single
step for other factors was taken proportional to the value of the adopted step of factor X5. Since
the parameters of the optimum region corresponding to the minimum value of the optimization
parameter were determined, the step process of the implementation movement with signs
replaced by the opposite ones. The experiments conducted according to the steep ascent program
showed that the zero point gave the best results, while the unevenness of the heap leveling was
9.50%, i.e. it has the lowest value. The further step process in accordance with the program leads
to an increase in the optimization parameter.
The results of the steep ascent give reason to assume that the previously selected center of the
experiment is near the optimum region.
In this regard, the center of the experiment was left the same. The validity of this conclusion is
also confirmed by the analysis of the signs and absolute values of the regression coefficients.
The interval of variation of the factors and the center of the experiment were chosen correctly,
since the absolute values of the regression coefficients for the factors are commensurable,
while two of them have the (+) sign, and one has the (-) sign.
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