Volume 8
Issue 2
Agricultural Engineering
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
Available Online: http://www.ejpau.media.pl/volume8/issue2/art03.html
A STUDY USING A MULTIVARIATE ANALYSIS ON THE MACRO AND MICRODAMAGE OF GRAIN IN A THREEDRUM THRESHINGSEPARATING SET
Andrzej Kornacki
Chair of Applications of Mathematics,
Agricultural University of Lublin, Poland
The paper examined the macro and microdamage of grain occurring in the course of the threshing and separating of grain in a combine harvester. Results of the experiment conducted on a stand with a threedrum threshingseparating set in the threshing of wheat, rye and barley were analyzed. Because macro and microdamages are strongly interrelated, studying them separately does not give the proper picture of the situation. A multivariate variance analysis (MANOVA) is an adequate instrument to describe the dependent properties. The present study adopted a twovariate model of a four way cross classification with interaction. Variance analysis as well as practical conclusions resulting from the former are presented.
Key words: process of threshing and separating the grain macrodamage, microdamage, multivariate variance analysis, four way cross classification.
INTRODUCTION
Combine harvesters are now commonly used in harvesting grain crops and other cultivated plants. Multidrum threshingseparating sets are used more and more frequently. The course of the threshing and separating the grain in these sets is mainly dependent on such exploitation parameters as: angular velocity of separating drums, transfer function, the size of the slot and grain moisture [1, 8]. The effect of the work of the threshing set of a combine harvester can be measured by means of three basic indexes. These are the degree of grain separation by the concave and the losses, energy consumption for threshing and degree of grain damage [2, 6]. The grain from the moving grain mass in the working slot is subjected to different quasistatic and dynamic loads. These loads have both positive, such as grain separation from the spike, and negative consequences. The main negative effect of the loads is mechanical damage. It lowers the biological value of the grain [4, 5]. The size of the damage is especially important in the harvest of seeds for the sowing material.
In practice, both macrodamage and microdamage occur in the course of threshing and separating the grain. So far, authors analyzed the effect of exploitation parameters on macrodamage and microdamage separately. This is not the proper procedure. Both kinds of damage are strongly interdependent [14]. In order to consider the correlation of the damage a multivariate variance analysis should be carried out, which follows from the fact that the conclusions from a lot of onedimensional analyses do not overlap the results from one, multivariate analysis. It may even happen that the properties that are studied individually do not show any level of significance and hence they are mot often ignored in a traditional onevariant variance analysis. However, in a multidimensional scheme they carry a great informative power [13].
The purpose of the present paper is to study the damage of the grain taking place during the threshing of wheat, rye and barley in a threedrum threshingseparating set at different levels of transfer function, the slot size, angular velocity of the separating drums and the grain moisture, taking into consideration a multivariate analysis.
METHODS
In view of considerable interest [9, 11] on the part of constructors and scientists in multidrum threshingseparating sets, a special research stand was constructed at the Chair of Agricultural Machines at the Agricultural University of Lublin. There a threedrum threshingseparating device was studied during the threshing of wheat, rye and barley.
The scheme of submitting the cereal mass consisted of a belttype level conveyor and a sloping chainboard conveyor. Thanks to the use of a nograduation chainshim conveyor it was possible to change the linear velocity smoothly (from 0.8 to 1.6 m.s^{1}) of the level conveyor. This allowed for different ranges of transfer function. The experiment made use of the following levels of transfer function: 2.5, 4.0, 5.5, 7.0 kg.s^{1}. The slanting conveyor was a typical construction used in Polish combine harvesters.
The experiment used a traditional flail threshing set of the combine harvester "Bizon". The width of the threshingmachine was 1.0 m, and the diameter of the threshing drum was 0.6 m. Because of construction respects, the angle of the drum fastening by the concave was reduced to 95°. The angular velocity of the threshing drum was constant and it was 96.6 radian.s^{1}. There was a possibility of regulating the threshing slot within the range from 15 to 32 mm at the inlet and from 9 to 20 mm at the outlet.
The separating set consisted of eight sections. Each section was made up of a drum with separating boards and a modified concave with a constant division of boards and rods. The experiment used three sizes of the working slot: 10, 25, 40 mm. Three rotary velocities were used at each of the slots, namely 53, 78, 103 radian.s^{1}. Channels catching the separated grain were situated under each section. The studies were conducted for three levels of relative moisture levels of the grain.
The experiment measured the size of the macro and microdamage of the grain [3]. The macrodamage is the kind of damage seen with a naked eye. Samples of 100 g of grain were taken (5 replications) and then they were manually separated and the damaged grain was weighed. The microdamage is the kind of damage that cannot be seen with a naked eye. In the experiment samples of 100 grains (5 replications) were taken, which were next washed in 1% Lugol liquid. The damaged grains were coloured brown. After counting the damage, the results were provided in percentages.
A multivariate analysis of variance is used in order to estimate the effect of the exploitation parameters: transfer function, the size of the working slot, the angular velocity of the separating drums and the grain moisture, on the size of the damage. This is the method of mathematical statistics making it possible to evaluate the significance of the effect of the considered factors on a few properties measured simultaneously [10, 12]. Moreover, interactions of any category can be studied in this analysis.
The model of observations for which we use the multivariate analysis of variance has the following form:
(1) 
where U is n×p matrix of n observations of p properties, X n×qmattrix of the experimental plan of the order f, B if q×p matrix of parameters, while E is the matrix of errors. The general linear hypothesis has the following shape in the multidimensional case:
(2) 
and the alternative hypothesis
(3) 
where matrix C g×q has the order of g and M p×u has the order of u.
Verification of hypothesis (2) is most frequently performed using Wilks´ test Λ [10]. The test statistics has the following form:
(4) 
where H and E mean the matrixes of the sum of square numbers and the products correspondingly for the hypothesis and for the error, while the mark M defines the determinant of matrix M. The present paper uses Rao test. The test function of this test has the following form:
(5) 
where:
(6) 
With the veracity of hypothesis (2) function (5) has approximately distribution F with gu and (m´s´21´) of freedom degrees.
A model of four way cross classification
The study uses a twovariate model of a four way cross classification. In our case: factor A is the angular velocity of the separating drums (radian.s^{1}), factor B  working slot (mm), factor C  transfer function (kg s^{1}) and factor D  grain moisture (%). Macroand microdamage of the grain perform the function of properties. The applied model has the following form:
(7) 
In this model y_{ijklmh} means observation of m^{th} replication of h^{th} damage (macro or micro) for i^{th} angular velocity of separating drums, j^{th } slot, k^{th} transfer function and l^{th} grain moisture; where:
Besides u_{h} means the mean value of h^{th} damage, α_{ih}  the effect of the influence of i^{th} angular velocity on h^{th} damage, δ_{lh}  the effect of the influence of l^{th} grain moisture on h^{th} damage, (αβ)_{ijh}  interactive effect of the influence of i^{th} angular velocity with j^{th} slot on h^{th} damage, (βχδ)_{jklh}  interactive effect of the influence of j^{th} slot with k^{th} transfer function and l^{th} moisture on h^{th} damage, while (εβχδ)_{ijklh}  the interactive effect of the influence of i^{th} angular velocity with j^{th} slot z, k^{th } transfer function and l^{th} moisture on h^{th} damage.
The matrix notation of this model, the forms of the operators of projection and the matrix notation of hypotheses are described in greater detail in the author´s previous paper [7].
RESULTS AND DISCUSSION
The theory presented in the former chapters is based on the results achieved during the threshing of wheat, rye and barley in a threedrum threshingseparating set. The data concerning the macro and microdamage of drain that took place during the threshing can be found in the paper [3]. The present paper made use of a twovariate analysis of variance. Statistics Rao in the notation (5) was applied to test the significance of particular effects. In order to guarantee the fulfillment of assumptions required in the analysis of variance in reference to the results of microdamage, transformation arcsin stabilizing the variance was used. The final effect of the applied statistical method is presented in tables 13.
Table 1. A multivariate analysis of variance for macro and microdamage of wheat grain in a threedrum threshingseparating set 
Source of transfer function 
ω  angular velocity, c  working slot, Q  transfer function, w  grain moisture 

effect 
RaoF^{0 }test function 
degrees of freedom 
degrees of freedom 
P(F>F^{0}) 
significance 
ω 
272.5282 
4 
286 
0.000000 
* 
c 
583.0890 
2 
143 
0.000000 
* 
Q 
486.2067 
6 
286 
0.000000 
* 
w 
154.9669 
4 
286 
0.000000 
* 
ωc 
0.7079 
4 
286 
0.587085 

ωQ 
16.4819 
12 
286 
0.000000 
* 
cQ 
2.5164 
6 
286 
0.021742 
* 
ωw 
3.2257 
8 
286 
0.001577 
* 
cw 
2.5986 
4 
286 
0.036487 

Qw 
11.5827 
12 
286 
0.000000 
* 
ωcQ 
6.5568 
12 
286 
0.000000 
* 
ωcw 
0.2294 
8 
286 
0.985315 

ωQw 
3.6929 
24 
286 
0.000000 
* 
cQw 
0.9442 
12 
286 
0.503006 

ωcQw 
1.3346 
24 
286 
0.139656 
Table 2. A multivariate analysis of variance for macro and microdamage of rye grain in a threedrum threshingseparating set 
Source of variability 
ω  angular velocity, c  working slot, Q  transfer function, w  grain moisture 

effect 
RaoF^{0 }test function 
degrees of freedom 
degrees of freedom 
P(F>F^{0}) 
significance 
ω 
607.960 
4 
286 
0.000000 
* 
C 
2433.522 
2 
143 
0.000000 
* 
Q 
622.005 
6 
286 
0.000000 
* 
w 
326.385 
4 
286 
0.000000 
* 
ωc 
30.721 
4 
286 
0.000000 
* 
ωQ 
44.891 
12 
286 
0.000000 
* 
cQ 
7.685 
6 
286 
0.000000 
* 
ωw 
14.065 
8 
286 
0.000000 
* 
cw 
9.669 
4 
286 
0.000000 
* 
Qw 
79.554 
12 
286 
0.000000 
* 
ωcQ 
8.151 
12 
286 
0.000000 
* 
ωcw 
9.510 
8 
286 
0.000000 
* 
ωQw 
27.684 
24 
286 
0.000000 
* 
cQw 
33.148 
12 
286 
0.000000 
* 
ωcQw 
11.502 
24 
286 
0.000000 
* 
Table 3. A multivariate analysis of variance for macro and microdamage of barley grain in a threedrum threshingseparating set 
Source of variability 
ω  angular velocity, c  working slot, Q  transfer function, w  grain moisture 

effect 
RaoF^{0 }test function 
degrees of freedom 
degrees of freedom 
P(F>F^{0}) 
significance 
ω 
17.86908 
4 
286 
0.000000 
* 
c 
10.13214 
2 
143 
0.000077 
* 
Q 
19.90301 
6 
286 
0.000000 
* 
w 
5.63182 
4 
286 
0.000224 
* 
ω c 
0.66647 
4 
286 
0.615744 

ωQ 
0.87473 
12 
286 
0.573258 

cQ 
1.51394 
6 
286 
0.173319 

ωw 
1.43258 
8 
286 
0.182432 

cw 
1.95790 
4 
286 
0.101048 

Qw 
1.78261 
12 
286 
0.050583 

ωcQ 
1.33569 
12 
286 
0.197472 

ωcw 
0.73901 
8 
286 
0.656986 

ωQw 
1.07600 
24 
286 
0.370592 

cQw 
1.02374 
12 
286 
0.426834 

ωcQw 
1.72176 
24 
286 
0.021106 
* 
The mark^{*} in the last column of the tables means the significance of a given effect 
Analyzing the data from tables 13 of the variance analysis we state that all the considered exploitation parameters, namely angular velocity of the separating drums, the size of the slot, transfer function and grain moisture have a significant effect on the macro and microdamage of the grain. Such a conclusion is correct for all the studied species of cereals: wheat, rye and barley. It is confirmed in the numbers from the last but one column of tables 13. If a factor significantly affects the size of the damage, then the corresponding probability contained in this column is smaller than the assumed level of significance α = 0.01. In the present experiment these probabilities are for all factors smaller than 10^{3}.
The factors considered in the experiment in various degrees affect the macro and microdamage of the grain. This is testified to by the values of the test function Rao in tables 13.
In the case of wheat, a considerable influence on the damage is exerted by the transfer function and the working slot  the values of the test function Rao range between 486 and 583. The damage is much less affected by the grain moisture and the angular velocity of the separating drums  the test function Rao has the values from 155 to 273.
For rye, the greatest influence on the damage is exerted by the working slot, transfer function and the angular velocity of separating drums. For these factors test function Rao has the values between 608 and 2434. The effect of grain moisture is much smaller with the value of Rao function of about 326.
For barley, the greatest influence on the damage is exerted by transfer function and angular velocity of separating drums. For those factors test function Rao has the values ranging from about 18 to 20. Grain moisture and the size of the working slot have a smaller effect on the damage  the values of Rao function range from 5.6 to about 10.
For rye and wheat the values of test function Rao are of 100600 (and even 2400 at the slot), while for barley they are of 520. It means that wheat and rye grains are much more susceptible to damage than the grain of barley.
Table 4. A multivariate analysis of ariance for macro and microdamage of wheat grain in an eightdrum threshingseparating set 
Source of variability 
ω  angular velocity, c  working slot, Q  transfer function, w  grain moisture 

effect 
Rao F^{0 }test function Rao 
degrees of freedom 
degrees of freedom 
P(F>F^{0}) 
significance 
ω 
797.989 
4 
286 
0.000000 
* 
c 
455.160 
2 
143 
0.000000 
* 
Q 
1376.369 
6 
286 
0.000000 
* 
w 
848.44 
4 
286 
0.000000 
* 
ωc 
5.286 
4 
286 
0.000403 
* 
ωQ 
42.340 
12 
286 
0.000000 
* 
cQ 
9.207 
6 
286 
0.000000 
* 
ωw 
25.428 
8 
286 
0.000000 
* 
cw 
0.260 
4 
286 
0.903182 

Qw 
40.102 
12 
286 
0.000000 
* 
ωcQ 
3.782 
12 
286 
0.000000 
* 
ωcw 
6.497 
8 
286 
0.000000 
* 
ωQw 
10.589 
24 
286 
0.000000 
* 
cQw 
5.192 
12 
286 
0.000000 
* 
ωcQw 
4.456 
24 
286 
0.000000 
* 
The damage is considerably determined by the number of separating drums of the threshing set. Such a conclusion is arrived at when we compare the values of test function Rao for a threedrum set (table 1) and an eightdrum set (table 4) [7]. For a threedrum set the test function is of 155283, while for an eightdrum one it is of 4551376. This means that wheat damage in an eightdrum set is clearly greater than in a threedrum set.
CONCLUSIONS
The analysis showed that all the considered factors, namely angular velocity of the separating drums, the size of the working slot, grain moisture and transfer function of a threedrum threshing set affect the macro and microdamage of the grain occurring during the threshing process. This conclusion is correct for all the studied species of cereals: wheat, rye and barley.
The smallest influence on the damage during the threshing is exerted by grain moisture. This was stated for all the examined cereal species: wheat, rye and barley.
The grain of rye and wheat turned out to be the most sensitive to the damage, while barley grain proved to be the most damage resistant.
Grain damage increases together with the number of the drums in the threshing set.
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Andrzej Kornacki
Chair of Applications of Mathematics,
Agricultural University of Lublin, Poland
13. Akademicka Street, 20950 Lublin, Poland
phone: (+ 48 81) 4456010
email: akornac@ursus.ar.lublin.pl
Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed 'Discussions' and hyperlinked to the article.