A STUDY USING A MULTIVARIATE ANALYSIS ON THE MACRO- AND MICRO-DAMAGE OF GRAIN IN A THREE-DRUM THRESHING-SEPARATING SET

Andrzej Kornacki
Chair of Applications of Mathematics, Agricultural University of Lublin, Poland

ABSTRACT

The paper examined the macro- and micro-damage 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 three-drum threshing-separating set in the threshing of wheat, rye and barley were analyzed. Because macro- and micro-damages 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 two-variate 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 macro-damage, micro-damage, multivariate variance analysis, four way cross classification.

INTRODUCTION

Combine harvesters are now commonly used in harvesting grain crops and other cultivated plants. Multi-drum threshing-separating 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 quasi-static 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 macro-damage and micro-damage occur in the course of threshing and separating the grain. So far, authors analyzed the effect of exploitation parameters on macro-damage and micro-damage separately. This is not the proper procedure. Both kinds of damage are strongly inter-dependent [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 one-dimensional 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 one-variant variance analysis. However, in a multi-dimensional 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 three-drum threshing-separating 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 multi-drum threshing-separating sets, a special research stand was constructed at the Chair of Agricultural Machines at the Agricultural University of Lublin. There a three-drum threshing-separating device was studied during the threshing of wheat, rye and barley.

The scheme of submitting the cereal mass consisted of a belt-type level conveyor and a sloping chain-board conveyor. Thanks to the use of a no-graduation chain-shim 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 threshing-machine 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 micro-damage of the grain [3]. The macro-damage 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 micro-damage 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×q-mattrix 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 two-variate 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 (%). Macro-and micro-damage 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 three-drum threshing-separating set. The data concerning the macro- and micro-damage of drain that took place during the threshing can be found in the paper [3]. The present paper made use of a two-variate 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 micro-damage, transformation arcsin stabilizing the variance was used. The final effect of the applied statistical method is presented in tables 1-3.

Analyzing the data from tables 1-3 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 micro-damage 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 1-3. 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 micro-damage of the grain. This is testified to by the values of the test function Rao in tables 1-3.

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 100-600 (and even 2400 at the slot), while for barley they are of 5-20. It means that wheat and rye grains are much more susceptible to damage than the grain of barley.

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 three-drum set (table 1) and an eight-drum set (table 4) [7]. For a three-drum set the test function is of 155-283, while for an eight-drum one it is of 455-1376. This means that wheat damage in an eight-drum set is clearly greater than in a three-drum set.

CONCLUSIONS

1. 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 three-drum threshing set affect the macro- and micro-damage of the grain occurring during the threshing process. This conclusion is correct for all the studied species of cereals: wheat, rye and barley.

2. 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.

3. 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.

4. Grain damage increases together with the number of the drums in the threshing set.

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