Performance evaluation of the universal steerage hoe design using the Harrington’s desirability function

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Introduction
Effective agricultural production is determined primarily by the best machines [1][2][3], optimization of their parameters and operating modes [4], advanced cultivation technologies [5][6] and operation of equipment [7].It is the equipment, mainly determining costs, energy intensity, and labor efficiency.These indicators form the basis of competitiveness of agricultural producers and their survival within unstable economy.
Making the right decision in choosing machine design from among alternatives is a "tough row to hoe".According to some evaluation indicators, the selected machine may be superior to those ones, being compared, while, in others, it may be inferior to them.Therefore, a comprehensive evaluation, based on composite index, is needed.Composite index maximum value of comprehensive evaluation of each alternative machine has been taken as a criterion for assessing compared machines.
Complete soil cultivation is a necessary agricultural operation in tilling any crop [8].Its purpose is to loosen the soil surface layer to a fine-crumbly condition at a given depth, to level it, to destroy seedlings and weeds, to improve the water balance and air regime of soil, and to prevent the capillary moisture rising and its intense evaporation.For each operation, including complete cultivation, the All-Union Research Institute of Agricultural Mechanization (VIM), together with the Ministry of Agriculture of the Russian Federation, have developed initial requirements [9], which the recommended machines must satisfy.In the list of initial requirements [8][9], important place is given to the uniformity of tillage depth with deviation from the specified one of no more than ±1 cm, complete weed cutting, cultivated surface leveling with an acceptable ridge height and furrow depth of no more than 4 cm, conservation of moisture in the soil with absence of eversion of lower wet layers.In production, hoes are necessarily equipped with a train of drawbar machines for them, which level the field surface, improve crumbling, and comb out weeds on the surface to create an erosion-resistant layer.

Materials and methods
Series-produced hoes fulfill the listed requirements in different ways, which affects the work quality performed and the future harvest volume.All this determines the quality of evaluated machines, their impact on the yield, costs, and takes part in decision-making in choosing a particular machine.Such approach is especially necessary in assessing agricultural machinery that has not yet shown its advantages in production conditions, which makes it difficult to make a decision on its choice and requires new methodological approaches to assess the machine quality and to facilitate decision-making.Development of such a methodology in relation to the selection of best cultivator of the METI ULTIMA system is the goal of our work.The work has been carried out at the Kuban State Agrarian University, based on studies of the METI ULTIMA universal cultivators of the MTZ-NORTHWEST trading house [10].
The METI ULTIMA universal hoe includes 230 mm duck-foot tines (V-shaped sweeps) on an S-shaped 65x12 stand, arranged in three rows.The feature of the family of cultivators under consideration, is the complexity of composition of the machine-tractor unit (MTU) for performing works.A rod-shaped trail roller and a two-row harrow are attached to hoe's frame.This MTU composition allows not only to remove weeds, but also to level the soil after passing, reduce ridgeness, improve crumbling degree and create optimal density of compacted layer.Attachment of the tines to an S-shaped stand is as current as: it provides important advantages in cleaning the working bodies from crop residues, adhering soil and reducing working bodies resistivity.A rod-shaped trail roller, a spring harrow and a leveling bar improve soil evenness, crumbling, and weed comb-out from soil.This configuration of machines, most assuredly, contributes to its uniformity and subsequent high-quality seeding-down of cultivated crops, contributing to increase in yield.

Results and Discussions
Distinctive features of the universal steerage hoes, under consideration, are shown in Figure 1.Proposed advantages of complex aggregation of the considered METI ULTIMA hoes will contribute not only to improving the cultivation quality, compared to domestic models, but also to the combination of operations, performed in one pass of the unit, which contributes to better soil preservation, its less destruction, and lower work costs.The listed advantages should be considered in choosing the best design (Figure 2).Sequence of work, according to the proposed method, is as follows.At the first stage, based on the chosen machine designs, a certain number of partial estimated j-factors with natural units of measurement, are substantiated, and desirability scales are built, based on them, using the Harrington's function graph (Figure 3).At the second stage, the constructed desirability scales are transferred to the y' scale with dimensionless evaluation indexes.Main requirement in choosing the j-th evaluation indexes, which must be met, is the reflection of essence of the evaluated structure, i.e. each selected private index must reflect essence of the design and its mandatory impact on total effectiveness.Only in this case we will receive an objective prerequisite for making a decision.If we are talking about assessing the designs of grain seeders, for example, partial evaluation indexes of desirability scales should reflect the machine operation quality (seeding-down depth evenness, seed distribution over the feeding area, compliance with the norm of sowing seeds and fertilizers).If grain harvesters are assessed, the estimated indexes consider crop loss, energy intensity, grain crushing, productivity, operator labor comfort, costs, and whether the combine is equipped with necessary devices for high-performance and highquality work.To evaluate universal steerage hoes, we have chosen four indicators, based on the tractor engine specific power consumption, the hoe's price, its metal consumption per 1 m of the machine working width, as well as the specific energy intensity of the hoe working process.Without mathematical calculations, it is impossible to objectively evaluate the best design; a unified approach to all compared machines and a general indicator of a comprehensive design assessment, are needed.Figure 3 presents the estimated indexes, their units of measurement, formulas for calculating the composite index of comprehensive assessment, as well as the relationship of the estimated indexes with the desirability dimensionless scale and the curve of desirability indicators d ij .
Particular evaluative j-th indexes are placed on their scales in the interval 0-4 on the dimensionless scale y'.Quality of the analyzed structure is assessed by the d ij quality index, using the Harrington's scale (Figure 3): it is excellent in the curve interval from 0.8 to 1, good in the interval 0.6 -0.8, satisfactory in the curve interval 0.37 -0.6 and less than satisfactory in the curve interval below 0.37.dj -the desirability of each j-th estimated index of i-constructions; y' -the scale of dimensionless j-th estimated indexes of i-constructions; N -the tractor engine specific power for working with construction, kW/m; C -the construction unit cost, ths.rub./m;W -the specific construction weight, kg/m; E -the specific energy intensity of construction work process, MJ/ha; For example, in evaluating universal steerage hoes, we will analyze the fourth evaluation index -the specific energy intensity E of the operation process for each of the five hoes (Table 1).
In order of priority for the analyzed machines, this indicator has had its values respectively: 67.5 MJ/ha; 66.7 MJ/ha; 74.0 MJ/ha; 77.8 and 90.9 MJ/ha.Translation of these data to the y' dimensionless scale and then to the intersection with the desirability scale the d ij functions (Figure 3) determined the following values of the latter, respectively, 0.66; 0.68; 0.4; 0.38; 0.37 (Table 2).The highest index of the process energy intensity has been obtained for the hoe (90.9 MJ/ha) that corresponds to the minimum value of the desirability function (d ij =0.37).This indicator is used in the calculations of the composite index of a comprehensive evaluation of the D i construction.However, other j partial evaluation indexes for the last hoe are preferable to other machines.High power-to-weight ratio (21.45 kW/m), low unit price (195.8ths.rub./m), and metal consumption (537.5 kg/m) made it possible to give preference in terms of the overall comprehensive evaluation index to the METI ULTIMA 15000 wide-span universal steerage hoe.
What particular evaluation indexes provided the advantage of the best construction of universal steerage hoe?According to the data in the Table 1, it can be assumed that this is the tractor engine specific power that aggregates the hoe, and its low specific cost.More clear idea of the advantages of evaluation indexes is given by the desirability function d ij of each index (Table 2) and its weighting factor (Table 1).For the best design (METI ULTIMA 15000 cultivator), the maximum value of the desirability function first two values and the high weighting factor of the second index provided it with priority, and even the highest weighting factor of the fourth index (process energy intensity) could not raise the level of the composite index of the comprehensive evaluation.
Table 3 shows the composite indexes for evaluation of cultivators.Analysis of the data obtained, emphasizes the advantage of the METI ULTIMA 15000 wide-span universal steerage hoe, which should be given preference to.Decision to select the best hoe from the alternatives has been made, based on the maximum value of the composite index of the complex evaluation D i (Table 3).This indicator has the greatest significance with both consideration of the evaluation indicator weighting (D i = 0.86) and without consideration of it (D i =0.59) for the METI ULTIMA 15000 cultivator.Specifically, using this machine in agricultural enterprise, the greatest useful effect will be given by it.Advantages of the latter cultivator are obtained due to its high performance (Table 4), low machine unit price and metal consumption.Calculations of technic-economic indicators have been performed for the MTU operating speed of 8 km/h.They clearly confirm the effectiveness of the selected METI ULTIMA 15000 universal cultivator.Compared with the first machine, the MTU performance increases by 2.5 times, with the second -by 2.1, with the third -by 1.9 and with the fourth -by 1.5 times.Also, great benefits have been obtained by reducing labor costs (Table 4).Compared to the list of cultivators studied, they are reduced by 3, by 2.6 times, by 2.3 times and by 1.9 times, respectively.This increase in performance will ensure work timely completion, observing optimal deadlines, which will also help reduce production costs and increase yield.The use of a wide-span hoe with a folding frame (Eurofolding) allows this MTU composition to perform work not only in one's own agricultural enterprise, but also to help neighboring ones with insufficient technical equipment [12].

Conclusions
Proposed decision-making technique for selecting the best universal cultivator showed the possibility of its application, using the Harrington's desirability function.It can also be used to select machines for other purposes (sowing, harvesting, etc.) Thus, we can formulate the following stages of work for decision-making, using proposed methodology:  Justification of partial evaluation j-indexes with actual units of measurement and construction of desirability scales, using the Harrington's function graph.
 Translation of the constructed desirability scales to the y' scale with dimensionless evaluation indexes. Determination of weighting factors for partial evaluation indexes. Calculation of the desirability d ij of each particular evaluation index for each evaluated construction. Calculation of composite index of the complex assessment D i for each structure in two versions: with consideration of weighting factors of partial evaluation indexes and without consideration of them. Analysis of the results obtained and decisions made.
The high efficiency of the selected universal steerage hoe confirms the validity of our chosen solution.Performance of the priority design exceeds analogues by 1.5-2.5 times, and labor costs are reduced by 1.9-3 times.Other advantages of the design of a wide-span hoe -high maneuverability, combination of technological operations in one pass across the field, operation quality -will also contribute to its effectiveness compared to alternative cultivators.

Fig. 2 .
Fig. 2. The METI ULTIMA hoe schematic constructionDecision-making technique in choosing the best design of a universal steerage hoe is based on the use of Harrington's desirability function (Figure3)[11].It is based on calculation of a composite index of comprehensive evaluation of each design of a universal cultivator.Sequence of work, according to the proposed method, is as follows.At the first stage, based on the chosen machine designs, a certain number of partial estimated j-factors with natural units of measurement, are substantiated, and desirability scales are built, based on them, using the Harrington's function graph (Figure3).At the second stage, the constructed desirability scales are transferred to the y' scale with dimensionless evaluation indexes.Main requirement in choosing the j-th evaluation indexes, which must be met, is the reflection of essence of the evaluated structure, i.e. each selected private index must reflect essence of the design and its mandatory impact on total effectiveness.Only in this case we will receive an objective prerequisite for making a decision.If we are talking about assessing the designs of grain seeders, for example, partial evaluation indexes of desirability scales should reflect the machine operation quality (seeding-down depth evenness, seed distribution over the feeding area, compliance with the norm of sowing seeds and fertilizers).If grain harvesters are assessed, the estimated indexes consider crop loss, energy intensity, grain crushing, productivity, operator labor comfort, costs, and

Fig. 3 .
Fig. 3. Graph of the Harrington's function and the desirability scale of partial j-th evaluation indexes of the compared cultivator models.

Table 1 .
Evaluated indexes of universal steerage hoes and their weighting factors.

Table 2 .
Value of Harrington's desirability function of estimated j-indexes.

Table 3 .
Values of the composite index of comprehensive evaluation for universal steerage hoes, with consideration of the partial evaluation indicator weighting and without consideration of it.

Table 4 .
Performance of compared universal cultivators for 1 hour of principal time.