STATISTICAL MODEL FOR CALCULATION OF MASS, POWER AND TRACTION CHARACTERISTICS OF AGRICULTURAL TRACTORS

全文:

introduction
Currently, the share of tractors powered by wheeled (CD) and tracked (D) engines is 50% of the total number of agricultural machines (Fig. 1), because the tractor is the main machine for a significant number of technological operations. It turned out that the market for tracked propulsion is 9 times smaller than that for wheeled propulsion. The low applicability of agricultural tractors with HD is due to the fact that they are effective only for arable work, in other cases they cannot compete with wheeled tractors (Fig. 2, a) according to the following criteria: The cost of operation, maintainability, speed, maneuverability, etc. However, tracked tractors (Fig. 2, b) have high cross-country ability, that is, high quality of interaction with the support surface and at the same time low specific pressure on the ground, which allows tractors to be used on low-bearing soils and on a snowy base.

An adjacent structure is also highlighted – a wheeled-tracked propulsion system (Fig. 2, c). As a rule, the wheel arrangement of propellers is 4x4 and sometimes includes paired wheels. The crawler propulsion scheme can be either consisting of two longitudinal crawler modules or four modules (4x4). The types of propellers are described in detail in [1]. After analyzing the tractor equipment of all major global manufacturers, it turned out that the wheeled and tracked propulsion is present only on combine harvesters or other latrines. All the listed leading tractor models have standard types of propulsion.

The introduction of digital and intelligent systems into agro-industrial production requires a new approach to agricultural activities. Agricultural tractors should be equipped with autonomous operation technology, which will allow the owl to work without a human operator of the machine tractor unit (MTA), that is, to be operated around the clock. At the same time, the design of the autonomous mobile complex (AMC) should allow it to function in all-weather conditions. 
Accordingly, the design of such AMCs must be approached at a fundamental level, taking into account the natural and climatic features of the operating area. At the same time, the AMK chassis must be designed to be the most versatile and adaptive. The versatility of the chassis means the use of CD and HD on the same chassis with the possibility of replacing the propellers. The concept of adaptability has the following meaning: the chassis is capable of adapting to variable physical and mechanical parameters of the driving surface and traction mode. 
The purpose of this work is to obtain mathematical relationships between the mass, power and traction characteristics of existing agricultural tractors in order to develop a statistical model for the selection of primary technical and structural parameters of agricultural machinery.

1. METHODOLOGY FOR COMPILING A STATISTICAL ANALYSIS MODEL
The essence of statistical analysis is to find an adequate mathematical pattern between independent parameters: technical and structural. The study [1] has already provided a statistical model for selecting the primary parameters of tracked vehicles, but it is quite generalized, since it does not take into account the specifics of the work of agricultural tracked tractors. So, unlike the study [1], we do not determine the dependencies related to speed and load capacity, since they are not significant for agricultural tractors. The most important is the amount of traction resistance on the hook, since the degree of interaction of the propulsor with the moving surface depends on it. 
The statistical analysis model is to obtain a linear regression equation and determine its adequacy using the confidence coefficient R2. To compile the model itself, it is necessary to form a sample of technical and structural parameters, between which a mathematical relationship is determined.
Compiling a sample of agricultural tractors is a laborious task, since the agricultural machinery market is represented by a large number of brands, and leading tractor manufacturers have a wide range of models. At the same time, tractors are equipped with energy carriers with different traction and power characteristics. Sampling can be carried out according to the State Standard 27021-86 [2], dividing all tractors by traction classes. However, this approach is not effective, since most of the popular wheeled and tracked tractors are in higher classes or are not included in them. Secondly, compiling a selection of tractors for each class will not give us an objective statistical model in terms of its involvement in production. This can be explained by the fact that the tractor's traction and power capabilities can be used in different ways, for example, a tractor with a traction force of 40-50 kN is designed to perform tillage, but at the same time it can be used both in sowing, harvesting, and auxiliary work with lower traction costs. In this case, the design of the tractor chassis can be either 4x2 or 4x4. Based on the above, we decided to compile a statistical model of tractors based on the technological operation of tractors, taking into account the wheel formula: universal (4x2), universal-row (4x4) and row tractors (4x4). A statistical model of tractors for GD will be compiled separately. It should be noted right away that they are used only for energy-intensive work. Thus, each group consists of twenty tractors with different traction and power characteristics (Table 1).

The data processing procedure was limited to the establishment of mathematical dependencies between the structural and technical parameters of the chassis. The fundamental technical parameter is the traction resistance on the hook, which is formed when moving the trailer unit during interaction with the ground. In particular, traction resistance affects the adhesion of the propulsion system to the trackbed. Examining the process of forming traction resistance on a hook, three types of interaction between the unit and the soil can be distinguished: 1) interaction of cutting elements of tillage units and soil; 2) the interaction of the seeder coulters and the soil; 3) the interaction of the wheel and the soil. These types of interactions are listed in the direction of reducing traction resistance, since the interaction with the soil occurs at different depths with different hardness. Therefore, the highest resistance value is formed during mechanical processing of the soil by the cutting elements of the plow, and the lowest value is formed when the wheel is rolling on the bearing surface. In addition, the following factors influence the interaction process, which can be grouped into groups: 1) physical and mechanical characteristics of the soil (humidity, density, modulus of deformation, etc.); 2) terrain (plain, hilly terrain, mountainous terrain, etc.); 3) agrotechnological requirements (speed of movement, method of movement according to the site, the design of the unit, etc.). In view of all this, it was decided to build on the tractor's developed traction force, since aggregation with one device or another implies the tractor's traction capabilities. Based on all of the above, we must determine the relationship between the traction resistance on the hook, the gross weight, the power of the internal combustion engine and other specific characteristics of the chassis necessary for the selection of the initial parameters of the AMP.

2. OBTAINING A STATISTICAL ANALYSIS MODEL
Based on the analysis and processing of the parameters of the main characteristics of tractors on CD, graphs were obtained (Figure 3-6) and the following regression equations (Table 2.3).

Since an agricultural tractor acts as a traction and pushing system in many operations, the main parameter is the traction force on the hook. Trailed agricultural machines and aggregates generate large resistance forces during operation, and the tractor's energy carrier must develop the power necessary to overcome them. It is known that the power flow from the energy carrier is distributed among the chassis elements, but for agricultural tractors there is a concept of "useful power" [10], which is distributed to the power take-off shaft (PTO) and the coupling device. Since a part of the developed power is spent on developing the required traction force, there is already a well-known mathematical pattern between them, therefore it is necessary to determine the relationship between the unobvious characteristics of the MT. Graphic information is an important part of the research (Fig.3-6), as it gives an idea of the nature of the relationship.

3. RESULTS OF STATISTICAL MODELING OF AGRICULTURAL TRACTORS
An analysis of the technical and structural parameters of agricultural tractors shows that there is some mathematical pattern between them, discovered using graphs. The results for each graph report the following:
1. The following results were obtained between the tractor's traction force and its gross weight: with increasing traction, the tractor's weight increases, except for the 4x2 class of universal tractors. A large number of wheeled tractors are represented in the range of traction from 20 to 50 kN, and the gross weight is 7-8 tons. Tractors on HD have the highest gross weight density from 15 to 20 tons, with a traction range from 50 to 75 kN.
2. The total mass – engine power relationship shows a similar growth trend of one parameter following the second; a more detailed analysis shows that most tractors on CD with a mass of 7-8 tons are in the power range up to 300 kW. For tractors on CD with the same weights, the power ranges from 300 to 400 kW.
3. For the same weights of tractors on CD, the specific engine power is mainly in the range of up to 40 kW/t, for tractors on HD - 20 kW/t.
4. The graph total tractor weight – specific ground pressure shows a downward trend: with an increase in the mass of wheeled tractors, the specific ground pressure decreases to 60 kPa/t with a mass of 10 tons, and for tracked tractors, on the contrary, there is a slight increase from 38 kPa/t to 42 kPa/t with an increase in weight from 15 tons. up to 27 tons .

conclusion
The statistical model shows that analytical dependencies can be identified between the technical and structural parameters of agricultural transport and technological machines. The obtained dependencies make it possible to select the initial parameters of the AMC in such a way that the TTM could at least compete with traditional types of chassis, and at most could function around the clock in all-weather conditions. Of course, this study establishes the relationship between the parameters of traditional chassis schemes, but at the same time presents a concept for building the same model between specialized TTMS, of which there are a sufficient number in agricultural production, for example, gantry and low-clearance tractors.

作者简介

Sergey Zhukov

State Budgetary Educational Institution of Higher Education ‘Nizhny Novgorod State University of Engineering and Economics’

Email: ser-9.02.94@yandex.ru
ORCID iD: 0000-0002-8090-5461

Senior Lecturer, Department of Mathematics and Computer Science 

俄罗斯联邦

Vladimir Makarov

ФГБОУ ВО НГТУ им. Р.Е. Алексеева

Email: makvl2010@gmail.com

профессор, доктор технических наук

俄罗斯联邦

Vladimir Belyakov

ФГБОУ ВО НГТУ им. Р.Е. Алексеева

Email: nauka@nntu.ru

профессор, доктор технических наук

Anton Klushkin

Nizhny Novgorod State Technical University named after R.E. Alekseev.

编辑信件的主要联系方式.
Email: aak-nntu@ya.ru
ORCID iD: 0009-0009-3141-6029
SPIN 代码: 2266-8679

Assistant of the Building and Road Machines Department

俄罗斯联邦, г. Nizhny Novgorod, Minina str. 24, bld.1

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