The study of controllability of motion of tractor aggregate of module type

Adamchuk V., Bulgakov V., Nadykto V., Holovach І., Prysiazhniuk D., Parakhin О. NSC «Institute of Mechanization and Electrification of Agriculture» 11 Vokzalna Str., Hlevakha township, Vasylkiv district, Kyiv oblast, 08631, Ukraine 2, National University of Life and Environmental Sciences of Ukraine 15 Heroiv Oborony Str., Kyiv, 03041, Ukraine 3, Tavria State Agrotechnological University named after Dmytro Motornyi 18 B. Khmelnytskoho Ave., Melitopol, Zaporizhzhia oblast, 72312, Ukraine Ladyzhyn College of Vinnytsia National Agrarian University 5 Petra Kravchyka Str., Ladyzhyn, Vinnytsia oblast, 24321, Ukraine e-mail: vvadamchuk@gmail.com, vbulgakov@meta.ua, volodymyr.nadykto@tsatu.edu.ua, holovach.iv@gmail.com, m09049@meta.ua, oleksandr.parakhin@tsatu.edu.ua ORCID: 0000-0003-0358-7946, 0000-0003-3445-3721, 0000-0002-1770-8297, 0000-0003-1387-4789, 0000-0002-6369-5781, 0000-0003-1972-3762


Fig. 1. Machine and tractor unit of the modular type with a five-hulled plough
The technological module of this machine and tractor unit is a separate bridge, whose wheels are driven from the synchronous power take-off shaft of the energy module (tractor). At the front of the technological module has a coupling device by means of which it is connected to the rear-mounted mechanism of the energy module, ie tractor. Coordination of circular linear speeds of the technological module wheels and rear wheels of the power module is carried out by means of the special reducer located on a frame of the technological module.
For coupling with agricultural implements, the technological module is equipped with a hydraulic attachment system, its own PTO shaft, a fifth wheel and a brake system.
The horizontal construction has an energy module for a technological module construction with vertical hinge. Its presence ensures the rotation of the technological module relative to the energy module by ± 30 о when the modular energy unit is moving on the return lane.
In the longitudinal-vertical plane, the energy module is connected to the technological module by a horizontal hinge. Thanks to it, the machine and tractor unit of the modular type can perform satisfactory copying of the longitudinal field profile.
Limited return of the energy module in the horizontal plane is provided by two hydraulic cylinders connecting the frames of the energy module and the technology module.
For oil flow from the overpiston cavity of the hydraulic cylinder into the underpiston cavity, they (cavities) are connected to each other by a hydraulic hose. However, during the testing of the modular energy unit it was found that when it moves as part of the unit on the return line, the technological module may have excessive fluctuations in the horizontal plane. As a consequence, there was a need to reduce the speed of the modular energy facility on the return field lane. And this, as we know, leads to a decrease in the productivity of the machine and tractor unit. So, increasing the controllability of a machine and tractor unit motion of modular type, consisting of an energy module (tractor) and an additional technological module is an actual scientific and technical problem.
Therefore, in order to reduce the fluctuations of the technological module in the horizontal plane and, consequently, to increase the controllability of the modular energy unit (tractor), in the hydraulic hose of one of the hydraulic cylinders connecting the energy and technological module, a throttle with a coefficient of resistance Кm = 1.03×10 6 •N•m•s•rad -1 was installed. Fig. 2 shows the connection scheme of the energy (tractor) and technological modules, which shows the installation in one of the hydraulic cylinders of the mentioned throttle.

Fig. 2. Installation diagram of the throttle in the hydraulic cylinder connecting the energy and technological modules: EM -energy module; TM -technological module; Кm -throttle, which creates a resistance coefficient
Justification of the value of this coefficient based on data obtained from field experimental studies and is the subject of research in this article.
Analysis of research and publications. Traffic controllability of machine and tractor units of modern technical level is a significant problem in the field of agricultural mechanization. Therefore, the development of conditions and technical devices ensuring controlled movement of machine and tractor units, especially arable and tilled ones, is based on scientific research and engineering developments aimed mainly at ensuring the straightness of the movement trajectory and minimizing the "side tracking", etc. These issues are particularly acute for machine and tractor units built on a modular principle. In the scientific literature questions of controllability of movement of agricultural machine-and-tractor units are given many questions [1][2][3][4][5][6][7][8][9][10][11], especially at theoretical research of planeparallel movement of units [3][4][5].
However, thorough controllability researches of movement of machine-and-tractor units of modular type at their movement on turn lanes and at transport crossings are not sanctified enough now in the literature.
The purpose of the research -to increase the controllability level of movement of the machine and tractor unit of modular type with a mounted plough by equipping one of the hydraulic cylinders connecting the power and process modules with a special throttle and scientific substantiation of the degree of its influence on the controllability of the mentioned unit.
Materials and methods of research. Experimental research of the machine and tractor unit of modular type with a mounted plough was carried out in the field on stubble after its flaking after winter wheat.
Technical characteristics of the machine and tractor unit of modular type are presented in the table. Thus preliminary before carrying out field experimental researches humidity and density of soil in layer 0...10 cm was measured, and also amplitude and frequency of fluctuations of unevenness of a field along future movement of the given machine-tractor unit.

Technical characteristics of the machine and tractor unit of modular type
Movement of this arable unit on the return lane was carried out in the same gear with an installed throttle (Кm = 1.03×10 6 •N•m•s•rad -1 ) in and out of a hydraulic cylinder (Кm = 0). The travel path of the unit was 50 m. Based on the fact that the machine was moving evenly, the speed a V of his movement was determined by this expression: where t -the time of the unit's passage of a 50 m long section.
To record the travel time of a mobile machine and tractor unit of the modular type with a plough on the return lane, an electronic stopwatch with the accuracy of the measurement ± 0.1 s was used.
In the movement process of the machine and tractor unit of modular type with the help of special equipment the rotation angle α of controlled wheels of the power module (tractor) and its course angle φ were registered.
To measure soil moisture W the electronic measuring device MG-44 (Ukraine) was used with the accuracy of measurement ± 1%. Measurement of soil density q  were carried out by our developed device according to the method [5]. The number of measurements of each parameter W and q  was no less 50.
The angle α of rotation of the controlled wheels of the energy module of the modular energy unit was recorded using an SP-3A resistor with a linear characteristic and rating of 470 Ohm. The resistor was mounted on the rotation axis of the left front wheel of the energy module.
To measure fluctuations in the longitudinal profile of the field, a special registration device was used, the element of which was an SP-3A resistor with a linear characteristic and a nominal value of 470 ohms.
The course angle φ of the energy module of the machine and tractor unit of modular type was recorded with a GY-521 gyroscope with the Arduino device (China).
Electrical signals from the gyroscope and resistors to record the angle φ, as well as fluctuations in the longitudinal profile of the field were fed to an analog-to-digital converter (Ukraine) and then to a PC. The measurement repeatability of these parameters is 3.
The following statistical characteristics, such as dispersions, as well as normalized correlation functions and spectral densities, were calculated from the data sets obtained in this case.
For the analysis of movement controllability of the machine and tractor unit of modular type with a plough at various values of throttling of the hydraulic cylinder the normalized mutual correlation function connecting fluctuations of an angle α of rotation of operated wheels of the power module with fluctuations of its rate angle φ was used.
Research results. At carrying out of experimental researches of the machine-tractor unit movement of modular type with a hinged plough on a return strip average value of humidity of soil of a field in a layer 0...10 cm was equal to 15.3%.Density of soil in the same layer did not exceed 1.24 gr•sm -3 .
The average speed for this modular arable machine and tractor unit on the return lane was 2.4 m • s -1 . The analysis of the data characterizing the fluctuations of the longitudinal field profile showed the following. The length of the correlation relation of the normalized correlation function of this process is 1 m (Fig. 3).

Fig. 3. normalized correlation function of fluctuations in the longitudinal field profile
By knowing the speed of the machine, you can easily determine the time of the correlation link. In this case, at the speed of this machine 2.4 m•s -1 it is equal: 1•(2.4) -1 = 0.42 s. It can be said that oscillations of the longitudinal field profile have almost no hidden periodic component. The information about changes in the correlation function, which takes place in Fig. 3, is not enough to determine the source of their generation.
The dispersion of oscillations of the process under consideration is equal to 0.91 sm 2 . Mostly it is concentrated in a fairly narrow range of frequencies 0…2 m -1 (Fig. 4). Taking into account the speed of this machine and tractor unit 2.4 m•s -1 this range is equal to 0…4.8 s -1 or 0…0,76 Hz.

Fig. 4. Spectral density of vibrations of the longitudinal field profile
The frequency of the spectral density cut, as can be seen from the data in Fig. 4, practically does not exceed 6 m -1 or 14.4 s -1 , which is equal to 2,3 Hz.
When the unit was moving on an agronomic background with such characteristics of longitudinal profile oscillations, the control action in the form of rotation angle α of the controlled wheels of the modular energy unit was changed in a very narrow range. Thus, the main part of the dispersion of vibrations of this parameter is concentrated in the frequency range of 0…2.0 s -1 or 0…0.32 Hz (Fig. 5).

Fig. 5. Normalized spectral density of oscillations of the rotation angle α of the modular energy unit controlled wheels
The maximum value of the normalized spectral density of oscillations of the angle α falls on a rather narrow frequency range: 0.30…0.35 s -1 . All this points to the desired low-frequency nature of the changes in the manipulated value in question.
As it turned out, the block-module unit worked out the fluctuations of the input effect differently. In the absence of throttling of the hydraulic cylinder of the technological module of the modular energy unit between the parameters α and φ a positive correlation relation was revealed. But, firstly, it is weak enough as the maximum value of the mutual correlation function does not exceed the estimate of 0.34 (curve 2, Fig. 6). Secondly, the maximum value of this function is shifted to the left of the zero coordinate by about 1 s. This means that the input of this dynamic system is not the angle α of rotation of the controlled wheels of the energy module, but its course angle φ. That is, that the control action α is a reaction to the change of the heading angle φ with time delay at 1 s.
The reason for changing the course angle φ of the modular energy unit in this case may be variations of the turning moment acting on the side of the technological module, or some other disturbances.
At the same time, the introduction of the hydraulic damper in the hydraulic cylinder of the technological module of the modular energy unit with a resistance coefficient Кm = 1.03×10 6 •N•m•s•rad -1 principally changes the behavior of the mutual correlation function  -. Moreover, both qualitatively and quantitatively (curve 1, Fig. 6).
First, the force of correlation between changes in α and φ increases sharply. In comparison with the variant Km = 0 the maximum of the mutual correlation function increases by 2.6 times, reaching the score of 0.89.
Secondly, the maximum of the evaluated function (curve 1, Fig. 6) is shifted to the right from the zero coordinate. This means that the control action (i.e. angle α) is the input, and the exchange rate angle φ of the modular energy facility is the output of the considered dynamic system.
Thirdly, the latency of the reaction of the course angle φ to the change of the control action α of the wheels of the energy module of the modular energy unit is almost reduced by half. In this case it is approximately equal to 0.51 s. Such a result is desirable, because the reaction of the dynamic system under consideration to the change of the control action should ideally be momentary. So it must be done with zero delay. But as it is impossible to reach it in practice, any constructive and technological solution aimed at reduction of reaction of a dynamic system to an input useful signal is desirable. In our case, such a solution is the installation of a throttle in the hydraulic cylinder of the technological module of the modular energy unit.

Conclusions
To increase movement controllability of the machine and tractor unit of modular type consisting of energy and technological modules, it is possible by throttling of one of hydraulic cylinders which limit mutual return of these modules among themselves in a horizontal plane.
Equipping the hydraulic cylinder of the modular energy unit with a choke with resistance coefficient at the level of 1,03×10 6 N m s rad -1 allows: -to bring the maximum value of the mutual correlation function between the control action, i.e. the angle α of rotation of the controlled wheels of the energy module of the modular energy unit, and its exchange rate angle φ to the level 0.89; -shift the maximum value of the given mutual correlation function to the right of the zero coordinate, thus providing the angle α of rotation of the controlled wheels of the energy module the role of the input (not the initial) influence; -to reduce by almost half the delay of the response of the course angle φ of the energy module to the change of the angle α of its controlled wheels.