Scientific and experimental substantiation of the key geometric and kinematic parameters of vibrocutting machines

The process of cutting with a blade is largely applied in technological equipment used in the agricultural production complex and is used to process raw materials with different 10 physical and mechanical properties. Nonetheless, the relation between the parameters of processing with vibroblade and the rheological properties of the processed material is insufficiently studied, while it is an important issue of practical significance. As a result of laboratory experiments, it became possible to obtain the power characteristics of vibrocutting of common reed, establish an optimal combination of factors: 15 vibration amplitude, frequency and the speed of the blade delivery to ensure the minimum vibro-cutting force. As a desirable kinematic regime, K = V Vτ , the following relation of speed of delivery and vibration speed of the toothed blade: ≅ 0.004. Introduction 20 The wide use of mechanization means of agricultural production processes, as a priority objective, is aimed at raising the agricultural production to the industrial level. For such progress, it is necessary to create a complex of machinery with high technical and economic indicators that will ensure the high quality of implementation of the required technological processes. 25 1 Head, Division of Mechanization of Field Cultivation and Livestock Breeding, arturaltunyan@gmail.com *Corresponding author 2 Principale scientist, arshaluystar@gmail.com Design of such machines and equipment should be based on new principles of intensification of technological process through developing relevant technical equipment, which will rely on more efficient working principles. Most of the tools and equipment used by man, starting from the tools of primeval period up to the latest equipment in the present day, work with the principle of Archimedean lever. 30 And we can say that only a small segment is occupied by technological equipment and devices working by the principle of vibration. Numerous theoretical and scientific and experimental studies have been carried out related to the issues of chopping and cutting of material with a blade, and a considerable experience has been gained; however, despite the urgency of the issue, vibrocutting of 35 materials as a specific and prospective version of cutting with a blade has not gained enough attention. As it is known, all phenomena in nature that take place in the micro and macro world are related to fluctuations. Therefore, it is considered that everything that moves, simultaneously performs also fluctuation (Yarullin R.B., 2007, Blekhman I.I., (1994)). In the 40 world of flactuations, mechanical flactuations have a special place, among which those fluctuations have a considerable role which have comparatively small amplitude and not so low frequency, and this is what is called vibration (Vibrations in the technology, 1978). In our days machines working by the vibration principle are largely spread, being an important factor of intensification and optimization of technological processes. The directions 45 of using vibration are really amazing both in terms of the sector, technology, and the working parameters, starting from vibro-arc fusing of renewable machine parts up to combing goat fur, and from construction vibration tool to massage of cow udders (Blekhman I.I., (2013)). In soil cultivation vibration harrows, cultivators and plows are widely known, with their working body subjected to self-excited vibrational motion (Fedorenko I.Ya., 2016, 50 Vasilenko V.V., Vasilenko S.V., Achkasova N.N., 2018, Loveykin V., Dyachenko L., 2013). As a result of the laboratory experiments carried out by the authors (Vasilenko V.V, Vasilenko S.V., Achkasova N.N., 2018) it was revealed that in case of vibration amplitude of 2...4mm and frequency of 22...24Hz, the angle of contact between the soil and the steel decreases by about 16%. In addition, it facilitates the high-quality mplementation of the 55 technological process, excluding soil sticking and accumulation of weed mass on the working body. During one of the tests, when the vibration amplitude of the working body was chosen 5mm and the frequency 8...10Hz, a 14% decrease in tractive resistance was recorded. Analysis of the results of field tests by another group of researchers (Loveykin V., Dyachenko L., 2013) has indicated that vibration has a positive impact on the decrease of 60 tractive resistance of the plow. The working bodies of vibratory plow receive vibration motion from the hydraulic vibrator. The obtained data indicate that at α = 65°9 of location angle of vibrator and at the values of ν = 33,4 Hz of vibrational frequency, the tractive resistance decreases by 54%. The authors also mention that in case of using vibratory plow, the number of small fractions increases dramatically in soil. The number of 1mm...10mm size particle 65 almost does not change, and particles that are larger than 10mm are decomposed. At the same time deviation from the set depth of tillage does not exceed the permitted limits. There are a number of machines working by the developed vibrational technological principle (Tarverdyan A.P., 2014, Vasilenko V.V., Vasilenko S.V., Achkasova N.N., 2018), soil cultivation machines used in agriculture, vibrodrills, as well as mowers, devices cutting with 70 blade, etc. However, in the theory of their dimensioning, basics of rheological modeling are not used at all or not enough attention is paid to them, and the rheology of interaction of the cultivated medium and the working body has not been taken into consideration. The design of vibration machinery to be used in agriculture and processing enterprises become difficult in practice due to a number of circumstances. 75 The first circumstance is related to the processes underway in machine working by the principle of vibration, despite the fact that those machines can be very simple in terms of their structure. The main goal of vibrational impact is to assure such a dynamic state of the cultivated medium that will boost the intensification of the technological process and the improvement of quality indicators as well as the decrease of force parameters. 80 In this case a complicated interaction between the vibration working bodies and the cultivated medium take place, with transfer of the mass, impulse and energy, etc. The second circumstance, which makes the design works difficult, is the variety and the diversity of the cultivated medium, agricultural materials and raw products and their physical-mechanical and rheological properties. This makes it difficult to establish a causal 85 relationships between the parameters of the machine’s working process and the final result indicator of its action. In different times and in different phases of development of technologies and methods, researchers claim a simple truth that is still relevent (Reznik N.Ye., 1975): “In different phases of development of the theory of cutting with blade, one of the priorities and most important 90 objectives should be seeking a method of determination of those properties of a material that have the most direct impact on the cutting process.” And, despite the critical significance of the physical-mechanical properties of the material being cut for the entire cutting process and other circumstances derived from it, while studying the sector (cutting and chopping agricultural crops and plants with thick stems, feed crushers, silage and senage crushers, food 95 industry, consumer goods manufacturing, etc.), the researchers are mostly guided by traditional methods of studying the properties of materials. This experience is nothing more than borrowing from such advanced sciences as strength of materials and material science, from where not only the methodological forms of the study but also the group of properties under research have been borrowed. As such properties, the indicators of strength and 100 decomposition in cases of deformations of compressing, tension, sliding, and bending are the most relevant ones. Academician A. Tarverdyan has attached importance to the physicochemical and anatomical-morphological properties of the material being cut, in particular, to the stem of the plant (Tarverdyan A.P., 2004), mentioning that ignoring their roles during the study of those 105 properties and the process of cutting may seriously constraint the enhancement of the productivity of mowing machines. The resistance of the working environment in the form of dry contact, and demonstration of non-Newton viscosity, slip deformation, relaxation of tensions, and thixotropic properties leads to nonlinear deferential equations that characterize the processes 110 in the vibrational technological machines, and, as a consequence, makes their estimation and analysis difficult. On the other hand, the nonlinearity is a source of numerous positive impacts and demonstrations of vibration, which are available in different technologies. With this paper, we will try to identify the impact of purely mechanical properties of 115 vibration on static forces and motions. This creates basis for further research works related to theoretical analysis of the quantitative size of the mechanical impact of vibration through modeling of rheological properties of the material with the help of different physical values. This kind of approach will obviously enable to create cutting devices that are efficient from the standpoint of intensification of technological processes and at the same time energy 120 efficient. As the results of the research have shown (Yarullin R.B., 2007), the effective values of vibration amplitude and frequency in technological equipment working by vibration principle in the food and agriculture sector do not exceed 10 mm and 300 rad sec-1 (or 47.75 Hz), respectively, except for some technological processes (Fig.1). The author offers also an 125 empirical formula that establishes a correlation between the optimal parameters of vibration. It looks as follows:


Introduction 20
The wide use of mechanization means of agricultural production processes, as a priority objective, is aimed at raising the agricultural production to the industrial level. For such progress, it is necessary to create a complex of machinery with high technical and economic indicators that will ensure the high quality of implementation of the required technological processes. The design of vibration machinery to be used in agriculture and processing enterprises become difficult in practice due to a number of circumstances. 75 The first circumstance is related to the processes underway in machine working by the principle of vibration, despite the fact that those machines can be very simple in terms of their structure. The main goal of vibrational impact is to assure such a dynamic state of the cultivated medium that will boost the intensification of the technological process and the improvement of quality indicators as well as the decrease of force parameters. 80 In this case a complicated interaction between the vibration working bodies and the cultivated medium take place, with transfer of the mass, impulse and energy, etc.
The second circumstance, which makes the design works difficult, is the variety and the diversity of the cultivated medium, agricultural materials and raw products and their physical-mechanical and rheological properties. This makes it difficult to establish a causal 85 relationships between the parameters of the machine's working process and the final result indicator of its action.
In different times and in different phases of development of technologies and methods, researchers claim a simple truth that is still relevent (Reznik N.Ye., 1975): "In different phases of development of the theory of cutting with blade, one of the priorities and most important 90 objectives should be seeking a method of determination of those properties of a material that have the most direct impact on the cutting process." And, despite the critical significance of the physical-mechanical properties of the material being cut for the entire cutting process and other circumstances derived from it, while studying the sector (cutting and chopping agricultural crops and plants with thick stems, feed crushers, silage and senage crushers, food 95 industry, consumer goods manufacturing, etc.), the researchers are mostly guided by traditional methods of studying the properties of materials. This experience is nothing more than borrowing from such advanced sciences as strength of materials and material science, from where not only the methodological forms of the study but also the group of properties under research have been borrowed. As such properties, the indicators of strength and On the other hand, the nonlinearity is a source of numerous positive impacts and demonstrations of vibration, which are available in different technologies.
With this paper, we will try to identify the impact of purely mechanical properties of This kind of approach will obviously enable to create cutting devices that are efficient from the standpoint of intensification of technological processes and at the same time energy 120 efficient.
As the results of the research have shown (Yarullin R.B., 2007), the effective values of vibration amplitude and frequency in technological equipment working by vibration principle in the food and agriculture sector do not exceed 10 mm and 300 rad sec -1 (or 47.75 Hz), respectively, except for some technological processes (Fig.1). The author offers also an 125 empirical formula that establishes a correlation between the optimal parameters of vibration.
It looks as follows: where A is the amplitude, m, and is the frequency, rad sec -1 . During the trials, two types of serrate blades were used as cutting tools (Fig.3), the 160 geometric parameters of which are provided in Table 2. Table 2 Types of blade Move of tooth: (mm) Height of tooth: ℎ (mm)  The cutting trials were done with the stems of common reed. The samples were placed in a special container prepared for scientific experiments, which allowed to provide a 10 cm cutting width of the layer of stems, trying to imitate the cutting of stems in a dense medium.

185
The relevant signals characterizing the values of the normal and tangential components of the vibrocutting force were recorded independently from each other but simultaneously.
To make the conduct of trials, data recording and processing of the results more comfortable, the levels of the factors are encoded, specifying "+1" as the upper limit and "-1" as the lower limit, and "0" as the main one. Transition from coded values to actual values is 190 performed according to the linear law: where ̃ is the actual value of the i-th level, ̃2 is the actual value of the main level of the relevant factor, d is the range of misinterpretation of the particular factor, and is the coded value of the i-th level.

195
However, it is often impossible to make a transition from the coded value of the factor to the actual value, making use of the linear equation (2), as the values of the factors change with unsteady step; in this case other approaches are applied, one of which is the analytic method. In our case, vibration amplitude is such a factor (Table 1). In this case the transition from the coded value to the actual value as well as vice versa for our example is expressed as 200 follows: The following are the values of the vibration amplitude: ̃1 = 8mm,̃2 = 10 ,̃3 = 14 .
We will obtain a linear equation: through which the initial values of the factors will be brought to a coded shape: "+1", "-1" and 215 "0".
Taking into consideration all the above mentioned transformations, we will obtain the following laws that express the linkage between the actual and coded values: ̃= + (̃2 − ) • : Inserting the obtained values of and (3.6) into the equation and taking into 220 consideration that for the case under discussion ̃2 = 10mm (the main level), to determine the actual value of the variable factor from the coded value, we will obtain the following expression: where ̃ is the actual value of the i-th level of vibration amplitude (Table 1), ̃2 is the actual value of the main level of vibration amplitude (Table 1), and 225 is the coded value of the i-th level ( Table 1).
The scientific trials were conducted in two phases, and the same plan/matrixes were composed to perform vibrcutting with a large-toothed blade in one case ( Fig. 3.a) and with a fine-toothed blade in another case ( Fig. 3.b).
The data obtained as a result of the scientific experiments were processed according to Among the square impact factors, only the vibration frequency is significant; however, its effect on the normal component is negative.
As it is seen from the equation, the factor of vibration amplitude is not part of the equation as it is not significant according to the Student's t-test.
None of the factors has a linear effect. Among the interacting efficiency factors, only the frequency-speed couple is significant. Its effect on the force value of the tangential component is positive.

310
Among the factors, only vibration frequency has a square effect, being the largest among the coefficients of the other factors, also with its absolute value. However, its effect is negative on the force value of the tangential component. should be mentioned that the obtained force parameters do not refer to the cutting of just one stem of common reed but a sheaf placed in a container (Fig. 4), where the cutting width is 10 cm (the height of the container).
During the scientific trials the value of the tangential component of the cutting speed was determined from the following expression, which takes into account the structural To assess the normal and the tangential components, the experiments were carried out with the help of the second class trifactor orthogonal planning matrix.