Optimization of the kinematic mode of operation of the tractor-driven tillage tool

A traction-driven tillage tool with low traction resistance has been developed. A decrease in the tractive resistance of the implement is achieved by transferring the main share of the power consumed by the implement to the process of loosening the soil through the tractor power take-off shaft (PTO) to the drive needle discs, which in turn create a pushing force. The efficiency of the technological process of soil cultivation depends on the kinematic mode of operation of each row of disk working bodies of the tractiondrive tillage implements. To optimize their kinematic mode of operation, a multifactorial experiment was carried out, which made it possible to establish the optimal values of such factors as the kinematic parameters of the 1st and 2nd rows of needle disks at the set operating speed of the unit.


Introduction
In crop production, tillage is one of the most energyintensive operations, it accounts for up to 40 % of the energy costs of the entire technology [1,2]. Increasing the energy efficiency of tillage is one of the important tasks in increasing the profitability and environmental friendliness of agricultural production. In this regard, relevant and significant research is aimed at optimizing the technological parameters of machine-tractor units, allowing to increase the efficiency of the use of energy resources in crop production.
Improving the energy efficiency of tillage is possible by means of the use of traction-driven tillage tools with active working bodies that do not create high traction resistances and do not require a large traction-coupling weight of the aggregating tractor [2][3][4][5]. The possibility of increasing the energy efficiency of the unit by reducing the tractor wheel slip and rolling losses of the unit, which is achieved by transferring part of the power through the PTO to the drive needle working bodies, which compensate for the traction resistance of the tool and create a pushing force, reducing the rolling resistance.
The use of the proposed traction-drive tool will allow for loosening the soil by stretching with separation and reduce the traction resistance of the tool by transferring the main share of the power consumed by the tool through the shaft of the tractor power take-off mechanism to the drive rotary working bodies, which in turn create a pushing force.

Research objects
To increase the energy efficiency of soil cultivation, a traction-driven tillage tool has been developed ( Fig. 1), which creates a low traction resistance. A decrease in the tractive resistance of the implement is achieved by transferring the main share of the power consumed by the implement to the technological process of loosening the soil through the tractor power take-off shaft to the driven rotary working bodies, which in turn create a pushing force, minimizing the traction resistance of the tillage implement [6].
The traction-driven tillage tool works as follows. Before the start of the movement of the unit, in the transport position of the tool, the shaft of the tractor power take-off mechanism is turned on, from which the torque is transmitted to the front and rear shafts with rotary working bodies-needle disks. Further, the tool is transferred to the working position and the needle disks of the first row with loosening-bearing elements are buried in the soil, performing strip tillage with frontal loosening by separation, and the needle disks of the second row with loosening elements in the form of an isosceles triangle loosen the soil by stretching deformation in adjacent untreated strips by the impact from the line of their symmetry in opposite directions to the loosened strips. At the same time, the circumferential speed of the drive rotary working bodies exceeds by 5...15 % the theoretical speed of the tractor in the selected gear, which creates reactions directed towards the movement of the unit.
The tool ( Figure 1) contains driven rotary working bodies -needle discs, which are located in two rows. The rows of working bodies are located perpendicular to the direction of movement of the tool in a checkerboard pattern, and are made in the form of batteries of needle disks with needles of optimal curvature [7].
The efficiency of the technological process of the traction-drive tillage implement depends on the kinematic mode of operation of each row of its disc working bodies. To optimize their kinematic mode of operation, a multifactorial experiment was carried out.

Fig. 1.
Experimental traction-drive tillage tool: 1 -frame; 2hinged device; 3 -support and adjusting wheel; 4 -wheel lever; 5 -screw adjuster of working depth; 6 -front battery of drive disc-needle working bodies; 7 -rear battery of drive discneedle working bodies; 8 -disk-needle working bodies; 9cardan shaft for transmission of torque from the tractor PTO; 10 -bevel gearbox; 11 -propeller shaft for transferring torque from the bevel gear to the battery of drive disk-needle working bodies; 12 -torque flow distributor with a block of replaceable sprockets; 13 -chain drive circuit for transmitting torque to the front battery of disk-needle working bodies; 14 -chain drive circuit for transmitting torque to the rear battery of disc-needle working bodies; 15 -tensioning mechanisms of chain drives of circuits for transmitting torque to batteries of disk-needle working bodies.

Experimental research methods
The method of optimization of the kinematic operating mode of the traction-drive tillage unit includes a series of experiments according to the theory of multifactorial planning of experiments [8].
The quality of soil crumbling and the hourly fuel consumption for the implementation of the technological process of soil cultivation were selected as the estimated indicators of the operation of a machine-tractor unit with a traction-drive implement. The optimization criterion was the specific energy consumption Ec [g/(h‧%)] -a relative characteristic of the technological process of soil cultivation, showing the hourly fuel consumption for each percentage of crumbling quality.
Based on the results of preliminary studies, the factors that have the most significant impact on the estimated indicators were identified: • kinematic parameter of the 1st row of needle disks (K1); • kinematic parameter of the 2nd row of needle disks (K2); • unit operating speed (Vp), km/h.
The kinematic parameters of the operation of the rotary working bodies of the front and rear rows were set by changing the gear number of the speed row of the tractor and changing the gear ratio of the chain drive of the battery drive. For this, a set of replaceable drive sprockets with the required number of teeth was manufactured (Fig. 2). Thus, a variational series of gear ratios for the front and rear batteries was provided (Table 1). The specified set of interchangeable drive sprockets made it possible to vary the ratio of the peripheral speeds of rotation of the front and rear rows of rotary working bodies from 1.0 to 1.22 in accordance with Table 2.
where y is the optimization parameter; b0 is the free term equal to the response at xi = 0; bi is an estimation of the coefficient of the regression equation corresponding i-th factor; bij is an estimation of the coefficient of the regression equation corresponding to the interaction of factors; xi is a coded value of factors (i = 1, 2, 3 ...).
Since the factors of the process are heterogeneous and have different units of measurement, they brought them to a unified system of calculation by moving from the actual values of the factors to those coded according to the formula: (2) where Xi is the natural value of the factor; Хi0 is the natural value of the factor at the main level; ∆Хi is the natural value of the factor variation interval.
Introduced a conventional designation of the upper, lower and main levels of factors, respectively, +1; -1; 0 (table 3). The planning matrix was adopted according to table 4 [3].
To construct a mathematical model in natural variables, coding formulas were used (2). After substituting the natural values of the factors into equation (1), the regression equation was obtained in a decoded form. Using the regression equation in a decoded form, the response surfaces were built and, by the nature of the surfaces, the effect of the unit speed and the peripheral rotation speeds of the front and rear rows of rotary working bodies on the quality of soil crumbling and fuel consumption when performing early spring tillage was evaluated, based on which rational values of the indicated parameters. Table 4. Matrix of the symmetric quasi-D-optimal Pesochinsky design (k = 3)

Experiment number
Combinations of factor values X1 X2

Results
As a result of a series of experiments on the symmetric non-compositional quasi-D-optimal plan of Pesochinsky, the following values of the specific energy consumption Ec [g/(h‧%)] were obtained (Table 5).
Replacing the coded values of the factors in the regression equation with natural ones according to the formulas: At the operating speed of the unit Vp = 9.1 km/h, the regression equation will take the following form: According to the regression equation (6), a graphical dependence of the change in specific energy consumption (EU) is plotted depending on kinematic parameters of the 1st (K1) and 2nd (K2) rows of needle disks, in the form of a cross-section of the response surface ( Figure 2).

Fig. 3. Factor dependence of specific energy consumption
To determine the optimal values of the kinematic parameters of the 1st (K1) and 2nd (K2) rows of needle disks, we differentiate equation (2), determining the first-order derivatives with respect to each variable and equating them to zero: 1486,5 730 140 0.
Solving the resulting system of equations (7), the optimal values of the factors were found: kinematic parameter of the 1st row of needle disks K1 = 1.08; kinematic parameter of the 2nd row of needle disks K2 = 1.13 at the operating speed of the unit Vp = 9.1 km / h. With the given values of the factors, the specific energy consumption of the EU does not exceed 90 g / (h • %).

Discussion
As a result of a series of experiments following the Pesochinsky symmetric noncompositional quasi-D-optimal plan and regression analysis of the experimental results, a graphical dependence of the change in specific energy consumption (EY) was constructed depending on the kinematic parameters of the 1st (K1) and 2nd (K2) rows of needle discs, in the form of a cross-section of the response surface (Figure 2). A visual analysis of this graphical dependence clearly shows the ranges of the optimal values of the factors. The same ranges are confirmed by solving a system of first-order differential equations for each variable (7).

Conclusions
Highly energy efficient early-spring tillage can be achieved through the use of traction-driven tillage implements with active working bodies that do not create high tractive resistance and do not require a large traction-coupling weight of the aggregating tractor. A decrease in the traction resistance of such implements is achieved by transferring the main share of the power through the tractor PTO to the driven rotary working bodies, which create a pushing force, minimizing the tractive resistance of the tillage implement. The best energy efficiency of the traction-driven tillage implement is ensured by the optimal values of such factors as the kinematic parameter of the 1st row of needle disks K1 = 1.08; kinematic parameter of the 2nd row of needle disks K2 = 1.13, the optimal values of which are determined at the operating speed of the unit Vp = 9.1 km / h. With the given values of the factors, the specific energy consumption of the EU does not exceed 90 g / (h‧ %).