Optimization of plow adjustment

. Optimization of plow adjustment is very important for national economy, especially in solving problems of increasing agricultural production and reducing energy consumption during plowing. One of the ways to optimize the plow adjustment is to reduce the friction forces of the plow from pressure on the bottom of the furrow and the walls of the furrow. To optimize the configuration of the plow, various methods and techniques are proposed and used that have certain advantages and disadvantages. One of the promising directions of reducing the friction forces of the plow is a dynamic method that uses adjustments of specific devices of the plow and tractor linkage mechanisms. However, one of the significant drawbacks of these adjustments is the shift of the tractor traction point from the longitudinal axis of symmetry of the tractor. The accepted working hypothesis and the studies of the process dynamics made it possible to determine the optimal parameters of the calculated and structural displacement of the tractor thrust point from the resistance line of the plow, as well as to develop recommendations for manufacturers of plows and agricultural tractors.


Introduction
Plowing is one of the main and energy-intensive technological operations in the cultivation of crops. Despite the widespread introduction of various energysaving technologies in agriculture around the world, which involve minimizing or completely abandoning soil cultivation, it is currently not possible to replace plowing with anything else [1][2][3][4]. This operation is an integral (mandatory) part in the cultivation of row crops, many industrial and other crops. It is also an effective agricultural technique in the fight against weeds, diseases, pests and is necessary when applying organic fertilizers (manure) for its incorporation into the soil, etc. [5].
According to various scientists, depending on the technology adopted, the type of cultivated crops, it accounts for up to 40% of all energy costs [6].
In this case, the correct setting of the arable unit is of particular importance since it has a significant impact on energy costs when performing a technological operation. It is known that the general pulling resistance of a plow consists of the necessary efforts to perform useful work -cutting, crumbling and wrapping the soil layer, and to overcome the friction forces of the hulls against the bottom and furrow walls -"useless" work. Efficiency coefficient of the plow shows which part of its resistance is spent on useful work -overcoming the living resistance of the soil, and which for useless movement along the field of the plow [7][8][9].
It is known that the optimum value of the function is the extremum: maximum or minimum. In our case, when setting up the plow: obtaining the highest value of the efficiency of the plow or the lowest value of traction resistance. These tasks are solved in various ways; let us consider in more detail some of the most common.
For a stable plow in the furrow, you must attach the plow to the tractor so that line 0102 (Figure 1) of the traction force intersects track 02 of the gravity center of the plow and the hinge H for attaching the lower longitudinal rods to the tractor [10]. The trace of the center of gravity of the plow is in the middle of a straight line connecting the socks of the first and last bodies. For the correct aggregation of mounted and semimounted plows, draw a straight line from point 01 to point 02 and find the necessary shift E of the attachment on the tractor and the distance Fо from the suspension axis of the plow to the furrow of the front body share. Installation dimensions E and F depend on the number of enclosures. Therefore, to aggregate plows PLN-5-35 and PLP-6-35 in four-, five-and six-body variants with T-150 and T-150K tractors, it is possible to install the plow suspension in four positions: the middle of the suspension is placed against the toe of the third case (displacement т is equal to zero), the middle of the suspension is shifted to the left by 60, 120 and 220 mm.
An analysis of the circuit in Figure 1 shows that the tractor traction line is shifted to the left of the longitudinal line of the plow resistance. This leads to an increase in pressure on the walls of the furrows, an increase in the friction force and a decrease in the efficiency of the plow.
Lemken company offers its own option of setting up a plow for stable running in the furrow -the Optiquick system ( Figure 2) [11]. The plow is considered optimally tuned if the tractor-plow traction line is the line between points Z and PZ, passes through the middle of the rear axle of the tractor -point M. Point Z is the point at which imaginary elongated lower links intersect, point PZ is the middle of the plow frame (figure 2). From the analysis of the circuits in Figure 2, we can make several observations: 1st. Point Z is the point of the mass center of the tractor and the "pole" π of the articulated four-linklower links -top view.
2nd. Point Z in the lower figure 2 is "shifted" to the right relative to the longitudinal axis of the tractor.
3rd Point M -point of tractor traction, which is indicated in the center of the tractor' drive wheels, and is not really a point of tractor traction.
4th. The point T -traction of the tractor in Figure 2 was added for clarity by the authors of this article. Without an indication of the actual point T of the tractor's thrust, the analysis of the stability of the plow's travel is difficult and leads to erroneous conclusions.
The aim of the study is to reduce the energy costs for plowing the soil by reducing the friction forces of the plow bodies from pressure on the bottom and the furrow walls, as well as optimizing the setting of the arable unit by determining the optimal location of the plow traction point in the longitudinally-vertical and horizontal planes.

Working hypothesis
The plow is optimally adjusted in the longitudinalvertical plane if the line of tractor pull, the center of mass point, the tractor and plow pull and the application of the plow drag force are on the same line and intersect at the π pole -the point of the imaginary extended lower link of the tractor linkage mechanism.
To reduce the pressure of the field planks on the furrow wall and reduce the friction force, it is necessary to shift the plow thrust point in the horizontal plane from the longitudinal line of the plow resistance point by the optimal value e, which will allow balancing the moments of forces: tractor thrust Px and resistance Rx, as well as the moment of resistance Ry plow.

Materials and methods
The main results of the work are obtained on the basis of theoretical studies using methods of mechanics, analytical geometry and the laws of agricultural mechanics. The analysis of technological process dynamics of various arable units was carried out taking into account the design parameters of the plow plows, the chassis and tractor linkage, as well as the physicomechanical properties of the treated soil.

Results and Discussion
Consider the adjustment of the plow in the longitudinally vertical plane (Figure 3).
The linkage mechanisms of the tractor and the plow must be adjusted so that the line of force РXZ of the tractor's thrust passes through the pole A of the center of mass of the tractor -through point B of the tractor's thrust -through point C of the instantaneous center of force RXZ of the plow's resistance (points A, B, C were on the same straight line). This is ensured by adjusting the tractor linkage mechanism (central link, left and right link braces) and the linkage ("tower") of the plow so that the extension of the link line coincides with the π pole of the articulated four-link linkage of the tractor linkage and with point A of the tractor center of mass, as well as with point C of the instantaneous center of resistance of the plow of force RXZ.
The projection of the tractor pull force РXZ and the resistance of the plow RXZ are equal to each other, but opposite in direction and are on the same line drawn through the indicated points. It is known that to move a body along a plane with friction, a minimum tractor pull force P will be required when it is directed horizontally at an angle ε equal to or greater than the friction angle φ [12]. The angle of friction of steel on the soil is in the range of 14...42°, and its average value is 26°30'. To obtain specific data on the effect of friction forces on the lateral component, we will analyze the interaction of forces acting on the plow in the horizontal plane ( Figure 4).
Traction force Рx of the tractor overcomes the resistance of the plow Rx to undercut the formation, crumbling and rotation of the formation and friction forces from the pressure of the field boards on the wall fRy and the bottom fmg of the furrow. Lateral componentRyof the resistance force of the plow Rxy. presses against the furrow wall with field boards, as a result an additional friction force fRy appears.
It should be especially noted that the numerical value of this friction force fRy also depends on the magnitude of the displacement of the tractor thrust pointеbetween the lines of the tractor thrust force Рx and the size L of the lateral shoulder shoulder Ry of the component of the plow drag force. If the tractor thrust force line Рx is offset from the plow resistance line Rx from the open furrow wall, then the pressure on the furrow wall will increase. If the tractor thrust force line Рx is offset from the plow drag line Rx to the open furrow wall, then the pressure on the furrow wall will decrease. Consequently, the friction force of the field boards against the furrow wall will also decrease.
The plow friction force during plowing is the sum of the friction from the plow gravity force fmg to the bottom of the furrow and the pressure on the furrow wall of the lateral resistance component fРiy.
Calculation of the friction forces of the plow from the pressure on the furrow wall of the lateral resistance component Рiy where f is the coefficient of friction of the field board on the soil, we take 0.5; Рiy is the tractor traction force to overcome the friction forces of the plow from the pressure on the furrow wall of the lateral component of plow rotation, N; Riy is the pressure force on the furrow wall of the lateral component of the plow rotation, N; Rx is the plow coaxing force, N; K is the specific soil rotation during plowing; we accept 4.0 N/cm 2 = 40,000 N/m 2 for loamy soils; a is the depth of plowing, we take 0.25 m; i•bis the width of the plow, taken equal to the number i of buildings multiplied by the width of the capture of one body, b = 0.55 m.
The displacementе, obtained from the equation of moments of the pair of forces Рx and Rx, is conventionally called optimal. The magnitude of the optimal displacement e is determined from the equation of the moments of the pair of forces: the pull force Px of the tractor and the drag force Rx of the plow where еК is the magnitude of the structural displacement of the tractor traction point B from point C of the center of resistance of the plow, m; di is the distance from the point Сi of the center of resistance of the plow to the furrow wall, D is the tractor track, m; W -wheel width, m.
The distance d from the point of the center of resistance of the plow to the wall of the furrow is determined: where d is the distance from the point C of the center of resistance of the plow to the furrow wall, i is the number of buildings, b is the width of the housing.
Tractor design track with optimal shift of tractor traction point B:  Based on these results, the graphs were constructed, which are shown in Figure 4, from which it follows that with an increase in the number of bodies, the value of the angle of inclination of the traction force decreases curvilinearly. According to the calculations and the constructed schedule, it follows that the angle at the 5-body plow ε5 =13° is about 46 % of the optimal 26°30' value; the angle at the 9-body plow ε9= 8° is about 28 % of the optimal value, the angle at the 13-body plow ε13= 6° is about 20 % of the optimal value, etc.
The design of the linkage mechanism of the plow and the linkage mechanism of the tractor do not always fully ensure the optimal value of the angle of direction of the draft line.
An optimal 100 % balancing by the tractor traction force of the plow's gravity with the number of bodies 5 or more is not possible. Therefore, it is necessary to achieve the maximum angleεof the inclination of the tractor's longitudinal thrust to the horizon.
The calculated values of the friction force FfrG of multi-body plows from the pressure on the bottom of the furrow by the force of gravity РiG and the friction force FfrY from the pressure on the furrow wall of the lateral resistance component РiY are summarized in Table 2. From the analysis of the data obtained, the percentage of the total frictional forces to the traction resistance of the plow shows that the efficiency of the plow is in the range 38 ... 20 % ofRxor from 0.62 to 0.8.
Thus, the optimal heighthiof the point of the thrust of the plow is one that provides the angle ε of inclination of the thrust force Рхz of the tractor, equal to the angle φ of friction of the plow on the soil.
Also, calculations were made of the values of the structural displacement eK I of the distance di from the point of the center of resistance of the plow to the furrow wall, the calculated track of the tractor depending on the number I of plow bodies with different working widths of one body, the calculation results are shown in table 3.
Based on the results of the obtained data, graphical dependences were constructed showing the dependence of the optimal displacement e of the tractor traction line and distance d from the point of the center of resistance of the plow to the furrow wall on the number of bodies i (Fig. 6).  An analysis of Table 3 and the graphs of Figure 6 shows that for plows with a small number of bodies it is almost impossible to combine the tractor thrust point with the optimal shift of the plow thrust point.
Track tractors in class 0.6 tf; 0.9 tf; 1.4 tf; 3 tf; 5 tf is in the range from 1200 to 2744 mm, for example, at the tractor Standard equipment K-744 gauge D = 2100 mm and Premium equipment K-744 gauge D = 2115 mm, wheel width W = 750 mm.
The value of the optimum displacement e for smallbody plows with a working width of less than 2.0 m does not agree with the track of the tractor. Therefore, the thrust point of the plow is forced to be estimated towards the point of tractor pull. As a result, the pressure on the furrow wall will increase, and the friction force will increase accordingly.
For plows with a working width of more than 2.0 m, the lateral pressure of the plow on the walls of the furrows is not completely balanced (up to 80%).
For plows with a working width of 6 m or more, the traction points of the plow and tractor coincide, which allows you to completely (100%) balance the lateral pressure of the plow on the walls of the furrows.
With a working width of 0.3 m for all plows, the bridge construction of the chassis of the tractors does not