Determination of the traction resistance of the combined working body for moldboard-free tillage

The article proposes a method for calculating the traction resistance of a universal combined working body, consisting of a rack with a chisel, loosening and flat-cutting paws. The paws can have both a straight profile and a curved profile in various combinations.


Introduction
Compaction of soil horizons is a mechanical barrier to the penetration of the root system of cultivated plants into the subsurface layers, worsens the conditions for their development. Compacted soil has a reduced infiltration capacity, which is the reason for the loss of a significant amount of water to runoff and evaporation [1][2][3][4]. The need to decompact the soil, improve its structure and conditions for the development of the root system of cultivated plants, aeration, and accumulation of moisture, led to the development of loosening technology that provides crumbling of the soil, both in the upper layer and in the subsoil horizon. In Russia and all over the world, work is underway to create new and improve existing machines [4][5][6][7][8][9][10][11][12][13].

Materials and methods
The calculation of the working bodies of tillage machines is also presented by works [14][15][16].
A method of deep loosening of the soil was proposed, the essence of which is the complex effect of a system of deformers with the formation of a loosening zone expanding to the surface of the field. Loosening of the formation is carried out without mixing the layers and bringing them to the surface when the zones of loosening of the deformers are combined.
Let us carry out a theoretical analysis of the traction resistance of a combined working body equipped with a chisel, a stand, upper and lower flat-cutting shares, with curvilinear or flat plowshares.
The traction resistance is determined by the formula: Where P1traction resistance of the share of the upper share; P2traction resistance of the share of the lower share; P3traction resistance of the chisel rack; P4, P5the force required for lateral separation of the soil by the plowshares of the upper and lower paws, respectively. The traction resistances of the plowshares of each paw are determined by the formulas: Where P1, P2maximum values of the traction resistance of the ploughshare installed at an angle J1, J respectively for the upper and lower legs; P`1, P`2maximum values of the traction resistance of the same share when it moves in the soil perpendicular to the blade.
The basis for calculating the traction resistance of the paw is the calculation of the resistance to the movement of a straight wedge in an elastic deformable medium. As a soil model for the southern regions of Russia, we take a polydisperse system with rigid bonds of a solid component and consisting of solid and gaseous phases. G.N. Dyachenko in his work identified the minimal Pcmin share resistance: Where Qgravity of the soil located on the share; Nvforce of resistance to kickback of the painted volume of soil; Nytotal force of inertia of the soil layer on the curved surface of the share; βcforce deflection angle ܰ ௬ ; Dshare cutting angle; Mangle of friction of soil against steel.
According to experimental data carried out on dry cohesive soil between Pc and Pcmin the is dependency established: The quantity Km depends on the thickness of the treated layer a: when increasing a from 0,08 to 0,16 value Km decreases from 2,0 to 1,5.
Using formulas (2)-(5), can be expressed by the first two terms of the formula (1): For the considered working body with simultaneous movement in the soil of the upper and lower wedge, values Q and Nv require special theoretical research.
Consider by the two wedges ABC and DEF angled as D1 and D2 to the horizon and located relative to each other along the line АM (rear edge of the rack), inclined to the horizon at an angle 4. The height of the rear wall of the edge of each wedge above the bottom of the furrow is respectively h1 and h2, the depth of travel of the cutting edges relative to the surface of the medium, respectively: a1 and a (fig. 1). For the convenience of the calculation, we assume that the density of the medium on the share is constant and equal to U. The magnitude of the force of the weight of the medium Q, located on the share, was determined by the formula: where Sarea of the environment above the share in the plane of the drawing, m 2 ; lshare length, m. Using Figure 1, we assume that: for top wedge S1=HDuDF; (9) for bottom wedge S2=АNuAC+QNuND.
Expression (12) fair, only if 'а d btg4cosD2. If 'a > b tg4cosD2, then the formula (12), will take the form: Using formulas (8), (11) -(13), we matter Q for each share: Q2=U2gl2 'a(bcosD2+a1ctg4), при 'аd btg4cosD2; At the moment of the shift of the deformable volume of the medium relative to the main massif along the line АК the force of resistance to displacement of the displaced part of the volume begins to act Nv. Its vector is deviated from the vertical at an angle D/2 according to the vector of absolute speed Vа free incompressible bulk media. At the moment of shearing, the speed of the sheared volume increases to Vа, Vа=2 Vрsin(D/2). According to this force Nv define from the expression: where V0initial velocity of a deformable medium equal to zero; mmass of a deformed medium, separated from the main body and lying on a wedge.
The time 't defined as the ratio of the lifting height h (h=bsinD) to the absolute velocity of the formation moving at an angle D/2 in relation to the vertical: ( 1 8 ) After substitution in expression (17) values of the quantities included in it, the formula for determining the force Nv, takes the form: for the upper paw: for the lower paw: Formation inertia for each foot: .
In order to determine the traction resistance of the strut with the chisel, let us divide this element of the working body into two parts: the chisel and the strut. We assume that the chisel works below the critical depth of cut, and the upper part of the tine, which is above the chisel, works in the already slightly loosened soil with the lower and upper paws and therefore only moves the soil. Then the thrust resistance of the chisel rack includes two components where Pnforce required to press soil into the walls of the gap below the critical depth of cut; Pcforce required to shear the sturdy soil.
where а2bit depth, а2=l3sinD3; b2bit width, m; qsoil volumetric crushing coefficient, N/m 3 To consider the shear force of the soil Pc we will divide the rack into two parts, then: where Pc1the shear force of the soil by the strut positioned above the upper paw, at a depth а1; Pc2force of shearing of the soil by the stable, located above the lower paw, at a depth 'a.
In accordance with the expression for the force for a stable soil shear, we will have: ) )tg(ψ tg -) ( Where С0soil connectivity, N/m 2 ; Zlateral soil separation angle; M1soil friction angle; b3rack thickness. The forces required for lateral separation of the soil by the share of the upper and lower paws P4 and P5 will be determined in accordance with the methodology described in [5]: