The optimisation of the cylinder-spiral soil-cultivating roller

. Designed cylinder-tillage spiral s kating rink w ith s piral w ork items, which form a fine lumpy structure of the sowing layer of soil with grain size corresponding to agrotechnical requirements, while helping the soil surface, mulching the top layer of soil over the seeds, seal the depth of their placement, p roviding the r equired c ontact o f s eeds w ith s oil is necessary to ensure the uniformity of germination. At the theoretical level, it is determined that an increase in the pinching angle leads to an increase in the s ize o f the h ollow s mooth p ipe o f t he roller. T his o ccurs w hile increasing the depth of deformation of the layer of crushed soil and the radius of the clump of soil. However, a change in the radius of a hollow smooth roller of more than 0.3 m does not lead to a slight increase in the pinching a ngle. T herefore, i ncreasing t he r adius o f t he ho llow smooth roller over 0.3 m is not rational, as it will increase the metal content of the structure. After a nalyzing t he obtained m athematical m odels of t he s oil treatment p rocess w ith a roller, w e o ptimized t he parameters o f a cylindrical-spiral roller: speed of 11 km/h, mass of ballasting loads of 100 kg, step of the spiral turn of 40 mm, and the departure of the spiral screw of 35 mm. These modes ensure the formation of a qualitatively compacted soil l ayer in the z one of planting s eeds of a gricultural crops, w hich is confirmed b y the maximum va lue of t he p rocessing quality c riterion f or matching the density of the soil after rolling with a cylindrical-spiral roller CCS = 0 .98 (while the de nsity of t he sown layer a ddition 1185...1215 kg/m 3 ), which f ully s atisfies t he a grotechnical optimum. The y ield of barley o f t he Nutans-553 va riety be came higher a fter t he us e of a n innovative cylindrical-spiral roller by 6.4 % and 9.3 %, respectively, of the yield after the impact of serial КК Sh rollers and ring rollers of the seeding machine. In the course of evaluating the metal consumption of structures of the innovative cylindrical-spiral roller and the ring-spur roller, a difference of 70% per unit width of the grip was revealed.

In t he system of agricultural cultivation ope rations, pr oducers of crop pr oducts f ace the negative aspect: t he germination of seeds of cultivated p lants in r eal field conditions i s worse t han t hat de termined i n laboratory conditions. T he e limination of t his d iscrepancy remains relevant [1]. This negative phenomenon significantly reduces productivity and, as a result, leads to a l oss of income from production a ctivities. O ne o f the well-established factors of this difference in seed germination is surface treatment of the soil during sowing for the purpose of compaction and structuring. After treating the soil with rolling tools, the necessary compaction of the seed layer and the rise of moisture from the lower layers due to t he for mation of a c apillary s tructure is p rovided f or agricultural s eeds. Rolling agricultural tools should grind large soil aggregates and smooth the microrelief of the field [2]. Cons equently, t he operation of post-seeding c ompaction a nd s tructuring of the s oil layer in the area where t he seeds of agricultural c rops a re l ocated becomes a n i mportant aspect of agricultural cultivation, ensuring the uniformity of seedlings.
The above allows us to formulate the purpose of the study -to improve the quality of post-sowing compaction and structuring of the soil layer in the zone of seed location on the basis of the de velopment of a c ylindrical-spiral r oller, w hich e nsures t he achievement of agrotechnical indicators of the process and increase the yield of agricultural crops.
When inventing and modeling agromachines, it is possible to ensure high efficiency of their operation on the basis of mechanical and technological justification of new principles and technological order of interaction of working bodies of agricultural tools with the soil, based on t he c ombination of h eterogeneous effects a nd deformations of t he pro cessed medium to ensure its required technological properties [3].
Based on the analysis of the designs of rotary loosening and compacting working bodies of a gricultural tools, a cylindrical-spiral tillage roller (figure 1) made of a hollow smooth pipe 1 w as developed. Along the surface of the pi pe in the l ongitudinal di rection with an equal step, holes 2 a re made a long t he entire l ength of the hol low smooth p ipe 1 . I n the rectangular holes 2, spiral screws 3 are installed parallel to the axis of its rotation.  The w idth of the holes 2 is m ade less than t he d iameter of t he s piral s crews 3 . The distance between t he t urns of the s piral s crews 3 i s m ade l ess t han or equal to t he agrotechnically set maximum size of soil lumps. At the ends of the hollow smooth pipe 1, disks 5 are located on the axis 4, in the center of which bearing supports 6, are installed on the outer sides. A hollow cylinder 7 is installed coaxially Inside the hollow smooth pipe 1. To ensure the fixed position of the spiral screws 3 in the holes 2, the diameter of the hollow cylinder 7 is selected so that its outer cylindrical surface contacts the outer surfaces of the spiral screws 3. The ends of the hollow cylinder 7 touch the inner surface of the disks 5.
The working process of t he roller is a s follows: supports 6 connected to t he frame a re connected t o the h itch w ith the s eeder. R olling ov er t he surface of t he s oil, l arge s oil aggregates are d estroyed by s piral s crews 3 a nd the e dges of ho les 2. In t his case, s piral screws sinking into the soil affect its aggregates, creating a strain of tension-compression. This p rinciple of elastic e ffects o n l umps intensifies the process of t heir c rumbling. In addition, spiral screws 3 s eal t he subsurface soil layer. At this point, the part i s deformed lumps falls into the internal cavity bounded by a hollow smooth tube 1 outer surface of the hollow cylinder 7, crumble, hitting the turns of spiral screw 3. The outer cylindrical surface of the hollow smooth tube 1 between the spiral screws 3 when rolling tillage rink, creating stress state in the contact zone with soil, condenses, smoothes the surface and destroys large clods of soil, pressing them into the top layer of the soil. Spiral screws form a fine-lumped structure of the sown soil layer with t he size of t he fraction corresponding t o agrotechnical r equirements. In addition, s piral s crews align t he soil surface, mulch the top layer of soil over the seeds, and seal the soil at the depth of their embedding, e nsuring t he r equired c ontact of s eeds w ith the s oil, which i s necessary t o ensure uniformity of seedlings. In addition, the presence of spiral screws and edges of holes in the hollow smooth pipe, located perpendicular to the direction of movement, prevents the cylindrical surface of the smooth hollow pipe from slipping, which eliminates the formation of cracks on the soil surface and, as a result, reduces the intensity of moisture evaporation from the s oil layers, i n which the roo t s ystem of cultivated plants is for med. Thus, the above-mentioned distinctive features of the tillage roller contribute to improving the quality of soil compaction.
Pinching of soil clumps occurs between the outer surface of the hollow smooth pipe and the soil. At the same time, there should be no pushing of soil lumps forward in front of the roller under t he influence of the resultant forc e of surface pressure, which will l ead t o shifting of the s oil l ayers and t he formation of c racks. T his forc e i s ori ented t owards t he solution of the s urfaces and is balanced by the for ces of f riction, a dhesion and external forces. T he maximum value of t he a ngle of pinching χ of soil aggregates by t he roller, at which there i s a ne gative ph enomenon of pus hing ou t l arge s oil aggregates, i s du e t o t he sum of the angles of friction of lumps on the surface of a hollow smooth pipe φ1 and soil φ2. The main factor affecting the size of the pinching angle is the radius and material of the hollow s mooth pi pe. T herefore, t o e liminate the s hift in the groun d b efore the ho llow smooth tube of the rink and provide a guaranteed condition of crushing of soil aggregates is necessary and s ufficient fu lfillment of t he inequality χ ≤ (ϕ1 + ϕ2), th at is , t he angle between the tangent to the surfaces defined by the sum of the angles of friction φ1 and φ2 were less than or at least equal to this amount (figure 2,а). If this condition is met, the soil lump is not pushed out and it does not shift, resulting in displacement of the surface layers of t he s oil. T o s implify c alculations, w e a ssume t hat t he cross s ection of s oil l umps represents the shape of a circle. We accept parameter designations: the radius of a hollow smooth tube of a cylindrical-spiral roller R, the radius of a clump of soil r.
Imagine the equation of the circle in polar coordinates, we get: Write equation (1) in a rectangular coordinate system: where x and y -are the coordinates of the tangent at the current time, m; φ -is t he s econd polar coordinate, counted from the first polar coordinate in our case from the axis Ox to the segment OM, deg.
Having constructed a tangent straight line to the circle of the soil clod passing through the point of contact of the clod with the soil A, we write the tangent equation [4]: where уА and хА -instant coordinates of a point А, m.
From expression (4), we define the tangent line parameter [5]: Taking into account the expression (5) and as a result of mathematical transformations, we determine the distance from point O to point M: The r esulting expression (6) Then the parameter cos χ: Therefore, in order to avoid shifting the soil in front of the hollow smooth pipe of the roller and to ensure the condition of guaranteed pinching of soil aggregates, it is necessary and sufficient to perform the inequality: The interaction of the roller with the soil clump causes the appearance of the force R1, and the reaction of the soil R2 from the action of the clump on it ( figure 2, b). These forces can be decomposed into the normal components Fn1 and Fn2 and the friction forces Ff1 and Ff2, r espectively. If t he final value of the pro jections of friction for ces on the x -axis i s greater than the final pushing forces in the projection on the same axis, the soil aggregate will be delayed between t he outer surface of the hollow smooth pipe of t he roller a nd the soil surface and crushed, since the mass of the roller is much larger than the mass of the soil lump. Let's analyze the requirements under which a hollow smooth pipe of a roller interacts with a lump of soil. For the purpose of simplification, we assume that the hollow smooth pipe of the roller moves, rolling over the surface of the soil, and there is no slippage. The soil surface is solid and does not experience deformation. The soil lump is a ball with the main parameter -the diameter of dsc max, w hich i s due to the a grotechnical established a nd a cceptable s ize of large fractions. Let's make a system of equations for projections of all forces on the x and y axes: After appropriate mathematical transformations and taking into account Ff1 = µ1Fn1 and Ff2 = µ2Fn2, where µ1 and µ2 -the coefficients of friction of the hollow masonry pipe of the roller on the soil and the soil clump on the soil, respectively, were obtained: Since AC = BD, and taking into account the expression (12), the minimum diameter of the cylinder-spiral roller Mathematical transformations of t he e xpression (15) a llow us t o ob tain a d ependence for d etermining t he minimum r adius of a cylindrical-spiral rol ler, t aking into account t he angle of pinching of the soil lump and the geometric parameters of the lumps located on the soil surface: The graphic d ependence (16) of t he r adius of the hol low smooth pi pe o f t he r oller R relative to the angle of pinching χ for different radii of the soil clump r is shown in figure 3. Thus, formula (16) establishes the dependence of the minimum diameter hollow smooth tube of c ylinder-spiral ri nk t o t he he ight of a deformable s oil layer, a grotehnicheskij installed and the allowable size of the coarse particles, the friction coefficient between the ice rink and tillage of the clod of soil, depending on the material, hollow smooth tube roller.
The theoretical research shows that increasing the angle of pinching requires increasing the size of the hollow smooth pipe of the roller. This occurs while increasing the depth of deformation of t he layer o f crushed s oil and the r adius of the c lump of s oil. However, a change in the radius of a hollow smooth roller pipe of more than 0.3 m does not lead to a significant increase in the pinching angle.
For the production of an e xperimental model of t he developed a gricultural equipment, taking into account theoretical research, the diameter of a hollow smooth pipe of 0.265 m was t aken from the s tandard ra nge o f pi pe d iameters according to G OST 1 0704-91. T he model of a cylindrical-spiral roller (figure 4) is made of a hollow smooth pipe 1, with disks 2 installed a t t he e nds of i t. O n t he s urface o f t he p ipe 1, ho les a re m ade i n w hich s piralscrew working bodies 5 a re installed. These working elements provide a finely structured topsoil layer that prevents intensive evaporation of valuable soil moisture. A special feature of the design is the ability to change the departure of spiral-screw working bodies and the step of their turn. Such adjustments are provided to optimize these parameters. To regulate the pressure on the soil, there is a mechanism for attaching balancing weights 6.
The cylindrical-spiral roller during operation must form a qualitatively compacted to the optimal va lue and s tructured s mall-aggregate t opsoil. T herefore, for a comprehensive assessment of the process under study, we need a criterion that can reliably characterize the process under study and link the factors affecting it to the model [6]. As such, the criterion compliance of standard (CCS) has been developed. CCS is used to determine the quality of soil rolling by comparing the density indicators after its treatment with a cylindrical-spiral χ, deg. roller to the reference values of agricultural requirements (ρopt = 1200 kg/m 3 ). CCS is easy to calculate for any rolling agricultural tools, as it is a universal and visual indicator.
hs -departure of spiral screws r elative to t he surface of a smooth hollow pipe; l -spiral screw turn step; 1 -hollow s mooth pi pe; 2 -disk; 3 -bearing s upports; 4 -coupling; 5 -spiral s crews; 6mechanism for securing ballasting loads; CCS is calculated using the equation: where ρopt -is t he soil density at t he depth of seeding in accordance with agrotechnically established requirements for t he cultivation of a pa rticular c rop, kg /m 3 ; ρe -is th e experimentally obtained values of soil density, kg/m 3 . The s oil d ensity at t he d epth of s eeding of ρопт based o n the a nalysis of a gricultural requirements was s elected 1200 k g/m 3 , w hich corresponds to the op timal s oil d ensity for sowing grain crops. In full compliance with the soil density at the depth of the seed location agrotechnical optimal value CCS = 1.
Various factors affect the rolling of the soil with the proposed cylindrical-spiral roller. As c ontrolled f actors o f the pro cess, w e chose: v (х1) -speed of m ovement of t he cylindrical-spiral roller, km/h; m (х2) -mass of ballasting cargo, kg; hs (х3) -departure of the s piral-screw working body , m m; l (х4) -step of the s piral-screw w orking body , m m. Based on the analysis of w ell-known e xperiments on rol ling t he soil, conclusions from search studies, existing theoretical data, as well as on the basis of the design features of the developed r oller, the ra nges of changes i n fa ctors w ere s elected. Levels a nd i ntervals of changes i n fa ctors: t he s peed of the t illage r oller varied from 7 km /h to 1 5 km/h w ith a n interval of variation of 4 km/h, t he pitch of the spiral screw -from 30 to 60 mm with an interval of 15 mm; the weight of ballasting loads-from 0 to 300 kg with an interval of 150 kg; the departure of the spiral screw relative to the surface of a hollow smooth pipe -from 0 to 50 mm with an interval of 25 mm.
As a function approximating the optimization criterion and independent factors, we can use an e xpression t hat is a f ormatted s imulation of t he pr ocess of c ompaction and structuring of the surface seed layer of the soil developed by a cylindrical-spiral roller [7 ].
To form a mathematical model, it is sufficient to use the following regularity [8]: where y -is the o ptimized value; хi (i = 1, 2 …n) -parameters that affect the optimized value y after c onversion t o e ncoded va lues; bi, bij, bii -coefficients that de termine t he correlation component of the model.
As a r esult of a m ulti-factor experiment with a pos sible combination of f actor v alues and processing of the array of data obtained, mathematical models were obtained describing the pro cess of for ming a c ompacted s oil l ayer by a c ylindrical-spiral r oller, s howing the influence of i ndependent fa ctors on CCS . A s econd-order po lynomial de scribing the influence of m and v on CCS: ССS = 0,7758 + 0,0234v + 0,0004m -0,001v 2 + 0,00000257vm -0,0000021m 2 , Constructing and analysing models of the densification process a nd structure of t he sowing l ayer of s oil developed cylinder-spiral roller, ha s de termined that t he maximum value of CCS after e xposure of c ylinder-spiral r oller a mounted t o 0.98 ( corresponding t o the density of the soil ρ = 1185...1215 kg/m 3 ), which fully meets t he agronomic optimum and i s a chieved when the rate o f c ylinder-spiral ri nk 11 k m/h, the m ass of ba llasting o f cargo of 100 kg, step spiral of the working body 40 mm, the radius of the spiral screw of 35 mm.
In the s ubsequent testing of t he c ylindrical-spiral roller took place in a peasant farm. It was found that the yield of spring barley of the Nutans-553 variety (figure 6) after exposure to a c ylindrical-spiral ro ller fo r an average of t hree years exceeded by 6.4% a nd 9.3%, respectively, the y ield of this c rop a fter rol ling with a ri ng-spur r oller 3K KSh-6 a nd ring rollers of the SZ-5.4 seeder. Thus, the study theoretically determined that by increasing the depth of deformation of the s urface layer of s oil ro lled down a nd t he s ize of the l ump of s oil t he p inching a ngle increases as the radius of the hollow smooth tube, but when you increase this parameter, the rink more t han 0 .3 m, the c hange i n t he a ngle of the pi nching be comes insignificant. Therefore, increasing the radius of the roller over 0.3 m is not rational, since it will increase the m etal content of the s tructure. Experimental studies of t he pro cess of tillage w ith a cylindrical-spiral rol ler a llowed us t o justify i ts optimal p arameters, in w hich th e q uality criterion for soil density CCS was 0.98 (with a maximum equal to 1), which is respectively 7.1% and 14.2% more compared to ring-spur rollers and ring-shaped rollers of the seeder. The yield of barley of the Nutans-553 variety became higher after the use of an innovative cylindrical-spiral roller by 6.4 % a nd 9.3 %, re spectively, of t he yield after the impact of serial KKSh rollers and ring rollers of the seeding machine. In the course of evaluating the metal ca pacity o f t he i nnovative cylindrical-spiral r oller a nd t he r ing-spur roller, a difference of 70% per unit width of the grip was revealed.