MATHEMATICAL MODEL OF THE ENERGETIC CONSUMPTION FOR SOIL DIGGING MACHINES IN GREENHOUSES

Transcription

1 Bulletin of the Transilvania University of Braşov Vol. 3 (5) - 00 Series II: Forestry Wood Industry Agricultural Food Engineering MATHEMATICAL MODEL OF THE ENERGETIC CONSUMPTION FOR SOIL DIGGING MACHINES IN GREENHOUSES Gheorghe BRĂTUCU Abstract: Preparing the gerination bed in greenhouses can be done by several technologies, ost of the including soil digging with a special achine anufactured for this purpose. The ain disadvantage of this achine refers to the relatively high energetic consuption, which increases the work cost. Starting fro the working process executed by the achine, the total energetic consuption is decoposed in representative coponents, for which the energetic coputation relations are given. Finally a coplex and general relation of the energetic consuption is obtained, by which interesting processing optiization solutions are being offered for this iportant functional paraeter, available for designers and anufactures but also for users. Key words: greenhouses, atheatical odel, soil digging achine.. Introduction Matheatical odeling of the energetic of soil digging achines in protected spaces eans to establish the relations of calculation of the necessary energy coponents in ground processing and their analysis in order to find ethods of reducing energy consuption in the work of preparing the seed-bed in greenhouses [], [ ], [4]. Based on the study of the energetic of the achinery on the work of preparing the gerination bed in greenhouses, the total echanical energy coponents for each of the were deterined, which are shown in Figure. Energy consuption in works of the soil, in general, are characterized by [3]: specific cutting surface of the soil S sp and the specific echanical work, L s. Specific surface for cutting the unit volue of the soil is the ratio of area and volue of the displaced soil in / 3. Specific echanical work is the work necessary for processing the deployent of the unit volue of soil, J/ 3 [5], [6].. Material and Method Energy consued during soil processing with soil digging achine, E ts, is used for the oveent of the working achine, for cutting and deployent of soil slices, for throwing the deployed slices, for self pushing and for covering the loss fro the transission of the achine, is: Dept. of Food Products Engineering, Transilvania University of Braşov.

2 44 Bulletin of the Transilvania University of Braşov Vol. 3 (5) - 00 Series II Total echanical energy required, E t E work, the energy required for processing soil Energy required carrying the achine Energy necessary to carry out the echanical processing operations E loss, the energy required to cover the loss in transission Analysis of coponents Fig.. Methodology of the study and atheatical odeling of total echanical energy E = E E E E E [J]. () ts oveent cut trow push loss Starting fro equation (), the total energy required to drive achinery to dig the soil with plain working coponent is calculated with: E ts = f G s v s π a B ρ g tg ψ v ϖ µ ρ g a b ϖ z sin ψ cos ψ π s E loss [J], s v s B a ρ v v x s () where: f is the coefficient of tire rolling resistance between the soil and the achine; G s - weight of the achine, [N]; v - achine speed, [/s]; t s - tie of digging, [s]; µ - friction coefficient between the soil and spade; ρ - soil voluetric weight, [N/ 3 ]; a, b - excavated soil slice size, []; ψ - angle of attack of the spade, [º]; z - nuber of spades; ω - angular speed of the crankshaft, [rad/s]; B - working width of the achine, []; v x - coponent of the relative speed to the direction of advance of the achine, [/s], [7]. In equation () are soe eleents for which there is insufficient data, such as the angle of attack of the spade ψ; forward direction coponent of velocity of a spade, v x. This data is established by theoretical calculations and graphical deterinations. For the theoretical study of the angle of attack a atheatical odel is built achieving: ψ = π θ = arccos α = ϕ ( θ ) ϕ ( θ r r r3 r4 r r4 cos θ r sin θ o (3) arctg α [ ], r r r r r cos θ r4 r cos θ 4 4 ) α = where: θ is the angle of the rotation of the leading eleent of the quadrilateral echanis of the digging achine; θ - angle of rotation of the driven eleent; α - constant

3 Brătucu, Gh.: Matheatical Model of the Energetic Consuption for Soil Digging Machines 45 angle fro the built; φ, φ - angles dependent on the angle θ ; r, r, r 3, r 4 - rectangle side length echanis. Angle of attack of the spade during work tie varies as the angle of rotation of the crankshaft is also variable in tie according to the relation: θ = ϖ t. The ediu value of the angle of attack is deterined graphically for the specific case of soil digging achine MSS-, 40. Diensions of the rectangular echanis of the achine MSS-, 40 are: r = 0.7 ; r = 0.35 ; r 3 = 0.6 ; r 4 = 0.40, α = 8. The variation of the angle of attack of the spade is shown in Figure. In deterining the average coponent tg ψ during digging the deterination of the rotation angle range in which the actual digging is ade is necessary. Figure 3 shows the trajectory of the top of the spade and deterines this interval graphically. Fro the graphics presented we can see that the range of crankshaft rotation angle in which the digging is executed is between T, T being the period of otion, which in this case is 360. Thus, while digging tg ψ average is equal to: tg ψ ed = 0.6. The ediu value of sin ψ cos ψ is considered: sin ψ ed cos ψ ed = Fig. 3. Trajectory of the top of the spade Fig.. Variation of the spades angle of attack depending on the angle of the crankshafts rotation Substituting the average values of coponents, deterined graphically, the relationship of total energy consuption of the work of the soil with the digging achine, one gets: E ts µ ρ g a b ϖ s = f Gs v s z v s 0.45 π B a ρ v ( 4.37) π s 0.6 a B ρ g v ϖ s E loss [J]. (5) Matheatical odel of energy consuption of the work of the soil with the digging achine, expressed by equation (5), provides inforation necessary to optiize achine paraeters to iniize its energy consuption. Energy necessary for the oveent of the soil digging achine, E oveent, is transfored into echanical work necessary for the oveent of the achine and in echanical work of deforation of the soil and of the transport wheels. G s is directly proportional to the weight of the achine and rolling resistance coefficient f

4 46 Bulletin of the Transilvania University of Braşov Vol. 3 (5) - 00 Series II between the transportation wheel and soil: E = f f, G ). oveent ( s Reducing energy consuption for hauling the soil digging achine is to reduce these two eleents. Weight reduction of the achine starting fro the design and construction phase ay be obtained by using lighter aterials, but adequate in ters of resistance to echanical stress. The coponent of forward otion of the speed of the spade v x is deterined graphically for the case β = 0. The variation of the coponent of the speed of spade on the otion direction v x is shown in Figure 4. Fig. 4. Variation of the speed coponents of the spade during advancing direction Fro the chart presented results that the average speed of the spade during digging is equal to: v x = 4.37 [/s]. Reducing rolling resistance coefficient can be provided by using wheels with diaeters and widths as high as possible, with low tire pressure. Mechanical energy necessary to carry out operations, E cut and E trow is used to cut, deployent and disposal of soil slice. Energy required to cut and slice the soil displaceent depends on the diensions of the displaceent of the soil, being directly proportional to the depth and width of the spade so the nuber of spades in the soil at a tie and physical and echanical properties of soil, naely: E cut = f (a, b, z, µ, ρ). The energy for throwing the slices deployed depends on the diensions of the displaced soil and physical properties of the processed soil: E throw = f (a, B, ρ). Reduction of the energy required by the echanical spading operations ay be achieved by reducing the chip size of the displaced soil by doing the work once the soil has optiu physical and echanical properties in ters of work. Energy consued for self pushing, E push, occurs due to friction between the spade and the soil. It is an inconvenience which anifests itself by converting echanical energy of rotation received fro the tractor P.T.O for self pushing. Energy consued for this is directly proportional to the depth of work, width of the spade, forward speed, but inversely proportional to the rotational speed of the crankshaft: E push = f (a, b, ρ, v, /ω). It is indicated that forward speed be saller than the coponent of the speed of the spade in the direction of advance, which is confired in the specific case studied. Fig. 5. Slice diensions of soil displaced by the digging achine

5 Brătucu, Gh.: Matheatical Model of the Energetic Consuption for Soil Digging Machines 47 Energy consued by transission loss due to friction occurring in achine echaniss. The reduction of loss can be achieved by reducing the oving bodies and by reducing friction through lubrication. Specific cutting surface is a geoetrical paraeter of the displaced soil slices []. It is the ratio of the cutting surface of the soil displaced and its volue: St Ssp = V [ / 3 ], (6) where: S t cut surface of the displaced soil, in ; V - volue of soil displaceent in 3. The cut surface of the displaced soil is calculated fro the geoetry shown in Figure 5, such as: S = S t CBFG S EFGH S ABFE a b b s a s [ ], (7) the concrete conditions of work, b = 0. ; v = 0.3 /s; ω = 6 rad/s (Figure 6). Fig. 6. Influence of working depth on the variation of specific cutting surface of soil work with the digging achine Cutting surface area decreases with increasing work rate, which is observed fro the diagra drawn for the concrete conditions of work: a = 0.3, b = 0., ω = 6 rad/s (Figure 7). where notations correspond to those in Figure 5 and have the following eanings: a working depth in ; b - thickness of the slice at the surface of the soil, in ; s - the step of the achine in. Step of the achine is calculated: π s = v []. (8) ϖ Dislocated soil volue by a spade can be considered equal with: V = s a b [ 3 ]. (9) Substituting relations (7) and (9) in the forula of the specific cutting surface forula is obtained: S sts ω = [ / 3 ]. (0) π v a b Cutting surface area is inversely proportional to increasing working depth, which is observed fro the diagra drawn for Fig. 7. Influence of work speed on the variation of specific cutting surface of the work of the soil with digging achine Specific cutting surface is inversely proportional to the increase of the width of spades, which is observed fro the diagra drawn for the concrete conditions of work, a = 0.3, v = 0.3 /s, ω = 6 rad/s (Figure 8). Specific echanical work is the work needed for the deployent of the unit volue of soil, J/ 3. The specific echanical work in working of the soil by the digging achine is calculated reporting the echanical work done on a rotation of the crankshaft to the volue of soil displaced in a rotation, is:

6 48 Bulletin of the Transilvania University of Braşov Vol. 3 (5) - 00 Series II P rot - crankshaft rotation required power in W; τ - tie of a rotation, period of the crankshaft rotary otion, in s. 3. Results and Discussions Moveent during rotation is calculated as: Fig. 8. Influence of the width of the spades on the variation of the specific cutting surface in working the soil with the digging achine L L P τ rot rot ss = = [J], () Vrot Vrot where: L rot is the echanical work done by the digging achine at a rotation of the achine shaft in J; V rot - volue of soil displaced in a rotation of the rotor shaft, in 3 ; π τ = [rad/s]. () ω Dislocated soil volue to a rotation of the crankshaft is calculated with: V rot = s a B [ 3 ], (3) where B is the width of the digging achine, in. Crankshaft rotation power required is calculated as: µ ρ g a b v ω t B a ρ v vx rot = f Gs v z R sin P sinψ cosψ π ψ v [W]. (4) Making substitutions in equation () the forula of specific echanical work changes in: L s ss = x f G a B µ ρ g a b z ρ v B sin ψ cosψ π ρ g tg ψ v ϖ [J/ 3 ]. (5) In equation (5) notations correspond to those of equation (). Relationship (5) provides inforation on factors that influence specific echanical work and also on the energy consuption of the digging work. Working depth, working speed, width of spades influences the specific echanical work of the soil with digging achine with the soil. To study the influence of each factor, in the theoretical part are considered the concrete conditions of theoretical study as: f = 0.5, G s = 600 N, ρ = 500 kg/ 3, µ = 0.36 between soil and steel; tg ψ ed = 0.6; ω = 7 rad/s; B =.4 ; v xed = 4.37 /s; b = 0. ; z = 6; a = 0.3 ; v = 0.4 /s. Fro the graph shown in Figure 9 it results that the depth variation is inversely proportional to the variation of echanical work specifically. With increasing depth, occurs the decrease of the echanical work needed in the processing of the unit volue of soil by digging. Fro the graphics shown in Figures 0, results that by increasing the working speed and width of the spades results an increase in the necessary echanical work needed for processing the unit volue of the soil by digging.

7 Brătucu, Gh.: Matheatical Model of the Energetic Consuption for Soil Digging Machines 49 Fig. 9. Influence of the depth of working on specific echanical work of digging achine with the soil The energetic optiization possibility application on the soil digging work based on the atheatical odeling ade in this paper presuppose the collaboration between designers and anufactures for soil digging technical equipents, but also a superior training of the agriculture operators. These ust assure optial adjustent for technical syste oveent speed concordant to physicalcheical soil characteristics, to existent grass quantity etc. Through applying the research results obtained by the atheatical odeling proposed in this paper a contribution can be brought to the achieveent of soe agricultural works of superior quality in optial econoical conditions. 4. Conclusions Fig. 0. Influence of work speed on specific echanical work of digging achine with the soil Fig.. Influence of the width of the spades on the specific echanical work of the soil with the digging achine Using the soil digging achine in preparing the gerination bed in greenhouses is justified in working the soil at greater depths but with lower work speed. The digging achine which has wide spades requires a larger aount of echanical work for the unit volue of the soil processed. Conclusion that refers to the width of the spades is benefic when. Designing the achine or when purchasing it, it can serve as basis for decision. The reduced diensions of the deployed slices of the soil lead to higher specific surfaces, at the sae tie high energy consuption in working of the soil by digging achine. Higher working speeds result in high advances at oving forward, so big slices are deployed, reducing the energy required for processing by digging of the soil. Using the soil digging achine for preparation of the gerination bed in greenhouses is justified through the working of the soil at greater depths.

8 50 Bulletin of the Transilvania University of Braşov Vol. 3 (5) - 00 Series II References. Brătucu, Gh.: Agricultural Technologies. Braşov. Transilvania University Publishing House, Drunek, L.J.: Researches on the Energy Optiization of the Preparation Works of the Gerination Bed in Greenhouses. In: Ph.D. Thesis, Transilvania University of Braşov, Ros, V., et al.: Matheatical Model for Energetically Analysis of the Soil Work Process. In: Trans Agra Tech Conference, Cluj-Napoca, 7-8 October 998, p Rus, Fl.: Machines for Soil Works, Sowing and Crop Maintenance, Braşov. Transilvania University Publishing House, Şandru, A., at al.: Energetic Consuption Reduction through Rational Using of the Agricultural Aggregate. Craiova. Scrisul Roanesc Publishing House, Toa, D., et al.: Econoic Use of the Energy in Agricultural Mechanization. Bucureşti. Ceres Publishing House, Voican, V., Lăcătuş, V.: The Protected Cultivation of the Vegetables in Greenhouses and Solarius. Bucureşti. Ceres Publishing House, 004.