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Transactions of the ASAE Vol 47 5 1389 1404 2004 American Society of Agricultural Engineers ISSN 0001 23511389 ANALYSIS AND DESIGN PARAMETERS FOR INCLINED ROTORS USED FOR MANURE DISPERSAL ON BROADCAST SPREADERS FOR SOLID MANURE J Duhovnik J Benedi i R Bernik ABSTRACT The process of manure spreading is an important step in cultivating land for agricultural production For this rea son the technical process of manure spreading was studied using various methods of scientific research and analysis The focus was primarily on improving the working principles of manure spreading using so called wide angle manure spreaders Results of the analysis of material transport along the rotor revealed the most relevant parameters of manure spreading It was found that friction is not the most important parameter The initial position of pieces of manure and the rotational frequen cy of the rotor are far more important The coefficient of friction between the rotor and pieces of manure has a minimum influ ence on the tangential speed of a piece on the rotor which in turn also means a minimum influence on the range of spreading The initial position of the piece on the rotor has an influence on the tangential speed and travel of the piece on the rotor The tangential speed of the piece as it departs from the rotor is influenced by the size of rotor and the rotational frequency of the rotor Included are recommendations regarding the process of constructing a new spreading device or improving existing methods of spreading manure Keywords Broadcast application Manure spreaders Mathematical models Spreading he spreading of manure is an important step in culti vating land for agricultural production Solid ma nure is a side product of cattle raising and its direct use for field fertilization is a basic requirement Different technologies for spreading solid stable manure are known but all have certain characteristic parameters in com mon Redelberger and Kuyhlmann 1989 The most impor tant criterion is the maximum possible spreading capacity with respect to the relief of the surface to be fertilized Anoth er criterion is the maximum possible uniformity of spreading perpendicular to the line of spreading In addition certain parts of the field need to be covered properly such as the be ginning and end of manure spreading blind angles along the line of spreading corners large variations in the slope of the fertilized surface etc Frick et al 2001 These criteria constitute the functional requirements for defining the tech nical process of manure spreading Once the technical process has been properly defined the elements of the technical system that will fulfill the set of functional requirements in their entirety or partially can be determined VDI 1993 Therefore individual solutions for the technical system are as a rule adjusted to the technical process The conceptual design process defined in this manner for each piece of work equipment allows various technical solutions to be used in the spreading process avbi Article was submitted for review in December 2002 approved for publication by Power phone 38614771507 fax 38612527232 e mail joze duhovnik lecad uni lj si and Duhovnik 2001 avbi and Duhovnik 1996 A study of the literature and the equipment supplied by well known manufacturers that is currently available on the market has shown several methods of manure spreading as described below Frick et al 2001 Huschke 2001 Benedi i 2002 The most commonly used method for stable manure spreading uses vertical beaters e g Bergmann spreader L Bergmann GmbH Goldenstedt Germany Huschke 2001 Benedi i 2002 A manure spreader with horizontal beaters is also manufactured P ttinger spreader Alois P ttinger Maschinenfabrik GmbH Grieskirchen Austria Huschke 2001 Benedi i 2002 and recently there has been an increasing number of manure spreaders with wide angle spreading devices e g Kemper spreader Maschinenfabrik Kemper GmbH Stadtlohn Germany and Bergmann spread er L Bergmann GmbH Goldenstedt Germany Huschke 2001 Benedi i 2002 Most spreading devices do not permit adjusting the spreading width during operation In addition the coefficient of variation CV is very large over the entire width of spreading Frick et al 2001 The prEN 13080 standard stipulates CV measurement only for the case of overlapping Final Draft European Standard 2002 Thus no real data are available on the spreading of manure over small surfaces where there is no overlapping The effective spreading width depends on the type of the manure spreader If the desire is to have the surface uniformly fertilized then manure must be spread by overlapping the adjacent manure spreader swaths since the amount of manure along the edges of one spreading width is very small Frick et al 2001 Modern manure spreaders should provide a more uniform and precise spreading of organic manure over the desired surface This would increase the operator s control increase the quality of the spreading process and indirectly increase the utilization of the spread manure T 1390TRANSACTIONS OF THE ASAE Manure Spreading Unspread Bulk Manure Spread Manure Feeding of Manure Shredding of Manure Transport to Spreader Dispersal Figure 1 Division of the manure spreading function into partial functions Based on our research it was recognized that the most important parameter of the manure spreading process is the path that pieces of manure cover from the container of the manure spreader to the fertilized surface The best method for increasing the rate of manure application kg s from a manure spreader is by increasing the spreading width Increasing the rate of manure application by increasing the speed of the vehicle along the manure spreading line is limited both with respect to the relief of the ground and the performance of the tractor and trailer combination For this reason more recent development of manure spreaders has been oriented toward increasing only the spreading width An increasing number of manufacturers produce manure spread ers with wide angle spreading devices which achieve spreading widths of up to 24 m While defining the technical process it was found that the manure spreading width directly depends on the dispersal assembly essentially an ejection assembly of the manure spreader The dispersal assembly functions on the principle of centrifugal throw out and projectile motion Meriam 1993 If very homogeneous material flow is achieved of stable manure in this case then the centrifugal dispersal process can be defined in great detail However in this case material flow is highly non homogeneous Therefore the uniformity or maximum possible homogeneity of pieces of manure in the material flow prior to entering the dispersal assembly is an important condition for defining the quality of spreading In the analysis below the focus will be on the process of spreading manure pieces Our analysis showed a few important parameters that affect the technical solution All of the essential ones i e diameter rotational frequency size of manure pieces manure feeding area and manure spreading area were analyzed and are shown in figures for clearer presentation A numerical simulation of the manure spread ing process was also performed and the parameters that most affect the quality of spreading were identified Values of these parameters that would yield the best results for spreading under predefined conditions including the unifor mity of spreading and range which is the distance traveled by a manure piece thrown by a spreading device were determined This article provides the theoretical basis for numeric calculation of the flow of pieces of manure from the spreading device onto the fertilized surface It is not the only example of flow control of artificial manure on hydraulically driven rotors that was found in the literature Hesse and Keuper 2002 however a numeric analysis of stable manure dispersal has not been found yet Hesse and Keuper paid more attention to the energy consumption and mass flow control In our case the flow control and the quality of dispersal as a result of the flow control of mass pieces were given the priority Benedi i 2002 MANURE SPREADING PROCESS To understand the manure spreading process it is necessary to make a detailed and comprehensive description of the process It is evident from the literature avbi and Duhovnik 2001 that the spreading process can be described by the functional structure which shows what partial functions need to be performed in order to obtain the desired result i e dispersed manure Division into partial functions helps us to build the model of numeric analysis of dispersal A detailed review of the available manure spreader types showed that some spreaders differ only in the method of execution of the working principle while in a few the manure spreading function is divided into the partial functions of shredding and dispersal of pieces of manure fig 1 1 Feeding of Manure Stable manure is loaded into the manure spreader s container and needs to be transported to the shredding assembly The feeding of manure is performed by a drag apron This can be driven continuously or in a stepwise manner The amount of manure reaching the dispersal assembly depends on the speed of the feeding assembly 2 Shredding of Manure The pile of manure from the container which is trans ported by the feeding assembly to the shredding assembly needs to be cut into small pieces The shredding assembly typically consists of vertically or horizontally positioned beaters These mash and cut the manure from the container into small pieces and then distribute it evenly over the entire width of the spreading device 3 Transport to Spreader The partial function of transporting pieces of manure ensures that these are moved from the shredding assembly to the dispersal assembly of the manure spreader It is important to guide pieces of manure from the shredding assembly to a specific area of the dispersal assembly The pieces that do not fall directly onto the dispersal assembly because of their inappropriate direction will travel along the metal guard and then reach this area 4 Dispersal of Manure The partial function of manure dispersal is the most important one because the functionality of the entire device depends on it The range and uniformity of spreading varies The dispersal working principle must accelerate pieces of manure so that they exit from the spreading device at the highest possible speed and thus achieve the maximum dispersal length i e range Most manure spreaders available on the market have the following partial functions shredding transport and dis persal of manure pieces The construction of most manure spreaders on the market enables the performance of partial 1391Vol 47 5 1389 1404 Table 1 Static coefficient of friction of manure on unpainted steel Coefficient of Friction dimensionless Moisture Content wet basis Moist Manure m Dry Manure d Moist Manure Dry Manure 0 670 777970 functions with a single unit but lately manufacturers have in creasingly been offering manure spreaders wide angle manure spreaders that consist of only a shredding assembly and a dispersal assembly The shredding assembly has re mained unchanged and has vertical or horizontal beaters which crush the manure into pieces These pieces then leave the manure spreader via the dispersal assembly In the case of wide angle manure spreaders these partial functions are performed by separate devices that follow one another THEORY AND PROPERTIES OF THE MANURE SPREADING PROCESS In the manure spreading process dispersal is based on the principle of centrifugal throw out The mass flow into the centrifugal ejector is relatively large so the simulation was based on the analysis of the movement of manure pieces Input data constitute an important part of the analysis Among the essential factors is the material itself i e stable manure It is important to analyze the mechanical and physical properties of the manure in detail MECHANICAL AND PHYSICAL PROPERTIES OF ORGANIC MANURE All materials have certain properties that affect their usability For numerical simulations the coefficient of friction between manure and the surface on which it slides is required The coefficient of friction depends on the surface and on the density moisture content and type of the manure Therefore values for the coefficient of friction vary considerably from 0 6 to 0 98 for example with storage conditions e g poultry manure Pezzi and Rondel li 2002 The coefficient of friction is influenced by many factors In our case the coefficient of friction was measured on cattle manure according to the DIN 51131 standard DIN Standards 1999 The objective was to verify the influence of manure moisture content on the coefficient of friction Measurements were performed on two types of manure seven measurements on manure with a high moisture content and seven on manure with a low moisture content In both groups of measurements the lowest and highest values were eliminated The average value of the coefficient of friction for the remaining measurements was used in the numerical calculations table 1 Measurements indicated that cattle manure with a low moisture content has a higher coefficient of friction than cattle manure with a high moisture content The higher the density the greater the moisture content Similar results have also been stated in other literature Redelberger and Kuyhl mann 1989 Dohler and Biskupek 1993 Highnett 1985 MATHEMATICAL MODEL The selection of the mathematical model is an important step in developing the procedure for performing the calcula tions of a numerical simulation Benedi i 2002 Hesse and Keuper 2001 Meriam 1993 as the correctness of simula tion results considerably depends on it A mathematical model was thus made for the case of a rotor in which the blades rotate and the base is stationary fig 2 The selection of this type of rotor enabled numerical simulation of the Figure 2 Top view of blades and rotor surface showing the mathematical model 1392TRANSACTIONS OF THE ASAE movement of pieces of manure along the rotor surface The pieces move in two dimensions therefore the mathematical model was also made for a two dimensional space A manure piece on the rotor surface moves according to the laws of dynamics Meriam 1993 To simplify the analysis the problem was solved in a polar coordinate system The motion of a manure piece is fully described by equations in the radial direction re in relation to the movement and in the tangential direction e in relation to the movement Due to the forces acting on the piece as a result of the rotor rotation and the movement of the piece the manure piece moves in radial and tangential directions relative to the rotor In the radial direction re forces acting on the manure piece are the following the force of friction 1 T F between the manure piece and the stationary surface the force of friction 2 T F between the blade and the manure piece and the radial force r am In the tangential direction e in fig 2 the following forces act on a manure piece the tangential force am and the force of the blade F which causes the force of friction 2 T F between the blade and the manure piece fig 3 The force of friction 3 T F between the manure piece and the stationary surface on which it moves should also be taken into account When determining the mathematical model it is very important to know which influences and properties to take into account and which to neglect It has already been mentioned that the influence of air resistance will not be taken into account in the numerical simulation Air resistance affects only the magnitude of the results speed range etc but not the direction of movement or the selection or determination of the parameters having a significant effect on the quality of manure spreading Thus a simplified numeri cal simulation which does not take into account the influence of air resistance can be used to determine the most important parameters these parameters can later be used when designing new manure spreading mechanisms As a whole organic manure is a nonhomogeneous material but crushing during the manure spreading process yields small pieces The sizes of pieces also depend on the storage time Manure stored for relatively long times has a majority of pieces smaller than 12 mm Pezzi and Rondelli 2002 It was presumed that manure with small pieces can be treated as homogeneous so the mechanical and physical properties of all pieces can be considered nearly the same This is also true for the cattle manure Simulation of the movement of a manure pieces was performed in two steps 1 movement of manure pieces along the rotor surface and 2 movement of manure pieces after leaving the rotor Movement of Manure Pieces Along the Rotor Surface A manure piece falls onto the rotor surface fig 2 stays in the same location on the rotor until a blade reaches it and then starts a circular movement together with the blade The centrifugal force causes the manure piece to move toward the Figure 3 Top view showing movement of pieces of manure along the rotor surface 1393Vol 47 5 1389 1404 edge of the blade and rotor This movement is described by a differential equation in the radial direction re rTT amFF 21 1 and for the tangential direction e amFFT3 2 Equations 1 and 2 are solved as differential equations 2 22 ggrrr 3 The solution of equation 3 is given in equation 4 which defines the radius of motion as a function of time r t The movement of a manure piece along the rotor surface is also a function of time and is influenced by the coefficient of friction of the manure piece on the surface on which it moves the initial distance of the manure piece from the center of rotation r0 and the rotor angular velocity Equation 3 is not dependent on the mass of the manure piece which means that by solving equations 1 and 2 the effect of the mass has been eliminated The results of the calculations are thus independent of the si