Particle motion over a plane, which rotates about a horizontal axis and makes a certain angle with it

Differential equations of relative material particle motion over a plane, which rotates about a horizontal axis, have been set up. Plane location relative to a rotation axis is set by a certain angle, which value can range from zero to ninety degrees. If angle value is equal to zero, a plane passes through a rotation axis; if angle value equals to 90 degrees, it is perpendicular to a rotation axis. The equations have been solved using numerical methods. In case of end positions of an angle, analytical solution has been found

Harrow with screw-type operating tools: optimisation of design and process parameters

Received: August 1st, 2022 ; Accepted: September 8th, 2022 ; Published: September 9th, 2022 ; Correspondence: [email protected] new design of the harrow with screw-type operating tools is presented in the paper. It describes the theoretical and experimental investigations carried out for the purpose of optimising the design and process parameters of the harrow with screw-type operating tools. Such optimisation will provide for improving the soil fertility, when burying chaff and other plant residues as organic fertilisers into the soil during its tillage. On the basis of the results obtained in the comprehensive experimental investigations, new regression relations have been generated. These relations provide for determining the proportion of the field surface, where the after harvesting residues have been completely buried in the soil with the harrow with screw-type operating tools. It has been established that the dominant effect on the relative amount of the field surface area S with completely worked-in plant residues is produced by the soil tillage depth h, then follows the factor of the screw-type operating device battery approach angle β. The pitch distance Т of the screw-type operating device has the smallest effect. The results of the completed research prove that increasing the pitch distance Т of the screw-type operating tool from 0.18 m to 0.26 m results in the decrease in the area S of the field surface with the plant residues buried in the soil by 1.4%. An increase in the approach angle β from 20° to 40° results in the increase in the field surface area S with the plant residues completely worked into the soil by 5.6%. Increasing the soil tillage depth from 0.08 m to 0.12 m results in the increase in the above-mentioned surface S by 7.1%. The simultaneous action of the factors of the tillage depth h and the approach angle β results in the percentage of the surface S rising from 72% to 82%

PARTICLE MOTION OVER THE EDGE OF AN INCLINED PLANE THAT PERFORMS AXIAL MOVEMENT IN A VERTICAL LIMITING CYLINDER

Differential equations of a relative material particle motion over the edge of an inclined flat ellipse that rotates around the axis of a vertical limiting cylinder have been deduced. The position of a plane relative to the axis of the rotation is set by the angle ranging from zero to ninety degrees in its value. If the angle is equal to zero, the plane is perpendicular to the axis of rotation and if the angle is equal to ninety degrees, it passes through the axis of rotation. The equations have been solved using numerical methods. Analytical solution has been found for certain angles. The aim of the research is to investigate the transportability of a technological material in a vertical direction by a cascade operating element that rotates in a cylindrical cover. The working part of the operating element is an inclined rigid plane, which is limited by an ellipse — the line of its contact with a cover. The objective of the research is to analytically describe the movement of a single particle of the technological material on two surfaces, namely, an inclined plane and a vertical cover. The research methodology is based on the methods of differential geometry and the theory of surfaces, theoretical mechanics and numerical methods of solving differential equations. The paper presents a first developed analytical description of the relative particle motion in an ellipse — a contact line of an inclined plane and a limiting vertical cylinder, in which the inclined plane rotates. The kinematic characteristics of such motion have been determined

Transportation of a material particle by the operating mechanism of an agricultural machine in the form of a vertical screw confined by a coaxial stationary cylinder

The use of vertical augers in screw conveyors significantly expands the operational capabilities of such mechanisation equipment for performing loading and unloading technological operations. However, the existing designs of vertical screws do not fully meet the operational requirements. Their main disadvantages are increased energy consumption, especially with their significant overall dimensions, which depend on the influence of friction of the process material on the conveyor surfaces. Therefore, the study considers the movement of a material particle by the operating mechanism of an agricultural machine in the form of a vertical screw confined by a coaxial stationary cylinder and establishes the dependence of the speed of transportation of a material particle on the influence of the particle friction coefficient on the surface of the screw and on the surface of the limiting cylinder. The purpose of the study is to determine the parameters of the movement of agricultural material particles when they interact with the helical surface of the operating mechanism of a vertical conveyor in the form of a screw that rotates around the axis and the surface of a coaxial fixed cylindrical casing. Mathematical modelling of the processes of movement of soil particles along the helical surface of the operating mechanism is described on the basis of general laws and principles of analytical and differential mathematics, theoretical and analytical mechanics. As a result of the study, the differential equations of movement of a particle of agricultural material on the helical surface of the screw, which rotates around its axis in a fixed cylinder, were compiled. The equation is solved using numerical methods and the trajectories of the relative motion of the particle along the helical line – the edge of the screw, which is common to the surface of the screw and the limiting cylinder are constructed. The friction forces of the material particle on the surfaces of the screw and casing are also considered. The limit value of the helical line lifting angle is found when the particle lifting becomes impossible at a given angular velocity of screw rotation. The influence of the friction angles and radius of the limiting cylinder on the particle lifting speed is estimated. Graphs of kinematic characteristics as a function of time are given. The materials of the study can be used by researchers for further investigation and by practitioners in the selection of conveyors for transporting agricultural material

Study of the movement of soil particles on the surface of a screw tillage working body

This study considers the interaction of soil particles with a screw tillage body, the working surface of which is made in the form of a deployed helicoid and substantially differs from the screw. Furthermore, the unfolded surface is characterised by manufacturability of the working body, since it is possible to calculate the geometric dimensions of a flat workpiece, which is formed into a finished product by simple bending with minimal plastic deformations. The purpose of this paper was to conduct theoretical and experimental studies of the movement of soil particles along the helical surface of the tillage working body, which is made in the form of a deployed helicoid. Mathematical modelling of the processes of movement of soil particles along the helical surface of a tillage working body was described based on general laws and principles of analytical and differential mathematics, theoretical and analytical mechanics. Experimental studies were carried out using a methodology with elements of mathematical statistics, mathematical methods of optimal planning of a multifactor experiment. The analysis of the results of experimental and theoretical studies was performed using applied computer programmes and systems. Experimental studies were conducted according to standard and independently developed methods. Results: a mathematical model of the movement of soil particles along the helical surface of the tillage body was developed, and it was established that when the angle of attack of the helical tillage working body increases, the lifting value of soil particles increases and the area of their dispersion by the helical surface increases. The value of the coefficient of friction does not substantially affect the shape of the trajectory of the soil particle. The quality of loosening the soil most depends on the angle of attack of the screw surface and the angular speed of rotation of the working body. The materials of this paper can be used by scientists for further research and practices in the selection of tillage units

Justification and calculation of design and strength parameters of screw loaders

Existing designs of screw working bodies of transport and processing machines cannot always provide the required performance and avoid overloading, which causes deformation and damage to parts of the mechanisms. Thus, it is necessary to establish new efficient screw working bodies that would ensure the execution of the technological process. The purpose of the study was to substantiate and explore the design and methodology for calculating the main structural-power parameters of the developed screw loader, to synthesise screw loaders using the method of morphological analysis to obtain designs of mechanisms with better technical and economic characteristics. The methods of surface theory, analytical and differential geometry, computer graphics and mathematics were used to conduct the research. As a result of theoretical and experimental studies, the designs of screw conveyors with hopper loading and screw conveyors with nozzle loading are presented. In addition, a classification of loaders for screw transport and technological mechanisms is presented. The dependencies for calculating the design of screw conveyor loaders are determined. The synthesis of loaders and mixers by the method of morphological analysis was performed to obtain designs of mechanisms with the best technical and economic characteristics and competitive designs of mechanisms were established. A system of coding and synthesis of structural elements and mechanisms of screw implements with improved technological properties is proposed, and competitive designs of screw implement that perform technological processes efficiently and effectively are selected. A methodology for calculating the main structural and power parameters of a screw loader has been developed, which allows for determining the parameters of a screw loader. The materials of the research can be used in further studies of screw conveyors and, in particular, screw loaders to determine their design, technological, energy and power parameter