The article presents approaches to the formation of a general computational scheme for modeling (simulating) the particle motion on an axisymmetric rotating curved surface with a vertical axis of rotation. To describe the complex particle motion over a given surface, the fundamental equation of particle dynamics in a non-inertial reference frame was used, and by projecting it onto the axes of cylindrical coordinates, the Lagrange’s differential equations of the first kind were obtained. According to the proposed algorithm in C#, an application was developed that enables graphical and numerical control of the calculation results. The program interface contains six screen forms with tabular baseline data (input) and a table of a step-by-step calculation of results (output); particle displacement, velocity, and acceleration diagrams constructed along the axes of the system of cylindrical coordinates ρ and z; graphical presentation of the generate of the surface of revolution and the trajectory of the absolute motion of a particle over the axisymmetric rotating surface developed in polar coordinates. Examples of the calculation of the particle motion are presented. The obtained results can be used for the study and design of machines, for example, centrifugal rotary chopper machines.
Abstract.A design and technological scheme of the grain crusher of shock-reflective action has been developed. As a result of the conducted research, dependences have been established describing the relative motion of a particle along the rotor blade at particular values of the angular velocity of the rotor, the angular coefficient of the plane, the coefficient of friction, and time. Analysis of the impact of individual indicators was carried out with the help of a developed program, tested under laboratory conditions. The research allows developing an efficient grain crusher at the design stage, to determine such adjusting parameters by which it is possible to obtain a finished product with a minimum energy intensity and maximum productivity.Keywords: grain, crusher, rotor blades, particle movement. IntroductionGrain is a valuable source of feed for farm animals. However, in order to increase the digestibility of the nutritional elements and their quality, as well as to obtain various feed mixtures, appropriate processing and preparation for feeding are required, including crushing [1].Efficient methods of preparing grain for feeding are crushing and grinding. Grinding of grain is used more for the production of food flour for baking bread and confectionery products. Crushing of grain is widely used for the preparation of feed for animals on the farms and in the mixed feed industry. Due to their high efficiency and the wide range of grinding, rotary crushers are widely used [2].In the exploration process of the operation of rotary grain crushers, the main regularities determining the efficiency, the degree of crushing, the energy consumption, etc. were revealed [3][4][5][6]. However, with the development of the feeding technologies, new requirements are imposed on the operation of the crushers, and constant improvement of their structures is required.During the research [7; 8] it was revealed that one of the main problems of rotary crushers is the heterogeneity of the crushed grain by its fractional composition and the high energy intensity of the process. First of all, this is due to untimely removal of the finished product from the crushing chamber.Therefore, the development of these machines with justified optimal design parameters is an important and urgent task. Establishment of theoretical regularities of the crushing process allows us to determine the optimal ranges of parameters and, already at the design stage, to make appropriate corrections in the design.The aim of this work was a mathematical description of the interaction of grain with the rotor blades, and the development of a model for the movement of a particle in the crushing chamber of the rotary grain crusher.
The most important process that affects the quality of the product obtained during the processing of buckwheat into cereals is peeling -the separation of films (outer shells) from the grain, which is carried out by peeling machines that differ in different ways of affecting the grain and the design of working elements. The Kazan State Agrarian University is working on developing devices with a reversible deck for peeling buckwheat grains. Their practical significance lies in the fact that the use of such devices eliminates the need for preliminary separation of grain into fractions according to geometric dimensions, and also increases the efficiency of grain peeling due to the influence of a complex of balanced forces on it. We consider a new design of a device for peeling buckwheat grain with a variable deck, which differs from existing devices in its compactness, low metal consumption, and low energy costs. To determine the performance indicators of the proposed peeling device, a laboratory prototype was created that allows, by changing the rotation frequency of the blade rotor and deck, to determine the peeling coefficient (a quantitative indicator) and the core integrity coefficient (a qualitative indicator). According to the results of the conducted experiments, the best indicators of peeling efficiency are observed, when peeling buckwheat grain with the moisture content 14, and 15 % after hydrothermal treatment at the rotor speed varied from 2100 to 2250 min -1 and deck speed -from 950 to 1150 min -1 .
Increasing the efficiency of agricultural production, in particular the production of crop products in personal subsidiary plots, depends on the development and implementation of high-tech machines and their working units. The need for small-sized tillage equipment is increasing from year to year. But in order to increase the functionality of the equipment and the quality of soil preparation for sowing, it is necessary to study the possibility of using various additional working units. The purpose of the work is theoretical studies of the movement and kinematic connection of a trailed slatted-spiral roller with a walk-behind tractor, which make it possible to substantiate rational design and technological parameters of a small-sized tillage tool. The study used the provisions of classical mechanics and analytical geometry, methods of equilibrium and motion of mechanical systems based on differential and integral principles of mechanics. The design of active and passive rollers for a walk-behind tractor is considered, which allows to qualitatively prepare the soil for sowing at the depth of seeding, the influence of potential and non-potential effects on their generalized forces is revealed, the angular velocity and their acceleration are determined, as well as the dynamic characteristics of the moment of inertia of the rollers relative to the axes of rotation X4 and Z4 and their frames relative to the axes of rotation X3 and Z3. The difference in the generalized force for a passive roller relative to the angle φ 5.49 N∙m was obtained. The angular speed of the active roller is 23.0 rad/s higher than that of the passive roller, and as a result of research it was revealed that the moments of inertia of the active roller and its frame relative to the axles are significantly higher than that of the passive roller. Generalized forces for an active roller relative to the angle q = 2.58 N∙m and relative to the angle φ = 1.98 N∙m, for a passive roller - relative to the angle q = 2.32 N∙m and relative to the angle φ = 7.47 N∙m. The generalized forces for the potential effects of an active roller are Qθa=1.58 N∙m, Qφa=2.26 N∙m, for a passive roller Qθn=1.32 N∙m, Qφn= 4.60 N∙m. Mθa = 1 N∙m, Mφa = 114.63 N∙m; passive roller - respectively Mθn = 1 N∙m, Mφn = 178.9 N∙m
Establishing optimal technological and design parameters of tillage tools is essential for ensuring tillage quality and lowest possible energy consumption by the tillage process. For simple plane soil looseners, used on the majority of tillage machines, this task is successfully achieved. In the meanwhile, significant proportion of tillage machines has relatively complex tools, which combine translational motion of the tool with rotation around its axis. This article studies the process of soil interaction with a screw conical subsoiler mounted on bearings. The subsoiler can freely rotate around its axis. The surface of the subsoiler is described by the screw surface equation bounded by a circular cone. External action on the subsoiler body is a resultant of normal and tangential forces applied to screw surface and friction force in the bearings. Theoretical dependencies have been obtained which determine the resultant force of soil on the screw surface of the subsoiler. This force is composed of the sliding friction force and the force appearing due to frontal soil flow after destruction of soil structural cohesion. The article also gives results of numerical calculations. The obtained dependencies allow studying the influence of technological and design parameters of the screw tool on the tillage process and substantiate parameters’ optimal values.
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