Mathematical Planning Of Experiment Research Articles

THERMODYNAMIC-KINETIC RESEARCH AND MATHEMATICAL PLANNING ON THE OBTAINING OF PHOSPHORUS-CONTAINING COMPONENTS BASED ON COTTREL DUST FROM PHOSPHORUS PRODUCTION WASTE

The research work is designed to develop a technology for the disposal of phosphorus-containing waste through their complex processing to solve regional environmental problems. In this development, thermodynamic and kinetic patterns are determined and optimal process parameters are established using the method of mathematical planning of experiments.

Development of alkaline concrete on the basis of active aggregates

The object of the research is the process of directed structure formation in the body of alkaline concrete, made using a reactive aggregate, in this case, basalt, and the process of deformation development in such concrete. The problem with using reactive aggregates is that they cause alkaline corrosion. It manifests itself in the form of cracks and layers of gel-like substances that form at the point of contact of the aggregate with the cement stone. During the research, methods of physical and chemical analysis were used (X-ray phase, differential thermal and thermogravimetric analyzes, electron microscopy, infrared spectroscopy, microprobe analysis). And also methods of mathematical planning of experiments have been used for the dependence of the physical and technical properties of cements and the directions of their structure formation. Also, the research has been carried out based on the analysis of world achievements in solving the problem of alkaline corrosion of concrete. The possibility of joint operation of the matrix of alkaline cements and active aggregates, represented by basalt, has been determined. The component composition of alkaline cement has been optimized and the need to increase the amount of the alkaline component in the system for the normal course of structure formation processes has been proved. The study of the influence of technical factors and conditions of hardening on the development of processes of structure formation of the investigated compositions has been carried out. The deformation properties of fine-grained concrete based on slag-alkaline cement and basalt aggregate have been investigated. It is shown that the expansion deformations of the samples, which accompany the process of alkaline corrosion of the aggregate in concrete, are directly related to the component composition and hardening conditions of the material. The obtained research results confirm the possibility of using active aggregates for the manufacture of building materials, in particular, based on alkaline cements. But for the safe course of the processes of structure formation, the component composition of the system has to be adjusted by introducing an active mineral additive and an additional alkaline component. The use of hydrophobizing additives makes it possible to increase the strength of the material even when operating under normal heat and humidity conditions.

Developing the technology of associated gold recovery when concentrating copper-pyrite ore

Research objective is to address an up to date task of developing the technology of associated gold recovery from complex ore. Object of research is the gold-bearing copper-pyrite ore. Gold was recovered in laboratory conditions with the use of gravity methods of mineral separation. Research tools. Rational modes of machinery operation have been determined through mathematical planning of experiments including the obtained results processing by mathematical and statistical methods. Methods of research. Gold was recovered in the grinding-classification circuit based on a seriesinstalled short-cone hydrocyclone, a jigging machine and a shaking table. Research results. The developed jig mode differs from the existing ones by the closed-circuit of jig machine chambers: from the feed of the second (in the direction of the light fraction travel) jig chamber, the light fraction (tailings) and undersize product – fraction with the increased content of accessory minerals (rough concentrate) are separated. The rough concentrate in the second chamber is directed to the first chamber of the machine, where the finished jig concentrate is obtained in the form of an undersize product. The light fraction moves from the first chamber to the second and is removed from the machine through the tail board. When fine-tuning the heavy fraction of jigging on a shaking table, it is recommended to mix 1/2 part of the initial feed of the tables with the rough concentrate isolated from the other 1/2 of the original feed. The new jigging mode and the scheme of concentration on the tables provide an increase in the gold content in the initial feed of the apparatus, which is the reason for a decrease in gold losses with the tails of the gravity circuit. Research relevance. Gold recovery increment by 4.77% was obtained due to the use of all three recommended scientific and technical measures, namely sands concentration in a short head cone crusher on a jig, switching the jig chambers to a closed circuit, and jet motion of concentrates on shaking tables. Scope of the results. The results should be applied when concentrating ore containing free (amalgamable) gold, as well as gold-bearing pyrite.

Processing of finely dispersed technogenic raw materials for aluminum production in order to extract valuable components

The paper provides the results of experiments on the hydrometallurgical processing of finely dispersed technogenic raw materials for primary aluminum production in Soderberg cells (case study of the Irkutsk Aluminum Smelter) – aged sludge. The components of this sludge are dust from electrostatic precipitators (79.7 %), wet gas cleaning sludge (4.4 %) and coal froth flotation tailings (15.8 %). According to the grain-size analysis carried out, aged sludge sample particles have a size of –50 μm. According to the chemical composition analysis of the sludge sample, main components in it are carbon, cryolite, chiolite with a small amount of other compounds (corundum, ralstonite, spodumene, fluorite). Fluorine leaching experiments were carried out with a 2 % sodium hydroxide solution at a stirrer speed of ~1020 rpm. Using the mathematical planning of a three-factor experiment, it was found that the maximum concentration of fluorine in the solution (15.844 g/dm3) is achieved with the following optimal parameters of fluorine alkaline leaching: temperature of 90 °C, liquid-to-solid ratio of 9 : 1, and time of 90 min. The multidimensional polynomial equation was obtained for fluorine alkaline leaching from aged sludge. Cryolite was obtained from fluorine-containing solutions (by the reaction of sodium fluoride interaction with sodium bicarbonate and an aluminate solution), which was confirmed by X-ray phase analysis data.

ИССЛЕДОВАНИЕ ВОЗМОЖНОСТИ ПОВЫШЕНИЯ КАЧЕСТВА ПОДГОТОВКИ СУХИХ СТРОИТЕЛЬНЫХ СМЕСЕЙ В ГОРИЗОНТАЛЬНОМ ЛОПАСТНОМ СМЕСИТЕЛЕ

Paddle mixers with horizontal shafts are common at building materials enterprises for the preparation of concretes, mortars, dry mortars. A new design of a horizontal paddle mixer with rod elements located in front of the working surfaces of the blades, changing the trajectories of material particles, increasing their mobility, which leads to an increase in the degree of homogeneity of the mixed material, is considered. The aim of the study was to assess the influence of rod elements on the quality of preparation of a cement-sand mixture, to establish patterns of influence on it by the design and technological parameters of a two-shaft paddle mixer and to determine the areas of their rational values. The following tasks have been solved. A bench installation of a two-shaft horizontal paddle mixer with rod elements has been developed, on which experimental studies have been carried out on the preparation of dry cement-sand mixtures. For the criterion characterizing the quality of the mixture, the ultimate compressive strength of the prism specimens made from it is adopted. Regression equations are obtained that adequately describe the compressive strength of prism samples from the design and technological parameters of the mixer: the angle of the blades, the distance from the working surfaces of the blades to the rod elements, the rotational speed of the blade shafts, and their analysis is performed. The analysis of the change in the ultimate compressive strength of the prism specimens from the parameters under study is carried out, the rational ranges of their values are determined. It was found that a mixer with rod elements allows to obtain a dry cement-sand mixture, products from which have a higher compressive strength. During the work, the method of mathematical planning of experiments was used. As a result of the study, an assessment of the influence of rod elements on the quality of preparation of a cement-sand mixture was carried out, the regularities of the influence on it of the design and technological parameters of a two-shaft paddle mixer and the area of their rational values were established.

THE CHOICE OF FACTORS OF INFLUENCE ON VIBRO-CENTRIC SEPARATION OF LIQUID INHOMOGENEOUS RAW MATERSALS

The development of modern equipment and technology leads to healthy competition, which in turn allows you to freely choose a machine or installation for the separation of liquid inhomogeneous systems. Each production when choosing equipment takes into account the relevant factors and its specifics. Mathematical and statistical planning of a multifactorial experiment was used to refine the glycerin quality indicators and determine their weight. The article constructs the response surfaces of the optimization criteria, which allow us to clearly illustrate the dependences of the values of the mass fraction of pure glycerin and energy consumption on individual optimization parameters. The research method includes the selection of optimal modes of operation of the vibrocentric machine for purification of liquid glycerol-containing raw materials according to technical and economic criteria for evaluation and determination of quality indicators of purified glycerol with variation of processing time, process temperature, etc. During the study, special attention was paid to the main operating parameters of this vibrating machine, namely: amplitude-frequency, power and energy. The efficiency of the process of vibration-based purification of crude glycerol was evaluated on such parameters as vibration control, angular rate of flow, rate of temperature. The recommendations of the second basic parameters of the lateral period were determined in accordance with the second set of the second order. Analyzing the results of studies of vibration-centrifugal separation of liquid inhomogeneous raw materials, it can be argued that the most influential factors in the separation of these products are the rotor speed, vibration shaft speed, oscillation amplitude, power, temperature and processing time.

TO INVESTIGATE THE MATHEMATICAL MODELING OF THE PROPERTIES OF EFFECTIVE CERAMIC PASTE WITH BURNT ADDITIVES FROM AGRICULTURAL WASTE

Results of scientific research on determination of optimum prescription and technological parameters of effective ceramic brick with burn-out additives, obtained by the method of mathematical planning of experiments are given in the article.

Medicines with active pharmaceutical ingredient diosmin: plaining of sample preparation

BACKGROUND: Most drugs in the form of tablets contain diosmin in the micronized flavonoid fraction. This is the reason for the low level recovery by means of solid-liquid extraction.
 AIM: to determine optimal conditions for sample preparation of some drugs with active pharmaceutical ingredient diosmin with the use of mathematical experiment planning (Box-Behnken design).
 MATERIALS AND METHODS: The study subjects were tablets Detralex 1000 mg, Venarus 900 mg, Detravenol 1000 mg, Flebaven 1000 mg, Phlebopha 600 mg, Phlebodia 600 mg. Estimation of diosmin recovery by the method of solid-liquid extraction was made according to the algorithm of full factorial design with three level factors (Box-Behnken design).
 RESULTS: The effect of some factors determining the extraction of diosmin from tablets Detralex 1000 mg, Venarus 900 mg, Detravenol 1000 mg, Flebaven 1000 mg, Phlebopha 600 mg, Phlebodia 600 mg was estimated. Mathematical (regression) models of solid-liquid extraction of diosmin for each drug were developed. The most significant factor determining the diosmin recovery from drugs (tablet formulation) is the sodium hydroxide concentration. Other factors (acetonitrile concentration, extraction time, centrifugation time, addition of ammonium sulfate) fail to exert significant effect. The optimal value of sodium hydroxide concentration is 0.02 mol/l. Diosmin recovery doesnt increase after the increase of the sodium hydroxide concentration above 0.02 mol/l.

Study of the functional properties of dough

The paper presents the studies of gluten - free types of unleavened dough, it shows the effect of hydrocolloids on the structure of the dough. The aim of the work is to study the functional and technological properties of the dough depending on the type and concentration of the flour and hydrocolloids. The tasks of the research are the following: to determine the concentration of colloids that makes dough plastic and strong dough; to identify the dependence of the concentration of flour on the type and properties of hydrocolloids; to study organoleptic quality indicators. The dynamic viscosity of the dough was determined by using a Brookfield viscometer. The methods of mathematical experiment planning were used to design the recipes of the unleavened dough. To define the reference dependency of viscosity on shear rate, the coefficients of nonlinear model equations have been estimated by using the methods of regression analysis in the program Statistica v6. For the experimental samples, the equation of the viscosity dependence is determined as a model of non-linear multiple regression. The graphs of the viscosity dependence on the shear rate compared to the reference rate are made. The methods of mathematical programming have been used to find the optimal ratio of flour and each type of structure-forming agents (soy protein isolate, xanthan gum, and potato starch) in the dough to maximize the approximation of the viscosity curve to the reference one. For this purpose, an objective function with limits on the shear rate is compiled. Using the MathCAD v15, the optimal values of the content of the components such as rice flour - 27.78%, soy protein isolate - 7.22%, potato starch - 32.22%. xanthan gum - 0.28 % are found. The results of the control measurement of the viscosity of the sample with the optimal composition indicate that the selected mathematical model corresponds to the elastoviscoplastic properties of this dough and the curve changes depending on the composition of the dry dough mixture. The description of the mathematical model and the regression analysis make it possible to select the ratio of the prescription components so that the resulting product has rheological characteristics close to the control sample.

Foam Polyethylene Made of Recycled Polyethylene

The paper deals with the main principles of foam polyethylene production by the addition of recycled polyethylene and a modifier in the initial mixture. Obtaining of the modified foam polyethylene will accomplish two important tasks: solve the environmental problem of recycling polyethylene waste and reduce the cost of the material. The optimal consumptions of recycled polyethylene and a modifier were determined by using the methods of mathematical experiment planning. To predict the main characteristics of the modified foam polyethylene a special nomogram was worked out. The properties of the developed material were studied. Based on the obtained results, it was found that the modified foam polyethylene had quite proper physical and mechanical characteristics and could be recommended for use in insulation systems of frameless and frame buildings, as well as in floating floor systems.

Parameters of the angle-lift of the front plow for smooth, rowless plowing

To improve the quality and energy indicators on the front plow in front of the housings, the angle axes are installed in the form of a triangular wedge. The purpose of the study is to substantiate the parameters of the angle-lift of the front plow, which provides high-quality performance of the technological process according to agrotechnical requirements with the lowest energy costs for smooth, rowless plowing. The research uses the laws and rules of theoretical mechanics, mathematical statistics, mathematical planning of experiments, and methods of strain measurement, as well as the methods given in existing regulatory documents. Based on the study of the process of interaction of the carbon monoxide with the soil, analytical dependences are obtained that allow us to determine the parameters of the carbon monoxide. According to the results of theoretical and experimental studies, it was found that the required quality of tillage with a front plow following the established agrotechnical requirements with minimal energy consumption is provided at the height of 22 cm, a length of 27 cm, a wing angle of 32° and an angle of inclination of the side face of 36°.

Development of a front plow with active and passive working bodies

The existing plows of smooth, furless plowing do not ensure efficient use of the power of energy-rich arable tractors, high-quality soil preparation for sowing and an increase in the productivity of the unit. The aim of the study is to substantiate the parameters of the active working body of the combined frontal plow, which ensures the efficient use of the power of energy-saturated arable tractors, high-quality soil preparation for sowing and an increase in the productivity of the unit. A constructive scheme of a combined frontal plow with active working bodies has been developed. Analytical dependencies are obtained that describe the process of interaction of an active working body with the soil and, on their basis, rational parameters of an active working body are determined. In the research, the laws and rules of theoretical mechanics, mathematical statistics, mathematical planning of experiments and methods of strain gauge were applied. It was found that when the active working body of the combined plow is in the form of an active cutter, its diameter is 572 mm, the number of knives is 5 pieces, the length of the knives is 16 cm and the sharpening angle is 20°, the required quality of plowing is ensured with the least energy consumption. In this case, the longitudinal distance from the nose of the body share to the shaft of the active working body of the combined frontal plow should be 3 cm, the indicator of the kinematic operating mode of the active working body – 2.19 the transverse distance between adjacent working bodies along the shaft of the active working body -26 cm.

Technological process of uniform distribution of fertilizers over the width of the coulter

The applied methods of applying fertilizers for cotton in Uzbekistan do not fully ensure the supply of nutrients to the plant's root system. The study aims to substantiate the technological process of uniform distribution of fertilizers in the root development zone and the parameters of coulters. When the fertilizer is distributed in the root development zone in tiers and the right ratio, the coefficient of their use increases, and the yield of cotton increases. The research uses the laws and rules of theoretical mechanics, mathematical statistics, mathematical planning of experiments, and the methods given in existing regulatory documents. The technology of forming new ridges instead of existing ridges and new furrows instead of existing furrows in fields with harvested husk with simultaneous fertilization and an improved chisel cultivator-fertilizer with comb-forming agents for its implementation, as well as the results of theoretical studies to substantiate the main parameters of the tuk coulter chisel-cultivator are presented. The study determined the parameters of universal fertilizer Coulter chisel-cultivator of fertilizer: the base cone of the diffuser in the form of an ellipse with minor axis width 10 mm, height tool provider relative to the upper base of the truncated cone of 60 mm, and a diameter of a half-cylinder of 20 mm.

Development of a frontal plow for smooth, furless plowing with cutoffs

The existing plows of smooth furless plowing do not provide a full turnover of layers within their own furrow and the incorporation of weeds, they have a high energy consumption. The aim of the study is to substantiate the parameters of the frontal plow cut-off, which ensures a high-quality performance of the technological process according to agrotechnical requirements with the lowest energy consumption during smooth furless plowing. An improved technology of smooth furrowless plowing has been developed, in which at first the seam is given a polygonal shape, then turned 180° within its own furrow. A frontal plow with offsets has been developed to implement the proposed technology. In the research, the laws and rules of theoretical mechanics, mathematical statistics, mathematical planning of experiments and methods of strain gauge were applied. It has been established by theoretical and experimental studies that when the frontal plow is cut off in the form of a triangular wedge, its height is 22 cm, the wing opening angle is 32°, the side edge angle is 36°, the required quality of smooth plowing is provided with the lowest energy consumption. With longitudinal distances between the plowshares of the body and the cut-off of at least 27 cm and between the disc coulter and the cut-off of 16 cm, the required quality of soil cultivation of the front plow is ensured in accordance with the established agro technical requirements.

Mini crusher-shredder for farms

The purpose of the study is to substantiate the parameters of a mini crusher-shredder for processing coarse feed stalks in farms. The feasibility of using a mini crusher-shredder for processing coarse feed in the conditions of farms and farms with a small number of animals, which has a rotary-type shredder that combines the operations of grinding and crushing, is justified. The research uses the laws and rules of mathematical statistics, mathematical planning of experiments, and the methods given in existing regulatory documents. Experimental studies were carried out to study the influence of the rotor parameters of the mini crusher-shredder on its quality performance. A compact crusher-shredder has been developed, which has good visibility of the working bodies, high reliability, and quality of work due to zootechnical requirements. Experimental studies have established that when using a hammer of a flat-turned shape with a lower sharpening and a rotation angle of 60 or more, high-quality grinding of the stems is provided.

Optimization of the Process for Producing 5-Nitro-2-Acetylaminobenzimidazole and its Bactericidal and Fungicidal Activity

The main factors affecting production of 5-nitro-2-acetylaminobenzimidazole were identified. The process was optimized using mathematical experiment planning. A mathematical model was compiled. A regression equation was calculated. The optimum process conditions including the temperature, duration, and quantitative ratio of starting compounds were found. The bactericidal and fungicidal activities of 5-nitro-2-acetylaminobenzimidazole against Xanthomonas malvacearum culture were studied under laboratory conditions.

Optimization of technology of special-purpose mineral wool products

Insulation systems must have a number of special properties when used on construction sites located in the zone of significant negative temperatures, wind load, and associated air filtration through building struc-tures, under the influence of the coastal environment that forms salts on tech-nical facilities associated with the production and transportation of petro-leum products. Firstly, high operational stability, including under the influ-ence of aggressive environments. Secondly, they must be non-flammable and have significant fire resistance limits. Thirdly, do not contain compo-nents that are toxic during normal operation or are released in the event of a fire. The analysis of possibilities has shown that products based on stone wool meet these requirements to the greatest extent as a thermal insulation material. The research presented in the article is based on a hypothesis about the use of products based on stone wool and epoxy binder on latent hardeners, which will allow us to obtain an energy-efficient material that fully meets the conditions of polar construction. The purpose of the research was to develop a method for selecting the parameters of manufacturing mineral wool products that affect the properties of mineral wool slabs to the greatest extent and to opti-mize the temperature of heat treatment of mineral wool carpet. Re-search methodology set out in the article is based on the method of mathematical planning of experiment and statistical processing of the results, followed by analytical optimization.

A Study of the Potential Use of Red Mud to Obtain Compositions Based on Portland Cement


 
 
 The paper deals with the problem of utilization of red mud which is a waste product from alumina production using the Bayer method. The principal possible use for the red mud of JSC “Bogoslovsky aluminum plant” (Sverdlovsk region) for the compositions based on Portland cement is shown. It was found that the mud introduction accelerates beginning of the cement paste setting and thickens the paste reducing its mobility. It is concluded that the introduction of red mud up to 30 % is justified in terms of strength indicators. The work is carried out using mathematical planning of experiments.
 Keywords: red mud, Portland cement, active mineral additive, composition, properties, bauxite, chemical composition, cement stone strength, mathematical planning of experiments
 
 

Managing the Effectiveness of Teaching Boys Aged 10 Mawashi-Geri (Roundhouse Kick) Technique in Kyokushin Karate

The objective of the study was to substantiate the influence of selected independent variables for building optimal models of teaching a series of tasks aimed at motor skills development in boys aged 10. Materials and methods. The study involved 32 boys aged 10. The children and their parents were informed about all the features of the study and gave their consent to participate in the experiment. To achieve the objective set, the following research methods were used: study and analysis of scientific and methodological literature; pedagogical observation, timing of learning tasks; pedagogical experiment, methods of mathematical statistics, methods of mathematical experiment planning. In the process of teaching, a method of algorithmic instructions was used. Results. The effect size of the factor varied from series to series. The calculated Cochran's criterion showed that all the groups of experimental data were obtained from the same population. It was found that the variances do not differ for the selected significance level of 0.05. Each independent variable (X1, X2, X1X2) plays a role in changing the indicator of proficiency in the Mawashi-geri-jodan (roundhouse kick). The constructed mathematical models adequately describe the obtained data. The calculated regression coefficients are statistically significant (Fр < Fkр), which means that the regression model is effective. Throughout the experiment, the independent variable Х1 “number of sets” had a constant positive effect on the target feature (Y). The percentage contribution in the first series of learning tasks was 59.3%, in the second – 88.6%, in the third – 56%, in the fourth – 93.9%, in the fifth – 81.3%, in the sixth – 69.62%. The independent variable Х2 “rest interval” has a negative effect in the first series – 25.9%, in the second series – 10.6%, in the fifth – 9.9%, in the sixth – 13.1%. A positive effect of the first-order interaction (X1X2) was observed in the third series – 29.1%, the fifth – 8.9%, the sixth – 17.28%. Conclusions. The optimal combinations of conditions for the series of tasks when teaching boys aged 10 the Mawashi-geri-jodan (roundhouse kick) are the following: series 1 – 3 sets, rest interval 60 s; series 2 – 3 sets, rest interval 60 s; series 3 – 3 sets, rest interval 120 s; series 4 – 3 sets, rest interval 60–120 s; series 5 – 3 sets, rest interval 120 s; series 6 – 3 sets, rest interval 120 s.

Mathematical planning of a multi-factor experiment and optimization of the feed extrusion process

To increase the level of protein and fat in milk, it is necessary to increase the total amount of feed fed, the diet must be balanced in energy, protein, fiber, minerals and vitamins; the feed must be of high quality. Oilseed waste produced during post-harvest processing and industrial processing contains a sufficient amount of protein and raw fat that can be used in animal feeding diets to increase milk productivity, and when using advanced processing methods, such as extrusion, it becomes a source of environmentally friendly vegetable protein that can increase the nutritional value of the feed several times. In order to study the efficiency of the technological process, the dependencies of quality parameters were determined. Using mathematical methods of planning a multi-factor experiment, a mathematical model of the extrusion process of feed raw materials was developed. The obtained model is used to identify recommended modes of extrusion of feed raw materials from post-harvest waste.