Дослідження процесів поширення хвиль Лемба по пластині, що контактує із випадково неоднорідним гетерогенним середовищєм

We present results of research into the influence of characteristics of a heterogeneous medium on the Lamb wave propagation process parameters along a plate in contact with a given medium. A mathematical description of the Lamb wave propagation process in a metallic plate was formed. Analytical expressions are derived for determining the displacement potentials that describe, respectively, the longitudinal and transverse waves in a plate with a thickness of 2d at frequency ω. The possibility is shown of the existence under given conditions of a certain finite number of symmetric and antisymmetric Lamb waves. The mentioned waves are different one from another in phase and group velocities, as well as the distribution of displacements and stresses along the plate's thickness.We have investigated dependence of the Lamb wave attenuation on the characteristics of fluid in contact with the propagation medium. In the case when the Lamb wave propagation medium borders the fluid and the speed of sound in liquid Cl is less than speed C of the wave in a plate, the Lamb wave will attenuate radiating energy into liquid. It was established that the attenuation is due to the density of the studied medium. Viscosity and motion speed of a gas-containing suspension, for example iron ore pulp, have almost no effect on the magnitude of attenuation of the Lamb waves.The significance of the obtained results is emphasized by the fact that they could be used to develop improved methods and tools to control parameters of gas-containing suspensions. The use of Lamb waves makes it possible to avoid measurement errors associated with the presence of microdefects at the surface of propagation and gas bubbles in the examined liquid.From a practical point of view, the results obtained could be used for the calculation of parameters for the sources of ultrasonic waves in the systems of ultrasonic testing. Thus, there is an opportunity to improve efficiency of technological processes in the mining and metallurgical industry, specifically, the enrichment of ore.Представлены результаты исследования влияния характеристик неоднородной гетерогенной среды на параметры процесса распространения волн Лэмба по контактирующей с данной средой пластине. Рассмотрено влияние параметров исследуемой среды на величину затухания волн Лэмба. Установлено, что вязкость жидкости и скорость потока не влияют на процесс распространения волн Лэмба. Полученные результаты могут быть использованы при разработке методов и средств контроля параметров газосодержащих суспензийПредставлені результати дослідження впливу характеристик неоднорідною гетерогенного середовища на параметри процесу поширення хвиль Лемба по пластині, що контактує з цим середовищем. Розглянуто вплив параметрів досліджуваного середовища на величину загасання хвиль Лемба. Встановлено, що в'язкість рідини і швидкість потоку не впливають на процес поширення хвиль Лемба. Отримані результати можуть бути використані при розробці методів і засобів контролю параметрів газовмісних суспензі

Використання високоенергетичного ультразвуку для підвищення якості очищення часток залізорудної сировини у процесі її збагачення

The iron-magnetite raw material extracted in Ukraine is characterized by a complex texture, structure, and a high content of harmful impurities such as silicon dioxide, potassium oxides, sodium, magnesium, and sulfur. At the same time, the requirements for the quality of iron ore concentrates entering the further metallurgical processing are increasing, as the high quality of magnetite concentrates can significantly reduce the cost of metallurgical production.Meanwhile, the quality of concentrates decreases mainly due to the formation of technogenic micron splices in the iron ore pulp. The main reason for the formation of gaps is the presence of ion-electric and molecular fields on the surface of the ore particles. The formation of technogenic gaps reduces the difference in the properties of the surface of the ore and nonmetallic grains; it changes their magnetic susceptibility and, consequently, the efficiency of separation methods.Analysis of the results of studying the influence of the dynamic effects of high-energy ultrasound on the ore pulp showed the promising use of this approach.To improve the efficiency of cleaning the surfaces of minerals, it is proposed to pre-treat the iron ore slurry with the help of high-energy ultrasound. The optimum values of the intensity and the duration of ultrasonic treatment in the purification of mineral particles have been determined. When cleaning mineral particles, the intensity should be 1.2 W/cm2, and the processing time should not exceed 60 seconds. In this case, the yield of the purified product is increased by 0.8 %, and its quality grows by 0.9 %. It has been proven that the efficiency of ultrasonic treatment is associated with the renewal of particles surfaces, which leads to an increase in the contrast of magnetic and flotation properties of minerals.The study has shown that ultrasonic treatment of the iron ore pulp in the Kremenchuk iron ore region of Ukraine allows reducing the content of harmful impurities: potassium oxide – from 0.19 to 0.035–0.04 %; sodium oxide – from 0.14 to 0.027 %.Ухудшение качества концентратов в основном происходит в результате образования микронных техногенных сростков. Предложено использование высокоэнергетического ультразвука в кавитационном режиме для очистки поверхностей минералов. Доказано, что эффективность ультразвуковой обработки связана с обновлением поверхностей частиц, что приводит к увеличению контрастности магнитных и флотационных свойств минералов. Выполнен расчет устройства формирования высокоэнергетического ультразвукаПогіршення якості концентратів в основному відбувається внаслідок утворення мікронних техногенних зростків. Запропоновано використання високоенергетичного ультразвуку в кавітаційному режимі для очищення поверхонь мінералів. Доведено, що ефективність ультразвукової обробки пов'язана з оновленням поверхонь часток, що призводить до збільшення контрастності магнітних і флотаційних властивостей мінералів. Виконано розрахунок пристрою формування високоенергетичного ультразвук

Modelling of iron ore processing in technological units based on the hybrid approach

The process line of concentrating iron ore materials is considered as a sequence of connected concentration units, some of which partially return ore materials to the previous unit. The output product of the final concentration unit in the process line is the end product of the whole line. Characteristics of ore, such as distribution of ore particles by size and distribution of iron content by size classes, are considered. Processing of iron ore materials by process units (a cycle, a scheme) is characterised by a separation characteristic – namely the function of extracting elementary fractions depending on physical properties of ore particles. The results of fraction analysis of ore samples in different points of the process line provide an experimental definition of separation characteristics and numerical values of the Rosin–Rammler equation factors. To identify dependencies that cannot be analytically described, the hybrid approach accompanied by the Takagi–Sugeno fuzzy models, in accompaniment with triangular membership functions determining fuzzy sets in preconditions, are used. To identify fuzzy sets in rule preconditions, triangular membership functions are used. Introduction of a-priori data on iron ore concentration as constraints for model parameters is a promising trend of further research, since it enables increased accuracy of identification despite limited availability of experimental data

Дослідження процесів поширення хвиль Лемба по пластині, що контактує із випадково неоднорідним гетерогенним середовищєм

We present results of research into the influence of characteristics of a heterogeneous medium on the Lamb wave propagation process parameters along a plate in contact with a given medium. A mathematical description of the Lamb wave propagation process in a metallic plate was formed. Analytical expressions are derived for determining the displacement potentials that describe, respectively, the longitudinal and transverse waves in a plate with a thickness of 2d at frequency ω. The possibility is shown of the existence under given conditions of a certain finite number of symmetric and antisymmetric Lamb waves. The mentioned waves are different one from another in phase and group velocities, as well as the distribution of displacements and stresses along the plate's thickness.We have investigated dependence of the Lamb wave attenuation on the characteristics of fluid in contact with the propagation medium. In the case when the Lamb wave propagation medium borders the fluid and the speed of sound in liquid Cl is less than speed C of the wave in a plate, the Lamb wave will attenuate radiating energy into liquid. It was established that the attenuation is due to the density of the studied medium. Viscosity and motion speed of a gas-containing suspension, for example iron ore pulp, have almost no effect on the magnitude of attenuation of the Lamb waves.The significance of the obtained results is emphasized by the fact that they could be used to develop improved methods and tools to control parameters of gas-containing suspensions. The use of Lamb waves makes it possible to avoid measurement errors associated with the presence of microdefects at the surface of propagation and gas bubbles in the examined liquid.From a practical point of view, the results obtained could be used for the calculation of parameters for the sources of ultrasonic waves in the systems of ultrasonic testing. Thus, there is an opportunity to improve efficiency of technological processes in the mining and metallurgical industry, specifically, the enrichment of ore.Представлены результаты исследования влияния характеристик неоднородной гетерогенной среды на параметры процесса распространения волн Лэмба по контактирующей с данной средой пластине. Рассмотрено влияние параметров исследуемой среды на величину затухания волн Лэмба. Установлено, что вязкость жидкости и скорость потока не влияют на процесс распространения волн Лэмба. Полученные результаты могут быть использованы при разработке методов и средств контроля параметров газосодержащих суспензийПредставлені результати дослідження впливу характеристик неоднорідною гетерогенного середовища на параметри процесу поширення хвиль Лемба по пластині, що контактує з цим середовищем. Розглянуто вплив параметрів досліджуваного середовища на величину загасання хвиль Лемба. Встановлено, що в'язкість рідини і швидкість потоку не впливають на процес поширення хвиль Лемба. Отримані результати можуть бути використані при розробці методів і засобів контролю параметрів газовмісних суспензі

Дослідження впливу характеристик газовмісних суспензій на параметри процесу поширення ультразвукових хвиль

In the course of present study, we have investigated patterns of connection between fluctuations in the number and size of particles, suspended in a fluid, and characteristics of the field of volumetric ultrasonic waves.The presence of particles of the solid phase and gas bubbles introduces certain features to the process of attenuation and scattering of ultrasonic wave energy. The scattering of waves on the solid phase particles becomes considerable when the wavelength is commensurate with the size of the particles themselves.In order to characterize the absorption and scattering of acoustic oscillations by oscillating gas bubbles, we applied the concepts of effective cross-sections of damping, absorption and scattering. The dependence is presented of the magnitude of cross-section of ultrasound damping by air bubbles on frequency of the sound wave.It was established that the magnitude of attenuation of volumetric ultrasonic oscillations of high frequency (≥5 MHz) in an actual pulp depends almost only on the concentration of the solid phase and particle size of the crushed material.The frequency of volumetric ultrasonic waves, at which the components of their absorption and scattering by particles of the solid phase in suspension are equal, characterizes the average particle size. A given frequency does not depend on the particle concentration and can be applied to estimate their mean sizeВ работе выполнено исследование закономерностей связи флуктуаций числа и размеров взвешенных в жидкости частиц на характеристики поля объемных ультразвуковых волн. Обнаружено, что величина затухания объемных ультразвуковых колебаний высокой частоты (≥5 мГц) в реальной пульпе зависит практически только от концентрации твердой фазы и крупности частиц измельченного материалаУ роботі виконано дослідження закономірностей зв'язку флуктуацій числа і розмірів зважених у рідини часток на характеристики поля об'ємних ультразвукових хвиль. Виявлено, що величина згасання об’ємних ультразвукових коливань високої частоти (≥5 мГц) у реальній пульпі залежить практично тільки від концентрації твердої фази і крупності часток подрібненого матеріал

Синтез робастних регуляторів систем керування технологічними агрегатами рудозбагачувальних фабрик

In order to synthesize a robust system of control over technological units, an analysis of appropriate mathematical models was performed. The uncertainty of models of technological iron ore processing units was accounted for by connecting a diagonal block at the top using a fractional linear transformation.To study robust control systems of technological units, we applied the following types of robust controllers: suboptimal H∞-controller, a controller that was synthesized using the method of circuit formation, and µ-controller. We performed an analysis of results of the study into indicators of robust quality and stability of control, created on the basis of these types of controllers.The best results were obtained using μ-controller, which ensures a minimal overshoot value of 2 %. Reducing the order of the selected μ-controller to the fourth order was performed by approximation using the Hankel norm. Under such a condition, a root-mean-square error relative to the base controller is 0.027.Results of present research could be used in the synthesis of control over technological iron ore processing units under conditions of uncertainty in parameters. Для управления процессами обогатительного производства в условиях изменения параметров технологических агрегатов, как объектов управления, исследована возможность применения робастных регуляторов. Установлено, что по показателям номинального и робастного качества управления целесообразно применение робастного μ-регулятора для понижения порядка которого выполнен аппроксимация с применением Ганкелевой нормыДля керування процесами збагачувального виробництва в умовах зміни параметрів технологічних агрегатів, як об’єктів керування, досліджено можливість застосування робастних регуляторів. Встановлено, що за показниками номінальної і робастної якості керування доцільним є застосування робастного µ-регулятора, для зниження порядку якого виконано апроксимація з застосуванням Ганкелевої норм

Investigation of Mechanochemical Leaching of Non-Ferrous Metals

The research deals with metal extraction from off-grade ores and concentration tailings. There are provided results of simulating parameters of reagent leaching of metals in the disintegrator according to the metal recovery ratio. The research substantiates the method of waste-free processing of chemically recovered ores. Recovery of metals into solution is the same both under multiple leaching of tailings or ore in the disintegrator and agitation leaching of tailings or ore previously activated in the disintegrator with leaching solutions. The time of agitation leaching is more by two orders of magnitude than that of the disintegrator processing. Recovery of metals into solution is most affected by the content of sodium chloride in the solution. Then, in decreasing order, go the content of sulfuric acid in the solution, the disintegrator rotor rpm and L:S ratio

Investigation of the Effect of Characteristics of Gas­containing Suspensions on the Parameters of the Process of Ultrasonic Wave Propagation

In the course of present study, we have investigated patterns of connection between fluctuations in the number and size of particles, suspended in a fluid, and characteristics of the field of volumetric ultrasonic waves.The presence of particles of the solid phase and gas bubbles introduces certain features to the process of attenuation and scattering of ultrasonic wave energy. The scattering of waves on the solid phase particles becomes considerable when the wavelength is commensurate with the size of the particles themselves.In order to characterize the absorption and scattering of acoustic oscillations by oscillating gas bubbles, we applied the concepts of effective cross-sections of damping, absorption and scattering. The dependence is presented of the magnitude of cross-section of ultrasound damping by air bubbles on frequency of the sound wave.It was established that the magnitude of attenuation of volumetric ultrasonic oscillations of high frequency (≥5 MHz) in an actual pulp depends almost only on the concentration of the solid phase and particle size of the crushed material.The frequency of volumetric ultrasonic waves, at which the components of their absorption and scattering by particles of the solid phase in suspension are equal, characterizes the average particle size. A given frequency does not depend on the particle concentration and can be applied to estimate their mean siz

Basic Regularities of Assessing Ore Pulp Parameters in Gravity Settling of Solid Phase Particles Based on Ultrasonic Measurements

The article describes the method of controlling the recovered grade based on measuring the intensity of volume ultrasonic oscillations and Lamb waves covering a fixed distance through the test medium and on a metal plate contacting the test medium at various time points of deliberate motion of ground materials. The authors suggest a method of determining density of ground ore particles in the pulp periodically after isolating the pulp flow in the vertical part of the measuring vessel based on measuring attenuation change values in Lamb waves covering a fixed distance on a plate contacting the medium under study and high frequency volume ultrasonic oscillations that have come through it within a certain time period. There are given dependencies of amplitudes of measuring channels based on volume ultrasonic oscillations and surface Lamb waves, size distribution according to solid phase pulp particles for various types of ores under study, a set of curves for determining the recovered grade with regard to various types of ores under study