ИССЛЕДОВАНИЕ ЛИНЕЙНОГО ИМПУЛЬСНО-ИНДУКЦИОННОГО ЭЛЕКТРОМЕХАНИЧЕСКОГО ПРЕОБРАЗОВАТЕЛЯ ПРИ РАЗЛИЧНЫХ СХЕМАХ ПИТАНИЯ ИНДУКТОРА

Purpose. The goal of the paper is to investigate the influence of the power circuits of the linear pulse-induction electromechanical converters (LPIEC), which form the current pulse of excitation of the inductor from the capacitive energy storage (CES), to its electromechanical parameters. Methodology. A circuit mathematical model of LPIEC was developed, on the basis of which recurrence relations were obtained for calculating the interrelated electromagnetic, mechanical, and thermal parameters of the LPIEC. This model makes it possible to calculate the LPIEC parameters for various power circuits, the inductor of which is excited by the CES. Results. It is established that electromechanical LPEC parameters with power circuit forming an aperiodic current excitation pulse of an inductor are better than in LPIEC with excitation of an inductor by an unipolar current pulse, but worse than in LPIEC with excitation of an inductor by a vibrationally damped current pulse. In this converter, during operation, the inductor is heated most, and the armature is heated least. It is established that in LPIEC with power circuit that forms an aperiodic current pulse of excitation of an inductor with the connection of an additional CES, all electromechanical parameters are higher in comparison with the LPIEC with a power circuit that forms a vibrationally damped current excitation pulse of the inductor. However, in this LPIEC the excess of the temperatures of the active elements increases, especially strongly in the inductor, and the efficiency of the converter decreases. Originality. For the first time, the LPIEC has been investigated using the power circuit that forms an aperiodic current pulse of excitation of an inductor with the connection of an additional CES. It is established that in this LPIEC all electromechanical parameters are higher than for LPIEC with power circuits forming an unipolar or oscillating-damped current excitation pulse of the inductor. Practical value. In the LPIEC with power circuit that forms an aperiodic current pulse of excitation of the inductor with the connection of an additional CES, the electromechanical LPIEC parameters increase. This increases the temperature rise of the inductor, and the temperature rise of the armature decreases. The effectiveness of this LPIEC is also reduced.На основе разработанной цепной математической модели получены рекуррентные соотношения для расчета взаимосвязанных электромагнитных, механических и тепловых параметров линейного импульсно-индукционного электромеханического преобразователя (ЛИИЭП). Показано, что электромеханические показатели ЛИИЭП со схемой питания индуктора, формирующей апериодический токовый импульс возбуждения, лучше, чем у ЛИИЭП с возбуждением индуктора однополярным токовым импульсом, но хуже, чем у ЛИИЭП с возбуждением индуктора колебательно-затухающим токовым импульсом. В данном преобразователе в процессе работы наиболее сильно нагревается индуктор и наименее нагревается якорь. Показано, что в ЛИИЭП со схемой питания индуктора, формирующей апериодический токовый импульс возбуждения с подключением добавочного емкостного накопителя энергии, все электромеханические показатели выше по сравнению с ЛИИЭП со схемой питания индуктора, формирующей колебательно-затухающий токовый импульс возбуждения. Однако в этом ЛИИЭП возрастают превышения температур активных элементов, особенно сильно – индуктора и снижается КП

Experimental research of dynamic damping of lateral vibrations of a rigid cantilever beam

This work considers passive dynamic absorber (without additional energy source) of the simplest type: a non-controlled spring with one degree of freedom. Object of vibration suppression is transversal vibrations of rigid cantilever beam. The inertial element is connected to the vibration protection object by means of elastic metal element - nonlinear conical coil spring. Experiments were performed on the universal vibration system TM 150

Periodic Skeletons of Nonlinear Dynamical Systems in the Problems of Global Bifurcation Analysis

The construction of the periodic skeleton is a search for stable and unstable periodic regimes for a given parameter space of nonlinear dynamical periodicals systems. This stage of the main non-linear bifurcation theory, which is designed for a global analysis of nonlinear dynamical systems and the state of the parameter space that allows for complete bifurcation analysis, build complex bifurcation group and discover new previously unknown solutions

Bifurcation analysis by method of complete bifurcation groups of the driven system with two degrees of freedom with three equilibrium positions

This paper devoted to application of the new method of complete bifurcation groups (MCBG), which shows very good results in single-degree-of-freedom tasks, for global bifurcation analysis of systems with two degrees-offreedom on example of two-mass chain system with symmetrical elastic characteristic with two potential wells between masses. It is shown, that using of the MCBG allows to implement global bifurcation analysis of nonlinear oscillators with 2 DOF, and to find new nonlinear effects, bifurcation groups, and unknown before periodic and chaotic regime

INFLUENCE OF ARMATURE PARAMETERS OF A LINEAR PULSE ELECTROMECHANICAL CONVERTER ON ITS EFFICIENCY

Purpose. The evaluation of the effect of armature parameters on the efficiency of a linear pulsed electromechanical converter, taking into account the power, speed, constructive and environmental parameters. Methodology. First, the height of the electrically conductive, coil and ferromagnetic armature of a linear pulse electromechanical converter is determined, at which the highest velocity develops. An integral efficiency index is introduced, which takes into account, in a relative way, the power, speed, energy, electrical and field characteristics of the converter. Variants of the efficiency evaluation strategy are used that take into account the priority of each indicator of a linear pulse electromechanical converter using the appropriate weighting factor in the integral efficiency index. Results. A mathematical model of a linear pulsed electromechanical converter is developed. It is established that as the height of the electroconductive, coil and ferromagnetic armature increases, the force pulse increases. The greatest speed develops with the use of a coil armature, and the smallest with an electroconductive armature. In the converter with coil and ferromagnetic armature, practically the same values of the electrodynamic and electromagnetic force pulse are realized, while in the converter the electrodynamic force is 1.52 times smaller in the converter by the electrically conductive armature. It is established that with all efficiency evaluation strategies, the converter with a coil armature is the most effective, even in spite of its constructive complexity, and the converter with a ferromagnetic armature is the least effective, although it is constructively the simplest. Originality. For the first time, using the integral efficiency index, which takes into account the power, speed, energy, electrical and field indices in a relative way, it is established that with all efficiency evaluation strategies, the converter with a coil armature is the most effective, and the converter with a ferromagnetic anchor is the least effective. Practical value. The height of the electrically conductive, coil and ferromagnetic armature of a linear pulse electromechanical converter is determined, at which the highest speed develops. It is shown that when using an electrically conductive armature, the value of the electrodynamic force pulse is lower than when using a coil and ferromagnetic armature. It is established that the converter with a coil armature is the most efficient, and the converter with a ferromagnetic armature is the least effective

ВЛИЯНИЕ ПАРАМЕТРОВ ЯКОРЯ ЛИНЕЙНОГО ИМПУЛЬСНОГО ЭЛЕКТРОМЕХАНИЧЕСКОГО ПРЕОБРАЗОВАТЕЛЯ НА ЕГО ЭФФЕКТИВНОСТЬ

Purpose. The evaluation of the effect of armature parameters on the efficiency of a linear pulsed electromechanical converter, taking into account the power, speed, constructive and environmental parameters. Methodology. First, the height of the electrically conductive, coil and ferromagnetic armature of a linear pulse electromechanical converter is determined, at which the highest velocity develops. An integral efficiency index is introduced, which takes into account, in a relative way, the power, speed, energy, electrical and field characteristics of the converter. Variants of the efficiency evaluation strategy are used that take into account the priority of each indicator of a linear pulse electromechanical converter using the appropriate weighting factor in the integral efficiency index. Results. A mathematical model of a linear pulsed electromechanical converter is developed. It is established that as the height of the electroconductive, coil and ferromagnetic armature increases, the force pulse increases. The greatest speed develops with the use of a coil armature, and the smallest with an electroconductive armature. In the converter with coil and ferromagnetic armature, practically the same values of the electrodynamic and electromagnetic force pulse are realized, while in the converter the electrodynamic force is 1.52 times smaller in the converter by the electrically conductive armature. It is established that with all efficiency evaluation strategies, the converter with a coil armature is the most effective, even in spite of its constructive complexity, and the converter with a ferromagnetic armature is the least effective, although it is constructively the simplest. Originality. For the first time, using the integral efficiency index, which takes into account the power, speed, energy, electrical and field indices in a relative way, it is established that with all efficiency evaluation strategies, the converter with a coil armature is the most effective, and the converter with a ferromagnetic anchor is the least effective. Practical value. The height of the electrically conductive, coil and ferromagnetic armature of a linear pulse electromechanical converter is determined, at which the highest speed develops. It is shown that when using an electrically conductive armature, the value of the electrodynamic force pulse is lower than when using a coil and ferromagnetic armature. It is established that the converter with a coil armature is the most efficient, and the converter with a ferromagnetic armature is the least effective.Разработана математическая модель линейного импульсного электромеханического преобразователя (ЛИЭП), описывающая быстропротекающие и взаимосвязанные электромагнитные и электромеханические процессы, проявляющиеся при перемещении якоря относительно индуктора. Показано, что при увеличении высоты электропроводящего, катушечного и ферромагнитного якорей ЛИЭП происходит увеличение импульса силы. Наибольшая скорость развивается в ЛИЭП с катушечным якорем, а наименьшая – в ЛИЭП с электропроводящим якорем. В ЛИЭП с катушечным и ферромагнитным якорями реализуются практически одинаковые значения импульса электродинамической и электромагнитной силы, а в ЛИЭП с электропроводящим якорем импульс электродинамической силы в 1,52 раза меньше. Введен интегральный показатель эффективности, который в относительном виде учитывает силовые, скоростные, энергетические, электрические и полевые показатели. Установлено, что при всех стратегиях оценки эффективности наиболее эффективным является ЛИЭП с катушечным якорем, а наименее эффективным является ЛИЭП с ферромагнитным якорем

AN OPTIMIZATION APPROACH TO THE CHOICE OF PARAMETERS OF LINEAR PULSE INDUCTION ELECTROMECHANICAL CONVERTER

Purpose. The purpose of the paper is to select the main parameters of the linear pulse induction electromechanical converters (LPIEC) for high-speed and power use with the use of the optimization approach, which provides an increase in speed and power indicators with limited electric, thermal and mass-dimensions. Methodology. A technique for finding the maximum of the integral efficiency criterion of LPIEC in the search space using a global optimization method that randomly searches for parameters, preventing entry into a local maximum, and a local method ensuring the contraction of the range of parameters with a global maximum to minimum dimensions is developed. As a global optimization method, genetic algorithms are used, and the Nelder-Mead method is used as the local method. Results. The LPIEC inductor should have a maximum external and minimum internal diameter, and its height should be less than that of the LPIEC of the basic design. The armature should have a maximum outer diameter, and the thickness of its wire should be minimal. The armature should be made with a significantly higher height, a greater number of turns and a wider wire. The height of the LPIEC inductor for power purposes should be almost the same as that of the LPIEC of the basic design. In this case, the number of turns of the inductor and the cross section of its wire should be approximately the same. The armature should be made with a slightly larger inner diameter and a significantly higher height. This armature should have a larger number of turns of wire, which must be stacked in 4 layers, and a large width of the wire. The average energy value and voltage of the capacitive energy storage for the LPIEC for high-speed and power applications should be higher than for the LPIEC of the basic design. Originality. An optimization approach to the choice of LPIEC parameters with a multi-turn squirrel arm is developed, which consists in finding the maximum of an integral efficiency criterion that takes into account the maximum speed and efficiency in a high-speed converter, the amplitude and magnitude of the electrodynamic force pulse in a power converter, with minimum temperature excesses, the mass of active elements and current of the inductor. The optimization uses a chain mathematical model that takes into account the interconnected electrical, magnetic, thermal and mechanical processes of the LPIEC. Practical value. The electric parameters of the capacitive energy storage device and the geometric parameters of the LPIEC are determined, which ensure the largest values of the integral efficiency criterion depending on the adopted version of the efficiency evaluation strategy. In optimized speed and power transfer converters, the integral efficiency criteria are 2.2 times higher on average than in the basic performance of the LPIEC

ВОЗБУЖДЕНИЕ СЕРИЕЙ ИМПУЛЬСОВ ЛИНЕЙНОГО ИМПУЛЬСНОГО ПРЕОБРАЗОВАТЕЛЯ ЭЛЕКТРОДИНАМИЧЕСКОГО ТИПА, РАБОТАЮЩЕГО В СИЛОВОМ И СКОРОСТНОМ РЕЖИМАХ

Purpose. The aim of the article is to increase the efficiency of linear pulse electrodynamic type converter (LPEC) when operating in high-speed and force modes by reducing the amplitude of the recoil force by exciting its windings with a series of pulses from the capacitive energy storage (CES). Methodology. Using the LPEC mathematical model, in which the equations describing the interconnected electrical, magnetic, mechanical and thermal processes are presented in a recursive form, the electrodynamic and electromechanical characteristics of LPEC are simulated by excitation by a single and a series of pulses from CES sections. Results. It was found that when a single pulse is excited by an LPEC operating in a high-speed mode, in which the armature accelerates the actuator, compared with the force mode in which the armature is inhibited, the current amplitude in the windings decreases by 7.5 %, and the amplitudes of electrodynamic force (EDF) – by 21.8 %, impulse values of EDF – by 27.1 %. In this case, the armature winding with the actuating element accelerates to a speed of 7.1 m/s. When excited by a series of pulses from the same sections of the CES during LPEC operation in the force mode, the amplitudes of the current pulses and the EDF are practically unchanged, and when operating in high-speed mode, the amplitudes of the currents and the EDF gradually decrease. Both in power and in high-speed operating modes, an increase in the number of excitation pulses while conserving the energy of the CES leads to a decrease in the main indicators of LPEC. But by reducing the amplitude of the EDF, which manifests itself as a recoil force, the efficiency of LPEC increases. Originality. It is shown that the excitation of LPEC by a series of pulses increases the efficiency of LPEC when operating in high-speed and power modes, providing a minimum amplitude of the EDF, which determines the recoil force acting on the inductor winding. Practical value. For LPEC operating in high-speed mode, it is proposed to reduce the maximum current amplitudes and EDF due to the sequential increase in capacitances of sections of the CES, forming a series of excitation pulses. For LPEC, operating in force mode, it is advisable to use the same capacities of all sections of the CES.Представлена математическая модель линейного импульсного преобразователя электродинамического типа (ЛИПЭТ), в которой решения уравнений, описывающих взаимосвязанные электрические, магнитные, механические и тепловые процессы, представлены в рекуррентном виде. Исследованы электромеханические и электродинамические характеристики ЛИПЭТ при работе в скоростном режиме, обеспечивающем ускорение обмотки якоря с исполнительным элементом, и в силовом режиме, когда обмотка якоря заторможена. Показано, что при возбуждении одиночным импульсом ЛИПЭТ, работающего в скоростном режиме, по сравнению с силовым режимом происходит уменьшение амплитуды тока в обмотках на 7,5 %, амплитуды электродинамических усилий (ЭДУ) – на 21,8 %, значения импульса ЭДУ – на 27,1 %. При этом обмотка якоря с исполнительным элементом разгоняется до скорости  7,1 м/с. При возбуждении серией импульсов от одинаковых секций емкостного накопителя энергии (ЕНЭ) и работе ЛИПЭТ в силовом режиме амплитуды импульсов тока и ЭДУ практически неизменны, а при работе в скоростном режиме происходит последовательное уменьшение амплитуд токов и ЭДУ. Увеличение количества импульсов возбуждения при сохранении энергии ЕНЭ приводит к уменьшению основных показателей ЛИПЭТ. Но за счет уменьшения амплитуды ЭДУ, которая проявляется как сила отдачи, эффективность ЛИПЭТ увеличивается. Для ЛИПЭТ, работающего в скоростном режиме, предложено уменьшение максимальных амплитуд тока и ЭДУ за счет последовательного увеличения емкостей секций ЕНЭ, формирующих серии импульсов возбуждения. Для ЛИПЭТ, работающего в силовом режиме, целесообразно использовать одинаковые емкости всех секций ЕНЭ

ЭЛЕКТРОМЕХАНИЧЕСКИЕ ПРОЦЕССЫ В ЛИНЕЙНОМ ИМПУЛЬСНО-ИНДУКЦИОННОМ ЭЛЕКТРОМЕХАНИЧЕСКОМ ПРЕОБРАЗОВАТЕЛЕ С ПОДВИЖНЫМ ИНДУКТОРОМ И ДВУМЯ ЯКОРЯМИ

Purpose. The purpose of the paper is to determine the influence of the height of the mobile and stationary disk electrically conductive armatures covering the movable inductor on the electromechanical processes of linear pulsed-induction electromechanical converter (LPIEC). Methodology. With the help of the developed mathematical model that describes electromechanical and thermal processes of LPIEC, the influence of the heights of the armatures on electromechanical processes, the values of the electrodynamic forces acting on the inductor and armature, and the moving speed of the movable armature (MA) is established. Results. It is shown that if the height of the stationary armature (SA) is twice the height of the MA, then the inductor at the initial instant of time is acted upon by electrodynamics forces pressing it to the SA, and the displacement of the inductor begins with a delay of 0.35 ms. If the height of the MA is twice the height of the SA, then the electrodynamics forces act on the inductor at the initial instant of time, repelling it from the SA, and its movement begins with a delay of 0.1 ms. If the heights of the SA and the MA are equal, then until the time 0.15 ms on the inductor, the electrodynamics forces practically do not act and the inductor moving relative to the SA begins with a delay of 0.25 ms. Originality. The effect of the geometric parameters of the SA and MA on the velocity of the inductor moving relative to the SA, MA relative to the inductor and the MA relative to the SA is established. It has been established that the highest velocity of the MA relative to the SA develops the lowest MA, and the height of the SA does not affect it practically. However, with the increase in the height of the MA, the effect of SA begins to affect. In this case, it is expedient to select the height of the SA to be 0.4-0.42 of the height of the inductor. Practical value. It is shown that as the weight of the actuating element increases, the currents in the active elements of the LPIEC increase, the induction velocities of the inductor relative to the SA and the MA decrease relative to the inductor. At the same time, the maximum the electrodynamic forces values acting on the inductor decrease, and the armatures increase. Moreover, the maximum the electrodynamic forces acting on the MA are less than similar forces acting on the SA.Разработана математическую модель, которая описывает электромеханические процессы в линейном импульсно-индукционном электромеханическом преобразователе с подвижным индуктором, взаимодействующим со стационарным якорем (СЯ) и подвижным якорем (ПЯ), ускоряющим исполнительный элемент. Установлено влияние высот якорей на электромеханические процессы в преобразователе. Если высота СЯ в два раза больше высоты ПЯ, то на индуктор в начальный момент времени действуют электродинамические усилия (ЭДУ), прижимающие его к СЯ и перемещение индуктора начинается с задержкой 0,35 мс. Если высота ПЯ в два раза больше высоты СЯ, то на индуктор в начальный момент времени действуют ЭДУ, отталкивающие его от СЯ, и его перемещение начинается с задержкой 0,1 мс. Если высоты СЯ и ПЯ равны, то до момента времени 0,15 мс на индуктор практически не действуют ЭДУ и перемещение индуктора начинается с задержкой 0,25 мс. Установлены комбинации геометрических параметров якорей, при которых действуют как наибольшие, так и наименьшие импульсы ЭДУ. Наибольшие скорости развивает наиболее низкий ПЯ, причем высота СЯ на них практически не влияет. С увеличением массы исполнительного элемента происходит увеличение токов в активных элементах преобразователя и уменьшение скоростей индуктора и ПЯ. При этом максимальные значения ЭДУ, действующих на индуктор, уменьшаются, а на якоря – увеличиваются

ЭКСПЕРИМЕНТАЛЬНЫЕ ИССЛЕДОВАНИЯ ВЛИЯНИЯ ПАРАМЕТРОВ ФЕРРОМАГНИТНОГО СЕРДЕЧНИКА НА ЭЛЕКТРОМЕХАНИЧЕСКИЕ ПОКАЗАТЕЛИ ЛИНЕЙНОГО ИНДУКЦИОННО-ДИНАМИЧЕСКОГО ПРЕОБРАЗОВАТЕЛЯ

Experimental studies of ferromagnetic core parameters action on electromechanical characteristics of a linear induction-dynamic converter are conducted. An experimental installation is designed and built to determine the converter electromechanical parameters during its operation. A ferromagnetic core with four radial slots made allows regulating the height of the base and the outer shell. The core geometric parameters providing the highest speed of the armature are specified. Under certain parameters, the ferromagnetic core increases the converter efficiency up to 50%. The experimental results confirm the analytical studies within 6 % error.Проведены экспериментальные исследования влияния параметров ферромагнитного сердечника на электромеханические показатели линейного индукционно-динамического преобразователя. Разработана экспериментальная установка, позволяющая определять электромеханические параметры преобразователя в течение рабочего процесса. Изготовлен ферромагнитный сердечник с четырьмя радиальными разрезами, позволяющий регулировать высоту основания и наружной обечайки. Установлены геометрические параметры сердечника, обеспечивающего наибольшую скорость якоря. При определенных параметрах ферромагнитный сердечник повышает эффективность преобразователя до 50%. Экспериментальные исследования с погрешностью до 6 % подтверждают теоретические расчеты.Проведені експериментальні дослідження впливу параметрів феромагнітного осердя на електромеханічні показники лінійного індукційно-динамічного перетворювача. Розроблена експериментальна установка, яка дозволяє визначати електромеханічні параметри перетворювача на протязі робочого процесу. Виготовлене феромагнітне осердя з чотирма радіальними розрізами, яке дозволяє регулювати висоту основи та зовнішньої обичайки. Визначені геометричні параметри осердя, які забезпечують найбільшу швидкість якоря. При певних параметрах феромагнітне осердя підвищує ефективність перетворювача до 50 %. Експериментальні дослідження з похибкою до 6 % підтверджують теоретичні розрахунки