342 research outputs found

    The impact of grain boundary character on the size dependence of Bi- crystals

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    The deformation behavior of metallic single crystals is size dependent, as shown by several studies during the last decade [1]. Nevertheless, real structures exhibit different interfaces like grain, twin or phase boundaries. Due to the possibly higher stresses at the micron scale, the poor availability of dislocation sources and the importance of diffusion in small dimensions the mechanical behavior of samples containing interfaces can considerable differ from bulk materials. Within this study we will show the size scaling behavior of general high angle grain boundaries in copper. The first boundary presented is believed to show extensive dislocation slip transmission at bulk dimensions. The second example acts as perfect obstacle for dislocation slip transfer. In the talk results from in situ scanning electron microscopy (SEM) and in situ Β΅Laue diffraction will be shown. While the SEM data is used to proof slip transmission, Β΅Laue is probing the occurrence of dislocation pile-ups at the grain boundary. The results show that at low plastic strains the size scaling behavior of single and bi-crystalline samples is identical in cases where the grain size is assumed as the critical length scale [2]. It can therefore be concluded that the initial number and size of dislocation sources is dominating not only the deformation behavior of single crystalline pillars, but also for bi-crystals (at low plastic strains) (see Fig. 1a). Thus, the character of the boundary does not play any role for the mechanical properties at the onset of yield! Please click Additional Files below to see the full abstract

    Insights into dislocation grain-boundary interaction by X-ray ΞΌLaue diffraction

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    The deformation behavior of metallic single crystals is size dependent, as shown by several studies during the last decade. Nevertheless, real structures exhibit different interfaces like grain, twin or phase boundaries. Due to the possibly higher stresses at the micron scale, the poor availability of dislocation sources and the importance of diffusion in small dimensions the mechanical behavior of samples containing interfaces can considerable differ from bulk material. In the talk we show the first in situ Β΅Laue compression experiments on micron sized, bi-crystalline samples. Three different grain-boundary types will be presented and discussed (i) Large Angle grain Boundaries (LAGBs) acting as strong obstacle for dislocation slip transfer; (ii) LAGBs allowing for easy slip transfer and (iii) coherent sigma 3 twin-boundaries. The talk will focus on pile-up of dislocations, slip transfer mechanisms, storage of dislocations and dislocation networks at the LAGB

    A METHOD FOR CALCULATING MECHANICAL CHARACTERISTICS OF INDUCTION MOTORS WITH SQUIRREL-CAGE ROTOR

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    Purpose. Development of a method for calculating mechanical characteristics of induction motors, taking into consideration saturation of the magnetic path and displacement of the current in the rotor bars. Methodology. The algorithm is based on calculating the steady-state mode of induction motor operation for a set slip, described by a system of non-linear algebraic equations of electrical equilibrium, whereas the mechanical characteristic is evaluated as a set of steady-state modes using parameter continuation method. The idea of the steady-state mode calculation consists in determining vectors of currents and flux linkages of the motor circuits, using which makes it possible to evaluate the electromagnetic torque, active and reactive powers, etc. Results. The study resulted in the development of a method and algorithm for calculating static characteristics of induction motors, which allows looking into the effect of different laws of voltage regulation on the mechanical characteristics, depending on the frequency change. Originality. An algorithm for calculating mechanical characteristics of the squirrel-cage induction motor was developed based on the mathematical model of the induction motor in which electromagnetic parameters are calculated using real saturation curves for the main magnetic flux and leakage fluxes, and displacement of the current in the rotor bars is evaluated by presenting the rotor winding as a multi-layer structure. Applying the transformation of the electrical equilibrium equations into the orthogonal axes enabled a significant reduction of calculation volume without impairing the accuracy of the results. Practical value. The developed algorithm allows studying the effect of different laws of scalar regulation of the voltage on the mechanical characteristics of the induction motor in order to obtain the necessary torque-speed curves for their optimization. It can be used for programming frequency converters

    KOPEKΠ¦IΠ― OΠ‘'Π„MΠ£AMHIOTИЧHOΠ‡ Π Π†Π”Π˜ΠΠ˜ Π£ BAΠ“ITHИΠ₯ ПРИ IΠ”IOПATИЧHOMΠ£ MAΠ›OBOΠ”Π”I.

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    It was estabiished that theΒ deveiopment of idiopathic oiigohydramnios important roie of increasing piasma osmoiarity mother. Hidratatsiyna therapy can not oniyincrease the amount of amniotic fiuid butaiso improve the iife support systems of the fetus.Π£cΡ‚aΠ½oΠ²Π»Π΅Π½o, Ρ‡Ρ‚ΠΎ Π² Ρ€Π°Π·Π²ΠΈΡ‚ΠΈΠΈ ΠΈΠ΄ΠΈoΠΏaΡ‚ΠΈΡ‡Π΅cΠΊoΠ³o маловодия ваТная Ρ€ΠΎΠ»ΡŒ ΠΏΡ€ΠΈΠ½Π°Π΄Π»Π΅ΠΆΠΈΡ‚ ΠΏΠΎΠ²Ρ‹ΡˆΠ΅Π½ΠΈΡŽ ocΠΌoляpΠ½ocΡ‚ΠΈ ΠΏΠ»Π°Π·ΠΌΡ‹ ΠΊΡ€ΠΎΠ²ΠΈΒ ΠΌΠ°Ρ‚Π΅Ρ€ΠΈ. Гидратационная тСрапия позволяСт Π½Π΅ Ρ‚ΠΎΠ»ΡŒΠΊΠΎ ΡƒΠ²Π΅Π»ΠΈΡ‡ΠΈΡ‚ΡŒ объСм Π°ΠΌΠ½ΠΈΠΎΡ‚ΠΈΡ‡Π΅^ΠΎΠΉ Тидкости, Π½ΠΎ ΠΈ ΡƒΠ»ΡƒΡ‡ΡˆΠΈΡ‚ΡŒΒ ΠΆΠΈΠ·Π½Π΅ΠΎΠ±Π΅Ρ‚Π΅Ρ‡Π΅Π½ΠΈΠ΅ ΠΏΠ»ΠΎΠ΄Π°. ВстановлСно, Ρ‰ΠΎ Π² Ρ€ΠΎΠ·Π²ΠΈΡ‚ΠΊΡƒΒ Ρ–Π΄Ρ–ΠΎΠΏΠ°Ρ‚ΠΈΡ‡Π½ΠΎΠ³ΠΎ маловоддя Π²Π°ΠΆΠ»ΠΈΠ²Π° Ρ€ΠΎΠ»ΡŒ Π½Π°Π»Π΅ΠΆΠΈΡ‚ΡŒ ΠΏΡ–Π΄Π²ΠΈΡ‰Π΅Π½Π½ΡŽ ocΠΌoляpΠ½ocΡ‚i ΠΏΠ»Π°Π·ΠΌΠΈ ΠΊΡ€ΠΎΠ²Ρ– ΠΌΠ°Ρ‚Π΅Ρ€Ρ–. Π“Ρ–Π΄Ρ€Π°Ρ‚Π°Ρ†Ρ–ΠΉΠ½Π° тСрапія дозволяє нС Ρ‚Ρ–Π»ΡŒΠΊΠΈ Π·Π±Ρ–Π»ΡŒΡˆΠΈΡ‚ΠΈ ΠΎΠ±'Ρ”ΠΌ Π°ΠΌΠ½Ρ–ΠΎΡ‚ΠΈΡ‡Π½ΠΎΡ— Ρ€Ρ–Π΄ΠΈΠ½ΠΈ Π°Π»Π΅ ΠΉ ΠΏΠΎΠΊΡ€Π°Ρ‰ΠΈΡ‚ΠΈ ТиттєзабСзпСчСння ΠΏΠ»ΠΎΠ΄Π°

    The innovative component of the system of economic security of Ukrainian transportation industry enterprises

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    РассматриваСтся Π½Π΅ΠΎΠ±Ρ…ΠΎΠ΄ΠΈΠΌΠΎΡΡ‚ΡŒ Π°ΠΊΡ‚ΠΈΠ²ΠΈΠ·Π°Ρ†ΠΈΠΈ ΠΈΠ½Π½ΠΎΠ²Π°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ Π΄Π΅ΡΡ‚Π΅Π»ΡŒΠ½ΠΎΡΡ‚ΠΈ Π² транспортной отрасли. Π˜ΡΡΠ»Π΅Π΄ΡƒΡŽΡ‚ΡΡ возмоТности кластСрной ΠΊΠΎΠ½Ρ†Π΅ΠΏΡ†ΠΈΠΈ Π² Ρ„ΠΎΡ€ΠΌΠΈΡ€ΠΎΠ²Π°Π½ΠΈΠΈ систСмы экономичСской бСзопасности прСдприятий транспортного комплСкса Π·Π° счСт Π°ΠΊΡ‚ΠΈΠ²ΠΈΠ·Π°Ρ†ΠΈΠΈ ΠΈΠ½Π½ΠΎΠ²Π°Ρ†ΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ развития

    ΠœΠ°Ρ‚Π΅ΠΌΠ°Ρ‚ΠΈΡ‡Π΅ΡΠΊΠ°Ρ модСль ΠΈ характСристики асинхронного двигатСля ΠΏΡ€ΠΈ ΠΏΠΈΡ‚Π°Π½ΠΈΠΈ ΠΎΡ‚ источника Ρ‚ΠΎΠΊΠ°

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    . Methods and mathematical models for studying the modes and characteristics of the three-phase squirrel-cage induction motor with the power supplied to the stator winding from the current source have been developed. The specific features of the algorithms for calculating transients, steady-state modes and static characteristics are discussed. The results of the calculation of the processes and characteristics of induction motors with the power supply from the current source and the voltage source are compared. Steady-state and dynamic modes cannot be studied with a sufficient adequacy based on the known equivalent circuits; this requires using dynamic parameters, which are the elements of the Jacobi matrix of the system of equations of the electromechanical equilibrium. In the mathematical model, the state equations of the stator and rotor circuits are written in the fixed two-phase coordinate system. The transients are described by the system of differential equations of electrical equilibrium of the transformed circuits of the motor and the equation of the rotor motion and the steady-state modes by the system of algebraic equation. The developed algorithms are based on the mathematical model of the motor in which the magnetic path saturation and skin effect in the squirrel-cage bars are taken into consideration. The magnetic path saturation is accounted for by using the real characteristics of magnetizing by the main magnetic flux and leakage fluxes of the stator and rotor windings. Based on them, the differential inductances are calculated, which are the elements of the Jacobi matrix of the system of equations describing the dynamic modes and static characteristic. In order to take into account the skin effect in the squirrel-cage rotor, each bar along with the squirrel-cage rings is divided height-wise into several elements. As a result, the mathematical model considers the equivalent circuits of the rotor with different parameters which are connected by mutual inductance. The non-linear system of algebraic equations of electrical equilibrium describing the steady-state modes is solved by the parameter continuation method. To calculate the static characteristics, the differential method combined with the Newton’s Iterative refinement is used.Π Π°Π·Ρ€Π°Π±ΠΎΡ‚Π°Π½Ρ‹ ΠΌΠ΅Ρ‚ΠΎΠ΄Ρ‹ ΠΈ матСматичСскиС ΠΌΠΎΠ΄Π΅Π»ΠΈ для исслСдования Ρ€Π΅ΠΆΠΈΠΌΠΎΠ² ΠΈ характСристик Ρ‚Ρ€Π΅Ρ…Ρ„Π°Π·Π½ΠΎΠ³ΠΎ асинхронного двигатСля с ΠΊΠΎΡ€ΠΎΡ‚ΠΊΠΎΠ·Π°ΠΌΠΊΠ½ΡƒΡ‚Ρ‹ΠΌ Ρ€ΠΎΡ‚ΠΎΡ€ΠΎΠΌ ΠΏΡ€ΠΈ ΠΏΠΈΡ‚Π°Π½ΠΈΠΈ ΠΎΠ±ΠΌΠΎΡ‚ΠΊΠΈ статора ΠΎΡ‚ источника Ρ‚ΠΎΠΊΠ°. Π˜Π·Π»ΠΎΠΆΠ΅Π½Ρ‹ особСнности созданных Π½Π° ΠΈΡ… основС Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΠΎΠ² расчСта ΠΏΠ΅Ρ€Π΅Ρ…ΠΎΠ΄Π½Ρ‹Ρ… процСссов, ΡƒΡΡ‚Π°Π½ΠΎΠ²ΠΈΠ²ΡˆΠΈΡ…ΡΡ Ρ€Π΅ΠΆΠΈΠΌΠΎΠ² ΠΈ статичСских характСристик. ΠŸΡ€ΠΈΠ²Π΅Π΄Π΅Π½ΠΎ сравнСниС Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚ΠΎΠ² расчСта процСссов ΠΈ характСристик асинхронных Π΄Π²ΠΈΠ³Π°Ρ‚Π΅Π»Π΅ΠΉ ΠΏΡ€ΠΈ ΠΏΠΈΡ‚Π°Π½ΠΈΠΈ ΠΎΡ‚ источника Ρ‚ΠΎΠΊΠ° ΠΈ источника напряТСния. ИсслСдованиС ΡƒΡΡ‚Π°Π½ΠΎΠ²ΠΈΠ²ΡˆΠΈΡ…ΡΡ ΠΈ динамичСских Ρ€Π΅ΠΆΠΈΠΌΠΎΠ² Π½Π΅ ΠΌΠΎΠΆΠ΅Ρ‚ Π±Ρ‹Ρ‚ΡŒ осущСствлСно с достаточной Π°Π΄Π΅ΠΊΠ²Π°Ρ‚Π½ΠΎΡΡ‚ΡŒΡŽ Π½Π° основС извСстных схСм замСщСния ΠΈ Ρ‚Ρ€Π΅Π±ΡƒΠ΅Ρ‚ использования динамичСских ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€ΠΎΠ², ΡΠ²Π»ΡΡŽΡ‰ΠΈΡ…ΡΡ элСмСнтами ΠΌΠ°Ρ‚Ρ€ΠΈΡ†Ρ‹ Π―ΠΊΠΎΠ±ΠΈ систСмы ΡƒΡ€Π°Π²Π½Π΅Π½ΠΈΠΉ элСктромСханичСского равновСсия. Π’ матСматичСской ΠΌΠΎΠ΄Π΅Π»ΠΈ уравнСния состояния ΠΊΠΎΠ½Ρ‚ΡƒΡ€ΠΎΠ² статора ΠΈ Ρ€ΠΎΡ‚ΠΎΡ€Π° составлСны Π² Π½Π΅ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΠΎΠΉ Π΄Π²ΡƒΡ…Ρ„Π°Π·Π½ΠΎΠΉ систСмС ΠΊΠΎΠΎΡ€Π΄ΠΈΠ½Π°Ρ‚. ΠŸΠ΅Ρ€Π΅Ρ…ΠΎΠ΄Π½Ρ‹Π΅ процСссы ΠΎΠΏΠΈΡΡ‹Π²Π°ΡŽΡ‚ΡΡ систСмой Π΄ΠΈΡ„Ρ„Π΅Ρ€Π΅Π½Ρ†ΠΈΠ°Π»ΡŒΠ½Ρ‹Ρ… ΡƒΡ€Π°Π²Π½Π΅Π½ΠΈΠΉ элСктричСского равновСсия ΠΏΡ€Π΅ΠΎΠ±Ρ€Π°Π·ΠΎΠ²Π°Π½Π½Ρ‹Ρ… ΠΊΠΎΠ½Ρ‚ΡƒΡ€ΠΎΠ² двигатСля ΠΈ ΡƒΡ€Π°Π²Π½Π΅Π½ΠΈΠ΅ΠΌ двиТСния Ρ€ΠΎΡ‚ΠΎΡ€Π°, Π° ΡƒΡΡ‚Π°Π½ΠΎΠ²ΠΈΠ²ΡˆΠΈΠ΅ΡΡ Ρ€Π΅ΠΆΠΈΠΌΡ‹ – систСмой алгСбраичСских ΡƒΡ€Π°Π²Π½Π΅Π½ΠΈΠΉ. Π’ основу Ρ€Π°Π·Ρ€Π°Π±ΠΎΡ‚Π°Π½Π½Ρ‹Ρ… Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΠΎΠ² ΠΏΠΎΠ»ΠΎΠΆΠ΅Π½Π° матСматичСская модСль двигатСля, Π² ΠΊΠΎΡ‚ΠΎΡ€ΠΎΠΉ ΡƒΡ‡ΠΈΡ‚Ρ‹Π²Π°ΡŽΡ‚ΡΡ насыщСниС ΠΌΠ°Π³Π½ΠΈΡ‚ΠΎΠΏΡ€ΠΎΠ²ΠΎΠ΄Π° ΠΈ явлСниС скин-эффСкта Π² стСрТнях ΠΊΠΎΡ€ΠΎΡ‚ΠΊΠΎΠ·Π°ΠΌΠΊΠ½ΡƒΡ‚ΠΎΠΉ ΠΎΠ±ΠΌΠΎΡ‚ΠΊΠΈ. Для ΡƒΡ‡Π΅Ρ‚Π° насыщСния ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΡƒΡŽΡ‚ΡΡ Ρ€Π΅Π°Π»ΡŒΠ½Ρ‹Π΅ характСристики намагничивания основным ΠΌΠ°Π³Π½ΠΈΡ‚Π½Ρ‹ΠΌ ΠΏΠΎΡ‚ΠΎΠΊΠΎΠΌ ΠΈ ΠΏΠΎΡ‚ΠΎΠΊΠ°ΠΌΠΈ рассСяния ΠΎΠ±ΠΌΠΎΡ‚ΠΎΠΊ статора ΠΈ Ρ€ΠΎΡ‚ΠΎΡ€Π°. На ΠΈΡ… основС Π²Ρ‹Ρ‡ΠΈΡΠ»ΡΡŽΡ‚ΡΡ Π΄ΠΈΡ„Ρ„Π΅Ρ€Π΅Π½Ρ†ΠΈΠ°Π»ΡŒΠ½Ρ‹Π΅ индуктивности, ΠΊΠΎΡ‚ΠΎΡ€Ρ‹Π΅ ΡΠ²Π»ΡΡŽΡ‚ΡΡ элСмСнтами ΠΌΠ°Ρ‚Ρ€ΠΈΡ†Ρ‹ Π―ΠΊΠΎΠ±ΠΈ систСм ΡƒΡ€Π°Π²Π½Π΅Π½ΠΈΠΉ, ΠΎΠΏΠΈΡΡ‹Π²Π°ΡŽΡ‰ΠΈΡ… динамичСскиС Ρ€Π΅ΠΆΠΈΠΌΡ‹ ΠΈ статичСскиС характСристики. Π‘ Ρ†Π΅Π»ΡŒΡŽ ΡƒΡ‡Π΅Ρ‚Π° скин-эффСкта Π² ΠΎΠ±ΠΌΠΎΡ‚ΠΊΠ΅ ΠΊΠΎΡ€ΠΎΡ‚ΠΊΠΎΠ·Π°ΠΌΠΊΠ½ΡƒΡ‚ΠΎΠ³ΠΎ Ρ€ΠΎΡ‚ΠΎΡ€Π° ΠΊΠ°ΠΆΠ΄Ρ‹ΠΉ ΡΡ‚Π΅Ρ€ΠΆΠ΅Π½ΡŒ вмСстС с ΠΊΠΎΡ€ΠΎΡ‚ΠΊΠΎΠ·Π°ΠΌΡ‹ΠΊΠ°ΡŽΡ‰ΠΈΠΌΠΈ ΠΊΠΎΠ»ΡŒΡ†Π°ΠΌΠΈ разбиваСтся ΠΏΠΎ высотС Π½Π° нСсколько элСмСнтов. Π’ Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Π΅ Π² матСматичСской ΠΌΠΎΠ΄Π΅Π»ΠΈ Ρ€Π°ΡΡΠΌΠ°Ρ‚Ρ€ΠΈΠ²Π°ΡŽΡ‚ΡΡ эквивалСнтныС ΠΎΠ±ΠΌΠΎΡ‚ΠΊΠΈ Ρ€ΠΎΡ‚ΠΎΡ€Π° с Ρ€Π°Π·Π½Ρ‹ΠΌΠΈ ΠΏΠΎ Π·Π½Π°Ρ‡Π΅Π½ΠΈΡŽ ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Π°ΠΌΠΈ, ΠΌΠ΅ΠΆΠ΄Ρƒ ΠΊΠΎΡ‚ΠΎΡ€Ρ‹ΠΌΠΈ ΡΡƒΡ‰Π΅ΡΡ‚Π²ΡƒΡŽΡ‚ Π²Π·Π°ΠΈΠΌΠΎΠΈΠ½Π΄ΡƒΠΊΡ‚ΠΈΠ²Π½Ρ‹Π΅ связи. РСшСниС Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΠΎΠΉ систСмы алгСбраичСских ΡƒΡ€Π°Π²Π½Π΅Π½ΠΈΠΉ элСктричСского равновСсия, ΠΊΠΎΡ‚ΠΎΡ€ΠΎΠΉ ΠΎΠΏΠΈΡΡ‹Π²Π°ΡŽΡ‚ΡΡ ΡƒΡΡ‚Π°Π½ΠΎΠ²ΠΈΠ²ΡˆΠΈΠ΅ΡΡ Ρ€Π΅ΠΆΠΈΠΌΡ‹, выполняСтся ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠΌ продолТСния ΠΏΠΎ ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Ρƒ. Для расчСта статичСских характСристик ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΡƒΠ΅Ρ‚ΡΡ Π΄ΠΈΡ„Ρ„Π΅Ρ€Π΅Π½Ρ†ΠΈΠ°Π»ΡŒΠ½Ρ‹ΠΉ ΠΌΠ΅Ρ‚ΠΎΠ΄ Π² сочСтании с ΠΈΡ‚Π΅Ρ€Π°Ρ†ΠΈΠΎΠ½Π½Ρ‹ΠΌ ΡƒΡ‚ΠΎΡ‡Π½Π΅Π½ΠΈΠ΅ΠΌ ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠΌ ΠΡŒΡŽΡ‚ΠΎΠ½Π°

    Orientation dependence of dislocation transmission through twin-boundaries studied by in situ ΞΌLaue diffraction

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    It is well known that the grain boundaries (GBs) act as a barrier for dislocation motion (Clark 1992), leading to the well-known strength increase with reduced grain size, as explained by the Hall-Petch relation. Unfortunately the strength increase often leads to a reduction of ductility, except one example: Nano-twinned microstructures. The twin-boundary (TB) dislocation interaction is still not thoroughly understood (Imrich 2014, Gumbsch 2006). Recent developments in deforming micron sized samples on synchrotron beamlines allow to study the interplay of the single dislocation with a specific grain boundary. In present work we conduct in situ compression on micron-sized copper specimens with differently oriented coherent Ξ£3 twin boundaries. The samples were grown by the Bridgman method and subsequently fabricated using FIB milling. The in situ Laue microdiffraction experiments (Β΅Laue) were performed on BM32 at the ESRF synchrotron light source. The experiments allow a clear insight into the stress state, and the density and type of geometrically necessary dislocations stored inside the material during compression. The complementary in situ scanning electron microscope (SEM) experiments further allow to analyze slip transfer by slip step analysis. The discussion will concentrate on the dislocation transmission mechanism through the TB and the necessity to store dislocations in some specific loading directions as against others

    Π£Π‘Π’ΠΠΠžΠ’Π˜Π’Π¨Π˜Π•Π‘Π― Π Π•Π–Π˜ΠœΠ« И Π‘Π’ΠΠ’Π˜Π§Π•Π‘ΠšΠ˜Π• Π₯ΠΠ ΠΠšΠ’Π•Π Π˜Π‘Π’Π˜ΠšΠ˜ Π’Π Π•Π₯Π€ΠΠ—ΠΠžΠ“Πž АБИНΠ₯Π ΠžΠΠΠžΠ“Πž Π”Π’Π˜Π“ΠΠ’Π•Π›Π― ПРИ ПИВАНИИ ОВ ΠžΠ”ΠΠžΠ€ΠΠ—ΠΠžΠ™ Π‘Π•Π’Π˜

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    A mathematical model is developed to study the operation of three-phase asynchronous motor with squirrel-cage rotor when the stator winding is powered from a single phase network. To create a rotating magnetic field one of the phases is fed through the capacitor. Due to the asymmetry of power feed not only transients, but the steady-state regimes are dynamic, so they are described by differential equations in any coordinate system. Their study cannot be carried out with sufficient adequacy on the basis of known equivalent circuits and require the use of dynamic parameters. In the mathematical model the state equations of the circuits of the stator and rotor are composed in the stationary three phase coordinate system. Calculation of the established mode is performed by solving the boundary problem that makes it possible to obtain the coordinate dependences over the period, without calculation of the transient process. In order to perform it, the original nonlinear differential equations are algebraized by approximating the variables with the use of cubic splines. The resulting nonlinear system of algebraic equations is a discrete analogue of the initial system of differential equations. It is solved by parameter continuation method. To calculate the static characteristics as a function of a certain variable, the system is analytically differentiated, and then numerically integrated over this variable. In the process of integration, Newton's refinement is performed at each step or at every few steps, making it possible to implement the integration in just a few steps using Euler's method. Jacobi matrices in both cases are the same. To account for the current displacement in the rods of the squirrel-cage rotor, each of them, along with the squirrel-cage rings, is divided in height into several elements. This results in several squirrel-cage rotor windings which are represented by three-phase windings with magnetic coupling between them.Π Π°Π·Ρ€Π°Π±ΠΎΡ‚Π°Π½Π° матСматичСская модСль для исслСдования Ρ€Π°Π±ΠΎΡ‚Ρ‹ Ρ‚Ρ€Π΅Ρ…Ρ„Π°Π·Π½ΠΎΠ³ΠΎ асинхронного двигатСля с ΠΊΠΎΡ€ΠΎΡ‚ΠΊΠΎΠ·Π°ΠΌΠΊΠ½ΡƒΡ‚Ρ‹ΠΌ Ρ€ΠΎΡ‚ΠΎΡ€ΠΎΠΌ ΠΏΡ€ΠΈ ΠΏΠΈΡ‚Π°Π½ΠΈΠΈ ΠΎΠ±ΠΌΠΎΡ‚ΠΊΠΈ статора ΠΎΡ‚ ΠΎΠ΄Π½ΠΎΡ„Π°Π·Π½ΠΎΠΉ сСти. Для создания Π²Ρ€Π°Ρ‰Π°ΡŽΡ‰Π΅Π³ΠΎΡΡ ΠΌΠ°Π³Π½ΠΈΡ‚Π½ΠΎΠ³ΠΎ поля ΠΎΠ΄Π½Π° ΠΈΠ· Ρ„Π°Π· питаСтся Ρ‡Π΅Ρ€Π΅Π· кондСнсатор. ВслСдствиС нСсиммСтрии Π½Π΅ Ρ‚ΠΎΠ»ΡŒΠΊΠΎ ΠΏΠ΅Ρ€Π΅Ρ…ΠΎΠ΄Π½Ρ‹Π΅ процСссы, Π½ΠΎ ΠΈ ΡƒΡΡ‚Π°Π½ΠΎΠ²ΠΈΠ²ΡˆΠΈΠ΅ΡΡ Ρ€Π΅ΠΆΠΈΠΌΡ‹ ΡΠ²Π»ΡΡŽΡ‚ΡΡ динамичСскими, поэтому Π² любой систСмС ΠΊΠΎΠΎΡ€Π΄ΠΈΠ½Π°Ρ‚ ΠΎΠΏΠΈΡΡ‹Π²Π°ΡŽΡ‚ΡΡ Π΄ΠΈΡ„Ρ„Π΅Ρ€Π΅Π½Ρ†ΠΈΠ°Π»ΡŒΠ½Ρ‹ΠΌΠΈ уравнСниями. Π˜Ρ… исслСдованиС Π½Π΅ ΠΌΠΎΠΆΠ΅Ρ‚ Π±Ρ‹Ρ‚ΡŒ с достаточной Π°Π΄Π΅ΠΊΠ²Π°Ρ‚Π½ΠΎΡΡ‚ΡŒΡŽ осущСствлСно Π½Π° основС извСстных схСм замСщСния ΠΈ Ρ‚Ρ€Π΅Π±ΡƒΠ΅Ρ‚ использования динамичСских ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€ΠΎΠ². Π’ матСматичСской ΠΌΠΎΠ΄Π΅Π»ΠΈ уравнСния состояния ΠΊΠΎΠ½Ρ‚ΡƒΡ€ΠΎΠ² статора ΠΈ Ρ€ΠΎΡ‚ΠΎΡ€Π° составлСны Π² Π½Π΅ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΠΎΠΉ Ρ‚Ρ€Π΅Ρ…Ρ„Π°Π·Π½ΠΎΠΉ систСмС ΠΊΠΎΠΎΡ€Π΄ΠΈΠ½Π°Ρ‚. РасчСт ΡƒΡΡ‚Π°Π½ΠΎΠ²ΠΈΠ²ΡˆΠ΅Π³ΠΎΡΡ Ρ€Π΅ΠΆΠΈΠΌΠ° выполняСтся ΠΏΡƒΡ‚Π΅ΠΌ Ρ€Π΅ΡˆΠ΅Π½ΠΈΡ ΠΊΡ€Π°Π΅Π²ΠΎΠΉ Π·Π°Π΄Π°Ρ‡ΠΈ, Ρ‡Ρ‚ΠΎ Π΄Π°Π΅Ρ‚ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡ‚ΡŒ ΠΏΠΎΠ»ΡƒΡ‡ΠΈΡ‚ΡŒ зависимости ΠΊΠΎΠΎΡ€Π΄ΠΈΠ½Π°Ρ‚ Π½Π° ΠΏΠ΅Ρ€ΠΈΠΎΠ΄Π΅, Π½Π΅ прибСгая ΠΊ расчСту ΠΏΠ΅Ρ€Π΅Ρ…ΠΎΠ΄Π½ΠΎΠ³ΠΎ процСсса. Для этого исходныС Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½Ρ‹Π΅ Π΄ΠΈΡ„Ρ„Π΅Ρ€Π΅Π½Ρ†ΠΈΠ°Π»ΡŒΠ½Ρ‹Π΅ уравнСния Π°Π»Π³Π΅Π±Ρ€Π°ΠΈΠ·ΠΈΡ€ΡƒΡŽΡ‚ΡΡ ΠΏΡƒΡ‚Π΅ΠΌ аппроксимации ΠΏΠ΅Ρ€Π΅ΠΌΠ΅Π½Π½Ρ‹Ρ… кубичСскими сплайнами. ΠŸΠΎΠ»ΡƒΡ‡Π΅Π½Π½Π°Ρ нСлинСйная систСма алгСбраичСских ΡƒΡ€Π°Π²Π½Π΅Π½ΠΈΠΉ являСтся дискрСтным Π°Π½Π°Π»ΠΎΠ³ΠΎΠΌ исходной систСмы Π΄ΠΈΡ„Ρ„Π΅Ρ€Π΅Π½Ρ†ΠΈΠ°Π»ΡŒΠ½Ρ‹Ρ… ΡƒΡ€Π°Π²Π½Π΅Π½ΠΈΠΉ. Π•Π΅ Ρ€Π΅ΡˆΠ΅Π½ΠΈΠ΅ выполняСтся ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠΌ продолТСния ΠΏΠΎ ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Ρƒ. Для расчСта статичСских характСристик ΠΊΠ°ΠΊ Ρ„ΡƒΠ½ΠΊΡ†ΠΈΠΈ Π½Π΅ΠΊΠΎΡ‚ΠΎΡ€ΠΎΠΉ ΠΏΠ΅Ρ€Π΅ΠΌΠ΅Π½Π½ΠΎΠΉ данная систСма диффСрСнцируСтся аналитичСски, Π° Π·Π°Ρ‚Π΅ΠΌ интСгрируСтся числСнным ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠΌ ΠΏΠΎ этой ΠΏΠ΅Ρ€Π΅ΠΌΠ΅Π½Π½ΠΎΠΉ. Π’ процСссС интСгрирования Π½Π° ΠΊΠ°ΠΆΠ΄ΠΎΠΌ шагС ΠΈΠ»ΠΈ Ρ‡Π΅Ρ€Π΅Π· нСсколько шагов производится ΡƒΡ‚ΠΎΡ‡Π½Π΅Π½ΠΈΠ΅ ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠΌ ΠΡŒΡŽΡ‚ΠΎΠ½Π°, Ρ‡Ρ‚ΠΎ Π΄Π°Π΅Ρ‚ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡ‚ΡŒ ΠΎΡΡƒΡ‰Π΅ΡΡ‚Π²ΠΈΡ‚ΡŒ ΠΈΠ½Ρ‚Π΅Π³Ρ€ΠΈΡ€ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠΌ Π­ΠΉΠ»Π΅Ρ€Π° Π·Π° нСсколько шагов. ΠœΠ°Ρ‚Ρ€ΠΈΡ†Ρ‹ Π―ΠΊΠΎΠ±ΠΈ Π² ΠΎΠ±ΠΎΠΈΡ… случаях ΡΠΎΠ²ΠΏΠ°Π΄Π°ΡŽΡ‚. Для ΡƒΡ‡Π΅Ρ‚Π° вытСснСния Ρ‚ΠΎΠΊΠ° Π² стСрТнях ΠΊΠΎΡ€ΠΎΡ‚ΠΊΠΎΠ·Π°ΠΌΠΊΠ½ΡƒΡ‚ΠΎΠ³ΠΎ Ρ€ΠΎΡ‚ΠΎΡ€Π° ΠΊΠ°ΠΆΠ΄Ρ‹ΠΉ ΡΡ‚Π΅Ρ€ΠΆΠ΅Π½ΡŒ вмСстС с ΠΊΠΎΡ€ΠΎΡ‚ΠΊΠΎΠ·Π°ΠΌΡ‹ΠΊΠ°ΡŽΡ‰ΠΈΠΌΠΈ ΠΊΠΎΠ»ΡŒΡ†Π°ΠΌΠΈ разбиваСтся ΠΏΠΎ высотС Π½Π° нСсколько элСмСнтов. Π’ Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Π΅ Π½Π° Ρ€ΠΎΡ‚ΠΎΡ€Π΅ ΠΏΠΎΠ»ΡƒΡ‡Π°Π΅ΠΌ нСсколько ΠΊΠΎΡ€ΠΎΡ‚ΠΊΠΎΠ·Π°ΠΌΠΊΠ½ΡƒΡ‚Ρ‹Ρ… ΠΎΠ±ΠΌΠΎΡ‚ΠΎΠΊ, ΡΠΊΠ²ΠΈΠ²Π°Π»Π΅Π½Ρ‚ΠΈΡ€ΡƒΡŽΡ‰ΠΈΡ…ΡΡ Ρ‚Ρ€Π΅Ρ…Ρ„Π°Π·Π½Ρ‹ΠΌΠΈ ΠΎΠ±ΠΌΠΎΡ‚ΠΊΠ°ΠΌΠΈ, ΠΌΠ΅ΠΆΠ΄Ρƒ ΠΊΠΎΡ‚ΠΎΡ€Ρ‹ΠΌΠΈ ΡΡƒΡ‰Π΅ΡΡ‚Π²ΡƒΡŽΡ‚ ΠΌΠ°Π³Π½ΠΈΡ‚Π½Ρ‹Π΅ связи
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