Математичне та розрахункове моделювання розповсюдження електромагнітного поля та магніто-пружно-пластичного деформування технологічних систем. Огляд
DOI:
https://doi.org/10.20998/2078-9130.2025.1.330041Ключові слова:
математичне моделювання, розрахунковий аналіз, електромагнітне поле, електромагнітна обробка, електро-магніто-пружність, метод скінченних елементів.Анотація
У статті розглянуто стан проблеми стосовно математичного та розрахункового моделювання процесів розповсюдження електромагнітного поля та викликаного їм деформування технологічних систем. Електромагнітне поле є невід’ємним чинником функціонування різноманітних технічних і технологічних систем. Дія електромагнітного поля на тіла та середовища відрізняється в залежності від їх властивостей. У разі дії на електропровідні тіла і середовища основну роль відіграє силовий вплив (завдяки виникаючим електромагнітним силам) та вплив на зміну температури (завдяки виникаючим розповсюдженими джерелам тепловиділення згідно до закону Джоуля-Ленца). Силовий вплив електромагнітного поля використовується у величезній кількості технологічних процесів. Можна відзначити процеси геологічної розвідки (завдяки імпульсам електромагнітного поля), металургійні процеси (тут електромагнітне поле застосовується, наприклад, для перемішування розплавів), обробні процеси. Великий клас обробних технологічних операцій, який має загальну назву електромагнітна обробка матеріалів, використовує електромагнітні сили для незворотної формозміни заготовок завдяки виникненню зон пластичних деформацій. У даному випадку силовій дії піддається як заготовка так і джерело електромагнітного поля – індуктор (соленоїд). При розробці технологічних операцій магнітно-імпульсної обробки вельми необхідно забезпечити як потрібний ступінь деформування заготовки так і працездатність індуктора, яка визначається його міцністю. Ці потреби викликають необхідність проведення математичного та розрахункового моделювання, що дозволяє визначити раціональні кількісні значення конструкційних та експлуатаційних параметрів. Подібне моделювання повинно гуртуватись на відповідних теоретичних моделях стосовно розповсюдження електромагнітного поля та викликаного ним пружно-пластичного деформування. У випадку розгляду технологічних систем електромагнітної обробки для опису розповсюдження електромагнітного поля припустимим є використання макроскопічного підходу, а опис процесів деформування може базуватись на принципах теорії електро-магніто-пружності. Сучасний підхід до математичного моделювання та розрахункового аналізу у системах електромагнітної обробки потребує використання чисельних методів, найбільш вживаним з яких є метод скінченних елементів завдяки своїй універсальності. Метод скінченних елементах у даному випадку дозволяє моделювати практично реальну геометрію системи та враховувати більшість конструкційних та експлуатаційних особливостей, пов’язаних із властивостями матеріалів, умовами контактної взаємодії тощо.Посилання
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