Kirill V. Poletkin

A new analytical approach to modeling the nonlinear dynamics of an induction suspension based on a two-circuit approximation of the eddy current distribution in a thin conducting disk is presented. The method of multiple scales is used to obtain a uniformly valid solution describing both slow low-frequency oscillations of the levitation height and fast components associated with the frequency of the feeding field. A novel parametric identification technique is proposed that requires only a single experimental measurement of the steady-state levitation height to determine the effective geometric parameters of the system. Verification against TEAM Workshop Problem 28 data and results of finite-element modeling confirmed that the model provides the high accuracy in the steady-state regime (disagreement <1%) and correctly reproduces the qualitative characteristics of the transient process. Stability criteria for the equilibrium position are derived analytically and confirmed numerically.

Аналитически и численно исследуется устойчивость пространственного движения проводящего тонкого кольца в электромагнитном поле двух круговых катушек индуктивности и определяются области параметров, обеспечивающие устойчивую левитацию. Модель движения построена на основе уравнений Лагранжа-Максвелла, взаимная индуктивность между кольцом и катушками описана через эллиптические интегралы и верифицирована численными расчетами в программном комплексе Comsol Multiphysics. С применением метода многих масштабов получены условия устойчивости для вертикальных, горизонтальных и угловых движений кольца; анализ устойчивости выполнен с использованием критерия Сильвестра, бифуркационный анализ проведен в программном комплексе MatCont. Установлено, что при фиксированных параметрах, принятых в предшествующих исследованиях, устойчивая левитация невозможна, однако систематическое варьирование высоты левитации, радиусов катушек и кольца позволяет обнаружить область устойчивых движений во всех трех механических степенях свободы. Аналитические результаты подтверждены прямым численным интегрированием исходной системы. Полученные результаты могут служить основой для выбора геометрических и электрических параметров при проектировании микромеханических индукционных подвесов.

An approach for calculation of the magnetic force arising between two electric current-carrying filaments having a circular and closed-curve of arbitrary shape is developed. The developed approach is based on the recently formulated segmentation method applied for the calculation of the mutual induction for a similar filament system. Employing the fact that any curve can be interpolated by a set of line segments with the desired accuracy and deriving the set of formulas for calculating of the magnetic force between a circular filament and line segment, the developed approach was also successfully applied for the estimation of the distribution of magnetic force along the closed-curve in addition to the resulting one. As illustrative examples, the calculation of the magnetic force and its distribution between the circular filament and the following closed-curves such as polygons, circles and a 3D curve was efficiently performed by using the developed approach. Also, the developed method was applied for the calculation of the resultant magnetic force between the rigid bodies including permanent magnets and current-carrying coils. The results of calculation were validated successfully by using FEM method and the analytical formulas available in the literature.

An approach for calculation of the magnetic force arising between two electric current-carrying filaments having a circular and closed-curve of arbitrary shape is developed. The developed approach is based on the recently formulated segmentation method applied for the calculation of the mutual induction for a similar filament system. Employing the fact that any curve can be interpolated by a set of line segments with the desired accuracy and deriving the set of formulas for calculating of the magnetic force between a circular filament and line segment, the developed approach was also successfully applied for the estimation of the distribution of magnetic force along the closed-curve in addition to the resulting one. As illustrative examples, the calculation of the magnetic force and its distribution between the circular filament and the following closed-curves such as polygons, circles and a 3D curve was efficiently performed by using the developed approach. Also, the developed method was applied for the calculation of the resultant magnetic force between the rigid bodies including permanent magnets and current-carrying coils. The results of calculation were validated successfully by using FEM method and the analytical formulas available in the literature.

The article constructs and studies a nonlinear electromechanical model of the motion of a microscale conductive non-deformable ring in a non-contact electr

НЕЛИНЕЙНАЯ ДИНАМИКА МИКРОМЕХАНИЧЕСКОГО НЕКОНТАКТНОГО ИНДУКЦИОННОГО ПОДВЕСА