Torque calculation between circular coils with inclined axes in air

Abstract

SUMMARYIn this paper we derive new semi-analytical expressions for calculating the electromagnetic torque between inclined circular coils in air. The torque calculation has been obtained from the corresponding mutual inductance between inclined circular coils using the filament method. The coils of rectangular cross-section whose centers are at the same and the different axes have been considered. From this general case it is possible to calculate the torque between all possible coil combinations either with rectangular or neglected cross-section. Results obtained by the presented approach are in very good agreement with already published data. This method can be used for industrial electromagnetic devices such as torque sensors, transducers and torque-measuring devices.

Magnetic Force Between Inclined Circular Loops (Lorentz Approach)

“…The vast majority of this attention has been given to the purely coaxial geometries [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. More recently the focus has been shifted to calculation of the mutual inductance and magnetic force between circular coils with lateral and angular misalignments [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Using the powerful numerical methods, such as Finite Element Method (FEM) and Boundary Element Method (BEM) [27,28], it is possible to calculate accurately and rapidly this important physical quantity.…”

New Formulas for Calculating Torque Between Filamentary Circular Coil and Thin Wall Solenoid With Inclined Axis Whose Axes Are at the Same Plane

“…Obviously all centers of filamentary coils replacing the thin wall solenoid and the center of the thin filamentary inclined coil are lying at the axe of the solenoid. Applying the same logic for the filament method already given in [4][5][6][7][8][9][10][11] and Equation (3) the torque can be obtained in the next form,…”

“…The calculation of the torque between two coils, carrying current, is a subject closely related to the calculation of their mutual inductance. Evidently the torque can be calculated by simple differentiation in any case where a general formula for the mutual inductance is available [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In this approach we use Grover's formula for the mutual inductance between two filamentary circular coils with inclined axes whose centers are at the same plane to calculate the torque between them.…”

“…We used this formula for calculating the torque between the filamentary circular coil and the thin wall solenoid with inclined axes whose centers are at the same plane. The filament method is applied [11][12][13]. The thin wall solenoid is replaced by the set of thin filamentary coils.…”

Magnetic stiffness calculation for the corresponding force between two current-carrying circular filaments arbitrarily oriented in the space

“…Analytical methods applied to the calculation of mutual inductance between two circular filaments and arising magnetic force, magnetic torque and corresponding magnetic stiffness when such the filament system carries electric currents is a prime example. These methods have proved their efficiency and have been successfully employed in an increasing number of applications, including electromagnetic levitation [1,2], superconducting levitation [3], calculation of mutual inductance between thick coils [4], magnetic force and torque calculation between circular coils [5,6,7], wireless power transfer [8,9,10], electromagnetic actuation [11,12,13], micro-machined contactless inductive suspensions [14,15,16] and hybrid contactless suspensions [17,18,19,20], biomedical applications [21,22], topology optimization [23], nuclear magnetic resonance [24,25], indoor positioning systems [26], navigation sensors [27], noncontact gap measurement sensors [28], wireless power transfer systems [29,30], magneto-inductive wireless communications [31] and others.…”