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

Abstract

In this paper we present a novel approach for calculating the torque between two filamentary circular coils with inclined axes whose centers are at the same plane. 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. The filament method is applied to the combination comprising a filamentary circular coil and a thin wall solenoid. As the comparative method we give the new formula for this coil's combination which is derived from Chester Snow's formula for two solenoids with inclined axes.

Vector Potential, Magnetic Field, Mutual Inductance, Magnetic Force, Torque and Stiffness Calculation between Current-Carrying Arc Segments with Inclined Axes in Air

“…The current-carrying arc segments are with currents I P , I S . For circular segments (see Figure 1), we define [22][23][24]:…”

“…The current-carrying arc segments are with currents 𝐼 , 𝐼 . For circular segments (see Figure 1), we define [22][23][24]: (1) The primary circular segment of radius 𝑅 is placed in the plane XOY (Z = 0) with the center at O (0, 0, 0). An arbitrary point P (𝑥 , 𝑦 , 𝑧 ) of this segment has parametric coordinates, (1) The primary circular segment of radius R P is placed in the plane XOY (Z = 0) with the center at O (0, 0, 0).…”

Analytical Modeling of Rotary Electromagnetic Fault Current Limiter

“…In particular, in [32] the magnetic force between circular coils with nonparallel axes and rectangular cross section are computed by adding magnetic forces between all individual filaments. Using Grover's formula [37] and filament method Babic et al obtained the torque between two filamentary circular coils with inclined axes [34]. However, existing models have mostly been applied/reported to co-axial and/or leveled, stationary coils with simple/standard geometrical shape (e.g., solenoid coil, disk-shape coil).…”

Calculation of force and torque between two arbitrarily oriented circular filaments using Kalantarov-Zeitlin's method

“…In 1996, Kim et al developed the expression for calculation of the restoring force in a system of two non-coaxial coils based on magnetic potential method [33]. Employing Grover's formula for calculation of mutual inductance between two filament coils [34], Babič et al developed the formulas for calculation of force and torque in such filament coil systems, in which circles have the lateral misalignment [35] and whose ases are inclined at the same plane [36,37], respectively. The developed formulas were applied to the calculation of force interaction between superconducting magnets and coils having a rectangular cross-section.…”