Parametric design of tri-axial nested Helmholtz coils

Abstract

This paper provides an optimal parametric design for tri-axial nested Helmholtz coils, which are used to generate a uniform magnetic field with controllable magnitude and direction. Circular and square coils, both with square cross section, are considered. Practical considerations such as wire selection, wire-wrapping efficiency, wire bending radius, choice of power supply, and inductance and time response are included. Using the equations provided, a designer can quickly create an optimal set of custom coils to generate a specified field magnitude in the uniform-field region while maintaining specified accessibility to the central workspace. An example case study is included.

An Optimal Design of an Electromagnetic Actuation System towards a Large Homogeneous Magnetic Field and Accessible Workspace for Magnetic Manipulation

“…An arrangement of two electromagnetic coils generated a magnetic field adjustable by varying electrical current to control microrobots in the workspace provided by the distance between two coils (e.g., Helmholtz coil capable of uniform field generation, Maxwell coil capable of non-uniform field generation). Tri-axial nested Helmholtz circular/square coil which is a perpendicular arrangement of a three-coil pair, generates a 3D-uniform magnetic field [17]. Some of those coil configurations have been integrated with computer vision to precisely navigate and track microrobots [18].…”

Optimization Design and Characterization of Helmholtz Coils

“…Helmholtz coil is a parallel pair of two similar circular coils, spaced one radius apart with coils wound in series such that current passes in same direction in each coil (Abbott, 2015). Helmholtz coils are usually employed to create magnetic fields to null the earth's magnetic field, calibrate magnetic sensors, and used for other experiments in which a controllable amount of uniform magnetic field is required (Abbott, 2015). The basic principle of Helmholtz coils is that the coils produces uniform magnetic field at the center (Abbott, 2015;Daron et al, 2015).…”

“…Helmholtz coils are usually employed to create magnetic fields to null the earth's magnetic field, calibrate magnetic sensors, and used for other experiments in which a controllable amount of uniform magnetic field is required (Abbott, 2015). The basic principle of Helmholtz coils is that the coils produces uniform magnetic field at the center (Abbott, 2015;Daron et al, 2015). This arrangement of coil was invented by German physicist, Hermann von Helmholtz, over a century ago (Bhatt et al, 2010).…”

“…This arrangement of coil was invented by German physicist, Hermann von Helmholtz, over a century ago (Bhatt et al, 2010). The intensity of magnetic field is directly proportional to the number of turns and the current through the coils (Abbott, 2015). Starting with the desired dimension based on the radius/coil separation R and magnetic field strength B, the required current IC and the number of turn N can be traded and selected according to the following equation for field strength at the center of the Helmholtz coil (Bhatt et al, 2010)…”

“…(Bhatt et al, 2010) Each of the individual Helmholtz coils produces uniform magnetic field parallel to the axis of the coils (Bhatt et al, 2010), and the two coils form a system such that a controllable amount of uniform magnetic field can be accomplished by controlling the applied current (Abbott, 2015). The uniform field within the coil accounts from the summation of fields parallel to the axis and the difference of vertical component fields (Abbott, 2015). Helmholtz coil design is simple and there are many commercially available designs for all kinds of applications.…”