The induction motor

Abstract

We obtain analytical expressions for the torques and angular speed of an induction motor with a simple geometry, resembling the geometry of the first induction motor investigated by Arago in 1824. The rotor is a conducting disc rotating between the magnetic poles of two off-axis solenoids, displaced in space by 90°from each other. We apply our results to discuss a theory for the ubiquitous electromechanical watt-hour meter. For comparison of the theoretical result for the angular speed with measurements, we propose a simple experiment in which an induction motor with an aluminum disc rotor is constructed.

Analytical results for rotating and linear magnetic brakes

“…In the low-speed regime, where the magnetic field due to the eddy currents is negligible, this repulsion or attraction is a very small effect and can also be neglected. This expression of T nk (α) is in agreement with the results we can find in literature for the cases α = π [11,19] and α = π/2 [11]. Eq.…”

“…Plots of the field lines of J(ρ, φ) can be seen in Refs. [11,17,19]. Now we consider the presence of another magnetic pole with uniform magnetic field B 2 = B 2ẑ inside the circular region of radius a, with center at the distance c 2 located at (x = c 2 cos α, y = c 2 sin α).…”

“…Now we consider the presence of another magnetic pole with uniform magnetic field B 2 = B 2ẑ inside the circular region of radius a, with center at the distance c 2 located at (x = c 2 cos α, y = c 2 sin α). The expressions for the electric potential due to this pole can be obtained from [11] (α = π/2) and in Ref. [19] (α = π).…”

“…These space charges and the fields associated with them have been studied in a number of conducting systems rotating in static and uniform magnetic fields (see, for example, [6,7,8]). Depending on the geometries of the conductor and the magnetic field, these space charges may be accompanied by an electric current density J, as in the case of the Faraday's first dynamo [9,10] and the induction motor [11]. References to these space charges on a magnetic brake made up of a disk rotating under the magnetic field of a single pole can be found in literature, [12,13,14,15,16,17] in the context of analytical calculations of forces and torques.…”

Numerical investigation of the DC electric motor

“…There are several articles describing and investigating the use of the electric motor as a teaching resource in the classroom, but from an experimental perspective [5][6][7]. On the other hand there is a lot of literature about more conceptually complicated motors and dynamos, like Ampere's homopolar motor [8,9], Faraday's dynamo [10], induction motor [11][12][13], etc.…”