motor_notes - AA320 Background on Electromechanical Energy...

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AA320 Background on Electromechanical Energy Conversion (Motors) . Conversion of electrical energy to mechanical energy most commonly is carried out by use of magnetic fields . A magnetic field is characterized by the flux density, B, whose units are Tesla. [Sometimes B is just called the magnetic field.]. B-fields can be generated from permanent magnets, or by currents. Coils of wire with current flowing in them are commonly used to generate fields. Note that this is the same configuration used to make inductors. [Inductors store magnetic energy , whereas capacitors store electric- field energy .] For such a coil, illustrated below, the field inside the coil is B= μ NI/ l , where μ is called the permeability, N is the number of turns, I is the current, and l is the length of the coil. B-fields have a direction in addition to magnitude (they are vectors), and for the coil, the direction of the field is parallel to the axis of the coil. The permeability μ depends on whether any material is present within the coil: μ = μ o μ r where, μ o =4 π x 10 -7 is the free-space value (a constant) and μ r is the relative permeability (dimensionless) that ranges from 1 for vacuum (or air), to values of several thousand for highly permeable materials (iron or ferrites). Use of these high- μ r materials allows us to generate high B-fields from relatively low currents. Conversion of electric-to-mechanical energy results from the force that acts on a current that is in a magnetic field. The magnitude of the force on a wire of length l carrying a current I, in a magnetic field of strength B is: F= BI l sin( θ ), where θ is the angle between the direction of current and the direction of the magnetic field B. The direction of this force is given by cross product: B x I F r r r = l ; there is no force on a wire if the magnetic field is parallel to the wire, and the force is maximum if the field direction is perpendicular to the wire. A final consideration is that a voltage (sometimes referred to as electromotive force, emf ) will be developed in a wire that is exposed to a changing magnetic field, or equivalently in a wire that is moving with velocity u through a fixed magnetic field. For a single loop of wire in a field that is changing, the voltage E is given by: E =-AdB/dt, where A is the area enclosed by the loop. The field is assumed to point perpendicular to the
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motor_notes - AA320 Background on Electromechanical Energy...

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