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Unformatted text preview: 13 ELECTRIC MOTORS Modern underwater vehicles and surface vessels are making increased use of electrical ac- tuators, for all range of tasks including weaponry, control surfaces, and main propulsion. This section gives a very brief introduction to the most prevalent electrical actuators: The DC motor, the AC induction motor, and the AC synchronous motor. For the latter two technologies, we consider the case of three-phase power, which is generally preferred over single-phase because of much higher power density; three-phase motors also have simpler starting conditions. AC motors are generally simpler in construction and more robust than DC motors, but at the cost of increased control complexity. This section provides working parametric models of these three motor types. As with gas turbines and diesel engines, the dynamic response of the actuator is quite fast compared to that of the system being controlled, say a submarine or surface vessel. Thus, we concentrate on portraying the quasi-static properties of the actuator – in particular, the torque/speed characteristics as a function of the control settings and electrical power applied. The discussion below on these various motors is generally invertible (at least for DC and AC synchronous devices) to cover both motors (electrical power in, mechanical power out) and generators (mechanical power in, electrical power out). We will only cover motors in this section, however; a thorough treatment of generators can be found in the references listed. The book by Bradley (19??) has been drawn on heavily in the following. 13.1 Basic Relations 13.1.1 Concepts First we need the notion of a magnetic ﬂux, analagous to an electrical current, denoted ; a common unit is the Weber or Volt-second. The ﬂux density B = /A (167) is simply the ﬂux per unit area, given in Teslas such that 1 T = 1 W/m 2 . Correponding to electrical field (Volts/m) is the magnetic field intensity H , in Amperes/meter: B H = = ; (168) µ o µ r Aµ o µ r 58 13 ELECTRIC MOTORS µ o ⇐ 4 β × 10 − 7 Henries/meter is the permeability of free space, and µ r is a (dimensionless) relative permeability. The product µ o µ r represents the real permeability of the material, and is thus the analog of electrical conductivity. A small area A or low relative permeability drives up the field intensity for a given ﬂux . 13.1.2 Faraday’s Law The voltage generated in a conductor experiencing a time rate of change in magnetic ﬂux is given as d e = (169) − dt This voltage is commonly called the back-electromotive force or back-e.m.f., since it typically opposes the driving current; it is in fact a limiting factor in DC motors. 13.1.3 Ampere’s Law Current passing through a conductor in a closed loop generates a perpendicular magnetic field intensity given by I = Hdl. (170) An important point is that N circular wraps of the same conductor carrying current I induce the field H = βDN I , where D is the diameter of the circle....
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- Fall '04