barcode reader code in c# net Introduction to Electric Machines in Software

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Introduction to Electric Machines
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when the brushes switch to the next pair of segments In this machine, then, the torque angle, , is not always 90 , but can vary by as much as 30 ; the actual torque produced by the machine would uctuate by as much as 14 percent, since the torque is proportional to sin As the number of segments increases, the torque uctuation produced by the commutation is greatly reduced In a practical machine, for example, one might have as many as 60 segments, and the variation of from 90 would be only 3 , with a torque uctuation of less than 1 percent Thus, the DC machine can produce a nearly constant torque (as a motor) or voltage (as a generator)
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Ra Lf Rf + Vf (a) Separately excited + Ra Rf Vf Lf La Va + La Va +
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Con guration of DC Machines In DC machines, the eld excitation that provides the magnetizing current is occasionally provided by an external source, in which case the machine is said to be separately excited (Figure 1714(a)) More often, the eld excitation is derived from the armature voltage and the machine is said to be self-excited The latter con guration does not require the use of a separate source for the eld excitation and is therefore frequently preferred If a machine is in the separately excited con guration, an additional source, Vf , is required In the self-excited case, one method used to provide the eld excitation is to connect the eld in parallel with the armature; since the eld winding typically has signi cantly higher resistance than the armature circuit (remember that it is the armature that carries the load current), this will not draw excessive current from the armature Further, a series resistor can be added to the eld circuit to provide the means for adjusting the eld current independent of the armature voltage This con guration is called a shunt-connected machine and is depicted in Figure 1714(b) Another method for self-exciting a DC machine consists of connecting the eld in series with the armature, leading to the series-connected machine, depicted in Figure 1714(c); in this case, the eld winding will support the entire armature current, and thus the eld coil must have low resistance (and therefore relatively few turns) This con guration is rarely used for generators, since the generated voltage and the load voltage must always differ by the voltage drop across the eld coil, which varies with the load current Thus, a series generator would have poor (large) regulation However, series-connected motors are commonly used in certain applications, as will be discussed in a later section The third type of DC machine is the compound-connected machine, which consists of a combination of the shunt and series con gurations Figures 1714(d) and (e) show the two types of connections, called the short shunt and the long shunt, respectively Each of these con gurations may be connected so that the series part of the eld adds to the shunt part (cumulative compounding) or so that it subtracts (differential compounding) DC Machine Models
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(b) Shunt connected Ra La Lf + Vf Va +
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(c) Series connected Ra La Shunt winding (d) Short-shunt compound connection Series winding +
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Ra La Series winding
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Shunt winding (e) Long-shunt compound connection
As stated earlier, it is relatively easy to develop a simple model of a DC machine, which is well suited to performance analysis, without the need to resort to the details of the construction of the machine itself This section will illustrate the development of such models in two steps First, steady-state models relating eld and armature currents and voltages to speed and torque are introduced; second, the differential equations describing the dynamic behavior of DC machines are derived
Part III
Electromechanics
When a eld excitation is established, a magnetic ux, , is generated by the eld current, If From equation 172, we know that the torque acting on the rotor is proportional to the product of the magnetic eld and the current in the load-carrying wire; the latter current is the armature current, Ia (iw , in equation 162) Assuming that, by virtue of the commutator, the torque angle, , is kept very close to 90 , and therefore sin = 1, we obtain the following expression for the torque (in units of N-m) in a DC machine: T = kT Ia for = 90 (176)
You may recall that this is simply a consequence of the Bli law of 16 The mechanical power generated (or absorbed) is equal to the product of the machine torque and the mechanical speed of rotation, m (in rad/s), and is therefore given by Pm = m T = m kT Ia (177)
Recall now that the rotation of the armature conductors in the eld generated by the eld excitation causes a back emf, Eb , in a direction that opposes the rotation of the armature According to the Blu law (see 16), then, this back emf is given by the expression Eb = ka m (178)
where ka is called the armature constant and is related to the geometry and magnetic properties of the structure The voltage Eb represents a countervoltage (opposing the DC excitation) in the case of a motor, and the generated voltage in the case of a generator Thus, the electric power dissipated (or generated) by the machine is given by the product of the back emf and the armature current: Pe = Eb Ia (179)
The constants kT and ka in equations 176 and 178 are related to geometry factors, such as the dimension of the rotor and the number of turns in the armature winding; and to properties of materials, such as the permeability of the magnetic materials Note that in the ideal energy-conversion case, Pm = Pe , and therefore ka = kT We shall in general assume such ideal conversion of electrical to mechanical energy (or vice versa) and will therefore treat the two constants as being identical: ka = kT The constant ka is given by ka = where p = number of magnetic poles N = number of conductors per coil M = number of parallel paths in armature winding An important observation concerning the units of angular speed must be made at this point The equality (under the no-loss assumption) between the constants ka and kT in equations 176 and 178 results from the choice of consistent units, namely, volts and amperes for the electrical quantities, and newton-meters and radians per second for the mechanical quantities You should be aware that it pN 2 M (1710)
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