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consideration the energy losses associated with these devices Figure 173(a) and (b) represent the various loss mechanisms you must consider in analyzing the ef ciency of an electric machine for the case of direct-current machines It is important for you to keep in mind this conceptual ow of energy when analyzing electric machines The sources of loss in a rotating machine can be separated into three fundamental groups: electrical (I 2 R) losses, core losses, and mechanical losses
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No-load Stray load Armature Brush 2 loss Ia Ra contact rotational loss 2 loss loss 2Ia Rotational losses 3 to 15% Armature-circuit copper losses 3 to 6%
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Seriesfield loss Is2Rs
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Shuntfield loss I 2 Rf f
Field copper loss 1 to 5%
Figure 173(a) Generator losses, direct current
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Shuntfield loss I 2 Rf f
Seriesfield loss Is2Rs
Brush Armature No-load 2 contact loss Ia Ra rotational 2 loss loss 2Ia Armature-circuit copper losses 3 to 6%
Stray load loss
Field copper loss 1 to 5%
Rotational losses 3 to 15%
Figure 173(b) Motor losses, direct current
I 2 R losses are usually computed on the basis of the DC resistance of the windings at 75 C; in practice, these losses vary with operating conditions The difference between the nominal and actual I 2 R loss is usually lumped under the category of stray-load loss In direct-current machines, it is also necessary to account for the brush contact loss associated with slip rings and commutators Mechanical losses are due to friction (mostly in the bearings) and windage, that is, the air drag force that opposes the motion of the rotor In addition, if
17
Introduction to Electric Machines
external devices (eg, blowers) are required to circulate air through the machine for cooling purposes, the energy expended by these devices is also included in the mechanical losses Open-circuit core losses consist of hysteresis and eddy current losses, with only the excitation winding energized (see 16 for a discussion of hysteresis and eddy currents) Often these losses are summed with friction and windage losses to give rise to the no-load rotational loss The latter quantity is useful if one simply wishes to compute ef ciency Since open-circuit core losses do not account for the changes in ux density caused by the presence of load currents, an additional magnetic loss is incurred that is not accounted for in this term Stray-load losses are used to lump the effects of nonideal current distribution in the windings and of the additional core losses just mentioned Stray-load losses are dif cult to determine exactly and are often assumed to be equal to 10 percent of the output power for DC machines; these losses can be determined by experiment in synchronous and induction machines The performance of an electric machine can be quanti ed in a number of ways In the case of an electric motor, it is usually portrayed in the form of a graphical torque-speed characteristic and ef ciency map The torque-speed characteristic of a motor describes how the torque supplied by the machine varies as a function of the speed of rotation of the motor for steady speeds As we shall see in later sections, the torque-speed curves vary in shape with the type of motor (DC, induction, synchronous) and are very useful in determining the performance of the motor when connected to a mechanical load Figure 174(a) depicts the torquespeed curve of a hypothetical motor Figure 174(b) depicts a typical ef ciency map for a DC machine It is quite likely that in most engineering applications, the engineer is required to make a decision regarding the performance characteristics of the motor best suited to a speci ed task In this context, the torque-speed curve of a machine is a very useful piece of information
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To Torque output (% of rated) 250 200 150 100 50 0 500 n 1,500 2,500 Rev/min 1,000 2,000 Operating point
120 Torque (Nm)
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