tailieunhanh - Electromagnetic Field Theory: A Problem Solving Approach Part 46

Electromagnetic Field Theory: A Problem Solving Approach Part 46. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reliance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. This book instills problem solving confidence by teaching through the use of a large number of worked problems. To keep the subject exciting, many of these problems are based on physical processes, devices, and models. This text is an introductory treatment on the junior level for a two-semester electrical engineering. | Faraday s Law for Moving Media 425 Figure 6-17 Cross-connecting two homopolar generators can result in self-excited two-phase alternating currents. Two independent field windings are required where on one machine the fluxes add while on the other they subtract. grows at an exponential rate Gu R 29 The imaginary part of s yields the oscillation frequency ft o Im s Go L 30 Again core saturation limits the exponential growth so that two-phase power results. Such a model may help explain the periodic reversals in the earth s magnetic field every few hundred thousand years. 426 Electromagnetic Induction d Periodic Motor Speed Reversals If the field winding of a motor is excited by a de current as in Figure 6-18 with the rotor terminals connected to a generator whose field and rotor terminals are in series the circuit equation is di t Gma m I-----------1 -----h dt L L f 31 where L and R are the total series inductances and resistances. The angular speed of the generator oe is externally Generator Motor Figure 6-18 Cross connecting a homopolar generator and motor can result in spontaneous periodic speed reversals of the motor s shaft. L L rm Lrg Lfg R Rrm Rfg Rrg Generator Faraday s Law for Moving Media 427 constrained to be a constant. The angular acceleration of the motor s shaft is equal to the torque of 20 d u 32 at where J is the moment of inertia of the shaft and If Vf Rfm is the constant motor field current. Solutions of these coupled linear constant coefficient differential equations are of the form i le 33 a We which when substituted back into 31 and 32 yield 34 7 Ws 0 Again for nontrivial solutions the determinant of coefficients of I and W must be zero O 35 Lt 7 JLt which when solved for s yields K-G riR-G ftj --------ÏT IA-2ÏT l 36 For self-excitation the real part of s must be positive G at R 37 while oscillations will occur if 5 has an imaginary part Now both the current and shaft s angular velocity spontaneously oscillate with time. 6-3-4 Basic Motors and .