Chapter 6. Mechanical Design - 6. MECHANICAL DESIGN Summary...

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185 6. MECHANICAL DESIGN Summary During fault conditions when currents can increase to about 25 times their normal values, transformer windings are subjected to very high forces. Sufficient bracing must be provided so that little movement occurs. In addition, the mechanical design and material properties must be such that the resulting stresses do not lead to permanent deformation, fracture, or buckling of the materials. Although fairly accurate calculations of the forces can be made either analytically or via finite elements, because of the complex structure of the windings, it is difficult to obtain the resulting stresses or strains without resorting to approximations. Nevertheless, with sufficient allowances for factors of safety, design rules to limit the stresses can be reliably established. 6.1 INTRODUCTION Transformers must be designed to withstand the large forces which occur during fault conditions. Fault currents for the standard fault types such as single line to ground, line to line, double line to ground, and all three lines to ground must be calculated. Since these faults can occur during any part of the ac cycle, the worst case transient overcurrent must be used to determine the forces. This can be calculated and is specified in the standards as an asymmetry factor which multiplies the rms steady state currents. It is given by [IEE93] (6.1) where and x/r is the ratio of the effective ac reactance to resistance. They are part of the total impedance which limits the fault current in the transformer when the short circuit occurs. Using this factor, the resulting currents are used to obtain the magnetic field (leakage field) surrounding the coils and, in turn, the resulting forces on the windings. Analytic methods such as Rabins’ method [Rab56] as discussed © 2002 by CRC Press
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MECHANICAL DESIGN 186 in Chapter 5 or finite element methods can be used to calculate the magnetic field. An example of such a leakage field is shown in Fig. 6.1 which was generated by the finite element program Maxwell ® EM2D Field Simulator [Ansoft]. Since this is a 2D program, the figure is cylindrically symmetrical about the core center line and only the bottom half of the windings and core are shown because of assumed symmetry about a horizontal center plane. Although details such as clamps and shields can be included in the calculation using a finite element approach, they are not part of Rabins’ analytical approach which assumes a simpler idealized geometry. However, calculations show that the magnetic field in the windings and hence the forces are nearly identical in the two cases. The force density (force/unit volume), f , generated in the windings by the magnetic induction, B , is given by the Lorentz force law f=J×B (6.2) where J is the current density and SI units are used. These force densities can be integrated to get total forces, forces/unit length, or pressures depending on the type of integration performed. The resulting values or the maxima of these values can then be used to obtain stresses or maximum
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This note was uploaded on 10/19/2010 for the course ENGINEERIN ELEC121 taught by Professor Tang during the Spring '10 term at University of Liverpool.

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Chapter 6. Mechanical Design - 6. MECHANICAL DESIGN Summary...

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