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Unformatted text preview: 2/28/2006 Copyright 2003 S.D. Sudhoff Page 1 4 / Distributed Windings and Rotating Fields The objective of this chapter is to develop some analytical tools specifically useful in the analysis of rotational electric machinery. One of the most important properties in this class of machines is that the windings are distributed throughout the machine, rather than concentrated in a particular place, as we have mainly considered thus far. This chapter largely concerns the treatment of distributed windings and how they can be used to create rotating magnetic fields. In particular, our objectives for this chapter are as follows. First, we need to establish methods to describe distributed windings. There are two methods of doing this a discrete description and a continuous description. The second objective of this chapter is to set forth a method to determine the flux linked by a distributed winding, and the flux caused by a distributed winding. As it turns out, a concept referred to as a winding function will be very useful in both of these problems. Next, we will turn our attention to the fields caused by distributed windings, and see how, with proper excitation, a rotating field can be established. This rotating field is responsible for the rotation of the rotor. Finally, we will turn our attention to calculating the electrical parameters of distributed winding systems. In particular, we will establish methods to calculate the self inductances, mutual inductances, and resistances of distributed windings. 4.1 NOTATION Before embarking into the subject of windings and rotating fields, it is convenient to first set forth some notation which will be used throughout this work. In particular, consider Figure 4.1. Therein, a generic electrical machine is depicted. The outside of the machine is stationary and is referred to as the stator. The inner portion of the machine rotates and is referred to as the rotor. In Figure 4.1, half the rotor is shaded so rotor position is evident. Three angles are defined in Figure 4.1. These include sm - Position as measured relative to the stator rm - Position as measured relative to the rotor rm - The position of the rotor relative to the stator Clearly, the position of a feature (such as the location of part of a winding) can be described by either sm or rm ; however, if we are describing the same feature using both of these quantities, then these two measures of angular position are related by sm rm rm = + (4.1-1) 2/28/2006 Copyright 2003 S.D. Sudhoff Page 2 sm rm rm Stator Reference Axis Arbitrary Position Rotor Reference Axis Figure 4.1-1. Definition of Position Measurements. Finally, much of the analysis presented herein may be expressed either in terms of sm measured relative to the stator or rm measured relative to the rotor....
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