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Brushless Permanent Magnet Motor Design- P4

Brushless Permanent Magnet Motor Design- P4: You've just picked up another book on motors. You've seen many others, but they all assume that you know more about motors than you do. Phrases such as armature reaction, slot leakage, fractional pitch, and skew factor are used with little or no introduction. You keep looking for a book that is written from a more basic, yet rigorous, perspective and you're hoping this is it. | Brushless Motor Operation 83 because the layout of the end turns is subject to few restrictions and a set magnetic field distribution is impossible to define. As a result the end turn inductance is often roughly approximated e.g. Liwschitz-Garik and Whipple 1961 . The approach followed here for computing end turn leakage inductance is to use the coenergy approach expressed by 4.17 and to assume that the magnetic field is distributed about the end turns in the same way that it is about an infinitely long cylinder having a surface current as illustrated in Fig. 4.19. If the current I is equal to ni then from 4.17 the inductance of a section of the cylinder of length Z out to a radius R is jn 2tt r 4.20 Application of this expression to find the end turn leakage inductance requires finding appropriate values for Z R and r. If the end turns are semicircular as shown in Fig. 4.20 then these parameters can be approximated by 4.21 Figure 4.19 Magnetic field about a cylindrical conductor. Brushless Motor Operation 85 Mutual Inductance The mutual inductances between the phases of a brushless PM motor are typically small compared with the self inductance. Just as the self inductance has three components the mutual inductance does also. Of these components the air gap mutual inductance is the most significant. The mutual slot leakage inductance is negligible because of the relatively high permeability of the stator teeth and back iron and the end turn mutual inductance is extremely difficult to model because end turn placement is not well defined and the field distribution about the windings is difficult to define. As a result only the air gap mutual inductance will be discussed here. Mutual inductance is defined in terms of the flux linked by one coil due to the current in another. Air gap mutual inductance is a function of the relative placement of the slots and therefore is a function of the number of phases in the motor. In general mutual inductance of the jth phase due .