TAILIEUCHUNG - Brushless Permanent Magnet Motor Design- P2

Brushless Permanent Magnet Motor Design- P2: 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. | Magnetic Modeling 21 Figure Circular-arc straightline permeance model. In this equation X the extent that the fringing permeance extends up the sides of the blocks is the only unknown. In those cases where X is not fixed by geometric constraints it is commonly chosen to be some multiple of the air gap length. The exact value chosen is not that critical because the contribution of differential permeances decreases as one moves farther from the air gap. Thus as X increases beyond about 10g there is little change in the total air gap permeance. Slot modeling v Often electrical machines have slots facing an air gap which hold current-carrying windings. Since the windings are nonmagnetic flux crossing an air gap containing slots will try to avoid the low relative permeability of the slot area. This adds another factor that must be considered in determining the permeance of an air gap. To illustrate this point consider Fig. where slots have been placed in the lower block of highly permeable material. Considering just one slot and the tooth between the slots there are several ways to approximate the air gap permeance. The simplest and crudest method is to ignore the slot by assuming that it contains material of permeability equal to that of the rest of the block. In this case the permeability is simply Pg g AIg where A is the total cross-sectional area facing the gap. Obviously this is a poor approximation because the relative permeability of the slot is orders of magnitude lower than that of block material. Another crude approximation is to ignore the flux crossing the gap over the slot giving a permeance of Pg Mo A - As g where As is the cross-sectional area of the slot facing the air gap. Neither of these methods is very accurate but they do represent upper and lower bounds on the air gap permeance respectively. 22 Chapter Two a Figure A slotted structure. There are two more accurate ways of determining air gap permeance in the presence of slotting. The

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