SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Appendix C - Sinusoidal and Nonsinusoidal Motors
This appendix elaborates the distinction between sinusoidal and nonsinusoidal motors.
Chapter 2 introduced the important concept of flux linkage. It was shown that the interaction
between the distributions of the rotor flux and the stator winding requires a spatial analysis but
that the end result (the rotor-stator flux linkage, R ) is a function of rotor position r . It was
mentioned that the physical details of motor construction were irrelevant in elementary analysis
since the bEMF/torque functions are derived from the rotor-stator flux linkage. The emphasis was
thus placed on R in order to see how it related to torque and bEMF. Simple motors were
studied to introduce the concept of sinusoidal and trapezoidal motors. Now that the basics have
been presented, these same concepts can be studied in greater detail.
Chapter 2 discussed the difference between sinusoidal and trapezoidal motors; that material is
relevant to understanding their operation and control. But it was mentioned that the trapezoidal
motor is not well defined. Similarly, although a sinusoidal motor was said to have a sinusoidal
R( r)
this can be achieved in various ways. The purpose of this appendix is to present a better
understanding of the constructional features that determine the shape of the rotor-stator flux
linkage. While this material is not directly useful from a motor control perspective it is required
to be able to define “sinusoidal” and “nonsinusoidal” motors. Eventually this information will aid
in the understanding of what happens when a model (space vector theory) or control scheme
(FOC)—both of which stipulate a sinusoidal motor—are used with a nonsinusoidal motor.
The first section discusses the fundamental relationships. The different types of windings are
discussed and their influence on MMF and rotor-stator flux linkage is investigated. Thus the first
section provides the link between motor construction and R( r)
. The second section
reexamines the how R( r)
influences torque and bEMF. Finally, the third section provides a
practical summary that defines the “sinusoidal” motor and the effective number of turns ( N e ) that
are used throughout this report.
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