12: Permanent magnet "Brushless DC" motors

Last updated
Save as PDF

Page ID: 54450

James Kirtley
Massachusetts Institute of Technology via MIT OpenCourseWare

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

This chapter is a brief introduction to the design evaluation of permanent magnet motors, with an eye toward servo and drive applications. It is organized in the following manner: First, we describe three different geometrical arrangements for permanent magnet motors:

Surface Mounted Magnets, Conventional Stator,
Surface Mounted Magnets, Air-Gap Stator Winding, and
Internal Magnets (Flux Concentrating).

After a qualitative discussion of these geometries, we will discuss the elementary rating parameters of the machine and show how to arrive at a rating and how to estimate the torque and power vs. speed capability of the motor. Then we will discuss how the machine geometry can be used to estimate both the elementary rating parameters and the parameters used to make more detailed estimates of the machine performance.

Some of the more involved mathematical derivations are contained in appendices to this note.

12.1: Motor Morphologies
There are, of course, many ways of building permanent magnet motors, but we will consider only a few in this note.
12.2: Zeroth Order Rating
In determining the rating of a machine, we may consider two separate sets of parameters. The first set, the elementary rating parameters, consist of the machine inductances, internal flux linkage and stator resistance. From these and a few assumptions about base and maximum speed it is possible to get a first estimate of the rating and performance of the motor. More detailed performance estimates, including efficiency in sustained operation, require estimation of other parameters.
12.3: Parameter Estimation
We are now at the point of estimating the major parameters of the motors.
12.4: Current Rating and Resistance
The last part of machine rating is its current capability. This is heavily influenced by cooling methods, for the principal limit on current is the heating produced by resistive dissipation. Generally, it is possible to do first-order design estimates by assuming a current density that can be handled by a particular cooling scheme.
12.5: Appendix 1- Air-Gap Winding Inductance
12.6: Appendix 2- Permanent Magnet Field Analysis
12.7: Layout