Table Of ContentDC MOTORS
SPEED CONTROLS
SERVO SYSTEMS
AN ENGINEERING HANDBOOK
prepared by
ELECTRO-CRAFT CORPORATION, USA
PERGAMON PRESS
Oxford · New York · Toronto · Sydney · Paris · Frankfurt
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copyright © Electro-Craft Corporation 1972
First published by Pergamon Press Ltd., 1977
All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system or transmitted in
any form or by any means: electronic, electrostatic,
magnetic tape, mechanical, photocopying, recording or
otherwise, without permission in writing from the
publishers
Library of Congress Catalog Card No. 76-56647
ISBN 0 08 021715 X F
0 08 021714 1 H
Printed in the United States of America
Foreword to the Third Edition
Since its first publication back in 1972 new P6000 series servomotor control sys-
Electro-Craft's engineering handbook, "DC tems.
MOTORS - SPEED CONTROLS - SERVO
SYSTEMS", has become a standard refer- Chapter 6 — An entirely new chapter dis-
ence in the field of motor control. In all cussing the new and exciting developments
35,000 copies have been sold averaging made by Electro-Craft in the field of DC
about 1,000 per month. Many of these Brushless Motors.
books are used by professional engineers
to provide day to day assistance in their Chapter 7 — Data sheets on Electro-Craft
system design work, and many are playing products have been revised, updated, and
a useful role in colleges and universities expanded. The new models now available
helping to train the engineers of the future. in the MOTOMATIC range of Speed
Controls, Servomotor Controls, and Digital
As a result of the continuous feedback Positioning Systems are described in full.
received from users of this book, we have
prepared a new, third edition, which has Once again Electro-Craft Corporation cor-
been expanded by about 100 pages to a dially invites your comments and criticisms
total of little over 500. Apart from the so that the next edition of this book will
correction of errors this new edition remain one of the foremost reference
includes the following changes: works in its field.
Chapter 5—The application section has
been expanded to include, more applica- ELECTRO-CRAFT CORPORATION
tions and notes on the application of the August 1975
XV -
Foreword to the Second Edition
Since October 1972, when the first edition a new section Phase-Locked Servo Systems
of this book was published, we have distri- has been added.
buted 15000 copies to interested engineers
Chapter 5 - The Applications section has
and designers. The overwhelming majority
been expanded, sections of Application Clas-
of the comments which we received from
sification and Specification, and Motor Selec-
our readers have been favorable and com-
tion Criteria have been added.
plimentary to our effort for creating this
book. We have also received some construc- Chapter 6 - Data sheets on motors and
tive criticism and requests for expanding the amplifiers have been revised, updated and
treatment and discussion on certain subjects. expanded. Electro-Craft's new line of servo
In preparing this expanded second edition, amplifiers is also presented in this chapter.
we have taken into account all these requests
which we could accommodate. All the
Two new Appendices have been added; a
changes and additions enlarge this book by
description of the SI System of Units (Metric
about 30 percent from the first edition to
System) and a Units' Conversion Factors
approximately 400 pages.
and Tables.
Listed below are the nature of the various It is the continuing interest of the authors
changes and additions by chapter: and editors of this engineering handbook to
make it a most useful, relevant and informa-
Chapter 7 - Recognizing the need for in-
tive source of knowledge regarding all aspects
clusion of the metric system, we revised the
of DC motors, speed controls and servo
Terminology and Symbols sections and have
systems. To this end we again wish to solicit
added the Systems of Units section.
the constructive comments of our readers.
Chapter 2 - The treatment of Motor Equa- These comments, together with the results
tions, Transfer Functions, Power Dissipation of our continually expanding search for
and Thermal Characteristics has been re- valuable, pertinent technical information,
written and expanded. will be incorporated into future editions of
this book.
Chapter 3 - Minor revisions.
Chapter 4 - Servo Components treatment ELECTRO-CRAFT CORPORATION
has been revised and expanded. The section
on Servo Amplifiers has been rewritten, and September 1973 n
- XVII -
Foreword to the First Edition
THE ELECTRO-CRAFT STORY
Electro-Craft is a growing, publicly held companies which make both. It is this
corporation started in 1960. For close to special "system-oriented" approach, coupled
ten of these twelve years, the company has with constant technological innovation, that
specialized in the development and manu- is perhaps most responsible for the com-
facture of fractional horsepower permanent pany's success in the field.
magnet DC motors, generators and control
amplifiers. WHY THIS BOOK
Around the turn of this century, AC motors
In the early years, business centered around
won out over DC machines as the generally
patented, integrally constructed motor-gen-
accepted sources of electric motive power.
erators and matching transistorized "Class
The deciding factor then was the state of
A" control amplifiers, marketed under the
technology and materials, rather than the
MOTOMATIC®trademark. These smaller
size, transistorized motor speed control sys- inherent characteristics of each device.
tems found their first applications mostly
Automation and the need for controlled
in office equipment, medical electronics,
speed and torque, rather than just raw mo-
and instrumentation products.
tive power, have brought about a resurgent
interest in the use of DC motors. High
Over the years, the product line has ex- energy permanent magnets, epoxy resins,
panded into larger sizes, higher performance improved brushes and other new materials
servomotors, low ripple tachometer-gener- and technologies have also made possible
ators, and increasingly sophisticated servo DC machines which are more reliable, smaller
control amplifiers to meet the growing de- and less expensive to produce.
mands of our customers.
The combination of the above factors pro-
During 'the past decade, Electro-Craft has duced a great deal of change during the last
sold over half a million precision DC motors decade in the variety and performance of
and controls to more than 1000 customers DC motors. The greatest innovation took
for approximately 300 different applications.
place in the fractional horsepower sizes. The
concurrent rapid advances in semiconductor
There are many motor manufacturers who technology, especially in low cost, high
do not make matching controllers, and vice power SCR's and transistors, facilitated the
versa; Electro-Craft is one of the very few
emergence of a variety of matching control
XIX -
amplifiers, from economy models to the index and the definitions in Chapter 1
very sophisticated ones. should help the reader to decide how much
background he needs to cover.
Due to this fast growth of technology,
Some of the information presented is stan-
much of what is available today is not
dard reference material, and some probably
described in the standard textbooks. The
purpose of this book is to offer a basic will not be found elsewhere. Some chapters
background in DC motors, speed controls are quite theoretical, while others focus on
and servo systems, and to describe new the more practical "how to" aspects.
developments in the field. The presentation
This is a handbook which will probably be
is aimed at the designer and user in industry,
consulted as a reference as problems arise,
with emphasis on many practical problems
rather than being read cover to cover as a
from testing to applications engineering.
student's textbook.
The selection of the power drive system
ABOUT THE AUTHORS
for an application is greatly facilitated by
proper communication: a specific under- Approximately twenty people contributed
standing of the problem between the user to the preparation of this book. They com-
and the manufacturer. Another aim of this prise the technical staff of Electro-Craft,
book is to make this task simpler by with backgrounds in design engineering,
attempting to share the accumulated techni- research and development, testing, teaching,
cal knowledge of our company, which has systems development, sales, application en-
specialized in this field for the past decade. gineering, and - most of all - practical prob-
lem solving. The authors collectively have
HOW TO USE THE BOOK over 200 man-years of experience in DC
motor and control technology.
This book was prepared as a compendium
In addition to their regular daily work, the
of articles on many related subjects. The
authors gave their time generously over the
editors made no attempt to homogenize
the styles of the different authors. An past year to make this book possible.
effort was made, however, to make the
ELECTRO-CRAFT CORPORATION □
chapters self-contained and to organize the
subject matter in a meaningful way. The October 1972
- xx -
Chapter 1
Terminology, Symbols, Systems of Units
1.1. TERMINOLOGY
Acceleration, Maximum from Stall - the Characteristic Equation - the characteristic
angular acceleration of an unloaded motor, equation of a servo system is 1 + GH = 0
initially at rest, when the peak armature where G is the transfer function of the
current I . is applied. forward signal path and H is the transfer
function of the feedback signal path.
Ambient Temperature - the temperature of
the cooling medium immediately surround- Circulating Current - the current in armature
ing the motor or another device. conductors which are short-circuited during
commutation.
Armature Reaction - the production of a
magnetic field shifted by 90 electrical de- Cogging - the non-uniform rotation of a mo-
grees with respect to the direction of stator tor armature caused by the tendency of the
magnetic field. This magnetic field is pro- armature to prefer certain discrete angular
duced by armature current. positions.
Bandwidth - the frequency range in which Coupling Ratio - a general term to define the
the magnitude of system gain expressed in relative motion between motor armature
dB is within the 3 dB band. and the driven load.
Block Diagram - a simplified representation Critical Damping - a critically damped sys-
of a system, with each component repre- tem's response to a step disturbance is the
sented by a block, and each block posi- return to its equilibrium state without over-
tioned in the order of signal flow through shooting the equilibrium state in minimum
the system. possible time.
Bode Plot - a plot of the magnitude of sys- Crossover Frequency - the frequency at
tem gain in dB and the phase of system gain which the magnitude of the product of the
in degrees versus the sinusoidal input signal forward path gain and the feedback path
frequency in logarithmic scale. gain is unity.
Break Frequency - the frequency(-ies) at Damping (in servo theory) -a term to describe
which the asymptotes of the gain curve in the amplitude decay of an oscillatory signal.
the Bode plot intersect.
1-1
Damping Ratio - a measure of system damp- Flux Biasing - a method for controlling the
ing expressed as the ratio between the actual torque constant of a servomotor by varying
damping and the critical damping. the magnetic field intensity of a separate
wound field assembly.
Dead Band - a range of input signals for
which there is no system response. Form Factor - the form factor of a harmonic
signal is the ratio of its RMS value to its
Decibel (dB) - a measure of system gain (A).
average value in one half-wave.
AdB = 20l°9lOA
Full Load Current - the armature current of
Dielectric Test - a high voltage test of the
a motor operated at its full load torque and
motor insulation ability to withstand an AC
speed with rated voltage applied.
voltage. Test criterion limits the leakage
current to a specified maximum at test
Full Load Speed - the speed of a motor
voltage of specified magnitude and fre-
operated with rated voltage and full load
quency, applied between the motor case and
torque.
winding.
Gain - the ratio of system output signal to
Dynamic Braking - a method for braking a
system input signal.
DC servomotor by controlling armature cur-
rent during deceleration. Gain Margin - the magnitude of the system
gain at the frequency for which the phase
Efficiency - the ratio of output power to in- angle of the product of the forward path
put power. and feedback path gains is —180°.
Hunting - the oscillation of system response
about theoretical steady-state value due to
Electrical Time Constant - the electrical time insufficient damping.
constant of a DC servomotor is the ratio of
armature inductance to armature resistance. Incremental Motion System - a control sys-
tem which changes the load position in
Fall Time - the time for the amplitude of discrete steps rapidly and repetitively.
system response to decay to 37% of its
steady-state value after the removal of steady- Inertia! Match - an inertia I match between
state forcing signal. motor and load is obtained by selecting the
coupling ratio such that the load moment of
Field Weakening - a method of increasing inertia referred to the motor shaft is equal
the speed of a wound field motor by re- to the motor moment of inertia.
ducing stator magnetic field intensity by
reducing magnet winding current. Lag Network - an electrical network which
1-2
increases the delay between system input Phase Margin - the phase angle of the loop
signal and system output signal. gain minus 180° at the crossover frequency.
Lead Network - an electrical network which Pole - a term of root locus plotting for the
decreases the delay between system input frequency(-ies) at which system gain goes to
signal and system output signal. infinity.
Safe Operating Area Curve (SOAC) - the
Lead Screw - a device for translating rotary
boundary on the speed-torque characteristic
motion into linear motion consisting of an
of a motor inside of which the motor may
externally threaded screw and an internally
be operated continuously without exceeding
threaded carriage (nut).
its thermal rating.
Lead Screw, Ball - a lead screw which has its Speed Regulation - for a speed control sys-
threads formed as a ball bearing race and the tem, speed regulation is the variance in actual
carriage contains a circulating supply of balls speed expressed as a percentage of set speed.
for increased efficiency.
Speed Regulation Constant - the slope of the
Linearity - for a speed control system it is motor speed-torque characteristic.
the maximum deviation between actual and
set speed expressed as a percentage of set System Order - the degree of the system
speed. characteristic equation.
Loop Gain -the product of the forward path
System Stiffness - a measure of system
and feedback path gains.
accuracy when subjected to disturbance sig-
nals.
Mechanical Time Constant -the time foran
unloaded motor to reach 63.2% of its final System Type - is given by the number of
velocity after applying a DC armature voltage. poles located at the origin of the loop gain
characteristic in the complex plane.
Motor Constant - the ratio of motor torque
Torque Ripple - the cyclical variation of
to motor input power.
generated torque at a frequency given by
No Load Speed - motor speed with no the product of motor angular velocity and
external load. number of commutator segments.
Phase-Locked Servo System -a hybrid control Transfer Function - the ratio of the Laplace
system in which the output of an optical transforms of system output signal and sys-
tachometer is compared to a reference square tem input signal.
wave signal to generate a system error signal Zero - a term of root locus plotting for the
proportional to both shaft velocity and frequency(-ies) at which system gain goes to
position errors. zero.
1-3
1.2. SYMBOLS
Unit |
Symbol Definition si British
, dv
a linear acceleration a = — m/s2 in/s2
dt
— I
A gain —
— I
gain expressed in dB —
AdB
AC alternating current (symbol)
B magnetic flux density T line/in2 I
C capacitance F F
CW clockwise rotation
CCW counterclockwise rotation
D viscous damping factor D = AdB Nm/rad s"1 oz-in/rad s'1 1
CO
— 1
dB decibel —
DC direct current (symbol)
deg I temperature degree °C, K not used 1
— 1
I e (2.71828) base of natural logarithms —
E internal voltage (emf) V V
internally generated voltage (counter emf) V V
E9
Eg=l<E
ί "
f frequency Hz Hz, c/s, cps 1
1-4
