Mathematics for Machine Technology

495 Pages·1998·56.022 MB·English

by  Robert D. Smith

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Library of Congress Cataloging-in-Publication Data:
Smith, Robert Donald, 1931 -
Mathematics for machine technology / Robert D. Smith. - 4th ed.
p. cm.
Includes index.
ISBN 0-8273-7942-0
I. Shop mathematics. I. Title.
TJ1165.S713 1998 98-6660
621.9'02'015 131 3-dc21 CIP

CONTENTS vii
UNIT57 ComplexPracticalMachineApplications..................... 361
UNIT58 TheCartesianCoordinateSystem........................... 371
UNIT59 ObliqueTriangles:LawofSinesandLawofCosines........... 375
UNIT60 AchievementReview-Section Five .. ..... .. ............ 385
SECTION 6 Compoun~Angles 390
UNIT61 IntroductiontoCompoundAngles. ......................... 390
UNIT 62 Drilling andBoring Compound-Angular Holes: Computing
Apgles of Rotation and TiltUsing Given Lengths. ............. 393
UNIT 63 Drilling and Boring Compound-Angular Holes: Computing
Angles of Rotation andTiltUsing Given Angles. .............. 397
UNIT 64 Machining Compound-Angular Surfaces: Computing Angles
ofR. otationandTilt. ..................................... 404
.
UNIT 65 Computing Angles Made by theIntersection of'!\vo
AngularSurfaces........................................ 412
UNIT66 ComputingCompoundAnglesonCuttingandFormingTools. ... 418
.
UNIT 67 Achievement Review-Section Six. . ...................... 425
SECTION 7 Computer Numerical Control (C~C) 428
UNIT 68 Introduction to Computer Numerical Control (CNC) ..... 428
UNIT 69 Control Systems, Absolute Positioning, Incremental
Positioning............................................. 432
.
UNIT 70 Binary Numeration System. ......... ..................... 439
UNIT71 AchievementReview-Section Seven. ...................... 443
Appendix. ..................................................... 446
Answers to Odd-Numbered ApplicatipDS ..... ..... ...... ...... ...... 450
Index , 477
PREFACE
Mathematics for Machine Technology is written to overcome the often mechanical
"plug in" approach found in many trade-related mathematics textbooks. An under-
standing of mathematical concepts is stressed in all topics ranging from general arith-
metic processes to oblique trigonometry, compound angles, and numerical control.
Both content and method are those used by the author in teaching applied machine
technology mathematics classes for apprentices in the machine, tool-and-die, and tool
design trades. Each unit is developed as a learning experience based on preceding
units-making prerequisites unnecessary.
Presentation of basic concepts is accompanied by realistic industry-related exam-
ples and actual industrial applications. The applications progress from the simple to
those with solutions which are relatively complex, Many problems require the student
to work with illustrations such as are found in machine trade handbooks and engineer-
ing drawings.
An analytical approach to problem solving is emphasized in the geometry, trigo-
nometry, compound angle, and numerical control sections. This approach is necessary
in actual practice in translating engineering drawing dimensions to machine working
dimensions. Integration of algebraic and geometric principles with trigonometry by
careful sequence and treatment of material also helps the student in solving industrial
applications. The Instructor's Guide provides answers and solutions for allproblems.
Changes from the previous edition have been made to improve the presentation of
topics and to update material.
A survey of instructors using the third edition was conducted. Based on their com-
ments and suggestions, changes inthe text revision were made. The result is an updated
and improved fourth edition in both content and sequencing of content.
.
The majority of instructors surveyedstatedthat theirstudentsarerequired to
perform basic arithmetic operations onfractions anddecimals prior tocalculator
usage. Thereafter, the students use the calculator almost exclusively inproblem-
solving computations. The structuring of calculator instructions and examples
in this text reflect in the instructors' preferences. Calculator instruction and ex-
amples have been updated and greatly expanded in this edition. The scientific
calculator is introduced in the Preface. Extensive calculator inst~ction and
examples are given directly following the units onfractions and mixed numbers
and the units on decimals. Further calculator instruction and examples are given
throughout the text wherever calculator applications are appropriate to the mate-
rial presented. A Calculator Applications Index is provided at the end of the
Preface. It provides a convenient reference for all the material in the text for
which calculator usage is presented. Often there are differences in the methods
of computation among various makes and models of calculators. Where there
are two basic ways of performing calculations, both ways are shown.
. Three new units on percent, units 17-19, havebeen added. 'ftle survey indicated
that the topics of percent andpercentages arerelevant tomanufacturing technol-
ogy. Applications are presented, primarily in problems involving machining
times, material shrinkage and expansion, alloy material composition, manufac-
turing costs, production rates, and percent defective product.
.
In Section 5, Trigonometry, trigonometric function tables and interpolation have
been eliminated. All computations involving trigonometric functions are done
with acalculator. Calculator examples have been greatly increased.
ix
/'
x
MATHEMATICSFORMACHINETECHNOLOGY
. Section 7, Computer Numerical Control, hasbeen updated. The revised material
is centered on computer numerical control (CNC) rather than onnumerical con-
trol (NC) as in previous editions.
Robert D. Smith has experience in bOththe manufacturing industry and in educa-
tion. He held positions as tool designer, quality control engineer, and chief manufactur-
ing engineer prior to teaching. Mr. Smith has taught applied mathematics, physics, and
industrial materials and processes on the secondary school level and in Machine Trade
Apprentice Programs. Mr. Smith is Associate Professor Emeritus of Industrial Technol-
ogy at Central Connecticut State University, New Britain, Connecticut. He is the author
of Delmar's Technical MathematicS.
...
0
0, Introduction to the Scientific Calculator
I
Scientific Calculator
A scientific calculator is to be used in conjunction with the material presented in
this textbook. Complex mathematical calculations can be made quickly, accurately, and
easily with a scientific calculator.
Aithough most functions areperformed in the sameway,there are some differences
among different makes and models of scientific calculators. In this book, generally,
where there are two basic ways of performing afunction, both ways are shown. How-
ever, not all of the differences among the various makes and models of calculators can
be shown. It is very important that you become familiar with the operation of your sci-
entific calculator. An owner's manual or reference guide is included with the purchase
of ascientific calculator. The manual explains the essential featUresandkeys of the spe-
cific calculator and provides detailed information on the proper use of the calculator. It
isessential that the owner's manual be studied and referredtowhenever there isaques-
tion regarding calculator usage.
For use with this textbook, the most important feature of the scientific calculator is
the Algebraic Operating System (AOSTM).This system, which uses algebraic logic,
permits you to enter numbers and combined operations into the calculatot in the same
order as the expressions are written. The calculator performs combined operations ac-
cording to the rules of algebraic logic, which assigns priorities to the various mathe-
matical operations. It isessential that you know ifyour calculator uses algebraic logic.
Most scientific calculators, in addition to the basic arithmetic functions, have alge-
braic, statistical, conversion, and program or memory functions. Some of the keys with
their functions are shown. Scientific calculators have functions in addition to those
shown.
General Information
Since there is some variation among different makes andmodels of scientific calcu-
lators, your calculator function keys may be different from the descriptions that follow.
Torepeat, it isvery important that you refer tothe owner's manual whenever there isa
question regarding calculator usage.
.
Solutions to combined operations shown in this text are performed ona calcula-
tor with algebraic logic (AOSTM).
. Turning the Calculator On and Off
The method of turning the calculator on with battery-powered caleulators de-
pends on the calculator make and model. When a calculator is turned on, 0
and/or other indicators are displayed. Basically, acalculator isturned on and off
by one of the following ways.
I
IWithcalculatorswith anon/clear,I ON/C ~ key,pressI ON/C to turn on. Press the
OFF key to turn off.
I
'-..
xi
PREFACE
SOME TYPICAL KEY SYMBOLS AND FUNCTIONS FOR
A SCIENTIFIC CALCULATOR
Key(s) Function(s)
G, G, 0, G, G, or EXE or IENTERI Basic Arithmetic
[81 ] 1
+/- or Change Sign
1 IT1 ] Pi
W,rn
Parentheses
IT[] ScientificNotation
or EXP
1 1
IEng EngineeringNotation
I 1
STO I,1RCLI,IEXC1 Memory or Memories
[TI, I I
fi Square and Square Root
IWlorlrl Root
[ZIor [2] Power
[}Jorra Reciprocal
Percent
Fractions and Mixed Numbers
Logarithm
IDRGI Degrees,Radians,andGraduations
IDMSlorD Degrees,Minutes,andSeconds
,,
Trigonometric Functions
~ [KJ
With calculators with an allclear power on/power off, key,press to
[KJ
turn on. Generally, the key is also pressed to turn off.
With calculators that have an on-off switch, move the switch either on or off.
The switch is usually located on the left side of the calculator.
> Note: In order to conserve power, most calculators have an automatic
power off featurethat automatically switchesoffthe powerafter approxi-
mately5 minutesofnonuse.
.
Clearing the Calculator Display and All Pending Operations
To clear or erase all entries of previous calculations, depending on the calcula-
tor, either of the following procedures isused.
I I
With calculators with an on/clear, ~ON/C ~ key,press [ONK/CJ1.twice.
Withcalculatorswiththeallclear, key,press
.
Erasing (Deleting) the Last Calculator Entry
A last entry error can be removed and corrected without erasing previously en-
tered data and calculations. Depending on the calculator, one of the following
procedures is used.
I
With calculators with the on/clear, ON/C ~ key,press I ON/C ~
I I
With calculators with a delete, DEL key,press DEL
~ I.
With calculators with a clear, W, key,press W.
.
Alternate-Function Keys
Most scientific calculator keys can perform more than one function.
~ ~
Dependingonthecalculator,the and keysor SHIFTkeyenableyou
1 1
to use alternate functions. The alternate functions are marked above the key
and/or on the upper half of the key.Alternate functions are shown and explained
in the book where their applications are appropriate to specific content.