A course for shop mathematics
653 114 5MB
English Pages 123
Polecaj historie
Citation preview
A COURSE FOR SHOP MATHEMATICS
A Project Presented to the Faculty of the School of Education The University of Southern California
In Partial Fulfillment - of the Requirement for the Degree * Master of Science in Education
by Frank J. Ziol February, 1950
UMI Number: EP46157
All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion.
Dissertation PwWisMrtg
UMI EP46157 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code
ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346
&
T h is p r o je c t r e p o r t, w r it t e n u n d e r the d ir e c t io n o f th e ca n d id a te ’s a d v is e r a n d a p p r o v e d by h im , has been p re se n te d to a n d a c ce p te d by the F a c u l t y o f the S c h o o l o f E d u c a t io n in p a r t i a l f u l f i l l m e n t o f the re q u ire m e n ts f o r
th e degree
o f M a s te r of
Science in E d u c a t io n .
Date...............................
A d v is e r
Dean
il TABLE OP CONTENTS CHAPTER
PAGE PART I.
GENERAL PROBLEMS
HOW TO SOLVE MATHEMATICAL DIFFICULTIES OF INSPECTION OR BENCH JOBS 1.
BLUEPRINTS;
HOW TO READ AND CALCULATE DIMENSIONS
' FROM SHOP DRAWINGS . A.
MOTIVATION:
...........
2
How the ability to read and work
from shop drawings can pay o f f ............. B.
DIRECTIONS:
2
Suggestions for Improving your
ability in working with shop drawings........... 1.
DRAWING LANGUAGE: directions
How to read blueprint
. . . . . . . .
2.- CUMULATIVE DIMENSIONS:
..................
MISSING DIMENSIONS:
.
MISSING ANGLES:
SOURCES FOR THIS CHAPTER:
ACTIVITY ASSIGNMENTS:
.
5
Where to get
further d a t a ................. C.
5
How to determine
additional angular v a l u e s ................. 5.
4
How to solve for
needed linear d a t a ........... 4.
2
Ho w to calculate
overall l e n g t h ............................ 3.
2
8
Some experiences that
will help you become more familiar with blue p rints.......................... D.
EVALUATION:
8
A sample check of your knowledge
in reading and calculating from shop drawings .
8
iii PAGE
CHAPTER 2.
LINEAR DIMENSIONS: LENGTH, A.
B.
WIDTH, OR THICKNESS..........................
MOTIVATION: how
HOW TO INSPECT MATERIALS FOR
Advantages arising from knowing
to make accurate measurements...............
DIRECTIONS:
COMMON PRACTIONS:
12
How to measure a length
in fractions of an inch...................... 2.
12
Some key points to guide you In
working with linear dimensions .................. 1.
12
CONVERSION TO DECIMALS:
12
How to adapt a
fractional length for measurement with a micrometer . . . . .
........................
13
How to "mic" a shaft...........
14
3.
MICROMETER:
4.
VERNIER CALIPER:
How to measure with a
vernier caliper............... 5.
PRECISION BLOCKS:
14
How to arrange precision
gage blocks for accurate measurement . . . .
16
6.
GAGES:
17
7.
VARIOUS SYSTEMS:
How to measure with fixed gages.
. .
How to select numbered,
lettered, or fractional drills ............. 8.
FOREIGN METHODS:
How to convert measure
ments to the metric scale.................... 9.
FOUNDRY REQUIREMENTS:
SHEET METAL PROBLEMS:
18
How to make allow
ance for shrinkage in a casting............. 10.
18
18
How to make allow
ances for bending in sheet m e t a l ...........
20
Iv PAGE
CHAPTER 11.
PRODUCTION NEEDS:
How to estimate lengths
of raw material for cutting in small p i e c e s ........................................ 12.
DESIGN DATA:
How
to measure the displace
ment of a cam. 13.
SOURCES FOR THIS CHAPTER:
ACTIVITY ASSIGNMENTS:
.
21
. . .
21
Where to get
further assistance . . . .“ . . . . . . C.
20
Learning experiences to
help you become more proficient in handling linear dimensions................................. D.
EVALUATION:
A sample check of your mastery in
measurements of length, width, or thickness. 3.
ANGULAR DIMENSION:
HOW TO INSPECT THE
. .
MOTIVATION:
Outcomes
.
DIRECTIONS:
25
of angle measurement
ability............................................ B.
22
RELATIONS OF
VARIOUS SURFACES OF MACHINE PRODUCTS A.
22
Suggestions
25
for handling some of
the problems of mathematical relationship of ........................
various surfaces 1.
MEASUREMENT:
How
to measure an angle with
a vernier protractor ......................... 2.
3.
SINE BAR:
25
25
How to set up an angle with a
sine b a r ......................................
26
TAPER ANGLE:
27
How to Inspect a
taper angle .
CHAPTER
PACE 4.
COMPOUND ANGLE:
How to inspect the angles 27
of a compound angle............... 5.
DOVETAIL CHECK:
How to check dovetails by
placing wires, rods, or b a l l s ................ 6.
HOLE CENTERS:
How to measure the distance
between drilled holes............... 7.
TOOL ANGLES:
. . . .
30
How to measure the cutting
angles of a t o o l .................
31
8.
RIGHT ANGLES:
32
9.
SOURCES FOR THIS CHAPTER: Where to .secure
How to make a square corner .
d a t a ............................... C.
30
ACTIVITY ASSIGNMENTS:
32
Performances which may
be used to develop your skill in making ang ular calculations................... D.
EVALUATION:
33
A sample of evaluation technique
which may be applied to your knowledge of ang ular dimension calculation ...................... 4.
AREA AND VOLUME:
HOW TO CALCULATE SURFACES AND
S O L I D S ................................................. A.
MOTIVATION:
DIRECTIONS:
35
Advantages of being able to make
area and volume c a l c u l a t i o n s .................... B.
33
Helpful hints on the development
35
of
skill In dealing with problems of surfaces and s o l i d s ............................................
35
Vi PAGE
CHAPTER 1.
FORMED METAL:
How to calculate sheet metal 35
requirements for box construction........... 2.
LIQUID DISTRIBUTION:
How to estimate paint
r e q u i r e m e n t s ............. . . ................ 3.
RAW SOLID MATERIAL:
36
How to calculate the
amount of wood necessary for pattern con struction. 4.
CASTING NEED:
36 How to determine volume re
quirements for casting . . . . . 5.
SOURCES FOR THIS CHAPTER:
37
Where to secure
d a t a ............................ C.
ACTIVITY ASSIGNMENTS:
37
Work to do to help you
gain experience in calculating areas and vol umes D.
............................
EVALUATION:
38
Sample evaluation instrument for
possible checking of your surface and solid calculations . . . . . . . 5.
LAYOUTS:
.......................
H O W TO DIAGRAM THE DIRECTIONS FOR WORK .
A.
MOTIVATION:
Returns from skill in layout work
B.
DIRECTIONS:
Suggestions for the development of
38
.
41
.
41
your ability to diagram work directions......... 1.
CENTER LOCATION:
How to locate the center
of round work for center-drilling......... 2.
CENTER OF GRAVITY:
41
How to locate the center
41
vll PAGE
CHAPTER ......................
42
How to lay out a c a m ...........
42
of irregular work. 3 . CAM LAYOUT: 4.
EQUAL DIVISION:
How to divide aboard into
a number of equal widths . 5.
PARALLEL LINES:
................
How to draw a line parallel
to a straight or curved l a y o u t ............. 6.
SCALE:
43
How to reduce or increase the scale
of a drawing 7.
VERTIGAL LINE:
.................
44
How to establish a vertical
reference line 8.
44
SOURCES FOR THIS CHAPTER:
Where to seeure
further d a t a ............. C.
ACTIVITY ASSIGNMENTS: to
D.
.
45
Some learning experiences
enhance your skill in layout w o r k ...........
EVALUATION:
42
45
A sample of a way in which you may
check your ability to diagram directions for shop wo r k .............
fART II.
46
MACHINE PROBLEMS
HOW TO SOLVE PROBLEMS INVOLVING MACHINING OPERATIONS 6.
SETUP: A.
HOW TO POSITION WORK IN A M A C H I N E . .........
MOTIVATION:
Advantages of being able to set up
your own w o r k ............. B.
DIRECTIONS:
48
Some helpful hints regarding
**•
48
viii CHAPTER
p kQE
positioning of w o r k ............................... 1*
CENTERING:
How to locate centers in milling
machine work 2.
.................. ..
ECCENTRICITY:
48
How to remove eccentricity
in lathe work................; ............. .. 3.
OFFSET:
......................
TABLE ANGLES:
50
How to set grinding table
a n g l e s ........................................ 5.
LEVELING:
50
How to level a workpiece in a
shaper vise. 6.
. . . . . . . . . . . . . . .
SOURCES FOR THIS CHAPTER:
.
ACTIVITY ASSIGNMENT:
EVALUATION:
MACHINE SPEED:
MOTIVATION:
DIRECTIONS:
54
Advantages that ordinarily result
from an ability to calculate machine speed . . . B.
52
HOW TO CALCULATE REVOLUTIONS OR
STROKES PER M I N U T E .................................... A.
52
A sample check of your knowledge
of positioning work in a m a c h i n e ................ 7.
51
Some experiences to help
you become familiar with machine set-ups . . . . D.
51
Where to secure
d a t a .......................................... C.
49
How to locate centers for off cen
ter lathe xvork 4.
48
54
Suggestions for handling the cal
culations of revolutions and
strokes per minute
of machine w o r k . ............................... ..
54
ix PAGE
CHAPTER 1.
LATHE SPEED:
How to calculate lathe speed
for cutting steel....... .... 2.
SHAPER SPEED:
How to calculate shaper
speed for cutting 3.
54
MILLING SPEED:
cast iron ................
55
How to calculate milling
machine speed for cutting a l u m i n u m .......... 4.
SAW SPEED:
How to calculate band saw speed
for’ cutting wood 5.
................
GRINDING SPEED:
6 . PULLEY RATIOS:
56
How to keep within the
maximum surface speed of a grinding wheel.
.
57
.
.
57
How to compound gears .
.
58
How to select a pulley
ratio to produce a needed machine speed. 7.
56
COMPOUND GEARING:
8 . SOURCES FOR THIS CHAPTER:
Where to get fur
ther assistance C.
ACTIVITY ASSIGNMENT:
59 Performances to give you
experience in calculating machine speeds . . . . D.
EVALUATION:
59
Samples of some evaluation tech
niques which may be applied to your knowledge of machine speeds............................... 8.
MACHINING TIME:
HOW TO DETERMINE PRODUCTION PERFOR
MANCE. A.
MOTIVATION:
59
62 Rewards to you for knowing the
facts about machine operations .
.............
62
X PAGE
CHAPTER B.
DIRECTIONS;
Some pointers that will help you
in determining production performance........... 1.
LATHE PERFORMANCE;
How to estimate the
machine time for a lathe o p e r a t i o n ......... 2.
HOURLY OUTPUT;
SHAPER PERFORMANCE;
......................
SPOILED MATERIALS;
...
64
How to calculate the 64
percentage of scrap................... 5.
SOURCES FOR THIS CHAPTER; data
C.
Where, to secure
...............................
ACTIVITY ASSIGNMENTS;
EVALUATION;
64
Work to help you get
started in determining production performance. D.
63
How to estimate the
machining time for a shaper operation. 4.
62
How to calculate per-hour
output of a machine. . 3.
62
.
65
Samples of some check-ups that
m a y be applied to your ability to determine machining time . . . . . . 9.
DRILLS AND TOOL BITS;
...........
. . . . .
HOW TO SET ANGLES OF CUTTING
TOOLS A.
*
MOTIVATION;
DIRECTIONS;
67
Advantages of knowing how to §et
up the angles of drills and tool bits. B.
65
. . . . .
67
Suggestions to help you in cor-
ectly setting the angles of cutting tools.
. . .
67
angle of cutting edges on a drill...........
67
1 . DRILL ANGLES;
How to grind the correct
xi PAGE
CHAPTER 2.
TOOL BIT ANGLES:
How to measure clearance
arid, rake angles of 3.
COMBINED ANGLES:
atool b i t ................
68
How to set up a tool bit
to grind two rake angles as a single compound a n g l e ............................... 4.
SPECIAL ANGLES:.. How.to grind special pur pose t o o l s
5.
.
SOURCES FOR THIS CHAPTER:
69 Where to get
■additional assistance. C.
68
ACTIVITY ASSIGNMENTS:
.........
69
Some experiences to help
you perfect your ability in setting up drill and tool bit angles.......... ..................... .. D.
EVALUATION:
Samples of a way to check your mast
ery of cutting tool a n g l e s ...................... 10.
SCREW THREADS:
MOTIVATION:
DIRECTIONS:
72
Outcomes of thread calculating
a b i l i t y .......................................... B.
70
HOW TO MAKE CALCULATIONS FOR CUT
TING THREADS ON A L A T H E . ............................. A.
69
72
Suggestions for the handling of
some calculations that arise in screw thread cutting p r o b l e m s .................... 1.
CHOICE:
How to select thread pitch for a
specific job .................... 2.
TOOLS:
72
How to grind the tool bit for var-
72
Xll PAGE
CHAPTER ious p i t c h e s .............................. 3.
DEPTH:
74
How to calculate the depth of cross 74
slide feed thread cutting.................... 4.
COMPOUND FEED:
How to determine the amount
of feed for off-set compound thread cutting. 5.
INSPECTION:
77
How to check thread dimensions
by the three wire m e t h o d ................. 6.
MULTIPLE THREADS:
77
Ho w to cut multiple
threads.............................. ... 7.
HELIX ANGLE:
79
How to calculate the helix
angle of the thread for grinding operations. 8.
INTERNAL THREADS:
80
How to determine the root
diameter of internal threads.. .............. 9.
SOURCES FOR THIS CHAPTER:
82
Where to get fur
ther assistance. C.
ACTIVITY ASSIGNMENTS:
82 Some laboratory assign
ments that may help you in becoming more skilled in screw thread calculations .................... D.
EVALUATION:
Samples of ways In which your
mastery of thread calculations may be checked. 11.
TAPERS:
83
•
83
*HOW TO MAKE CALCULATIONS FOR CUTTING TAPER
ON A L A T H E ....................................... . A.
MOTIVATION:
Advantages that result from ability
to make taper c a l c u l a t i o n s ................... B.
DIRECTIONS:
86
Some key points to guide you in
86
xiii PAGE
CHAPTER your calculations 1.
of taper w o r k .................
MACHINE ACCURACY:
How to check a lathe for
taper with a dial indicator.................. 2.
OFFSET METHOD:
86
H o w to calculate tallstock
set-over for taper turning ..................
87
3.
ANGLE:
87
4.
TAPER ATTACHMENT:
How to calculate taper angle . . . . How to set a taper attach
ment in taper per foot 5.
SHORT TAPER:
..................
6.
EXTREMITY DIAMETERS:
..............
TAPER STANDARDS:
SOURCES FOR THIS CHAPTER:
90
Where to get fur
ther data. ACTIVITY ASSIGNMENTS:
90
How to identify a milling
machine or lathe taper correctly . . . . . . 8.
88
How to calculate the
large and small diameters.................... 7.
88
How to set the compound rest
for turning a taper.
C.
86
92 Learning experiences to
help you become proficient in handling taper calculations . . . . . . . . . . D.
12.
..
93
ability to calculate tapers may be checked . . .
93
EVALUATION:
INDEXING:
...........
Samples of ways in which your
HOW TO DIVIDE THE CIRCLE IN MILLING
MACHINE WORK ............................... A.
MOTIVATION:
. . . . .
95
Advantages of being able to solve
indexing problems......................
95
xiv PAGE
CHAPTER B.
DIRECTIONS:
Suggestions on the solution of
problems involving division of thecircle. 1.
COMMON DIVISIONS:
COMPLEX DIVISIONS: indexing .
3.
indexing 4.
......................
CONTINUOUS DIVISION:
SOURCES FOR THIS CHAPTER:
ACTIVITY ASSIGNMENTS:
98
How to cut a spiral 99
Where to get
further assistance ........... C.
96
How to perform angular
on a milling m a c h i n e ......................... 5.
95
How to perform compound
.................................
DEGREE DIVISION:
95
How to perform simple
....................................
indexing 2.
. . .
99
Some experiences that
will help you in becoming more familiar with indexing D.
EVALUATION:
......................
100
Samples of evaluation techniques
which m ay be applied to checking your ability to make machine division ofthe c i r c l e ............. 100 RESERVE SHELF L I S T : ........................................
103
XV
LIST OF FIGURES FIGURE
PAGE ......... . ................... . .
3
1.
Relation of Views
2.
Length of Diagonal Calculation......................
6
3.
Chord. Length Calculation...............
7
4.
Trigonometric Formulas.
5.
Reading a Micrometer..........
6.
. . . . . . .
.............
15 . . . .
19
7.
Compound Angle Correction ..........................
28
8.
Dovetail Angle Checking ............................
29
9.
Standard Thread Dimensions..........................
73
10.
Screw Thread Forms.
75
11.
American Standard Thread F o r m .....................
76
12.
Three Wire Thread Checking..........................
78
13.
Helix Angle . .
...................................
81
14.
Taper Angle C a l c u l a t i o n ..........
15.
Standard Taper Dimensions . . . . . . . .
16.
Numbered and Lettered Drill Sizes
9
.............................
89 ........
Compound Indexing C a l c u l a t i o n ................... .
91 .
97
XV i
PREFACE Many mathematics books have been published and are in use today in various school programs.
If we set aside the
texts that make the traditionally theoretical approach, there remain but a few whose intent is distinctly functional.
Even
these few have Varying degrees of similarity to the past in their classification of real problems according to their math ematical area.
What is needed is a text whose action pattern
will cut across all boundaries and deal with problems in their entirety. Writing a syllabus as a curriculum project has given this author an opportunity to make a gesture In the direction of a better course and a better textbook.
The author has ex
perienced teaching shop m a t h classes from various texts and sincerely feels this need.
This syllabus will also reflect
several experiences of teaching adults who were actually em ployed In machine shop work.
It Is this last mentioned ex
perience, conducted without benefit of text,
that prompts
the development of a good course. The problems of this syllabus have been collected by the slip technique.
The author learned this technique from
Dr. Crawford several years ago and has been able to profit from Its use ever since.
The courses In shop math the auth
or taught to adults were developed from difficulty slips col lected in the first session of each program.
Saving these
slips has made this work much easier and certainly more real.
xSii Thanks are due to many students and fellow students who made this syllabus possible.
Appreciation of Dr. Crawford’s
guidance cannot be adequately expressed.
His satisfaction
must certainly come from knowing that his students are suc ceeding. Prank J. Zlol
1
. PART I,
GENERAL PROBLEMS
H O W TO SOLVE MATHEMATICAL DIFFICULTIES OF INSPECTION OR BENCH JOBS The simplest as well as the most complex jobs of modern industry are found on the bench.
We ordinarily associate the
best paying jobs with the most complicated machines, however this does not necessarily follow.
To the man at the bench,
there is a constant opportunity of finding, greater personal security by becoming competent In the mathematical handling of his problems.
The bench job of the uneducated man will
always be simple, repetitive, paid.
insecure, and not very well
To the man who can read blueprints and solve the prob
lems they create, there will come a greater feeling of person al satisfaction plus security and worth. The first five chapters are devoted to increasing your competency In the basic mathematical operations common to all the shop problems.
Study them carefully.
2
CHAPTER 1.
BLUEPRINTS
HOW TO READ AND CALCULATE DIMENSIONS PROM SHOP DRAWINGS A.
MOTIVATION:
H o w the ability to read and work from shop
drawings can pay o f f . 1.
HIGHER RATING:
Being able to work directly from blue
prints is generally accompanied by higher placement on the salary schedule. 2.
LESS LOST TIME:
A high degree of skill in operating
a machine is of no value if you must wait for some one else to solve each mathematical problem that arises. B.
DIRECTIONS:
Suggestions for improving your ability in
working with shop drawings. 1.
DRAWING LANGUAGE: a.
How to read blueprint directions.
All. three dimensions of any object are repressented on the shop drawing in the appropriate v views.
b.
The views of an object are related to each other as illustrated in Pig. 1.
c.
Dimensions that indicate the width of the object are placed horizontally: (1)
Above the top view.
(2)
In the top view.
(5)
Between the top and front views
(4)
In the front view.
U f r lN D
FMht
BOTTOM
(5) d.
Below the front view.
Dimensions that indicate the height of the object are horizontally placed:
e.
(1 )
To the left of the front view.
(2 )
Within the front view.
(3)
Between the front and side view.
(4)
Within the side view.
(5)
To the right of the side view.
Dimensions that indicate the depth or length of the object are placed:
f.
(1)
Horizontally above or within theside
view.
(2)
Vertically to the left of the top view.
(3)
Vertically within the top view.
(4)
Vertically to the right of the top view.
Dimensions conveying information about angles, holes,
and other features are placed so as to be
best recognized and related to the object or its parts. g.
It is generally assumed that all dimensions are in inches unless otherwise indicated.
CUMULATIVE DIMENSIONS: a.
How to calculate overall length.
Generally overall length is indicated directly in the appropriate view of the drawing.
b.
In some cases it is necessary to add together var ious part dimensions.
c.
Dimensions that are to be added together must be
carefully selected as they may overlap others and result In an Incorrect length. d.
When dimensions are added to each other they should be converted entirely to fractions or decimals.
MISSING DIMENSION: a.
How to solve for needed linear data.
Frequently dimensions are omitted intentionally to prevent their use.
b.
If the objeet cannot be made from the dimensions that are found on the drawing, it ma y be necessary to calculate others.
c.
Diagonal distances may be obtained by squaring the lengths of each of two perpendicular sides and ex tracting the square root of their sum. (See Fig. 2.)
d.
Distances between holes on a common diameter may be solved by the formula:
Chord equals diameter
of hole circle multiplied by the sine of one-half the included or central angle. (See Fig. 3.) e.
Some missing dimensions are solved b y adding the dimensions of parts and subtracting the total from the overall length.
MISSING ANGLES:
How to determine additional angular
values. a.
Frequently angle desired is complement of given angle and is obtained b y subtracting known angle from 90 degrees.
b.
In some Instances angle desired Is supplement of
6
jt
/*
a. +~ b
- c
*
or* q + a
*
zf
2.S * 2 f
c
»
|/«. t
FIGURE S LENGTH OF DIAGONAL CALCULATION
7
CHORD
C H O R D = J?tRAl£r£R X S/Hf j
C£ h TR*L A H S I L
FIGURE 3 CHORD LENGTH CALCULATION
8 given angle and is obtained by subtracting given angle from 180 degrees. c.
Angle may be a part of a circle in which case it may be calculated by determining the value of that fractional part of 360 degrees.
d.
Some angles may have to be calculated from linear data available by using the many trigonometric formulas of the angle.
5.
(See Pig. 4.)
SOURCES FOR THIS CHAPTER; a.
Where to get further data,
Bages to read in the books which are cited repeat edly.
Dooley 223-224;
Edwards 4-10, 39-69, 103-
115, 129-136, 145-148, 157-175; 123-128;
Ewing-Hart 1-5,
French 87-137, 229-255;
306-322, 327-333; Nicholson 10-13;
Jones 80-85,
McMackin-Shaver 257-282; Oberg-Jones 169-177;
Bibb 128-140, 167-176,
541-624;
Palmer-
Slade-Margolis
247-273. C.
ACTIVITY ASSIGNMENTS:
Some experiences that will help you
become familiar with blueprints. 1.
LABORATORY OR CLASSROOM:
Select a blueprint from the
group made available to you by the instructor and sup ply the needed information as indicated by the instruct o r ^ red question marks upon the copy. D.
EVALUATION:
Sample check of your knowledge in reading and
calculating from shop drawings.
9
B
S/N£ f i n e OH 'Ta n fi t k>
/?
Cos f i x e C o t f i x cl
FIGURE 4 TRIGONOMETRIC FORMULAS
10 TRUE-FALSE:
Place an X in the correct space for
true or false. a.
T F ( )( ) The relation of the views in a shop draw ing must be varied to suit the object.
b.
(
)( ) The height of the object ma y be generally found in the top view.
c.
(
)( ) Dimensions chord involves the cosine of the angle.
h.
( )( ) The width of the object should not be taken from the top view.
i.
( )( ) It is correct to subtract an angle from 90 degrees to find its complement,
j.
( )( ) Supplementary angles should be calculated in the case of all angle problems,
h.
( )( ) Subtracting the total of all known parts from the overall length is an incorrect
11 T
F way of finding the missing dimension.
1.
( )( ) Distances between holes on the same hole circle should be found by the chord formula,
m.
( )( ) It is correct to find an angle by applying the square root formula,
n.
( )( ) Angles that are part of a circle should be stated in .fractional form,
o.
( )( ) It is incorrect to place an overall length on the drawing,
p.
( )( )A shop drawing is useful because it shows one view of the object,
q.
( )( ) Length, width, or height dimensions should appear on the shop drawing in a consistent manner.
r.
( )( ) The top view of a drawing is correctly placed below the side view,
s.
( )( ) The height of an object should appear in all three views,
t.
{ )( )It is incorrect to have shop drawing dim ensions overlap each other.
12 CHAPTER 2.
LINEAR DIMENSIONS
HOW TO INSPECT MATERIALS FOR LENGTH, WIDTH, OR THICKNESS
A.
MOTIVATION;
Advantages arising from knowing how to make
aecurate measurements. 1.
ACCURATE WORK:
Almost all work Involves some type of
measuring which you must do right. 2.
UNIVERSAL LANGUAGE:
If you do not know how to measure
you are unable to communicate with technical people. 3.
ECONOMY OF MATERIALS: to most
B.
DIRECTIONS:
Modern production requires you
efficiently utilize raw materials. Some key points to guide you in working with
linear dimensions. 1.
COMMON FRACTIONS:
Ho w to measure a length in fractions
of an inch. a.
The
popular division of the inch is into halfs,
quarters, eighths,
sixteenths,
thirty-seconds, and
sixty-fourths. b.
Occasionally fractions of one-tenth and one-hundreth of an inch are used.
c.
The degree of division of the Inch may be stamped on the measuring instrument.
d.
When not indicated,
the type of division should be
determined by Inspection.
13 e.
When measuring the instrument shall be so placed that its one end coincides with the end of the measured length.
f.
Where it is not possible to begin at the end of the measuring instrument,
the value of the be
ginning point should be subtracted from the deter mined length. g.
When attempting to read the graduation coinciding with the end of the piece,
the measuring instrument
should be placed with its graduated edge as close to the work as possible. h.
The full number of inches should be noted first.
i.
The varied lengths of the smaller graduations should be used to assist in identifying the value of the coinciding graduation.
j.
The following typical reasoning process should be used:
Greater than a half, less than three quar
ters, more than five-eighths and then by narrowing down exactly eleven-sixteenths. CONVERSION TO DECIMALS:
How to adapt a fractional
length for measurement with a micrometer. a.
Reference should be made to decimal equivalent charts that are readily accessible.
b.
A fraction is converted to a decimal by dividing the numerator by the denominator.
c.
The value of the decimal should be carried out to
14 four decimal places to determine a three place significant value for use on the regular micrometer d.
A ten-thousandths micrometer requires a four place significant decimal obtained from five decimal places.
e.
The additional decimal is used to determine if the preceding digit should be raised or retained.
MICROMETER: a.
How to "mic” a shaft.
The micrometer must be held perpendicular or square with the work to obtain the best reading.
b.
A reading should be made without disturbing the position of the thimble.
c.
The graduations on the barrel of the micrometer are spaced .025 inch apart.
d.
Numbers on the barrel are placed each four divis ions and represent .100 inch.
e.
The fine divisions are read on the thimble as 25 parts of one turn of the thimble or .001 inch a piece.
f.
A reading should consist of the total number of .100 Inch units plus the excess amount of .025 inch unlt3 plus the number of divisions on the thimble. (See Fig. 5.)
g.
The number of full Inches Indicated by the size of the micrometer should be added to the decimal ob tained.
VERNIER CALIPER:
How to measure with a vernier caliper
FIGURE 5 READING A MICROMETER
16 a.
The v e r n ie r d e c im a l
b.
c a lip e r
is
used
to
m e a s u re
le n g th
in
In c h e s .
Pull inches are read the same as on any other meas uring instrument.
c.
The of
in c h
space to
The d iv is io n m eans o f
e.
d iv id e d
is io n s
in d ic a te
of
th e
o f
th e
in
.1 0 0
.025 i n c h
40 s p a c e s e a c h
in c h . space is
m ade b y
s c a le .
d iv is io n s
c o in c id e
in to
a n d g e n e r a l ly n u m b e re d e a c h
th e v e r n ie r
T w e n ty - fiv e m ade t o
f.
fu rth e r
.025 i n c h v a l u e
fo u rth d.
is
of
th e
le n g th
v e r n ie r
w it h
r e g u l a r m e a s u r in g
s c a le
a re
tw e n ty -fo u r d iv s c a le .
When reading the vernier the value of a partial .025 inch space is determined by finding the vern ier line that most nearly coincides with the reg ular scale and noting its value.
g.
The f i r s t th e re
h.
is
and la s t no
v e r n ie r
lin e
w ill
c o in c id e
w hen
space.
The value of the space is added to the
reading of
full inches, .100 inch spaces, and .025 inch spaces to obtain the total reading. PRECISION BLOCKS:
How to arrange precision gage
blocks for accurate measurement. a.
Precision gage blocks are manufactured with an ac curacy of from .000002 to .000008 inch.
b.
Gage blocks should be carefully cleaned and wrung
17 or wiped together. c.
Assembling the blocks to use is made by first se lecting a gage block that eliminates the last dec imal digit of the desired dimension.
d.
The second block is selected to eliminate the se cond last decimal digit.
e.
.A third block i 3 selected to eliminate the third last decimal digit.
f.
The blocks selected should be totaled and the dif ference made up by adding a block of the necessary tenths.
g.
When assembled the blocks are used with various accessories to measure length.
GAGES: a.
How to measure with fixed gages.
Fixed gages are generally used to rapidly inspect production runs of manufadtured articles.
b.
The single gage which is set at the exact size is not generally used as it does not allow for permissable variations.
c.
A “Go” or ”No Go” gage is superior in that it may be used to exclude the oversize and undersize piece.
d.
The ”G o ” portion should not allow the large piece to pass but should pass the tolerable size.
e.
The ”No Go” portion should not allow the undersize piece to pass but should pass the tolerable size.
18 7.
VARIOUS SYSTEMS:
How to select numbered, lettered,
or fractional drills. a.
The American drill system is without duplicate except for the one-fourth inch and the letter E.
b.
The f r a c t io n a l v a r ie s
c.
s y s te m
is
b y s ix ty - fo u r th s
th e
m o s t com m on a n d
o f an in c h .
Numbered drills range from .0135 inch (number 80) to .2280 inch (number 1 ) and following no part icular pattern must be selected by means of a chart.
d.
(See Pig. 6 .)
The lettered drills begin at the end of the nu m bered series and should also be selected by chart.
e.
(See Pig. 6 .)
There are no lettered drills over .4130 Inch (Letter Z).
8.
FOREIGN METHODS:
How to convert measurements to the
metric scale. a.
A measurement In inches should be converted to centimeters by multiplying by 2.54.
b.
When measurements are to be in millimeters,
the
number of inches are multiplied by 25.4. c.
The number of meters Is found by dividing the number of inches by 39.37.
9.
FOUNDRY REQUIREMENTS:
How to make allowance for
shrinkage in a casting. a.
Shrinkage allowance should be made on the pattern.
19
DIA M ETERS OF N U M B E R ED D RILLS
DIA M ETERS OF
Drill No.
Diameter Inches
Drill No.
Diameter Inches
Drill No.
Diameter Inches
80 79 78 77
.0135 .0145 .0160 .0180
53 52 51 50
.0595 .0635 .0670 .0700
26 25 24 23
.1470 .1495 .1520 1540
76 75 74 73
.0200 .0210 .0225 .0240
49 48 47 46
.0730 .0760 .0785 .0810
22 21 20 19
.1570 1%) 1610 1660
72 71 70 69
0250 0260 .0280 .0292
45 44 43 42
.0820 .0860 .0890 .0935
18 17 16 15,
1695 .1730 .1770 .1800
68
.0310 .0320 .0330 .0350
41 40 39 38
.0960 .0980 .0995 .1015
14 13 12 11
.1820 .1850 .1890 .1910
.0360 .0370 .0380 .0390
37 36 35 34
.1040 .1065 .1100 .1110
10 9 8 7
.1935 .1960 .1990 .2010
.0400 .0410 .0420 .0430
33 32 31 30
.1130 .1160 .1200 .1285
6 5 4 3
.2040 .2055 .2090 .2130
67
66 65 64 63 62 61 60 59
58 57 56 55 54
. .
.0465 .0520 .0550
29 28 27
.1360 .1405 .1440
2 1
.2210 .2280
FIGURE 6 NUMBERED AND LETTERED DRILL SIZES
Drill Letter
Diameter Inches
A B C D
.2340 .2380 .2420 .2460
E F G H
.2500 .2570 t 261° .2660
I K L
2720 .2770 .2810 .2900
M N O P
.2950 .3020 .3160 .3230
Q
✓ .3320 .3390 .3480 .3580
J
R S T U V X
.3680 .3770 .3860 .3970
Y Z
.4040 .4130
w
b.
20 The amount allowed Is dependent upon the metal to be used and the various lengths Involved.
c.
A patternmaker’s shrink scale Is used to avoid calculating this allowance each time.
d.
The shrink scale Is constructed b y
adding the
shrink per foot for the particular
metal and then
redividing the length. e.
Reasonable care must be exercised to prevent misusing a shrink scale or using a
regular scale
in its place. f.
Metal shrinkage varies up to one-fourth inch per foot and should be determined for each case from a table of shrinkage values.
10
.
SHEET METAL PROBLEMS:
How to make allowances for
bending in sheet metal. a.
Bend allowances should be made in specifying fin ished material lengths that are to be bent or in layouts.
b.
An approximate formula that may be used in cal culating allowance is: times bend radius plus
Allowance equals (.01745 .0078 times the metal
thickness) multiplied by the number of degrees in the bend. 11.
PRODUCTION NEEDS;
How to estimate lengths of raw
material for cutting in small pieces. a.
Raw material sizes should be carefully selected to
21 keep material removal requirements to a minimum. b.
Stock sizes should be employed whenever possible to avoid extra charges or time delays.
c.
The overall dimension is obtained or calculated from the blueprint.
d.
The width of the saw cut, subsequent finishing op eration allowance and the overall length are added together to establish the multiple for material calculation purpose.
e.
Stock lengths should be taken into consideration in determining number of pieces.
12
.
DESIGN DATA; a.
How to measure the displacement of a cam.
The displacement of a cam is the total lift that it imparts to its follower.
b.
The base circle of a cam is the smallest concentric circle that can be drawn touching the outline of the cam.
c.
The greatest distance between the base circle and the cam outline is the displacement of the cam.
13.
SOURCES FOR THIS CHAPTER;
Where to get further assis
tance. a.
Pages to read in the books which are cited repeat edly.
Dooley 419-422;
Hart 6-74, 114; Shaver 1-87;
Edwards 3-4, 10-53;
Hesse 85-97;
Ewing-
Jones 54-55; McMackin
Oberg-Jones 1117-1118, 1369-1374;
Palmer-Bibb 18-69;
Slade-Margolis 1-37, 199-204;
Wagener-Arthur 1-5, 18-28.
22 C.
ACTIVITY ASSIGNMENTS:
Learning experiences to help you
become more proficient In handling linear dimensions. 1.
LABORATORY:
Select four drills from a miscellaneous
group and after measuring each with a micrometer, vern ier caliper, gage, and precision block arrangement, id entify the drill size as numbered, lettered, or frac tional . 2.
CLASSROOM:
Calculate the amount of 16 gage sheet met
al to rim the outside of three hundred 3 inch lift cams whose base circles are 2 inches and whose width is onehalf inch. 3.
CLASSROOM:
Working from an English drawing, provided
by the instructor convert the metric units to inches and make allowance for casting shrinkage in order to make the pattern. D.
EVALUATION:
A sample check of your mastery in measurements
of length, width, or thickness. 1.
COMPLETION:
Place the appropriate missing word in the
blank space. a.
The smallest division you can measure with the com mon six inch rule i s ____________ .
b.
When measuring with the regular micrometer, the val ue of a fraction must be converted to a_________
c.
.
The angle at which a micrometer must be held to the work to obtain the best reading i s _______________
.
d.
The divisions on the thimble of the micrometer should be read as ____________
e.
.
The measure of length for which the vernier caliper is used is t h e ______________.
f.
The proper place to read thousandths on the vernier caliper is t h e ______________ .
g.
One full turn of the micrometer thimble should be counted as______________ .
h.
When making a vernier reading you should look for _______________lines.
i.
The decimal accuracy that is possible with pre cision gage blocks I s ___________
j.
The method of assembly of
gage blocks i s ________
k.
The first gage block dimension
.
that is selected
should eliminate the_______________ decimal of the desired value. 1.
The gage which does not allow for permissable var iation is t h e _____________ _
m.
The size of pieces not passed by the ”G o” portion of a gage i s __________ than
n.
the specification.
The size of pieces passed by the ”Go” portion of a gage and not passed by the ”No Go” portion Is within t h e _____________
o.
of the specification.
The largest letter drill that is available measures
24 The factor by which inches are multiplied to ob tain centimeters is q.
The smallest numbered drill m a y ing for a ______________
be secured
by ask
.
r.
The meter should be converted t o _____
s.
The allowance on
t.
The additional length of the patternmaker’s scale
the pattern in casting
is for_____________ u.
is for
.
Sheet metal that is to be cut before it is formed must contain a _____________
v.
inches,
allowance.
The allowances that are added to the length of the piece in estimating production requirements are the finishing and ____________
w.
dimensions.
The greatest radius of a cam is a total of its base circle radius plus its _____________.
25 CHAPTER 3.
ANGULAR DIMENSION
HOW TO INSPECT THE RELATIONS OP VARIOUS SURFACES OP MACHINE PRODUCTS
A.
MOTIVATION: 1.
Outcomes of angle measurement ability.
GREATER RESPONSIBILITY:
Angle problem solution Is
not as common as linear
measurement, therefore great
er value is placed upon
your ability to do it.
2'. INDIVIDUAL DEVELOPMENT:
Problems in angular relation
ships develop third dimensional concepts and make subsequent problems easier for you to solve. B.
DIRECTIONS:
Suggestions for handling some of the problems
of mathematical relationship of various surfaces. 1.
MEASUREMENT:
How to measure an angle with a vernier
protractor. a.
^he angle is measured by the number of degrees included between its sides or rays.
b.
The radii of a circle acting as sides ma y be con sidered to generate an angle of 0 to 360 degrees.
c.
An angle should be measured in the same degree units regardless of the length of the sides.
d«
The vernier protractor is used to measure the number of degrees and minutes in an angle,
e.
The head and blade of the vernier protractor should be accurately set to angle of the work.
26 f.
Full degrees are the first to be read from the protractor and care should be exercised to read the scales correctly.
g.
The vernier scale is read to divide the degree spaces into 5 minute units.
h.
The lines of the vernier scale should be inspected to determine whibh graduation is aligned with a graduation on thd degree scale.
i.
The total angle is determined by adding the full degrees and the vernier scale reading of nearest five minutes.
SINE BAR: a.
How to set up an angle with a sine bar.
The sine bar is a precision length of metal gener ally five or ten inches long.
b.
A n angle is set up by elevating one end of the bar to correctly set an angle.
c.
The correct height of the elevated end is based on the value of the sine of the desired angle.
d.
A 10 inch sine bar m a y be elevated correctly by obtaining the sine of the desired angle from the trigonometric tables and multiplying it by ten. (Shift the decimal point one place to the right.)
e.
The five inch sine bar values are based on multi plying the sine value by 5 or dividing b y 2 and shifting the decimal point one place to the right.
f.
A n established angle may be determined by dividing
the elevation of a 10 inch sine bar by 10 (shift the decimal point one place to the left) and find ing the corresponding angular value in the trigon ometric sine tables. TAPER ANGLE: a.
How to Inspect a taper angle.
k taper angle is the angle between the two uniform ly increasing or decreasing sides.
b.
The angle m ay be inspected with a vernier or reg ular protractor or with the sine bar.
c.
Care must be exercised to avoid measuring the incorrectltaper angle that is the angle between a side of the work and its axis.
d.
Some taper angles are inspected by gages or plugs that have been previously established as perfect angles.
COMPOUND ANGLE:
How to inspect the angles of a compound
angle. a.
A compound angle may be created by the result of two angles at right angles to each other. (See Pig.7)
b.
These component angles should be checked at and parallel to the surfaces to which they have been specified.
c.
T h e co m p o u n d a n g le m ay b e th e
d.
d ia g o n a l o f
th e
s p e c if ie d
and ch e cke d
as
w o rk p ie c e .
The angle may be set up on two sine or angle plates set at 90 degrees to each other.
TAN
C O A A Z C T E D ANGLE
»
TQ* & *
FIGURE 7 COMPOUND ANGLE CALCULATION
CHS
3
POVCTfitL JiNG lE COT-Z DOVETAIL ANGLE * HAP m s o f fiaj?
*
CHECK T N M E N S iQ N
@ + -V IA M L T C E
O f f i 6 Z > ( / J -C O T 1 j o r e j f i f t
ANGLE )
®
“0
*
* ( ® x CoT v o n m L
angle
FIGURE 8 DOVETAIL ANGLE CHECKING
)
e.
Some compound angles to not develop from two angles at right angles to each other and these cases should carefully be set up for their correct angular relationship.
DOVETAIL CHECK:
How to check dovetails by placing
wires, rods, or balls. a.
A wire, rod, or ball should be selected that will make contsct with both sides of the dovetail angle at approximately their middle.
b.
The check dimension over wires, rods,, or balls placed at both ends of a double dovetail is cal culated from the formula:
Base check dimension
equals base dimension plus diameter of the wire, rod, or ball multiplied by 1 plus the cotangent of one-half the dovetail angle. c.
(See Pig. 8 .)
The top or greater dovetail dimension is calculated b y the formula:
Top dovetail dimension equals base
dimension plus two times height of the dovetail times the cotangent of the dovetail angle. (See Pig. 8 .) HOLE CENTERS:
How to measure the distance between
drilled holes. a.
Hole to hole distance when the holes are on a com m o n circle should be determined by the formula: Check dimension (chord) equals diameter multiplied by the sine of one-half the central angle.
31 b.
When holes are equally spaced on a common circle, the central angle should be determined by dividing 360 degrees by the number of spaces between holes.
c.
Some hole to hole distances are the hypotenuse or the longest side of a right triangle.
d.
The hypotenuse of a triangle, when only the length of the other two sides is given,
should be solved
by squaring the length of each of the two sides, adding their squares together and extracting the square root. e.
Distances that are the hypotenuse of a right tri angle where an angle is given, should be solved by selecting a trigonometric relationship that involves the known factors and calculating the value.
TOOL ANGLES:
(See Pig. 4.) H o w to measure the cutting angles of a
tool. a.
The cutting angles of a tool and generally spec ified as rake angle, clearance angle, and angle of kee n n e s s.
b.
The rake angle may be to the back or to and in both cases should be measured as
the side a depart
ure from the horizontal or top side of the tool. c.
The clearance angle may be of the front
or sides
and should be measured as a departure from the ver tical or the front or side of the tool.
32 d.
A n g le
o f keenness
Is
th e m e ta l r e m a in in g a n g le s
have
RIGHT ANGLES: a.
d e t e r m in e d a fte r
th e
as
th e
a n g le
c le a r a n c e
of
and ra k e
•
been c u t aw ay,
Ho w to make a square corner,
A square corner is one whose 3ides are perpend icular or at 90 degrees to each other,
b.
The square, bevel protractor, right triangle, or any device whose sides are established to be at 90 degrees to each other m a y be used to create an other right angle or square corner.
c.
Large square corners m ay be laid out by utilizing the principle of the 3, 4, 5 right triangle.
d.
A right angle is determined when the relationship of the sides of a triangle Is 3 and 4 and the hypotenuse 5.
e. f.
Any convenient multiple of these values m ay be used. Another technique of constructing a square corner Is to inscribe an angle within a semi-circle,
g.
In inscribing an angle In a semi-circle,
the inter
secting of the diameter and the circle are connected to any point on the circumference of circle. h.
The right angle Is the angle between the sides that are drawn.
SOURCES FOR THIS CHAPTER: a.
Where to secure data.
Pages to read in the books which are cited re peatedly:
Edwards 103-119, 136-155;
Ewing-Hart
97-113, 236-239;
0.
Jones 323-326;
Oberg-Jones
1119-1120, 1134-1136;
Slade-Margolis 205-207;
Wagener-Arthur 31-33;
Wolfe-Phelps 1-144.
ACTIVITY ASSIGNMENTS:
Performances which may be used to
develop your skill In making angular calculations. 1.
LABORATORY:
Seeure a tapered gib from the instructor
and using vernier caliper,
sine bar, and wire rod or
ball calculate the angle of the dovetail, dovetail dimension,
the base
the taper in the length of the
dovetail and the compound angle represented by the dovetail surface. 2.
CLASSROOM:
Calculate the hole center distances for
11 holes equally spaced on a 5 inch hole circle. 3.
CLASSROOM:
Construct a right angle in the middle of
a sheet of paper by using the 3, 4, 5 triangle prin ciple. D.
EVALUATION:
A sample of evaluation technique which may
be applied to your knowledge of angular dimension calcul ation. 1.
RATING SCALE:
Place an X in each space for which you
can qualify. a. ( ) Correctly reading a vernier protractor angle. b.
( ) Setting a specific angle on the protractor.
c. ( ) Properly setting up a sine bar. d. ( ) Determining the angle of the sine bar from the
34 sine tables. e. ( ) Setting up an angle on a five inch sine bar. f. ( ) Measuring a taper angle. g. ( ) Measuring a compound angle. h. ( ) Checking the component angles of a compound angle. i. ( ) Placing the wires for dovetail measurement, j. ( ) Calculating the dovetail check dimension. k. ( ) Calculating the center to center distance for holes. 1. ( ) Measuring rake and clearance angles. m. ( ) Calculating the angle of keenness. n. ( ) Constructing a 3, 4, 5 triangle. o. ( ) Constructing a right angle in a semi-circle. (
) Total.
35 CHAPTER 4.
AREA AND VOLUME
H OW TO CALCULATE SURFACES AND SOLIDS
A.
MOTIVATION: Advantages of being able to make area and volume calculations. 1.
MONEY SAVING:
Over-buying results from your in
ability to accurately calculate requirements. 2.
WASTE REDUCTION:
Your production technique requires
some waste, but you can keep it at a minimum by knowing exactly what you need. B«
DIRECTIONS: H e l p f u l h i n t s o n the d e v e l o p m e n t of sk ill d e a l i n g w i t h p r o b l e m s of s u r f a c e s
1.
FORMED METAL:
in
a n d solld3.
How to calculate sheet metal require
ments for box construction. a.
A box that is to be made b y cutting and bending a single sheet requires more raw material than one which is fabricated.
b.
The sheet size for a rectangular box (without top) is determined by the formulas:
Length equals box
length plus two times its height; width equals box width plus two times its height. c.
Four square sections of the sheet are cut out and not used unless some portion is employed to lap the ends.
d.
Fabricated box sides and bottom should be laid out in the most economical manner considering the
36 available sheet sizes. e.
A width equal to the length of the box is desir able for cutting out three pieces with minimum waste.
LIQUID DISTRIBUTION:
How to estimate paint require
ments . a.
The coverage or spreading ability of a paint should be determined by test or from the manu facturer’s recommendations.
b.
The area of the surface to be painted is deter mined by adding together the component areas.
c.
Room areas may be calculated by multiplying the circumference of the room by its height and add ing the ceiling area.
d.
Window areas ma y be ignored unless excessive.
e.
The total area is divided by the paint coverage in number of square feet per gallon and the re sult is gallons required.
R A W SOLID MATERIAL:
How to calculate the amount of
wood necessary for pattern construction. a.
The unit of measure for lumber is the board foot.
b.
The board foot is best illustrated as a piece of lumber one inch thick, twelve inches wide and one foot long or its equivalent.
c.
Purchased lumber is ordinarily surfaced and has been reduced approximately a quarter inch In thick-
ness and three-quarters of an inch in width. d.
Lumber requirements must take into account the finished sizes and be within standard available widths, lengths,
e.
The
am ount o f w ood i s
ro u g h
f.
and thicknesses.
o r u n fin is h e d
le n g th
( a ll
144 to
d e te r m in e
d e t e r m in e d b y m u l t i p l y i n g
w id t h
e x p re s s e d b o a rd
in
tim e s in c h e s )
th ic k n e s s
tim e s
and d iv id in g
by
fe e t.
The number of board feet per lineal foot m a y ,be determined b y multiplying width times thickness and dividing b y 12.
CASTING NEED:
How to determine volume requirements
fo r
c a s tin g .
a.
The three dimensions of a simple piece ma y be multiplied together to obtain the volume of the metal required.
b.
Cubic inches or feet should be multiplied by the weight of the casting metal per corresponding unit in order to secure the foundry-needed data.
c.
The weight of metal for complicated patterns should be obtained b y multiplying the pattern weight by the specific gravity factor.
d.
The specific gravity factor is the ratio of the specific gravity of the casting metal to the specific gravity of the pattern material.
SOURCES FOR THIS CHAPTER: a.
Where to secure data.
Pages to read in the books which are cited re-
peatedly.
Dooley 10-20;
Ewlng-Hart 75-86, 141-186; Shaver 88-125;
Edwards 120-128; Jones 87-94; McMackin-
Oberg-Jones 148-168;
Palmer-Bibb
79-95, 156-165; Slade-Margolls 50-140, 292-502. C.
ACTIVITY ASSIGNMENTS:
Work to do to help you gain exper
ience In calculating areas and volumes. 1.
LABORATORY:
Select a v?ooden pattern and calculate
the amount of aluminum needed to cast the part. 2.
GIASSROOM:
Select a blueprint of a part requiring a
pattern and determine the amount of wood necessary to make it. 3.
CLASSROOM:
Calculate the sheet metal and paint re
quirements for building 15 waste paper containers as per the print available from your instructor. D.
EVALUATION:
Sample evaluation instrument for possible
checking of your surface and solid calculations. 1.
BEST ANSWER:
Place the number of the best answer in
the paranthesis. a. ( ) The smallest sheet is used when:
(l) The .box
is made from one piece that has been bent. (2) Each part is a separate piece of metal. (3) The four sides are made in one piece. (4) Two sides and the bottom are made in one piece. b. ( ) Paint requirements should be determined by: (1) Dividing the volume of the room by the paint
coverage factor.
(2) Multiplying the room
perimeter by the paint coverage factor,
(3)
Dividing the room area by the paint coverage factor.
(4) Multiplying the room size by the
number of coats to be applied. c. ( ) The board foot should be used when:
(1) Meas
uring the length of unfinished lumber. (2) Estimating and pricing lumber.
(.3) Judging
the width of finished lumber. (4) Calculating the' surface area of lumber. d. ( ) Purchased lumber that has been surfaced should be approximately:
(l) One-quarter inch thinner,
(2) One-quarter inch narrower.
(3) One-quarter
inch shorter. (4) Two inches shorter. e. ( ) Dineal board feet are determined by: (1) Multi plying width times thickness and dividing by 12. (2) Dividing width by 12. (3) Multiplying width times thickness and dividing b y 144. (4) Dividing the length by 12. f. ( 5 The weight of a casting may be determined by: (l) Multiplying its volume in cubic inches by its specific gravity.
(2) Multiplying its vol
ume in cubic inches b y the weight of a cubic inch of the metal. (3) Dividing its volume by its specific gravity. (4) Dividing its volume b y 1728.
40 g. ( ) The specific gravity factor is obtained by: (1) Weighing the casting.
(2) Dividing the
casting metal specific gravity by the pat tern lumber specific gravity. (3) Consulting a table of specific gravities. (4) Dividing volume by surface area.
41 CHAPTER 5.
LAYOUTS
H O W TO DIAGRAM THE DIRECTIONS FOR WORK
A.
MOTIVATION; 1.
Returns from skill in layout work.
SELF SUSTENANCE;
The ability to read blueprints
and
make your own layouts relieves you of considerable dependence upon others. 2.
SIMPLIFIED OPERATIONS;
Y ou may be able to get the
job done, eventually, but a little time spent In learning how to make layouts correctly will make your job much simpler and easier. B.
DIRECTIONS;
Suggestions for the development of your
ability to diagram work directions. 1.
CENTER LOCATION;
How to locate the center of round
work for center-drilling. a.
A centering head square is held firmly against the circumference of the work while a line is scribed against the blade of the square.
b.
The square Is turned at approximately right angle and the operation repeated.
c.
The intersection of the two lines should be center punched carefully as It is the center of the work.
d.
In the absence of a center head square, the herma phrodite caliper may be used.
e.
The caliper is set at approximately the radius of the work and then used to scribe several arcs in-
tersecting each other. f.
A center punch is used to make a mark within the scribed marks.
CENTER OF GRAVITY:
How to locate the center.of irreg'
ular work. a.
Rectangular work should be centered by drawing intersecting diagonal lines.
b.
A n y flat work may be centered b y suspending it from s e v e r a l rdifferent points, drawing vertical lines through the points and locating the inter section of these vertical lines.
c.
Flat work ma y be tested until it balances on a single point which also locates the center.
CAM LAYOUT: a. b.
How to lay out a cam.
The base circle for the cam is drawn first. Division of the circle is made by degrees so that the radii locate the various movements.
c.
The various stages of lift should these radii using the base circle
d.
be laid out
on
as a reference.
The located points are connected with a smooth curved line.
e.
If a roller
follower is used, arcs of such radius
should be drawn through the points and the
smooth
curve drawn tangent to these arcs. EQUAL. DIVISION: of equal widths.
How to divide a board into a number
43 a.
Simple equal divisions m ay be made by direct meas urement.
b.
Oddly dimensioned widths should be divided by the diagonal application of any other equally divided instrument.
c.
The equal divisions are selected so that their combined length exceeds the width of the board to be divided.
d.
In the diagonal position the ends of the dividing piece should coincide with the width of the board.
e.
When positioned diagonally a transfer of equal divisions is made to the board.
PARALLEL LIHES:
How to draw a line parallel to a
straight or curved layout. a.
Parallel lines to straight or curved lines are determined by establishing a series of equidis tant points.
b.
The arc method is the easiest and surest approach.
c.
A compass is set for a radius equal to the dis tance required between the parallel lines.
d.
With the center point on the original line an arc should be drawn that will Indicate the extreme per pendicular position of the distance.
e.
A straight or curved line is drawn tangent to the arcs.
SCALE:
44 How to reduce or increase the scale of a draw
ing. a.
Drafting is ordinarily done using a scale grad uated to indicate different scales of drawings.
b.
A drawing drawn to scale should be a completely proportioned image of the real object.
c.
To draw an object half size all the real dimen sions are divided b y two or the side of the draftsman's scale is used which reads one-half.
d.
Double size is indicated by dimensions that are twice the actual.
e.
Pull scale should be used whenever possible to assist the worker in reading the print.
f.
Objects drawn larger than their real size are used to help clear up small details.
g.
Reduced scale drawings should be used to conserve paper and reduced bulk if they do not sacrifice clarity.
VERTICAL LINE:
How to establish a vertical reference
line. a.
The truest vertical line is determined by a string freely suspending a plumb bob or reasonable weight.
b.
A perpendicular may be established from some hori zontal surface.
c.
A free liquid is an accurate criterion of a true horizontal line.
d.
The builder's level is based on the movement
of
a bubble in a free body of liquid. e.
A vertical line ma y be determined by placing
the
free liquid of the builder's level in a perpend icular position to the body. 8.
SOURCES FOR THIS CHAPTER: a.
Pages to read in the books which are cited re peatedly. 118;
Edwards 46-53, 87-103;
Faires 425-442;
Jones 187-225;
635;
Ewing-Hart 114-
French 62-82, 396-405;
McMackin-Shaver 190-223;
son 95-100, 145-154;
ACTIVITY ASSIGNMENTS:
Nichol
Oberg-Jones 270-280, 631-
Palmer-Bibb 143-153, 231-242;
golis 228-246; C.
Where to get further data,
Slade-Mar-
Wagener-Arthur 7, 85-87. Some learning experiences to en
hance your skill in layout work. 1.
LABORATORY:
Locate the center of a 3 inch round piece
of steel and lay out the detail of a 1 inch lift, 1 Inch base circle cam on the centered end. 2.
LABORATORY:
Selecting an irregular
available to you by the instructor,
piece of work made locate Its center
of gravity, construct the largest circle possible, divide the diameter of the circle into three equal parts and draw parallel lines through the ends of these equal divisions. 3.
CLASSROOM:
Establish a vertical line on one wall of
the room and indicate the height of
the blackboard and
46 other objects on the wall If the room were half scale. D.
EVALUATION:
A sample of a way in whleh you ma y check your
ability to diagram directions for shop work. 1.
HATING SCALE:
Place an X in each space for which you
can qualify. a.
(
Locating center of round work with the center** ing head square.
b. (
Using the hermaphrodite caliper to locate centers.
3
x \
"
53
J£1
hql£
ctQCi.es
2k z
*//
AW M & e R
6 £ HOLES
I n £ q c h fio< e C t R C t C
-£2
r