Download Machinery's Handbook Guide 27th Edition (Machinery's Handbook Guide to the Use of Tables PDF

TitleMachinery's Handbook Guide 27th Edition (Machinery's Handbook Guide to the Use of Tables
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LanguageEnglish
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Table of Contents
                            Title
THE PURPOSE OF THIS BOOK
THE METRIC SYSTEM
1 Dimensions And Areas Of Circles
2 Chordal Dimensions, Segments, And Spheres
3 Formulas And Their Rearrangement
4 Spreadsheet Calculations
5 Calculations Involving Logarithms Of Numbers
6 Dimensions, Areas, And Volumes Of Geometrical Figures
7 Geometrical Propositions And Constructions
8 Functions Of Angles
9 Solution Of Right-angle Triangles
10 Solution of Oblique Triangles
11 Figuring Tapers
12 Tolerances And Allowances For Machine Parts
13 Using Standards Data And Information
14 Standard Screw And Pipe Threads
15 Problems In Mechanics
16 Strength Of Materials
17 Design Of Shafts And Keys For Power Transmission
18 Splines
19 Problems In Designing And Cutting Gears
20 Cutting Speeds, Feeds, And Machining Power
21 Numerical Control
22 General Review Questions
23 Answers To Practice Exercises
INDEX
                        
Document Text Contents
Page 1

1

SECTION 1

DIMENSIONS AND AREAS OF CIRCLES

HANDBOOK Pages 66 and 76
Circumferences of circles are used in calculating speeds of

rotating machine parts, including drills, reamers, milling cutters,
grinding wheels, gears, and pulleys. These speeds are variously
referred to as surface speed, circumferential speed, and peripheral
speed; meaning for each, the distance that a point on the surface or
circumference would travel in one minute. This distance usually is
expressed as feet per minute. Circumferences are also required in
calculating the circular pitch of gears, laying out involute curves,
finding the lengths of arcs, and in solving many geometrical prob-
lems. Letters from the Greek alphabet frequently are used to desig-
nate angles, and the Greek letter π (pi) always is used to indicate
the ratio between the circumference and the diameter of a circle:

For most practical purposes the value of π = 3.1416 may be used.

Example 1:Find the circumference and area of a circle whose
diameter is 8 inches.

On Handbook page 66, the circumference C of a circle is given
as 3.1416d. Therefore, 3.1416 × 8 = 25.1328 inches.

On the same page, the area is given as 0.7854d2. Therefore, A
(area) = 0.7854 × 82 = 0.7854 × 64 = 50.2656 square inches.

Example 2: From page 76 of the Handbook, the area of a cylin-
drical surface equals S = 3.1416 × d × h. For a diameter of 8 inches
and a height of 10 inches, the area is 3.1416 × 8 × 10 = 251.328
square inches.

Example 3: For the cylinder in Example 2 but with the area of
both ends included, the total area is the sum of the area found in
Example 2 plus two times the area found in Example 1. Thus,

π 3.14159265… circumference of circle
diameter of circle

-------------------------------------------------------= =

Guide to Machinery's Handbook 27th Edition

Copyright 2004, Industrial Press, Inc., New York, NY

Page 2

DIMENSIONS AND AREAS OF CIRCLES2

251.328 + 2 × 50.2656 = 351.8592 square inches. The same result
could have been obtained by using the formula for total area given
on Handbook page 76: A = 3.1416 × d × (1⁄2d + h) = 3.1416 × 8 ×
(1⁄2 × 8 + 10) = 351.8592 square inches.

Example 4:If the circumference of a tree is 96 inches, what is its
diameter? Since the circumference of a circle C = 3.1416 × d, 96 =
3.1416 × d so that d = 96 ÷ 3.1416 = 30.558 inches.

Example 5:The tables starting on page 1018 of the Handbook
provides values of revolutions per minute required producing vari-
ous cutting speeds for workpieces of selected diameters. How are
these speeds calculated? Cutting speed in feet per minute is calcu-
lated by multiplying the circumference in feet of a workpiece by
the rpm of the spindle: cutting speed in fpm = circumference in
feet × rpm. By transposing this formula as explained in Formulas
And Their Rearrangement starting on page 8,

For a 3-inch diameter workpiece (1⁄4-foot diameter) and for a cut-
ting speed of 40 fpm, rpm = 40 ÷ (3.1416 × 1⁄4) = 50.92 = 51 rpm,

approximately, which is the same as the value given on page 1018
of the Handbook.

PRACTICE EXERCISES FOR SECTION 1

(See Answers to Practice Exercises For Section 1 on page 221)

1) Find the area and circumference of a circle 10 mm in diameter.

2) On Handbook page 1020, for a 5-mm diameter tool or work-
piece rotating at 318 rpm, the corresponding cutting speed is given
as 5 meters per minute. Check this value.

3) For a cylinder 100 mm in diameter and 10 mm high, what is
the surface area not including the top or bottom?

4) A steel column carrying a load of 10,000 pounds has a diame-
ter of 10 inches. What is the pressure on the floor in pounds per
square inch?

5) What is the ratio of the area of a square of any size to the area
of a circle having the same diameter as one side of the square?

rpm
cutting speed, fpm

circumference in feet
---------------------------------------------------=

Guide to Machinery's Handbook 27th Edition

Copyright 2004, Industrial Press, Inc., New York, NY

Page 138

138

SECTION 16

STRENGTH OF MATERIALS

HANDBOOK Pages 203 – 225
The Strength of Materials section of Machinery’s Handbook

contains fundamental formulas and data for use in proportioning
parts that are common to almost every type of machine or mechan-
ical structure. In designing machine parts, factors other than
strength often are of vital importance. For example, some parts are
made much larger than required for strength alone to resist extreme
vibrations, deflection, or wear; consequently, many machine parts
cannot be designed merely by mathematical or strength calcula-
tions, and their proportions should, if possible, be based upon
experience or upon similar designs that have proved successful. It
is evident that no engineering handbook can take into account the
endless variety of requirements relating to all types of mechanical
apparatus, and it is necessary for the designer to determine these
local requirements for each, but, even when the strength factor is
secondary due to some other requirement, the strength, especially
of the more important parts, should be calculated, in many
instances, merely to prove that it will be sufficient.

In designing for strength, the part is so proportioned that the
maximum working stress likely to be encountered will not exceed
the strength of the material by a suitable margin. The design is
accomplished by the use of a factor of safety. The relationship
between the working stress sw, the strength of the material, Sm , and
the factor of safety, fs is given by Equation (1) on page 208 of the
Handbook:

(a)

The value selected for the strength of the material, Sm depends
on the type of material, whether failure is expected to occur

sw
Sm
fs

------=

Guide to Machinery's Handbook 27th Edition

Copyright 2004, Industrial Press, Inc., New York, NY

Page 139

STRENGTH OF MATERIALS 139

because of tensile, compressive, or shear stress, and on whether the
stresses are constant, fluctuating, or are abruptly applied as with
shock loading. In general, the value of Sm is based on yield strength
for ductile materials, ultimate strength for brittle materials, and
fatigue strength for parts subject to cyclic stresses. Moreover, the
value for Sm must be for the temperature at which the part operates.
Values of Sm for common materials at 68°F can be obtained from
the tables in Machinery’s Handbook from page 474 and 554. Fac-
tors from the table given on Handbook page 421, Influence of
Temperature on the Strength of Metals, can be used to convert
strength values at 68°F to values applicable at elevated tempera-
tures. For heat-treated carbon and alloy steel parts, see data starting
on Handbook page 468.

The factor of safety depends on the relative importance of reli-
ability, weight, and cost. General recommendations are given in
the Handbook on page 208.

Working stress is dependent on the shape of the part, hence on a
stress concentration factor, and on a nominal stress associated with
the way in which the part is loaded. Equations and data for calcu-
lating nominal stresses, stress concentration factors, and working
stresses are given starting on Handbook page 208.

Example 1:Determine the allowable working stress for a part that
is to be made from SAE 1112 free-cutting steel; the part is loaded
in such a way that failure is expected to occur in tension when the
yield strength has been exceeded. A factor of safety of 3 is to be
used.

From the table, Strength Data for Iron and Steel, on page 474
of the Handbook, a value of 30,000 psi is selected for the strength
of the material, Sm.Working stress Sw is calculated from Equation
(a) as follows:

Finding Diameter of Bar to Resist Safely Under a Given
Load.—Assume that a direct tension load, F, is applied to a bar
such that the force acts along the longitudinal axis of the bar. From
Handbook page 213, the following equation is given for calculat-
ing the nominal stress:

sw
30 000,

3
------------------ 10 000 psi,= =

Guide to Machinery's Handbook 27th Edition

Copyright 2004, Industrial Press, Inc., New York, NY

Page 276

x

The metric material in the Handbook will provide considerable
useful data and assistance to engineers and technicians who are
required to use metric units of measurements. It is strongly sug-
gested that all readers, whether or not they are using metric units at
the present time, become familiar with the SI System by reading
the explanatory material in the Handbook and by studying the SI
units and the ways of converting English units to them.

Guide to Machinery's Handbook 27th Edition

Copyright 2004, Industrial Press, Inc., New York, NY

Page 277

vi

The Purpose Of This Book vii

The Metric System viii

1 Dimensions And Areas Of Circles 1

2 Chordal Dimensions, Segments, And Spheres 4

3 Formulas And Their Rearrangement 8

4 Spreadsheet Calculations 22

5 Calculations Involving Logarithms Of Numbers 32

6 Dimensions, Areas, And Volumes Of Geometrical Figures 42

7 Geometrical Propositions And Constructions 46

8 Functions Of Angles 50

9 Solution Of Right-angle Triangles 58

10 Solution of Oblique Triangles 78

11 Figuring Tapers 88

12 Tolerances And Allowances For Machine Parts 94

13 Using Standards Data And Information 108

14 Standard Screw And Pipe Threads 113

15 Problems In Mechanics 122

16 Strength Of Materials 138

17 Design Of Shafts And Keys For Power Transmission 150

18 Splines 159

19 Problems In Designing And Cutting Gears 169

20 Cutting Speeds, Feeds, And Machining Power 196

21 Numerical Control 205

22 General Review Questions 212

23 Answers To Practice Exercises 221
INDEX 254

SECTION PAGE

CONTENTS

Guide to Machinery's Handbook 27th Edition

Copyright 2004, Industrial Press, Inc., New York, NY

Machinery's Handbook Guide 27th Edition

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