This document provides information on measuring various elements of screw threads, including major diameter, minor diameter, mean diameter, and thread form. It defines each element and describes methods for measuring them using tools like micrometers, wires, and optical comparators. The document focuses on measuring ISO metric, unified, and Whitworth screw threads specifically. It provides formulas for calculating mean diameter and pitch diameter based on measurements taken using a 3-wire method.

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UNIT 1 SCREW THREAD
OBJECTIVES
General Objective: To understand the methods of testing and
measuring elements of ISO and BSW screw
threads.
Specific Objectives: At the end of the unit you will be able to :
Ø Identify the methods of measuring major diameter,
minor diameter and mean diameter.
Ø Measure and calculate major diameter, minor
diameter and mean diameter of a screw thread.
Ø To check the thread form by using the optical
comparator.

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INPUT
1.0 INTRODUCTION
All elements of the thread influence
the strength and interchange ability
of screw thread, but the pitch, angle
and effective diameter are much
more important than the other
elements
1.1 ELEMENTS OF A THREAD
To understand and calculate the thread elements, the following
definition relating to screw threads should be known (Fig. 1.1).
root
pitch
major diameter
mean diameter
minor diameter
thread angle
Figure 1.1 Screw thread terminology

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1.1.1. Major Diameter
It is the largest diameter of the thread. This is the distance between
the crests of the thread measured perpendicular to the thread axis.
1.1.2. Pitch/Mean Diameter
The diameter of the thread used to establish the relationship, or fit,
between an internal and external thread. The pitch diameter is the
distance between the pitch points measured perpendicular to the thread
axis. The pitch points are the points on the thread where the thread ridge
and the space between the threads are of the same width.
1.1.3. Minor Diameter
It is the smallest diameter of the thread. This is the distance
between the roots of the thread measured perpendicular to the thread
axis.
1.1.4. Thread Angle
This is the included angle of the thread form.
1.1.5. Pitch
It is the distance between the same points on adjacent threads. This
is also the linear distance the thread will travel in one revolution.
1.1.6. Root
The surface of the thread that joins the flanks of adjacent threads.
The distance between the roots on opposite sides of the thread is called
the root, or minor diameter.

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1.2. MEASURING THE MAJOR DIAMETER
To measure major diameter of the screw, a micrometer, with anvils of a
diameter sufficient to span two threads, may be used,( Fig. 1.2). To eliminate
the effect of errors in the micrometer screw and measuring faces, it is advisable
first to check the instrument to a cylindrical standard of about the same
diameter as the screw. For such purposes a plug gauge or a set of ‘Hoffman’
rollers is useful.
anvil
Figure 1.2 Checking the major diameter with a micrometer
1.3. MEASURING THE MINOR/CORE DIAMETER
The diameter over the roots of a thread may be checked by means of a
special micrometer adapted with a shaped anvils, (Fig. 1.3) or a micrometer may
be used in conjunction with a pair of vee pieces ( steel prisms ). The second
method is recommended ( Fig.1.5). The steel prisms on the micrometer are
pressed into the thread groove. The ends of the prisms are slightly curved and
parallel to the root thread. It is important , when making the test, to ensure
that the micrometer is positioned at right angles to the axis of the screw being
measured, and when a large amount of such work is to be done, a special
‘floating bench micrometer’ ( Fig. 1.4 ) is used. It is because, it supports the
screw and incorporates the micrometer elements correctly located, as well as
providing means for suspending the vee prisms.

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Fig. 1.3 Checking the core diameter of a thread with an
shaped anvil micrometer
Fig. 1.4. A Floating Micrometer

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The prism values are stated as,
Dm = W – 2T
Note:
Dm - mean diameter
W - distance between two prism
T - prism height (known)
T
prism
W
Figure 1.5 Checking minor diameter by using a micrometer and prisms
1.4. MEASURING THE MEAN/PITCH/EFFECTIVE DIAMETER
The three-wire method is recognized as one of the best methods of checking
the pitch diameter because the results are least affected by any error which may
be present in the included thread angle. For threads which require an accuracy
of 0.001 in. or 0.02 mm, a micrometer can be used to measure the distance over
the wires. For threads requiring greater accuracy an electronic comparator
should be used to measure the distance over the wires.
In the three-wire method, three wires of equal diameter are placed in the
thread; two on one side and one on the other side (Fig. 1.6). The wires used
should be hardened and lapped to three times the accuracy of the thread to be
inspected. A standard micrometer may then be used to measure the distance
over the wires. For greatest accuracy, the best size wire should be used.

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Figure 1.6 Three wire method
The hard round bars (wire) with the same size are positioned opposite to
the screw thread groove shown in the diagram above. The distance is measured
between the outside of the round bars. The most suitable wire size is 0.57735p.
In Fig. 1.7 P is the pitch of the screw thread. The suitable wire size is quite hard
to get, usually a size bigger than 0.57735p wire size will be used.
Fig. 1.7. Conditions when measuring with wires

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1.4.1. Best Size Wires.
Wires which touch the thread at the pitch diameter are known as
"Best Size" Wires. Such wires are used because the measurements of
pitch diameter are least affected by errors that may be present in the
angle of the thread.
The above analysis for the distance over wires holds good provided
the wire touches the thread somewhere on its right side, and provided the
thread angle is correct. The extremes of wire sizes which touch on the
straight sides and which can be measured are shown at (a) and (c),
Fig.1.9. For ISO metric, unified and Whitworth threads these limiting
sizes are given in Table 1.1
Table 1.1. Wire sizes for thread measurement ( p = pitch of thread)
Thread Max. Min. ‘Best Size range for
Form Wire Wire Wire’ Best wire
ISO metric and 1.01p 0.505p 0.557p 0.534p
Unified 0.620p
Whitworth 0.853p 0.506p 0.564p 0.535p
0.593p

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Pitch (P)
A
h r
W C
a H
B
DE a 60o
2
D E
P/2
Figure 1.8. Three-wire measurement
Note:
W = Distance over wires
DE = Pitch/ Effective Diameter
Dw = Wire diameter
a = 600
From the Fig. 1.8, mean/pitch diameter can be calculated by applying the
following formula;
a a
AD = AB cosec = r cosec
2 2
a P a
H = DE cot = cot
2 2 2
P a
CD = 0.5H = cot
4 2
a P a
h = AD – CD = r cosec – cot
2 4 2

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and distance over wires (W)
= DE + 2h + 2r
a P a
= DE + 2 {r cosec – cot } + 2r
2 4 2
a P a
= DE + 2r cosec - cot + 2r
2 2 2
a P a
= DE +2r ( 1 + cosec ) – cot
2 2 2
and, since 2r = d (the diameter of the wire),
a P a
W = DE + d ( 1 + cosec ) – cot (1)
2 2 2
From this general formula we may apply the special adaptation for
common threads.
Figure 1.9. a) ISO metric and unified b) Whitworth

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(a) ISO metric and unified Fig. 1.9 (a)
The effective diameter lies 0.3248p inside the crest of the thread,
Hence DE = D – 0.6496p
a
a = 60° and cosec =2
2
a
cot = 1.732
2
a P a
W (over wires) = DE + d (1 + cosec ) – cot
2 2 2
P
=D – 0.6496p + d(3) – (1.732)
2
= D +3d- 1.5156p (2)
(b) Whitworth Fig. 1.9(b)
Depth of thread = 0.64p, so that DE = D – 0.64p
a a
a = 55° and cosec = 2.1657 cot = 1.921
2 2
a P a
Hence W ( over wires) = DE + d { 1 + cosec } - cot
2 2 2
P
= D -0.64p + d 3.1657) - (1.921)
2
= D + 3.165d - 1.6 p (3)

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1.5. OPTICAL COMPARATOR
An optical comparator or shadowgraph (Fig. 1.10a and 1.10b) projects an
enlarge shadow onto a screen where it may be compared to lines or to a master
from which indicates the limits of the dimensions or the contour of the part being
checked. The optical comparator is a fast, accurate means of measuring or
comparing the work piece with a master. It is often used when the work piece is
difficult to check by other method. Optical comparators are particularly suited
for checking extremely small or odd-shaped parts, which would be difficult to
inspect without the use of expensive gauges.
Optical comparators are available in bench and floor models, which are
identical in principle and operation. Light from a lamp passes through a
condenser lens and is projected against the work piece. The shadow caused by
the work piece is transmitted through a projecting lens system, which magnifies
the image and casts it onto a mirror. The image is then reflected to the viewing
screen and is further magnified in this process.
The extent of the image magnification depends on the lens used.
Interchangeable lenses for optical comparators are available in the following
magnifications: 5 x, 10 x, 31.25 x, 50 x, 62.5 x, 90 x, 100 x, and 125 x.
A comparator chart or master form mounted on the viewing screen is used
to compare the accuracy of the enlarged image of the work piece being inspected.
Charts are usually made of translucent material, such as cellulose acetate or
frosted glass. Many different charts are available for special jobs, but the most
commonly used are linear-measuring, radius, and angular charts. A vernier
protractor screen is also available for checking angles. Since charts are
available in several magnifications, care must be taken to use the chart of the
same magnification as the lens mounted on the comparator.
Many accessories are available for the comparator, increasing the
versatility of the machine. Some of the most common ones are tilting work

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centres, which permit the work piece to be tilted to the required helix angle for
checking threads; a micrometer work stage, with permit quick and accurate
measuring of dimensions in both direction; and gauge blocks, measuring rods,
and dial indicators used on comparators for checking measurement. The surface
of the work piece may be checked by a surface illuminator, which lights up the
face of work piece adjacent to the projecting lens system and permits this image
to be projected onto the screen.
1.5.1. To check the angle of a 60o thread using an optical comparator
1. Mount the correct lens in the comparator.
2. Mount the tilting work centres on the micrometer cross-slide
stage.
3. Set the tilting work centres to the helix angle of the thread.
4. Set the work piece between centres.
5. Mount the vernier protractor chart and align it horizontally
on the screen.
6. Turn on the light switch.
7. Focus the lens so that a clear image appears on the screen.
8. Move the micrometer cross-slide stage until the thread image
is centralized on the screen.
9. Remove the vernier protractor chart to show a reading of 30o.
10. Adjust the cross-slides until the image coincides with the
protector line.
11. Check the other side of the thread in the same manner.

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Note: If the threaded angle is not correct or square with the centre line,
adjust the vernier protractor chart to measure the angle of the thread
image. Other dimensions of the threads, and width of flats, may be
measured with micrometer measuring stages or devices such as rods,
gauge blocks and indicators.
helix angle
Figure 1.10 (a). Checking a thread form on an optical comparator

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Figure 1.10 (b) Principle of the optical projector

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ACTIVITY 1
TEST YOUR UNDERSTANDING BEFORE YOU CONTINUE WITH
THE NEXT INPUT…!
1.1. Draw and label a schematic drawing of how you would check the
core diameter of an external V-thread.
1.2. Using ‘best’ wire sizes determine the distance of the wire for M 20 x
2.5 ISO metric thread.
1.3. Why is the three-wire method is one of the best method of
measuring the pitch diameter of a V thread?
1.4. With the aid of a labelled diagram, briefly explain how you would
use an optical comparator to check the thread angle of 60o

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FEEDBACK ON ACTIVITY 1
1.1
T
prism
W
Dm = W – 2T ; T = prism height (known)
1.2. 20 mm x 2.5 mm pitch
Best wire diameter = 2.5 x 0.577
= 1.443 mm.
From formula W = D + 3d – 1.5156P
= 20 + 3 (1.443) – 1.5756 (2.5)
= 20.54 mm
1.3. The results are least affected by any error which may present in the
included thread angle.

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1.4. Using an optical comparator to check the thread angle of 60o.
To check the angle of a 60o thread using an optical comparator
1. Mount the correct lens in the comparator.
2. Mount the tilting work centres on the micrometer cross-slide stage.
3. Set the tilting work centres to the helix angle of the thread.
4. Set the work piece between centres.
5. Mount the vernier protractor chart and align it horizontally on the
screen.
6. Turn on the light switch.
7. Focus the lens so that a clear image appears on the screen.
8. Move the micrometer cross-slide stage until the thread image is
centralized on the screen.
9. Remove the vernier protractor chart to show a reading of 30o.
10. Adjust the cross-slides until the image coincides with the protector
line.
11. Check the other side of the thread in the same manner.

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Note: If the threaded angle is not correct or square with the centre line,
adjust the vernier protractor chart to measure the angle of the thread
image. Other dimensions of the threads, and width of flats, may be
measured with micrometer measuring stages or devices such as rods,
gauge blocks and indicators.

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SELF-ASSESSMENT 1
1. Calculate the effective diameter of M35 x 5.5 threads by using three wire
method. The distance between wires is 35.60 mm.
Used formula E = M – 3d + 0.866P ; when d = 0.577P and P = pitch.
Sketch the measurement setup.
3
2. Using the ‘best’ wire sizes, determine the distance over wires for (a) in
4
Whitworth, (b) M 20 x 2.5 ISO metric threads.

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FEEDBACK OF SELF-ASSESSMENT 1
1. E = 23.263 mm
Three wire method
2. (a) 0.0564 in, (b) 1.4425 mm