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METROLOGY
MEASUREMENT OF
SCREW THREADS
Dr. M.Vijaya Kini,
Associate Professor (Senior Scale)
Department of Mechanical and Manufacturing Engineering
Manipal Institute of Technology,
MANIPAL
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Screw Threads Terminology1. Screw thread:
A screw thread is the helical ridge produced by
forming a continuous helical groove of uniform
section on the external or internal surface of a
cylinder or cone.
A screw thread formed on a cylinder is known as
straight or parallel screw thread, while the oneformed on a cone or frustum of a cone is known
as tapered screw thread.
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2. Axis of a thread:
This is imaginary line running longitudinally
through the centre of the screw.
3. Crest of thread :
This is defined as the prominent part ofthread, whether it be external or internal.
4. Root of thread :
This is defined as the bottom of the groovebetween the two flanks of the thread,
whether it be external or internal.
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5. Flanks of thread :
These are straight edges which connect the crestwith the root.
6. Angle of thread (Included angle):
This is the angle between the flanks or slope ofthe thread measured in an axial plane.
7. Flank angle:
The flank angles are the angles betweenindividual flanks and the perpendicular to the
axis of the thread which passes through thevertex of the fundamental triangle. The flankangle of a symmetrical thread is commonlytermed as the half-angle of thread.
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8. Pitch:
The pitch of a thread is the distance, measured
parallel to the axis of the thread, betweencorresponding points on adjacent thread forms in the
same axial plane and on the same side of axis.
The basic pitch is equal to the lead divided by the
number of thread starts. On drawings of thread
sections, the pitch is shown as the distance from the
centre of one thread crest to the centre of the next,and this representation is correct for single start as well
as multi-start threads.
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9. Depth of thread:
This is the distance from the crest or tip of the
thread to the root of the thread measuredperpendicular to the longitudinal axis or thiscould be defined as the distance measuredradially between the major and minor cylinders.
10.Fundamental triangle:
This is found by extending the flanks and joiningthe points B and C. Thus in Figure, triangle ABC
is referred to fundamental triangle. HereBC = pitch, and the vertical height of the triangleis called angular or theoretical depth. The pointA is the apex of the triangle ABC.
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11.Truncation:
A thread is sometimes truncated at the crest or
at the root or at both crest and root. Thetruncation at the crest is the radial distance
from the crest to the nearest apex of the
fundamental triangle. Similarly the truncationat the root is the radial distance from the root to
the nearest apex.
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12.Addendum:
For an external thread, this is defined as the
radial distance between the major and pitchcylinders. For an internal thread this is the radial
distance between the minor and pitch cylinders.
13.Dedendum:This is the radial distance between the pitch
and minor cylinder for external thread, and for
internal thread, this is the radial distancebetween the major and pitch cylinders.
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14.Major diameter:
In case of a straight thread, this is the diameter ofthe major cylinder (imaginary cylinder, co-axial
with the screw, which just touches the crests of anexternal thread or the root of an internal thread ).
It is often referred to as the outside diameter, crestdiameter or full diameter of external threads.
15.Minor diameter:
In case of straight thread, this is the diameter of theminor cylinder (an imaginary cylinder, co-axialwith the screw which just touches the roots of anexternal thread or the crest of an internal thread ).
It is often referred to as root diameter or conediameter of external threads.
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16.Effective diameter or pitch diameter:In case of straight thread, this is the diameter of the pitch
cylinder (the imaginary cylinder which is co-axial with
the axis of the screw, and intersects the flank of the
threads in such a way as to make the width of
threads and width of the spaces between the threads
equal ).
If the pitch cylinder be imagined as generated by a straight
line parallel to the axis of screw, that straight line is then
referred to as the pitch line. Along the pitch line, the
widths of the threads and the widths of the spaces are
equal on a perfect thread.
This is the most important dimension as it decides the
quality of the fit between the screw and the nut.
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Errors in Threads.In the case of screw threads there are at least fiveimportant elements which require consideration
and error in anyone of these can cause rejection ofthe thread.
In routine production all of these five elements
major diameter,
minor diameter,
effective diameter,
pitch and
angle
of the thread form) must be checked and method ofgauging must be able to cover all these elements.
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Pitch Errors in Screw Threads.
Classification:
Progressive Pitch Error.
Periodic Pitch Error.Drunken Thread.
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Progressive Pitch Error This error occurs when the tool
work velocity ratio is incorrect
though it may be constant. It can
also be caused due to pitch errors
in the lead screw of the lathe or
other generating machine.
The other possibility is by using an incorrect gear or an
approximate gear train between work and lead screwe.g., while metric threads are cut with an-inch pitch
lead screw and a translatory gear is not available. A
graph between the cumulative pitch error and the
length of thread is generally a straight
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Periodic Pitch Error This repeats itself at regular intervals
along the thread. In this case,successive portions of the thread are
either longer or shorter than the
mean. This type of error occurs when
the tool work velocity ratio is not
constant.
This type of error also results when a thread is cut from a lead
screw which lacks squareness in the abutment causing the
leadscrew to move backward it and forward once in eachrevolution. Thus the errors due to these cases are cyclic and pitch
increases to a maximum, then reduces through normal value to a
minimum and so on. The graph between the cumulative pitch error
and length of threads for this error will, therefore, be of sinusoidal
form.
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Drunken Thread.This is the one having erratic
pitch, in which the advance of
the helix is irregular in one
complete revolution of the
thread.
Thread drunkenness is a particular case of a periodic pitch errorrecurring at intervals of one pitch. In such a thread, the pitch
measured parallel to the thread axis will always be correct, the
only error being that the thread is not cut to a true helix. If the
screw thread be regarded as an inclined plane wound round acylinder and if the thread be unwound from the cylinder, (i.e.,
development of the thread be taken) then the drunkeness can
be visualised. The helix will be a curve in the case of drunken
thread and not a straight line as shown in Figure.
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Effect of Pitch Errors
An error in pitch virtually increases the
effective diameter of a bolt or screw anddecreases the effective diameter of a nut.
The meaning of the virtual change ineffective diameter is that if any screw isperfect except for pitch error, it will not
screw easily into a perfect ring gauge ofsame nominal size until its effectivediameter is reduced.
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Measurement of Major Diameter.
1
1
2
1 1 2
If D diameter of setting cylinder
R reading of micrometer on setting cylinder
R micrometer reading on thread
then major diameter D R R
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Measurement of Minor Diameter.
1 2
1 1 2 1
reading on setting cylinder with Vee-pieces in position =R and reading on thread =R
and diameter of setting cylinder =D . Then minor diameter =D + (R - R ).
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Effective Diameter Measurements
The effective diameter or the pitch diameter can
be measured by anyone of the followingmethods :
Micrometer method
One wire, Two wire or three wire
or rod method.
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Thread Micrometer MethodThe thread micrometer resembles the
ordinary micrometer, but it has special
contacts to suit the end screw thread from
that is to be checked.
In this micrometer, the end of the spindle is
pointed to the Vee-thread form with a
corresponding Vee recess in the fixed anvil.
When measuring threads only, the angle of the point and the sides
of Vee anvil. i.e. the flanks of the threads should come into contact
with the screw thread.
If correctly adjusted, this micrometer given the pitch diameter.This value should agree with that obtained by measurement by
oUtside diameter and pitch from the following relation :
Pitch dia = D - O.6403p (in case of Whitworth thread)
where O.6403p =depth of thread, D =outside dia., p =pitch.
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Two Wire Method
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The effective diameter of
a screw thread may be
ascertained by placing
two wires of identical
diameter between the
flanks of the thread, and
measuring the distance over the outside of these
wires. The effective diameter E is then calculated as
E = T + PWhere T =Dimension under the wires
=M - 2d
M =dimension over the wires,
d = diameter of each wire
Th i d d
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The wires used are made
of hardened steel to
sustain the wear and tear
in use. These are given a
high degree of accuracy
and finish by lapping to
suit different pitches.Dimension T can also be determined by placing
wires over a standard cylinder of diameter greater
than the diameter under the wires and noting thereading R1 and then taking reading with over the
gauge, say R2.
Then T = S - (R1 - R2 ).
P I i l hi h
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P = It is a value which
depends upon the dia of
wire and pitch of the
thread.
If p =pitch of the thread, then
P =0.9605p 1.1657d (for Whitworth thread),
P =0.866p d (for metric thread).
Actually P is a constant value which has to be added to thediameter under the wires to give the effective diameter.
Th i f h
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The expression for the
value of P in terms of p
(pitch), d (diameter of
wire) and x (thread angle)
can be derived as follows:
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In Figure, since BC lies on
the effective diameter line
1 1BC = pitch = P2 2
cosec / 2OR =
2
(cosec / 2 1)RA =2
d x
d x
cot / 2 cot / 24
p RQ QC x x
cot / 2 (cosec / 2 1)
4 2
p x d x AQ RQ AR
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AQ is half the value of P
P value cot / 2=2 cosec / 2 1A2
Q = p
x d x
Th Wi M th d
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Three Wire Method.
The same derivation may be used for this method.
The only change is in the sketch. The figure
shown above may be used instead of the two
wire method sketch.
B Si Wi
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Best Size Wire
The best size wire is one, in which case the wiremakes contact with the thread flank. i.e., the
contact points of the wires should be on the pitch
line or effective diameter.
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In other words, OB is
perpendicular to the flank
position of the thread. Let
half the included angle of
thread be x .
Then in OAP,
sin , AB
POAOB
0or sin (90 - )
AB x
OB
0or
sin(90 ) cossec
AB ABOB
x x AB x
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Since AB = r, and wire diameter =2r.
Best wire diameter 2 2 secb AB xd r
As AP lies on the pitch line,
AP (where p =pitch of the th4
)d= rea p
2sec sec4 2
b
p pd x x
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Pitch Measurement
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It is desired to measure the Effective diameter of
a 32 x 3.5 mm pitch metric plug screw gauge.
For this purpose, following readings (averagevalues) were noted.
Micrometer reading over the standardcylinder of 30.500 mm and the wires of 2.000
mm diameter as 13.3768 mm.
Micrometer reading over the gauge and wires
as 12.2428 mm.