This document discusses the measurement of screw threads. It defines various screw thread terminology such as crest, root, flank, pitch, and angle of thread. It describes common types of pitch errors in screw threads such as progressive, periodic, and drunken threads. It also outlines various methods for measuring important screw thread dimensions like major diameter, minor diameter, and effective diameter. These include using a bench micrometer, thread micrometer, and two-wire method. Accurately measuring thread features is important for evaluating thread quality and fit.

1. METROLOGY
MEASUREMENT OF
SCREW THREADS

4. Screw Threads Terminology
1. 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 one
formed on a cone or frustum of a cone is known
as tapered screw thread.

5. 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 of
thread, whether it be external or internal.
4. Root of thread :
This is defined as the bottom of the groove
between the two flanks of the thread,
whether it be external or internal.

6. 5. Flanks of thread :
These are straight edges which connect the crest
with the root.
6. Angle of thread (Included angle):
This is the angle between the flanks or slope of
the thread measured in an axial plane.
7. Flank angle:
The flank angles are the angles between
individual flanks and the perpendicular to the
axis of the thread which passes through the
vertex of the fundamental triangle. The flank
angle of a symmetrical thread is commonly
termed as the half-angle of thread.

7. 8. Pitch:
The pitch of a thread is the distance, measured
parallel to the axis of the thread, between
corresponding 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.

8. 9. Depth of thread:
This is the distance from the crest or tip of the
thread to the root of the thread measured
perpendicular to the longitudinal axis or this
could be defined as the distance measured
radially between the major and minor cylinders.
10.Fundamental triangle:
This is found by extending the flanks and joining
the points B and C. Thus in Figure, triangle ABC
is referred to fundamental triangle. Here
BC = pitch, and the vertical height of the triangle
is called angular or theoretical depth. The point
A is the apex of the triangle ABC.

9. 11.Truncation:
A thread is sometimes truncated at the crest or
at the root or at both crest and root. The
truncation at the crest is the radial distance
from the crest to the nearest apex of the
fundamental triangle. Similarly the truncation
at the root is the radial distance from the root to
the nearest apex.

10. 12.Addendum:
For an external thread, this is defined as the
radial distance between the major and pitch
cylinders. 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 distance
between the major and pitch cylinders.

11. 14.Major diameter:
In case of a straight thread, this is the diameter of
the major cylinder (imaginary cylinder, co-axial
with the screw, which just touches the crests of an
external thread or the root of an internal thread).
It is often referred to as the outside diameter, crest
diameter or full diameter of external threads.
15.Minor diameter:
In case of straight thread, this is the diameter of the
minor cylinder (an imaginary cylinder, co-axial
with the screw which just touches the roots of an
external thread or the crest of an internal thread).
It is often referred to as root diameter or cone
diameter of external threads.

12. 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.

13. Errors in Threads.
In the case of screw threads there are at least five
important elements which require consideration
and error in anyone of these can cause rejection of
the 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 of
gauging must be able to cover all these elements.

14. Pitch Errors in Screw Threads.
Classification:
Progressive Pitch Error.
Periodic Pitch Error.
Drunken Thread.

15. 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 screw e.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 line.

16. 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 and forward once in each revolution.
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.

17. 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 error
recurring 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 a
cylinder 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.

18. Effect of Pitch Errors
An error in pitch virtually increases the
effective diameter of a bolt or screw and
decreases the effective diameter of a nut.
The meaning of the virtual change in
effective diameter is that if any screw is
perfect except for pitch error, it will not
screw easily into a perfect ring gauge of
same nominal size until its effective
diameter is reduced.

19. Measurement of Major Diameter.

20. BENCH MICROMETER

21. Measurement of Minor Diameter.

22. Effective Diameter Measurements
The effective diameter or the pitch diameter can
be measured by anyone of the following
methods :
Micrometer method
One wire, Two wire or three wire
or rod method.

23. Micrometer method
Screw Thread Micrometer

24. Screw Thread Micrometer

25. Thread Micrometer
Method
The 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 gives 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.

26. Two Wire Method

39. 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 (average
values) were noted.
 Micrometer reading over the standard
cylinder 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.

40. Effective diameter =T + P .
1 2
dim - ( )
where T ensions under the wires S R R
  
S = diameter of standard = 30.500 mm
l
2
R =reading over wires located above the cylinder =13.3768 mm
R =reading over wires located over the gauge =12.2428 mm
30.500 (13.3768 12.2428) 29.3660 mm
T    
For metric threads P is a constant 0.866 -
0.866 3.5 2
1.0312 mm
p d

  

E =T + P =29.3660 + 1.0312 =30.3972 mm