This document discusses the metrology of threads. It begins by defining external and internal threads and providing examples. It then defines various thread terminology including pitch, lead, crest, flank, root, major diameter, minor diameter, effective diameter, depth of thread, angle of thread, and others. It describes various types of thread forms and types of errors in threads. The document outlines various measurement methods for elements of a thread like major diameter, minor diameter, effective diameter, and pitch. It also discusses gear terminology and types of gears like spur gears, helical gears, bevel gears, worm gears, and rack and pinion gears.

1. Metrology of Threads
By
Prof N D Sadaphal
Assistant Professor
Sanjivani College of Engineering,
Kopargaon (Maharashtra State) 423601
Mechanical Engineering

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Metrology of Thread
Prof. N.D.Sadaphal
TE Mechanical
Metrology & Quality Control
1Prof N D Sadaphal
Types of thread
External thread: a thread formed on outside of a work piece is
known as external thread. Example: on bolts or screw etc.
Internal thread: a thread formed on inside of a work piece is
known as internal thread. Example: nut.
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Screw Thread terminology
3Prof N D Sadaphal
Pitch: The distance from a point on a screw thread to a
corresponding point on the next thread measured parallel to the
axis.
Lead The distance moved by a nut or a bolt in axial direction in
one complete revolutions called lead.
Crest: The outer-most part of the thread is called crest.
Flank: It is the Thread surface that connects crest with root.
Root: The inner most part of the thread is called root.
Major Diameter: Diameter at the crest of the thread measured at
right angle to the axis is called as major diameter and is also
known as outside diameter.
Minor diameter: The diameter at the core or root of the thread is
called minor diameter. It is also called as core or root diameter.
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 Effective diameter or Pitch diameter: It is the diameter at the
pitch line.
 Depth of thread: It is the distance between crest and root
measured perpendicular to axis of screw.
 Angle of thread: Included angle between sides of thread
measured in axial plane.
 Helix angle: Angle that the thread makes with plane
perpendicular to thread axis at pitch line.
 Flank angle: It is half the included angle of the thread.
 Addendum: It is the distance between the crest and the pitch
line measured perpendicular to axis of the screw.
 Dedendum: It is the distance between the pitch line & the root
measured perpendicular to axis of the screw. 5Prof N D Sadaphal
Forms of Thread
Metric threadUnified thread
British Association (B.A.) thread
British Standard Whitworth (B.S.W.)
thread
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Buttress threads
Knuckle threads
Acme threads
Square threads
Sellers thread 7Prof N D Sadaphal
Errors in Thread
• Errors in major & minor diameter may cause interference with
mating parts & will lead to rapid wear & weakening of
threads.
• Pitch Error:-
The ratio of linear velocity of tool & angular velocity of
work must be correct & this ratio must be maintained
constant, otherwise pitch error will occur.
These are classified as,
a. Progressive error
b. Periodic error
c. Drunken error
d. Irregular error 8Prof N D Sadaphal

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1) Progressive error:
If the pitch of the thread is uniform but is longer or
shorter its nominal value then it is called as progressive error.
This error Caused:
•Incorrect ratio of linear velocity of tool &
angular velocity of work.
•Pitch error in lead screw of lathe machine.
•Fault in the saddle guide ways of lathe.
2. Periodic error
These error repeats itself at regular intervals along the thread.
If successive portion of thread is short or long than nominal value.
This error Caused:
•Incorrect ratio of linear velocity of tool
& angular velocity of work.
•Teeth error in thread.
•Lead screw error.Sinusoidal form
9Prof N D Sadaphal
3) Drunken error:
Drunken errors are repeated once per turn of the thread. In Drunken
thread the pitch measured parallel to the thread axis. If the thread is not
cut to the true helix the drunken thread error will form.
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Prof N D Sadaphal

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4) Irregular errors (Erratic error)
• It is vary in irregular manner along the length of
the thread.
• Error like variation in major & minor dia. at every
thread.
Irregular error causes:
1. Machine fault.
2. Non-uniformity in the material.
3. Cutting action is not correct.
4. Machining disturbances
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MEASUREMENT OF VARIOUS
ELEMENTS OF THREAD
1) Major diameter
2) Minor diameter
3) Effective or Pitch diameter
4) Pitch
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Ordinary Micrometer
•Micrometer is first adjusted on a standard (setting) cylinder having
approximately the same diameter as that of major dia. of thread & reading
R1 is taken.
•Then micrometer is set on the major dia. of the thread & reading R2 is
taken.
13Prof N D Sadaphal
Major diameter of screw thread
= S±(R1-R2)
S= dia. of standard cylinder
R1=micrometer reading over setting cylinder
R2=micrometer reading over screw thread
Prof N D Sadaphal 14

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Measurement by Bench micrometer:
Clam p
Fiducial
Indicator
M easuring
Anvils Holding centres
M icrom eter head
Supports
BENCH M ICROM ETER
In order to ensure that all measurement are made at the
same pressure, a fiducial indicator is used . It ensures constant
pressure for all measurement. 15Prof N D Sadaphal
Bench micrometer
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•Initially a calibrated setting (standard) cylinder having nearly same diameter
as that major diameter of the thread to be measured is used as setting
standard.
•The setting cylinder is held between anvils & reading is taken.
•The cylinder is then replaced by threaded workpiece & again micrometer
reading is noted.
•Measurement is taken at two or three positions along the thread to detect
any taper & Ovality.
Major dia. of screw
thread=
D=Dia. of setting cylinder.
R1=reading of micrometer on setting cylinder.
R2=reading of micrometer on screw thread.
Measurement of Major Diameter
17Prof N D Sadaphal
Measurement of Minor Diameter
•The threaded work piece is mounted between the centers of the instrument
and the V pieces are placed on each side of the work piece and then the
reading is noted.
•After taking this reading the work piece is then replaced by a standard
reference cylindrical setting gauge.
Two V-piece method
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Prof N D Sadaphal
Mainor diameter of screw thread
= D±(R2-R1)
D= dia. of standard cylinder
R1=micrometer reading over setting cylinder
R2=micrometer reading over screw thread

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Measurement of Effective(Pitch) Diameter
By Three wire Method
19Prof N D Sadaphal
E M
H
A
B C
D

P
h
E
M
Dia 'd'

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 This method ensures alignment of micrometer faces parallel to
the thread axis.
 Here, three wires of exactly known diameters are used, one on
one side & the two on the other side. The wires may be held in
hand or hung from a stand.
 From fig, M=diameter over the wires, E= effective diameter (to
be found)
d= diameter of wires, h=height of wire center above the pitch
line,
r=radius of wire, H=depth of thread, D=major diameter of the
thread.
21Prof N D Sadaphal
2
cot
22
cosec1dEMOr
2
cot
22
cosec122
2
cot
42
rcosec2EMi.e.
2r2hEMwires,over theDistance
2
cot
42
cosec
2
)(
2
cot
42
H
CDand
2
cot
22
cot
2
cosec
22
cosecABAD,ABDetriangl


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P
P
rEr
P
Pd
CDADhFurther
PP
DEH
d
theFrom








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
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
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


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


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o
Whitworth thread, 55 , of thread 0.64P
E D-0.64P, cosec 2.1657, and cot 1.921
2 2
3.1657 1.605 where Dis the major diameter of the thread.
For Metric threads, Depth of thread 0.6495P
For depth
M D d P
E

 
 
   
  

 0.6495 , 60 ,cos 2,cot 1.732
2 2
3 1.5155
measure the value of Mpractically&then
compare with the theoretical values using formulae derived above.
After finding the correct value o
o
D P ec
M D d P
We can
 
    
   
f M, as d is known, E can be found out.
23Prof N D Sadaphal
P
 


A
P/2
P/4
Pitch line
BEST SIZE OF W IRE
B
 If the size of the wire is such that, it contacts the flanks at the
pitch line, it is called as ‘best size’ of wire which can be
determined by geometry of screw thread.
BEST WIRE SIZE
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 
b
b
InthetriangleOAB, , orsin 90-
2
sec .
2cossin 90-
22
1
But OB radiusofwire ofbest sizewire(D )
2
i.e. D 2 2 sec . AlsosinceABliesonthepi
2
AB AB
Sin BOA
OB OB
AB AB
OB AB
dia
OB AB





 
  
 
   
 
 
 
  
   
P
tchline, AB
4
Pis thepitchofthethread.
2 sec sec
4 2 2 2
b
where
P P
D
 

  
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T= Dia. Under the wire, E= Effective/Pitch dia.
E=T+P (P=Pitch value)
For metric thread P= 0.866p-d (p=pitch of thread, d=dia. of wire used)
For whitworth thread P=0.9605p-1.1657d
T= (R2-R1)+Ds (R2= Reading over Screw thread
R1= Reading over master cylinder
Ds= dia. of master cylinder)

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Pitch measuring machine
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Prof N D Sadaphal
Pitch measuring machine

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GEAR…..
• Power transmission is the movement of energy
from its place of generation to a location where it
is applied to performing useful work
• A gear is a component within a transmission
device that transmits rotational force to another
gear or device
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TYPES OF GEARS
1. According to the position of axes of the
shafts.
a. Parallel
1.Spur Gear
2.Helical Gear
3.Rack and Pinion
b. Intersecting
Bevel Gear
c. Non-intersecting and Non-parallel
worm and worm gears
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SPUR GEAR
• Teeth is parallel to axis
of rotation
• Transmit power from one
shaft to another parallel
shaft
• Used in Electric
screwdriver, clock,
washing machine and
clothes dryer
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External and Internal spur Gear…
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Helical Gear
• The teeth on helical gears are cut at an angle
to the face of the gear
• This gradual engagement makes helical gears
operate much more smoothly and quietly than
spur gears
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Helical Gear…
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Rack and pinion
• Rack and pinion gears
are used to convert
rotation (From the
pinion) into linear
motion (of the rack)
• A perfect example of this
is the steering system
on many cars
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Straight and Spiral Bevel Gears
Used in differential
gear box of bus trucks
etc.
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WORM AND WORM GEAR
Used in Lathe machine
for movement of saddle
along axis of work-piece
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NOMENCLATURE OF SPUR GEARS
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Pitch circle- It is an imaginary circle which by pure rolling action would
give the same motion as the actual gear.
Pitch circle diameter(D) It is the diameter of the pitch circle. The size of
the gear is usually specified by the pitch circle diameter. It is also known
as pitch diameter.
Addendum-It is the radial distance of a tooth from the pitch circle to the
top of the tooth.
Dedendum- It is the radial distance of a tooth from the pitch circle to the
bottom of the tooth.
Addendum circle-It is the circle drawn through the top of the teeth and is
concentric with the pitch circle.
Dedendum circle-It is the circle drawn through the bottom of the teeth. It
is also called root circle.
Module. It is the ratio of the pitch circle diameter in millimeters to the
number of teeth. It is usually denoted by m. Mathematically,
41Prof N D Sadaphal
Circular pitch. It is the distance measured on the circumference of the
pitch circle from a point of one tooth to the corresponding point on
the next tooth. It is usually denoted by Pc ,Mathematically,
Note : If D1 and D2 are the diameters of the two meshing gears having
the teeth T1 and T2 respectively, then for them to mesh correctly,
Clearance. It is the radial distance from the top of the tooth to the
bottom of the tooth, in a meshing gear. A circle passing through the top
of the meshing gear is known as clearance circle.
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Total depth. It is the radial distance between the addendum and
the dedendum circles of a gear.
Face of tooth. It is the surface of the gear tooth above the pitch
surface.
Flank of tooth. It is the surface of the gear tooth below the pitch
surface.
Top land. It is the surface of the top of the tooth.
Face width. It is the width of the gear tooth measured parallel to
its axis.
43Prof N D Sadaphal
ERRORS in Gear
(i) Adjacent pitch error: Actual pitch—design pitch.
(ii) Cumulative pitch error:
Actual length between corresponding flanks—design length.
(iii) Profile error: Deviation of actual profile from Designed profile
(iv)The tooth thickness error:
Actual tooth thickness measured along the surface—design tooth
thickness.
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Gear tooth Vernier
Measurement of tooth thickness
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The tooth thickness is generally measured at pitch circle
•Since the gear tooth thickness varies from the tip to the base
circle of the tooth, the instrument must be capable of measuring
the tooth thickness at a specified position on the tooth.
•The gear tooth Vernier has two Vernier scales. The vertical
Vernier scale is used to set the depth (d) along the pitch circle
from the top surface of the tooth at which the width (w) has to be
measured. While the horizontal Vernier scale is used to measure
the width (w) of the teeth.
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• Considering one gear tooth, the theoretical
values of w and d can be found out which may
be verified by the instrument.
• As shown in the figure ,
w =chord ADB,
but tooth thickness is specified as an
= arc distance AEB.
Also, the depth d adjusted on the instrument is
slightly greater than the addendum CE“.
width w is therefore called chordal thickness and
d is called the chordal addendum.
W=AB=2AD
But for gear , θ=360/4N,
Where, N= number of teeth.
Pitch circle radius
Chordal thickness Method
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49Prof N D Sadaphal
Constant Chord Method
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51
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Base Tangent Method
Base tangent length = one base circular thickness + number of base pitches
Base tangent length is the distance
between the two parallel planes which
are tangential to the opposing tooth
flanks.
53
Prof N D Sadaphal
David Brown Tangent Comparator

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Base tangent length is,
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Gear Rolling Tester
Parkinson Gear Tester
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Gear Rolling Tester
Prof N D Sadaphal
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Parkinson Gear Tester

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59Prof N D Sadaphal
Working Principle
Construction :-
• A standard gear (master gear) is mounted on a fixed
vertical spindle & gear to be tested on another spindle
mounted on sliding carriage.
• These gears are maintained in mesh by spring pressure.
• Two spindles can be adjustable so that their axial distance
is equal to the designed gear center distance.
• A scale is attached to one carriage & vernier to other, to
measure center distance.
• A recorder is also fitted in form of circular chart.
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• As gears are rotated the movements of sliding carriage are
indicated by a dial indicator, and these variation are measure
of any irregularities in the gear under test.
• When these gears are in close mesh & rotated, any error in
the tooth form, pitch or concentricity of pitch line, will
cause a variation in center distance, and movements of
carriage are indicated by dial indicator.
• A recorder is used to record or trace the irregularities in the
gear under the test.
Working:-
61Prof N D Sadaphal
Limitation of Parkinson Gear Tester
• Generally Maximum 300mm diameter gear &
150 mm smaller diameter gears are also tested.
• The accuracy is upto .
• Errors are not clearly identified for type
profile, pitch, helix angle & tooth thickness.
• Measurements are directly depend upon the
master or reference gear.
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Profile Projector
• A profile projector is also referred to as an
optical comparator, or even known as a
shadowgraph, a profile projector is an optical
instrument utilized for measurement of screw
thread parameter.
• The projector magnifies the profile of the
specimen, and shows this on the built-in
projection on screen.
•The X-Y axis of the screen can be aligned
correctly using a straight edge of the machined
part to analyze or measure by moving work
table of Profile Projector.
Prof N D Sadaphal 63
Tool Maker’s Microscope
•It is an ideal measuring instrument for simplifying inspection and precision
measurement of diameter, forming tools, gauges as well as template
checking of thread and its angles.(it is based on optical system)
•Gear tooth flank profile can be tested by projecting on the screen.
•Projected profile can be compared with standard profile of tooth which can be
seen on projected screen.
STANDARD
SPECIFICATIONS:
Total Magnification :30x
Objective : 2x
Eyepiece: 15x
Working distance :65mm
Field of view : 6mmProf N D Sadaphal 64