1

Screw Thread Metrology

By

Syed Samsul Amin

Supervisor: Dr. Jay Raja

Summer 2004

Department of Mechanical Engineering and Engineering Science

The University of North Carolina at Charlotte

9201 University City Blvd. Charlotte, NC 28223-0001 USA

2

Title: Screw Thread Metrology

Contents:

1. Introduction

2. Classification of Threads

3. Profile of a screw thread

4. Elements of a Vee-form thread

I. Major Diameter

II. Minor Diameter

III. Form (Flank Angles)

IV. Pitch

V. Simple Effective Diameter / Pitch Diameter

VI. Virtual Effective Diameter

5. Pitch Errors in Screw Threads

I. Progressive Pitch Error

II. Periodic Pitch Error

III. Thread Drunkenness

6. Measurement of the Various Elements of Thread by Indicating Thread Gages

7. Measurement of the Various Elements of Thread by Individual Processes

I. Measurement of Major Diameter (External/Internal Threads)

II. Measurement of Minor Diameter (External/Internal Threads)

III. Measurement of Thread Form

a) Effect of Flank Angle Errors

IV. Measurement of Pitch Errors

a) Effects of Pitch Errors (Progressive / Periodic)

V. Measurement of Simple Effective Diameter

8. Conclusion

9. Reference

10. Appendix

3

1. Introduction Screw threads are composite design elements which in distinction to a cylindrical shaft or hole,

for example, are defined by specific forms and dimensional parameters, several of these

parameters are considered principal, others as complementary. Interchangeable screwed parts,

e.g. bolts and nuts, are produced in bulk quantity, one part by a process in a specializing

workshop; the counterpart, by a different process, often in a different workshop. The parts are

usually inspected independently before acceptance by using gages made to appropriate limits

which ensure that the accepted parts will assemble within the limits for quality of fit. Screw

thread inspection is performed based on the attributes and variables. For the inspection by

attributes, the applied methods and instruments are designed to determine whether the inspected

thread is within specific size limits which are defined to assure a particular function, such as

assembly with a mating part also having acceptable thread dimensions. Inspection by variables

provides more specific information on the actual size of the measured thread element. Depending

upon these factors inspection is performed either by using the indicating thread gages or

individual measuring instruments.

2. Classification of Threads The different thread classes have differing amounts of tolerance and allowance (Unified Standard

Series). Classes 1A, 2A, 3A apply to external threads; Classes 1B, 2B, 3B apply to internal

threads.

3. The Profile of a Screw Thread When viewed in the axial cross section of the threaded part, is most commonly a symmetrical V

shape, although screw threads other cross sectional shapes and also some with nonsymmetrical

profiles are used for particular purposes. In majority of screw thread types the symmetrical Vee

shape of both the groove and the ridge have a 60º included angle. The basic shape would result in

a shape crest on the top of the ridge and a sharp root at the bottom of the groove. Such thread

forms, however, are seldom specified and for manufacturing reasons due to tool wear, are never

produced perfectly. For replacing the uncertain effect of tool wear with more consistently

1

Fig-1 Classification of threads 1

4

producible specifications and also for such functional reasons as increased strength of the

threaded part and interference free assembly with the mating component, the specification of

most screw thread types define the thread form as a Vee with truncated crest and root.

Standard Screw Threads: (American National Standard Unified Screw Thread)

Fig-2 Screw thread terms relating to external thread

2 The basic form is shown in Fig-1. The drawings indicate the location of an important reference

line in the design of screw threads, that of the pitch line. This line is the boundary of an imaginary

cylinder, coaxial with the screw thread; on the surface of that cylinder the widths of the grooves

and of the ridges are theoretically equal. This conceptual line is an important reference element of

screw thread measurement because it represents the location where the pitch and the pitch

diameter are measured.

4. Elements of a V form Thread A V-form thread is mainly composed basically of the following elements:

I. Major Diameter is that of an imaginary cylinder (termed the major cylinder) which just

embraces the crests of an external thread or the roots of an internal thread.

II. Minor Diameter is that of an imaginary cylinder (termed the minor cylinder) which just

embraces the roots of an external thread or the crests of an internal thread.

III. Thread Form is the shape of one complete profile of the thread, between corresponding

points at the roots of adjacent grooves in an axial plane section. Included angle is the angle

between the flanks of the thread, measured in an axial plane section. Flank angles are the

angles between the individual flanks and the perpendicular to the axis of the thread,

measured in an axial plane section.

IV. Pitch is the distance, measured parallel to the axis, between corresponding points on

adjacent thread forms in the same axial plane and on the same side of the axis. Pitch is also

used to describe advance of the helix parallel to the axis with full or partial rotation of the

thread. Axis of a parallel thread is the axis of its pitch cylinder. The lead of the thread

designates the distance by which one of the two mating parts is moving axially when

rotated by a full turn while the other part is

stationary. The pitch and lead are identical in a

single start thread. The lead is twice the pitch

in a double start thread.

V. Simple Pitch (Effective) Diameter is that of an

imaginary cylinder (termed the pitch cylinder) Fig-3 Simple Pitch Diameter

3

5

which intersects the surface of the thread where the widths of the ridge and the groove are

each equal to half a pitch.

VI. Virtual Effective Diameter of a parallel thread is the simple pitch diameter of an imaginary

thread of perfect pitch and flank angles, cleared at the crests and roots but having the full

depth of straight flanks, which would just assemble with the actual thread over the

prescribed length of engagement. Thus the virtual effective diameter of a thread is the

simple effective diameter modified by corrections due to pitch errors and flank angle errors

and hence is the most important single dimension of a screw thread gauge.

5. Pitch Errors in Screw Threads If a screw thread is generated by a single point cutting tool, it‟s pitch depends on a) the ratio of

the linear velocity of the tool and angular velocity of the work being correct and b) this ratio

being constant. If these conditions are not satisfied then pitch errors will occur, the type of the

error being determined by which of the above conditions is not satisfied.

1) Progressive error of pitch is a gradual, but not necessarily uniform, deviation of the pitch of

successive threads from the nominal pitch. This error occurs when the tool work velocity ratio is

constant but incorrect. It may be caused by an incorrect gear train or an approximate gear train

between work and tool lead screw as when producing a metric thread with an inch pitch lead

screw when no translatory gear is available. If the pitch error per thread is δp then at any position

along the thread the cumulative pitch error is nδp where n is the number of threads considered.

2) Periodic error of pitch is a cyclical pattern of departures from nominal pitch which is repeated

regularly along the screw. This type of error occurs when the tool work velocity is not constant. It

may be caused by pitch errors in the gears connecting the work and lead screw or by an axial

movement of the lead screw due to the worn thrust faces. Such a movement would be

superimposed on the normal tool motion to be reproduced on the work. It will be appreciated that

errors due to these causes will be cyclic, i.e. the pitch will increase to a maximum, reduce through

normal to a minimum and so on. Maximum cumulative pitch error will be the total error between

the greatest positive and negative peaks within the length of the thread engaged in an approximate

sinusoidal graph.

3) Thread Drunkenness is a periodic variation of pitch where the cycle is of one pitch length. A

drunken thread is a particular case of a periodic pitch error recurring at intervals of one pitch.

This means that the pitch measured parallel to the thread axis will always be correct and all that is

in fact happening is that the thread is not cut to a true helix. A development of the thread helix

will be a curve and not a straight line. Such errors are extremely difficult to determine and except

on large threads will not have any great effects.

(c)

Fig-4(a) Progressive Pitch Error, (b) Periodic Pitch Error,4 (c) Thread Drunkenness

5

6

6. Measurement of Various Elements of Thread by Indicating Thread Gages According to the ASME classification, the three different thread gaging systems are,

“System 21- provides for interchangeable assembly with functional size control at the

maximum material limits within the length of standard gaging elements. These gages are

primarily go / no-go devices.”

“System 22- provides the functional size control of the minimum materials size limits

over the length of the full thread in addition to the control of maximum materials limit as

system 21”.This system confines the cumulative form variations of thread characteristics

such as lead, flank angle, taper and roundness within the maximum and minimum

material limits. But there is no specific control of their magnitude.

“System 23- provides the functional size control of the maximum material limits and also

control of the minimum material size limits that is control of the pitch diameter as system

22”. Besides, the magnitude of other thread characteristics such as lead, flank angle,

taper and roundness are further controlled with in these limits and hence this system is

used for safety critical applications (i.e. aerospace products). All the three systems

require the inspection of major and minor diameter size as applicable. According to the system-22, separate gage contact profiles are used for pitch diameter and

functional diameter size measurement1. For the pitch diameter indicating gage, Cone and Vee

Rolls are used for the gage contact and for functional diameter indicating gage either Multi Rib

Rolls or Full Form Segments are used for the gage contact.

The total amount of thread element differential is considered the size of the thread, with all the

variations in lead, flank angle, taper and out of round, minus the pitch diameter. This differential

is determined by first observing the largest functional diameter size on O.D. threads with respect

to taper and roundness simply by rotating the part and measuring along the thread length. Then

the smallest pitch diameter size on O.D. threads are observed and lastly determining the

difference. The inspection process further refines the total amount of thread element variation so

that the amount of variation for each individual element becomes known and hence termed as

singe thread element variation differential (as shown in the appendix-1).

7. Measurement of Various Elements of Thread by Individual Processes The methods discussed here are from the point of view of measurement of gauges, but they can

obviously be applied to precise work, threading tools, taps and hobs etc.

Fig-5 Pitch contact profile for pitch and functional diameter size measurement

7

I. Measurement of Major Diameter

It is most commonly measured by means of a bench micrometer. This instrument was designed

by N.P.L. to estimate some deficiencies inherent in the normal hand micrometer i.e. variations in

measuring pressure, pitch errors in micrometer threads etc. It uses constant measuring pressure

and with this machine the error due to pitch error in the micrometer thread is avoided. This is

done by using a fiducial indicator in place of a fixed anvil. In this machine there is no provision

for mounting the work piece between the centers and it is to be held in hand. This is so because

generally the centers of the work piece are not true with its diameter. This machine is used as a

comparator in order to avoid any pitch error of micrometers, zero error setting etc. A calibrated

setting cylinder is used as the setting standard.

The procedure consists of simply noting the reading obtained on the setting cylinder and that

obtained on the thread. The difference in these two readings is then the size difference between

the cylinder and the thread at that position. If this difference is added to the diameter of the

setting cylinder, the result is the major diameter of the thread.

If Dc=Calibrated diameter of the setting cylinder

Rc= Micrometer reading on setting cylinder

Rt =Micrometer reading on thread

Then, Major Diameter = Dc+(Rt-Rc)

Fig-6 Bench Micrometer5

In order to determine the amount of taper, the reading should be taken at various positions along

the thread and to detect the ovality, two or three reading must be taken at one place in angular

position. For the internal threads, an indirect approach is followed by making a cast of the thread

by plaster of paris, dental wax or sulphur and then measuring the major diameter of the thread of

the cast.

II. Measurement of Minor Diameter

This is also measured by a comparative

process using small Vee-pieces which make

contact with a root of the thread. The Vee-

pieces used consist of hardened steel prisms

having an angle of about 45°, with the front

edge finished to a radius somewhat smaller

than that of the curvature at the roots of the

finest thread which it is desired to measure.

It is found useful to have such Vees made in

a series of different sizes, to cover the range

of screws usually met. With this method, it is essential that the micrometer should be held at right

angles to the axis of the screw gauge being measured because F×p/2 Nm couple would tend to

rotate the thread through an angle depending on the pitch and an erroneous reading would result

otherwise. This is best secured by using a "floating micrometer" diameter measuring machine in

which the thread is mounted between the centers and a type of bench of micrometer is constrained

to move at right angles to the axis of the centers by a Vee ball slide. The readings are taken on the

Fig-7 Use of prism to measure minor diameter4

8

setting cylinder with the prisms in position and on the thread. If the prisms are considered as

extensions to the micrometer anvils, it is seen that their size is unimportant and

Minor Diameter = Dc+(Rt-Rc)

Minor diameter for internal threads are measured by using taper parallels if the thread diameter is

less than 20 mm and by using rollers otherwise.

III. Measurement of Thread Form

Measurement of the flank angle is the most important form measurement to be made on a screw

thread. It is measured by the optical methods although for large threads contact methods can be

applied. Optically it can be done by projection and measuring the angle of the flank image on the

screen or by using a microscope with a goniometric head.

For the screw thread projection method, a NPL projector is used. It consists of a lamp house

whose optical outlet contains condenser lens to give even illumination. The object to be projected

is mounted on a stage between the condensers and the projection lens which focuses an enlarged

image on the screen. To give the required degree of enlargement, the whole projector may be

moved on rails normal to the screen. The work stage may be moved relative to the projector lens

for focusing purposes. To accommodate screw threads, the work stage has centers and can be

swung out of normal to the optical axis to avoid interference due to helix angle. The thread axis is

made parallel with the light rays by swinging the thread through its helix angle. But this tends to

narrow the thread image as projected on the screen because the flank angle is defined as being

measured on a plane section parallel to the thread axis. This foreshortening effect is eliminated by

swinging the lamp house through the helix angle so that the light rays are not impeded as they

(a) (b) Fig-8 (a) Taper parallels

6 and (b) rollers to measure the minor diameter of IT.

5

Fig-9 (Left) NPL projector(courtesy of the N.P.L crown copyright)6 , (Right) (a) Projection normal to the

thread axis causes interference, (b) Turning thread through helix angle avoids interference but

foreshortens pitch and distorts profile.4

9

pass through the thread to the objective lens. Thus the measurement is actually carried out using a

shadow protractor mounted on a ledge on the screen.

The microscopic flank angle measurement method consists of a clear glass screen in the focal

plane of the objective lens carrying datum lines which can be rotated through 360º, the angle of

rotation being measured direct to 1' and by estimation to fraction of a minute. The thread gage is

mounted on centers, which is illuminated from below. The microscope is mounted above the

thread in such a way that it can be swiveled to be in line with the thread helix and avoid

interference of the image as shown in the Fig-8.

The centers are mounted on slideways which enable them to be moved through coordinate

dimensions on a rotary table. In operation the microscope is first focused with its axis vertical, on

a focusing bar set so that it is focused on a plane through the line of the centers i.e. the axis of the

thread to be measured. The thread is then set up in place of the focusing bar and the microscope

swung through the helix angle of the thread to avoid interference. The datum lines in the

microscope head are set to zero and the table rotated until the crests of the thread image coincide

with the horizontal datum. The table is then locked and the datum lines in the microscope

eyepiece rotated until they coincide with the thread flanks. The flank angles are then read off the

eyepiece scale or viewed on a screen.

Effect of Flank Angle Error:

The effect of the flank angle of an otherwise perfect thread is to foul the mating thread above the

pitch line if the error is positive and below the pitch line if the error is negative considering a Vee

thread having flat crests and roots. In either case the effective diameter of the thread must be

increased for an external thread of fouling is to be avoided, the diametral increase being δEd.

Fig-10 (Top left) With thread axis and screen parallel interference is avoided by turning light rays

through helix angle; (right) Microscopic measurement of flank angle.4

10

Fig-11 (left) Nut of a perfect form mating with a screw having a flank angle error δθ on one flank

only;(right) Enlarged view of fouling with a screw.4

According to the Fig-11,

If δθ is small and in radians, then

Again,

where, θ= nominal flank angle

δθ=flank angle error

h=depth of thread considering the straight portion of the flank only.

Making a similar correction for the opposite flank, the net increase in the effective diameter,

where δθ1 and δθ2 are the worst flank angle errors on the right hand and left hand flanks in

radians. (See appendix-2)

IV. Measurement of Pitch Error

Pitch errors can be determined by pitch measuring machines i.e. Pitter, Matrix etc. Basically all

the pitch measuring machine operates on the same principal. The screw under measurement is

essentially held stationary between centers in the Pitter machine while it is progressively moved

AC

GD

AD

GDsin

GDED sin

ED

GD

sin

ACEDACGD

cosAC

AD

cos

ABAC

2

hAB

2sinsincos2

hhED

)(2sin

21

h

Ed

Fig-12 (Left) Fiducial Indicator used on pitch measuring machine 4 ;(right) Matrix Pitch

measuring machine 5.

11

forward with the help of a micrometer in the Matrix machine. The stylus is allowed to traverse

along the thread axis with the help of a micrometer in the Pitter machine. Both these two motions

causes a relative motion of the indicator in relation to the work piece and hence disruption of the

null condition. A round nosed stylus engages the thread approximately at the pitch line and

operates a simple type of fiducial indicator. While the thread is traveling axially relative to the

axis, the micrometer readings are noted each time the indicator needle comes up to its fludicial

mark. The stylus is mounted in a block supported by a thin metal strip and a strut which together

gives a parallel type motion. If the side pressures on the stylus, P and P1 are unequal the strip

twists and the block pivots about the strut. The forked arm causes the crank to rotate and hence

the pointer deflects from the fludicial mark. Thus the pointer will only be against this mark when

P= P1. If thread to thread pitches are required then each micrometer reading is subtracted from the

next reading. The cumulative pitch error is determined by simply noting the micrometer readings

and subtracting them from the expected reading. For the internal threads an adaptor is used to

measure the pitch error in a standard machine (appendix-3).

Effects of Pitch Error

Whether the pitch error is positive or negative, a thread with a pitch error will only enter a nut of

perfect form and pitch if the nut is made oversize. Consider a thread having a cumulative pitch

error of δp over a number of threads. Hence the length is np+ δp. Hence this screw will mate with

a nut of perfect form and pitch if engaged. If δp is the cumulative pitch error over the length of

the engagement and δEd is the equivalent increase in the effective diameter, it can be seen that,

Also it is evident that the pitch error is almost doubled when the equivalent increase in effective

diameter is calculated.

V. Measurement of Simple Effective Diameter

The simple effective diameter can be measured by the one wire, two wire or three wire or rod

method. In the one wire method which is carried out in a bench micrometer, one wire is placed

between two threads at one side instead of the prism and on the other side the anvil of the

measuring micrometer contacts the crests. The wire size is chosen so that they pitch

approximately at the effective diameter and hence such cylinders are called „Best size‟ wires.

First a reading is taken with the cylinders, over a setting cylinder. A reading is then taken with the

cylinders engaged in the thread. The difference in the readings is the difference between the

diameter of the setting cylinder and the dimension T under the wires when engaged with the

thread.

cotpEd

Fig-13 Screw having cumulative pitch error δp in mesh with a nut of perfect form and pitch 4.

12

From the Fig-14, Ed=T+2x

In the ∆ABC , AB= BC cotθ

But, BC=¼ pitch=¼ P

Therefore, AB= ¼ P cotθ

In the ∆ADE ,

Now, x =AB-AF and AF =AE – EF =AE - d/2

Therefore,

where,

P= Nominal Pitch

D=Wire Diameter

θ= Nominal Flank Angle or semi angle of thread

For the two wire method, two wires or rods of identical diameter are placed between the flanks of

the thread and the effective diameter is determined by measuring the distance over the outside of

these wires. The effective diameter,

E=T+P

Where, T=dimension under the wires = M-2d

M= dimension over the wires,

D=diameter of each wire

In the case of three wire method, 2 wires on one side help in aligning the micrometer square to

the thread while the third placed on the other side permits taking of readings. The wires are

placed in the threads and a micrometer is used to measure over the top of the wires. Different

thread types and thread sizes require different size wires. The Approximate Three Wire Formula

"Simplified Version" should read as follows:

M = E - 0.86603P + 3W

Where, M = the measurement over the wires

E = the pitch diameter

P = the pitch or (1 divided by the number of threads per inch)

W= the wire size

The wire methods require the rake correction and compression correction in the measurement of

the effective diameter.

Conclusion: This document describes the processes and instruments used in measuring different parameters of

a screw thread. Measurement of thread on CMM is described vividly in the Appendix-4. Surface

ecd

ecDEAE cos2

cos

)1(cos2

ecd

AF

)1(cos2

cot4

ecdP

x Fig-14 Calculation of simple effective diameter.4

Fig-15 (Left) Two wire method 5; (right) three wire method

7.

13

roughness and roundness measuring instruments are described in reference 12 with the

corresponding procedure.

Figure Reference:

1. http://www.starrett.com/pages/77_advanced_thread.cfm

2. http://www.tpub.com/content/draftsman/14040/css/14040_52.htm

3. www.qualitymag.com/CDA/

4. „The measurements of screw threads,‟ Metrology for Engineers, pg 156-173

5. R. K Jain ,„Engineering Metrology‟, 1990, pg 879-920

6. H. Kunzaman, J. Lerch, F. Waldele, „Measurement of Threads on CCCMM,‟ 1981

7. History of Thread measuring wires and elastic deformation at NBS.

Additional Reference:

8. Indicating Gages , an independent study by Sudhakar, UNCC

9. Metrology of Screw Threads , an independent study by Murugesan Venkatapathi,

UNCC

10. Thread Gaging Debate, QUALITY, May 1997,pg 28-34

11. Websites of Johnson Gage, Roton, efunda.

12. Quality Control and Assembly, TMEH,Volume-4, Wick Veilleux, Fourth Edition, pg

4.54- 4.55

14

Appendix-1

15

16

Appendix-2

17

Appendix-3

Thread Specification

UNC Unified National Coarse

UNF Unified National Fine

UNS Unified National Special

Unified coarse and unified fine refer to the number of threads per inch on fasteners. A

specific diameter of bolt or nut will have a specific number of threads per inch of length.

For example, a ¼-inch diameter unified national coarse bolt will have 20 threads per inch

of length. This bolt will be identified by the following specifications:

¼-20-UNC

The ¼ is the major diameter and 20 refers to the number of threads per inch. A ¼ inch

diameter bolt with a fine thread would be identified by the following specifications:

¼-28-UNF

The ¼ is the major diameter and 28 refers to the number of threads per inch.

The Unified Special Series is identified the same way. A ¼ inch diameter UNS bolt may

have 24 or 27 threads per inch.

Fig (a) Illustrating that for best results the stylus point should make contact on or near the effective

diameter in a Pitter screw measuring machine, (b) Set up for measuring the pitch for an internal thread.

(a) (b)