7. screw threads

7/21/2019 7. Screw Threads

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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



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.



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.



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.



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.



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.



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.



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.



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.



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.



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.



Pitch Errors in Screw Threads.

Classification:

Progressive Pitch Error.

Periodic Pitch Error.Drunken Thread.



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



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.



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.



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.



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



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 ).



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.



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.



Two Wire Method



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



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



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



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:



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



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



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



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.



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



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



Pitch Measurement



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.

7. screw threads

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