Unit III

Introduction

Angular measurement is an important element in measuring. It involves the measurement

of angles of tapers and similar surfaces. In angular measurements, two types of angle measuring

devices are used. They are

Angle gauges corresponding to slip gauges.

Divided scale corresponding to line standard.

The most common instrument is sine bar. The main difference between linear and angular

measurement is the no absolute standard is required for angular measurement.

Sine bar

Sine bar are always used along with slip gauges as a device for the measurement of angles

very precisely. They are used to:

Measure angle very accurately.

Locate the work piece to given angle with very high precision.

Sine bars are made from high carbon, high chromium, and corrosion resistant steel.

These materials are highly hardened, ground and stabilised.

In sine bar, two cylinders of equal diameter are attached at the ends with its axes mutually

parallel to each other.

Two cylinders are also equal distance from the upper surface of the sine bar.

Mostly the distance between the axes of two cylinders is 100mm, 200mm or 300mm.

The working surfaces of the rollers are finished to 0.2µm Ra value.

The cylindrical holes are provided to reduce the weight of the sine bar and alsoto facilitate

handling.

Working principle of sine bar

The working of sine bar is based on trigonometry principle. To measure the angle of the

specimen, one roller of the sine bar is placed on the surface plate and another one roller is placed

over the surface of slip gauges. Now, ‘h’ be the height of the slip gauges and ‘L’ be the distance

between roller canters, then the angle is calculated as

sinh

L

1sinh

L

1

Principle of Sine bar

Accuracy requirements of sine bar:

The accuracy of sine bar depends on the following constructional features:

The rollers must have equal diameter and equal cylinder.

The rollers should be placed parallel to each other and also to upper face.

The accurate center to center of rollers must be known.

The top surface of the bar must be flat with high degree of accuracy.

Use of sine bar

Sine bar are used for

I. Locating any work to a given angle.

II. To check unknown angle.

III. Measurement of unknown angles for heavier components

IV. Measurement of unknown angles of heavier components with more accurate

readings.

I. Locating any work to a given angle

To set at a given angle, first ‘h’ of the slip gauge is calculated by the formula

sin =h/L.

After calculating the height ‘h’ ,the required height ‘h’ is made by suitable slip gauge

combinations.

After this, one of the roller is placed on the surface plate and other on is placed on the top

of the slip gauges combination.

II. To check unknown angle :

2

Before checking the unknown angle of the specimen, the angle of the given specimen is

found approximately by bevel protector.

Then the sine bar is set at angle of and clamped on the angle plate.

Now the work piece is placed on the sine bar and the dial indicator is set at one end of the

work and it’s moved across the work piece and deviations are noted.

Slip gauge is adjusted so that the dial indicator reads zero throughout the work piece.

III. Measurement of unknown angles for heavier components :

For heavy components, the sine bar is mounted on the work piece at inverted position (i.e.

the rollers are placed in such a way that the rollers should face upward).

The heights of the rollers are measured on the vernier height gauge.

The dial test indicator is mounted on the vernier height gauges to ensure constant

measuring pressure.

Now, the sine angle is calculated as the difference between two vernier height gauge

readings divided by center distance of sine bar rollers.

1 2sinh h

L

Limitations of sine bars

Sine bars are fairly reliable for angles less than 15 0.

It is physically difficult to hold in position.

Slight errors in sine bar cause larger angular error.

The size of parts to be inspected by sine bar is limited.

Sources of error in sine bar

The different sources of errors are listed below:

Error in distance between roller centers.

Error in slip gauge combination. 3

Error in equality of size of rollers and cylindricity.

Error in flatness of the upper surface of sine bar

Error in parallelism of roller axes with each other.

Bevel protractors

Bevel protractors are nothing but angular measuring instruments.

Types of bevel protractors:

The different types of bevel protractors used are:

1) Vernier bevel protractor

2) Universal protractor

3) Optical protractor

Vernier bevel protractor:

Working principle:

A vernier bevel protractor is attached with acute angle attachment.

The body is designed its back is flat and no projections beyond its back. The base plate is

attached to the main body and an adjustable blade is attached to the circular plate

containing vernier scale.

The main scale is graduated in degrees from 0° to 90° in both the directions. The

adjustable can be made to rotate freely about the center of the main scale and it can be

locked at any position.

For measuring acute angle, a special attachment is provided. The base plate is made fiat

for measuring angles and can be moved throughout its length. The ends of the blade are

beveled at angles of 45°and 60°.

The main scale is graduated as one main scale division is 1° and vernier is graduated into

12 divisions on each side of zero. Therefore the least count is calculated as

Least count = One main scale division/No. of on vernier scale

=10/12

4

=1/12*60

=5 minutes

Thus, the bevel protractor can be used to measure to an accuracy of 5 minutes.

Optical bevel Protractor

Stock

The working edge of the stock is about 90 mm in length and 7 mm thick. It is very

essential that the working edge of the stock be perfectly straight.

Blade

It can be moved along the turret throughout its length and can also be reversed. It is

about 150 or 300 mm long, 3 mm wide and 2 mm thick and ends bevelled at angles of 45° and

60° within the accuracy of 2 minutes of arc. It can be clamped in any position.

The values are obtained by means of an optical magnifying system. This optical

magnifying system is attached with the bevel protractor itself separate arrangement is provided

for adjusting the focus of the system for the normal variation of eyesight. The main and vernier

scale are arranged always in focus of the optical system.

Applications of bevel protractor

The bevel protractor can be used in the following applications.

1. For checking a ‘V’ block:

Checking ‘V’ block

2. For checking acute angle

5

Measuring acute angle

Auto- collimator:

An autocollimator is an optical instrument for non-contact measurement of angles.

It’s used for the measurement of small angular differences, changes or deflection, plane

surface inspection etc.

For small angular measurements, autocollimator provides a very sensitive and accurate

approach.

An auto-collimator is essentially an infinity telescope and a collimator combined into one

instrument.

Basic principle:

Principle of Auto-collimator

If a light source is placed in the flows of a collimating lens, it is projected as a parallel

beam of light.

If this beam is made to strike a plane reflector, kept normal to the optical axis, it is

reflected back along its own path and is brought to the same focus.

If the reflector is tilted through a small angle ‘’. Then the parallel beam is deflected twice

the angle and is brought to focus in the same plane as the light source.

The distance of focus from the object is given by

Note:

The position of the final image does not depend upon the distance of reflector from the

lens. i.e. distance x is independent of the position of reflection from the lens.

But if the reflector is moved too much back then reflected rays would completely miss the

lens and no image will be formed.

Working of auto-collimator:

There are three main parts in auto-collimator. 6

1. Micrometer microscope.

2. Lighting unit and

3. Collimating lens.

Fig. Shows a line diagram of a modern auto-collimator. A target graticule is positioned

perpendicular to the optical axis.

When the target graticule is illuminated by a lamp, rays of light diverging from the

intersection point reach the objective lens via beam splitter.

From objective, the light rays are projected as a parallel rays to the reflector.

A flat reflector placed in front of the objective and exactly normal to the optical axis

reflects the parallel rays of light back along their original paths.

They are then brought to the target graticule and exactly coincide with its intersection.

A portion of the returned light passes through the beam splitter and is visible through the

eyepiece.

If the reflector is tilted through a small angle (), the reflected beam will be changed its

path at twice the angle.

It can also be brought to target graticule but linearly displaced from the actual target by

the amount 2 *f.

Linear displacement of the graticule image in the plane tilted angle of eyepiece is directly

proportional to the reflector. This can be measured by optical micrometer.

The photoelectric auto- collimator is particularly suitable for calibrating polygons, for

checking angular indexing and for checking small linear displacements.

Applications of auto-collimator

Auto-collimators are used for

7

Measuring the difference in height of length standards.

Checking the flatness and straightness of surfaces.

Checking squareness of two surfaces.

Precise angular indexing in conjunction with polygons.

Checking alignment or parallelism.

Measurement of small linear dimensions.

For machine tool adjustment testing.

Angle Gauges

Angle gauges is a hardened steel block approximately 75mm long and 1mm wide which

lapped flat working faces lying at a very precise angle to each other. It can be constructed at any

angle from 0 to 360 degree by suitable combination of gauges.

Each angle gauge is marked with ‘V’ which indicates the direction of included angle. To

add the angles, all ‘V’ marks should be in same line and to subtract, ‘V’ marks should be in

opposite direction.

Total angle = 37° 9′ 18″ (Not to scale)

Uses of angle gauges

(i) Direct use of angle gauges to measure the angle in the die insert

(ii) Use of angle gauges with square plate.

CLINOMETER

A Clinometer is a spirit level mounted on a rotator member.

The angle of inclination of the rotary member relative to its base can be measured by a

circular scale.

There are various types of Clinometer.

Vernier Clinometer

Micrometer Clinometer

Dial Clinometer

Optical Clinometer

Vernier Clinometer:

It consists of a spirit level mounted on a rotator member carried in housing.

One face of the housing forms the base of the instrument.

There is a circular scale on the housing.

8

The angle of inclination of the rotary member relative to the base be measured by a

circular scale.

The scale may cover the whole circle or only part of it. Clinometers are generally used to

determine the angle included between two adjacent faces of a work piece.

The base of the instrument is placed on one of the surfaces and rotary member is adjusted

till zero reading of the bubbles is obtained.

The angle of rotation is then noted on the circular scale against an index.

The instrument is then placed on the other surface and the reading is taken in the similar

manner.

Micrometer Clinometer:

In this type spirit level is attached at one end of the barrel of a micrometer. The other end of the

spirit level is hinged on the base. The base is placed on the surface whose inclination is to be

measured.

The micrometer is adjusted till the level is horizontal. This type of clinometer is used for

measuring small angles.

Dial Clinometer:

The dial clinometer is similar in principle to the bevel protractor.

The spirit level is attached to a gear and a dial gauge.

The whole angle can be observed through an opening in the dial on the circular scale on

the gear and fraction of the angle can be read on the dial gauge. 9

Uses of clinometer:

It is used for checking included angles, relief angles as well as angular face on larger

cutting tools and milling cutter inserts.

It also used for setting inclinable tables on jig boring machines and angular work on

grinding machines,etc.

Screw Thread Measurement

Screw threads are used to transmit the power and motion, and also used to fasten two

components with the help of nuts, bolts and studs.

There is a large variety of screw threads varying in their form, by included angle, head

angle, helix angle etc.

The screw threads are mainly classified into

1) External thread

2) Internal thread.

External Thread Internal Thread

Screw thread Terminology

Screw thread: It is a continuous helical groove of specified cross-section produced on the

external or internal surface.

Crest: It is top surface joining the two sides of thread. 10

Flank: Surface between crest and root.

Root: The bottom of the groove between the two flanks of the thread.

Lead: Lead = number starts x pitch

Pitch: The distance measured parallel to the axis from a point on a thread to the corresponding

next point.

Helix angle: The helix is the angle made by the helix of the thread at the pitch line with the axis.

Flank angle: Angle made by the flank of a thread with the perpendicular to the thread axis.

Depth of thread: The distance between the crest and root of the thread.

Included angle: Angle included between the flanks of a thread measured in an axial plane.

Major diameter: Diameter of an imaginary co-axial cylinder which would touch the crests of

external or internal thread.

Minor diameter (Root diameter or Core diameter): Diameter of an imaginary co-axial cylinder

which would touch the roots of an external thread.

Addendum

Radial distance between the major and pitch cylinders For external thread.

Radial distance between the minor and pitch cylinder For internal thread.

Dedendum:

Radial distance between the pitch and minor cylinder for external thread.

Radial distance between the major and pitch cylinders for internal thread.

Measurement of various elements of thread

To find out the accuracy of a screw thread it will be necessary to measure the following:

1) Major diameter.

2) Minor diameter.

3) Effective or Pitch diameter.

4) Pitch

5) Thread angle and form.

1. Measurement of major diameter:

The instruments which are used to find the major diameter are by

Ordinary micrometre

Bench micrometre.

Ordinary micrometre:

The ordinary micrometre is quite suitable for measuring the external major diameter.

It is first adjusted for appropriate cylindrical size (S) having the same diameter

(approximately).This process is known as ‘gauge setting’.

After taking this reading ‘R the micrometre is set on the major diameter of the thread, and

the new reading is ‘R2

Then the major diameter, D =S± (R1 –R2)

11

Where,

S =Size of setting Gauge.

R1= Micrometre reading over setting gauge.

R2=Micrometre Reading Over thread.

Bench micrometre:

For getting the greater accuracy the bench micrometre is used for measuring the major

diameter.

In this process the variation in measuring Pressure, pitch errors are being neglected..

The fiducial indicator is used to ensure all the measurements are made at same pressure.

The instrument has a micrometre head with a vernier scale to read the accuracy of

0.002mm. Calibrated setting cylinder having the same diameter as the major diameter of

the thread to be measured is used as setting standard.

After setting the standard, the setting cylinder is held between the anvils and the reading is

taken.

Then the Minor diameter, D =S± (D2 –D1)

Where,

S =Diameter of setting Gauge.

R1= Micrometre reading on screw thread.

R2=Micrometre Reading on setting cylinder.

Measurement of minor diameter:

The minor diameter is measured by a comparative method by using floating carriage diameter

measuring machine and small V pieces which make contact with the root of the thread.

V piece are made up of hardened steel

These Pieces are made in several sizes, having radii at the edges.

The floating carriage diameter-measuring machine is a bench micrometer mounted on a

carriage.

12

The thread work piece is mounted between the centres of the instrument and the V pieces

are placed on the each of the work piece and then reading is noted.

After taking this reading the work piece is then replaced by standard reference cylindrical

setting gauge

The minor diameter of the thread = D± (R2 –R1)

Where, D=Diameter of cylinder gauge.

R2= Micrometer reading on the thread work piece

R1=Micrometer reading on cylindrical gauge.

Gear Measurements

The most commonly used forms of gear teeth are in volute & cycloid.

It is used to transmit power from one shaft to another shaft.

The various types of commonly used gears are:

Spur gear: it is a cycloid gear whose tooth traces is straight line.

Helical gear: it is a cylindrical gear whose tooth traces is straight helices.

Spiral gear: a gear whose tooth traces is curved line.

Straight bevel gear: a gear whose tooth traces is a straight-line generator of cone. It

is conical in form in operating and intersecting axes usually at angles.

Worm gear pair: the worm and mating worm wheel have their axes non-parallel and

non-intersecting

Gear terminology:

Addendum circle

It is a circle, which passes through the tip of the tooth.

Dedendum circle

It is a circle, which passes through the root of the tooth.

Tooth thickness

It is the thickness of the tooth measured along the pitch circle.

Space width

13

It is the distance between two adjacent teeth measured along the pitch circle.

Circular pitch

It is the distance from a point on one tooth to a similar point on the adjacent

tooth measured along the pitch circle. It is also the ratio of the circumference of the pitch circle to

the number of teeth.

Face width

It is the length of the tooth measured parallel to the axis of the gear.

Addendum

It is the radial height of the tooth between the pitch circle and addendum circle.

Dedendum

It is the radial height of the tooth between the pitch circle and dedendum circle.

Face

It is the working area of the tooth between addendum circle and pitch circle.

Flank

It is the working area of the tooth between pitch circle and dedendum circle.

Module (m)

It is the diameter measured per tooth of the gear. It is always represented in mm .

Diametral pitch (Pd)

It is a reciprocal of module of the number of teeth per mm of diameter.

Pressure angle

It is the angle between the line of contact and the common tangent at the

pitchpoint.

Clearance

It is the difference between the dedendum and addendum.

Backlash

It is the difference between the space width and tooth thickness.

Gear ratio (I)

14

It is the ratio of the gear diameter to the pinion diameter or the ratio of the pinion speed to

the gear speed or ratio of number of teeth on gear to that on pinion.

Measurement of Gear tooth thickness.

The tooth thickness is generally measured at pitch circle and is therefore, the pitch line

thickness of tooth. It may be mentioned that the tooth thickness is defined as the length of an arc,

which is difficult to measure directly. In most of the cases, it is sufficient to measure the chordal

thickness i.e., the chord joining the intersection of the tooth profile with the pitch circle. Also the

difference between chordal tooth thickness and circular tooth thickness is very small for gear of

small pitch.

The thickness measurement is the most important measurement because most of the gears

manufactured may not undergo checking of all other parameters, but thickness measurement is a

must for all gears.

There are various methods of measuring the gear tooth thickness.

Gear tooth vernier calliper (Chordal thickness method),

Constant chord method (gear tooth micrometre),

Base tangent method,

Measurement by dimension over pins.

Gear Tooth Calliper.

The tooth thickness can be very conveniently measured by a gear tooth vernier.

The tooth thickness is generally measured at pitch circle, and the instrument is capable of

measuring the tooth thickness at a specified position on the tooth.

The gear tooth vernier consists of two vernier scales and two perpendicular arms. In two

arms, one arm is used to measure the thickness and other arm is used to measure the depth.

Vernier gear tooth calliper

Horizontal vernier scale reading gives chordal thickness (W) and vertical scale gives the

chordal addendum.

The thickness of a tooth at pitch line and the addendum is measured by an adjustable

tongue, each of which is adjusted independently by adjusting screw on graduated bars. 15

This method is simple and inexpensive. However it needs different setting for a variation

in number of teeth for a given pitch and accuracy is limited by the least count of

instrument.

Since the wear during use is concentrated on the two jaws, the calliper has to be calibrated

at regular intervals to maintain the accuracy of measurement.

Disadvantage of tooth vernier method:

Not closer to 0.05mm

Two vernier readings

Measurement is done by edge of measuring jaw and not by face.

Base tangent method

In this method, the span of a convenient number of teeth is measured with the help of the

tangent comparator. The measurement is done by using micrometre with anvils. There are two

anvils used in this method.

David brown tangent comparator

One is fixed and another one is movable and micrometre on moving anvil has slightly

made either side of the setting. The distance for S no of teeth are calculated and set with the help

of slip gauges. The distance W theoretical and actual is verified for any difference.

PARKINSON GEAR TESTER

Working principle:

The master gear is fixed on vertical spindle and the gear to be tested is fixed on similar

spindle which is mounted on a carriage.

The carriage which can slide both side and these gears are maintained in mesh by spring

pressure.

When the gears are rotated, the movement of sliding carriage is indicated by a dial

indicator and these variations arc is measure of any irregularities in the car under test. Fig.

The variation is recorded in a recorder which is fitted in the form of a waxed circular

chart.

16

In the gears are fitted on the mandrels and are free to rotate without clearance and the left

mandrel move along the table and the right mandrel move along the spring-loaded

carriage.

The two spindles can be adjusted so that the axial distance is equal and a scale is attached

to one side and vernier to the other, this enables center distance to be measured to with in

0.025mm.

If any errors in the tooth form when gears are in close mesh, pitch or concentricity of pitch

line will cause a variation in center distance from this movement of carriage as indicated

to the dial gauge will show the errors in the gear test.

The recorder also fitted in the form of circular or rectangular chart and the errorsare

recorded.

Limitations of Parkinson gear tester:

Accuracy±0.001mm

Maximum gear diameter is 300mm

Errors are not clearly identified:

Measurement dependent upon the master gear.

Low friction in the movement of the floating carriage.

CO-ORDINATE MEASURING MACHINES

Measuring machines are used for measurement of length over the outer surfaces of a

length bar or any other long member.

The member may be either rounded or flat and parallel.

It is more useful and advantageous than vernier calipers, micrometer, screw gauges etc.

The measuring machines are generally universal character and can be used for works of

varied nature.

The co-ordinate measuring machine is used for contact inspection of parts.

When used for computer-integrated manufacturing these machines are controlled by

17

computer numerical control.

Types of Measuring Machines

i. Universal measuring machine.

ii. Co-ordinate measuring machine.

iii. Computer controlled co-ordinate measuring machine.

Constructions of CMM

Co-ordinate measuring machines are very useful for three dimensional measurements.

These machines have movements in X-Y-Z co-ordinate, controlled and measured easily

by using touch probes.

These measurements can be made by positioning the probe by hand, or automatically in

more expensive machines.

Reasonable accuracies are 5 micro in. or 1 micrometer.

The method these machines work on is measurement of the position of the probe using

linear position sensors.

Transducer is provided in tilt directions for giving digital display and senses positive and

negative direction.

Types of CMM

(i) Cantilever type

The cantilever type is very easy to load and unload, but mechanical error takes

place because of sag or deflection in Y-axis.

(ii) Bridge type

Bridge type is more difficult to load but less sensitive to mechanical errors.

(iii) Horizontal boring Mill type

This is best suited for large heavy work pieces.

Types of CMM

18

Working Principle

CMM is used for measuring the distance between two holes. The work piece is clamped

to the worktable and aligned for three measuring slides x, y and z. The measuring head

provides a taper probe tip which is seated in first datum hole and the position of probe digital

read out is set to zero.

The probe is then moved to successive holes, the read out represent the co-ordinate part

print hole location with respect to the datum hole. Automatic recording and data processing

units are provided to carry out complex geometric and statistical analysis. Special co-ordinate

measuring machines are provided both linear and rotary axes.

This can measure various features of parts like cone, cylinder and hemisphere. The prime

advantage of co-ordinate measuring machine is the quicker inspection and accurate

measurements.

Schematic Diagram

Causes of Errors in CMM

The table and probes are in imperfect alignment.

The weight of the work piece may change the geometry of the guide ways and therefore,

the work piece must not exceed maximum weight.

Variation in temperature of CMM, specimen and measuring lab influence the uncertainly

of measurements.

APPLICATIONS

Co-ordinate measuring machines find applications in automobile, machine

tool, electronics, space and many other large companies.

These machines are best suited for the test and inspection of test equipment, gauges

and tools. For aircraft and space vehicles, hundred percent inspections is carried out

by using CMM.

CMM can be used for determining dimensional accuracy of the components.

These are ideal for determination of shape and position, maximum metal condition,

linkage of results etc. which cannot do in conventional machines.

19

Advantages

The inspection rate is increased.

Accuracy is more.

A skill requirement of the operator is reduced.

Reduction in calculating and recording time.

Reduction in set up time.

No need of separate go / no go gauges for each feature.

Reduction of scrap and good part rejection.

Reduction in off line analysis time.

Disadvantages

The lable and probe may not be in perfect alignment.

The probe may have run out.

The probe moving in Z-axis may have some perpendicular errors.

Probe while moving in X and Y direction may not be square to each other.

There may be errors in digital system.

20