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UNIT III

LINEAR AND ANGULAR MEASUREMENT

Lecture by

Dr. J.Jeevamalar, M.E., Ph.D.

Associate Professor/ Mechanical

E.G.S. Pillay Engineering College, Nagapattinam

1702ME402 – MEASUREMENTS

AND METROLOGY

UNIT III LINEAR AND ANGULAR MEASUREMENTS 6 Hrs

Linear Measurements:

Vernier Caliper

Vernier Height

Depth Gauges

Micrometer and depth micrometer

Slip gauge

Limit gauge and its classification

Comparator

Mechanical

Electrical types

Pneumatic

Angular Measurements:

Sine bar

Bevel protractor

Autocollimator

Angle Decker

3

© Dr. J.Jeevamalar, Mechanical/EGSPEC

LINEAR MEASURING INSTRUMENTS

- Includes the measurement of lengths, diameters, heights and

thickness.

- Comparison with standard dimensions.

• Devices used for measuring the linear measurements are,

(i) Vernier calipers

(ii) Micrometers

(iii) Slip gauge or gauge blacks

(iv) Limit gauges

(v) Comparators

1. VERNIER CALIPER

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5


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One small division on main scale = 1 mm

No. of divisions on Vernier scale = 50

50 Vernier scale divisions = 49 divisions on main scale (or 49

mm)

Each division on Vernier scale = (49/50) mm

Least Count = 1 MSD – 1 VSD

= 1 - (49/50) mm

= (50 - 49)/50

= (1/50) mm

Least Count of Vernier = = 0.02 mm

a. TYPE-A VERNIER CALIPER

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b. TYPE-B VERNIER CALIPER

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c. TYPE-C VERNIER CALIPER

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2. VERNIER HEIGHT GAUGE

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3. VERNIER DEPTH GAUGE

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4. MICROMETER

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TYPES OF MICROMETER

1.Outside Micrometer

2. Inside Micrometer

3.DepthMicrometer

1. OUTSIDE MICROMETER

Pitch of the Barrel = 0.5 mm

Thimble graduation = 50 mm

So LC = 0.01 mm

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2. INSIDE MICROMETER

• Used to measure Inner Diameter

• 4 Parts – Measuring Heads, Extension Rods, Spacing Collars, Handles

• Used to measure cylinder Diameter, rings

• Ranges of IMM 25-150, 150-300, 300-450, 450-600mm

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3. DEPTH MICROMETER

• Used to measure depth of holes, slots

• Can side up & down & perpendicular to axis of hole

• Range of depth MM is 0 – 225 mm

• Length of extension rod equal to range of micrometer

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• Fixed Gauges are used for checking the size, shape

without a scale being used to check dimensions, and

form.

Example of fixed gauges:

1. Slip Gauges

2. Limit Gauges


GAUGE BLOCKS

These are small blocks of alloy steel.

Used in the manufacturing shops as length standards.

Rectangular blocks with thickness representing the dimension

of the block.

The measuring surfaces of the gauge blocks are finished to a

very high degree of finish, flatness and accuracy.

Come in sets with different number of pieces and a typical set

consisting of 88 pieces for metric units.


1. SLIP GAUGE (Gauge Block)

Grade II : Workshop grade for rough

checks.

Grade I : Used for setting up sine bars,

checking gap gauges and setting

dial test indicators to zero.

Grade 0 : Used in tool room and

inspection department.

Grade 00 : Kept in standard room and

used for high precision work such

as checking Grade I and Grade II

slip gauges.


TYPES OF SLIP GAUGE

• Wringing is defined as the property of the measuring faces of slipgauges to adhere to the measuring faces of other slip gauges.

• Wringing is nothing, but removing the atmospheric air betweentwo mating surfaces of any two gauge blocks, so that the blocksstick to each other due to vacuum.

• Due to do this, hold the two blocks edge-to -edge, and gently pushone of the blocks inside so as to make it sit on the other block,completely.


WRINGING OF SLIP GAUGE

2 LIMIT GAUGES


LIMIT GAUGES

• These are also called “GO” and “NO GO” gauges refers to

an inspection tool used to check a workpiece against its

allowed tolerances.

• To check the accuracy of a hole, a cylindrical bar with

highly finished ends of different diameters is used.

• Its name derives from its use: the gauge has two tests; the

check involves the workpiece having to pass one test (Go)

and fail the other (No Go).

• It is an integral part of the quality process that is used in

the manufacturing industry to ensure interchangeability of

parts between processes, or even between different

manufacturers.


TYPES of LIMIT GAUGES

1. Plug gaugesa. Double ended Plug gaugesb. Progressive type of Plug gauges

2. Taper Plug Gaugea. Taper plug gauge - Plainb. Taper plug gauge – tanged

3. Ring Gaugesa. Taper ring gauge - Plainb. Taper ring gauge – tanged

4. Combined Limit Gauges

5. Position Gauges

6. Snap gauges

a. Double ended Snap gauges

b. Progressive type of Snap gauges

c. Adjustable Snap gauges

d. Plate type Double ended Snap gauges

e. Plate type single ended Snap gauges


The ends are hardened and accurately finished

by grinding. One end is the GO end and the

other end is NOGO end.

Usually, the GO end will be equal to the lower

limit size of the hole and the NOGO end will be

equal to the upper limit size of the hole.

If the size of the hole is within the limits, the GO

end should go inside the hole and NOGO end

should not go.

If the GO end and does not go, the hole is under

size and also if NOGO end goes, the hole is

over size.

Hence, the components are rejected in both the

cases.© Dr. J.Jeevamalar, Mechanical/EGSPEC

1. PLUG GAUGES

1. PLUG GAUGES


a. Double ended Plug gauges

b. Progressive type of Plug gauges


2. TAPER PLUG GAUGE

• It is used to check the taper. It is also used to measure the

diameter of the taper at some point.


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a. Taper plug gauge - Plain

b. Taper plug gauge – Tanged


3. RING GAUGES


Ring gauges are mainly used for checking the

diameter of shafts having a central hole.

The hole is accurately finished by grinding and

lapping after taking hardening process.

The periphery of the ring is knurled to give more

grips while handling the gauges.

We have to make two ring gauges separately to

check the shaft such as GO ring gauge and NOGO

ring gauge.

But the hole of GO ring gauge is made to the

upper limit size of the shaft and NOGO for the

lower limit.

While checking the shaft, the GO ring gauge

will pass through the shaft and NOGO will not pass.

To identify the NOGO ring gauges easily, a red

mark or a small groove cut on its periphery.

a. Taper ring gauge - Plain

b. Taper Ring Gauge – Tanged


4. SNAP GAUGES

a. Double ended Snap gauges

• It is used for checking external diameters. Shafts are

mainly checked by the snap gauges.


b. Progressive type of Snap gauges


c. Adjustable Snap gauges


d. Plate type single ended Snap gauges


e. Plate type Double ended Snap gauges


5. COMBINED LIMIT GAUGES

In case of gauging of cylindrical holes, it is

impossible to combine both the 'Go' and 'No Go'

dimensions of plug gauge and thus a single

gauge doing the work of checking both the upper

and lower limits


6. POSITION GAUGES


It is designed for checking the

position of features in relation to

another surface.

Ex: Contour gauges, receiver

gauges, profile gauges etc.

An instrument, which provides the measurement

in terms of comparison, is called a comparator.

A comparator works on relative measurement.

Comparators are generally used for linear

measurements.

A comparator has to be set to a reference value

(usually zero setting) by employing a standard.

Once it is set to this reference value, all

subsequent readings indicate the deviation from

the standard.

The variation in the measured value may be in

terms of change in displacement, pressure, fluid

flow, temperature, and so on.

COMPARATOR

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40


TYPES OF COMPARATOR

1. Mechanicalcomparators

2. Electrical comparators

3. Pneumaticcomparators

a. Free Flow Type/ Velocity Type Pneumaticcomparators

b. Back Pressure Pneumaticcomparators

i. Solex AirGauge

ii. DifferentialComparator

MECHANICAL COMPARATOR

DIAL INDICATOR

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•It is primarily used to compare workpieces against a master.

•It consists of a body with a circular graduated dial, a contact point

connected to a gear train and an indicating hand, which directly

indicates the linear displacement of the contact point.

APPLICATIONS

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2. ELECTRICAL COMPARATORS



Electrical comparators generally depend on a Wheatstone bridge circuit for

measurement.

The plunger is the sensing element, the movement of which displaces an

armature inside a pair of coils. Movement of the armature causes change in

inductance in the two coils, resulting in a net change in inductance.

This change causes imbalance in the bridge circuit, resulting in an output.

Least count of the electrical comparator is 0.001mm

Ex: Linear Variable Differential Transformer (LVDT)

Advantages

1.Very less number of moving parts

2.High magnification

3.Pointer is very light and not sensitive to vibrations

Disadvantages

1.It is more expensive than the mechanical comparator

2.Heating of coils in the measuring unit may cause zero drift and alter thecalibration

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3. PNEUMATIC COMPARATORS (Pneumatic Gauge)

1. FLOW / VELOCITY TYPE

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2. PRESSURE TYPEa. SOLEX AIR GAUGE

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2. PRESSURE TYPEb. DIFFERENTIAL COMPARATOR

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Advantages

1. The operation is very simple and low price

2. Indicating & measuring is done at two different places

3. The gauging members are direct contact with the work

Disadvantages

1.These comparators are very sensitive are temperature and

humidity.

2.For different job, it requires different gauging heads

ADVANTAGES AND DISADVANTAGES OF

PNEUMATIC COMPARATORS

• Angle is defined as the opening between the two lines meet

at a point.

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ANGLE MEASUREMENT - INTRODUCTION

1. Sine Bar

2. Universal Bevel Protractor

3. Auto Collimator

4. Angle Dekkor


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INSTRUMENTS USED FOR ANGULAR MEASUREMENT

• It is a precision measuring instrument and is an excellent example

of combination of linear measurement and angular measurement

when used in conjunction with gauge blocks (slip gauges).

• Sine bar is made of high carbon, high chromium corrosion

resistant steel, suitably hardened, precision ground and stabilized.

• It consists of a bar carrying a suitable pair of rollers set a known

centre distance.

• Relief holes are provided for easy handling of sine bar and for

reducing the weight of the sine bar.


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SINE BAR

• The principle of operation of sine bar is relay upon the application of

trigonometry.

• The sine bar is placed on the surface plate with the slip gauges of the

required length (H) under one roller and opposite to the angle as

shown in figure.

WORKING PRINCIPLE OF SINE BAR

The angle is given by, Taper Angle, Sin = h / L in Degrees

h = Height of the Slip Gauge in mm. L = Length between two rollers in mm


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1. Checking unknown angles of small components:

When an angle of component to be compared is unknown, it is necessarily first

find out the approximate taper angle with the help of bevel protector.

If the angle is θ, then the sine bar is set at an angle θ with the help of slip gauges

and clamped to an angle plate as shown in figure.

A dial indicator is set at a one end of the work and moved to the other end and

the deviation is note down.

Again slip gauges are so adjusted (according to the deviation) such that dial

indicator reads zero as it move from one end to other end of the work piece.

If the deviation is noted down by the dial indicator .


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USE OF SINE BAR

2. For locating any work to a given angle

For this, assume surface plate is perfectly flat, so that its surface is

perfectly horizontal.

One roller of the sine bar is placed on the surface plate and the other is

placed on the slip gauge rack of height H.

Let the sine bar is set to an angle θ. Sine θ = h/L

where L is the distance between the center.

Thus knowing θ, H can be found and any work can be set out at this angle

as the top face of the sine bar is inclined at angle θ to the surface plate.

For better result both rollers must placed on slip gauge of height h1

and h2 respectively.


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3. Checking of unknown angles of heavy component:

When components are heavy and cannot be mounted on the sine bar, the sine bar

is mounted on the component as shown in figure.

The height over the rollers can be measured by a Vernier height gauge using a

dial gauge mounted on the anvil of it.

The difference in the two readings of height gauge divided by the centre distance

of sine bar gives the sine angle of the component to be measured.

ADVANTAGES AND DISADVANTAGES OF SINE BARS

• Advantages of sine bar

1. It is precise and accurate angle measuring device.

2. It is simple in design and construction.

3. It is easily available

• Disadvantages

1. It is not fairly reliable at angles less than 15 but become

increasingly inaccurate as the angle increases. It is

impractical to use sine bar for angle above 45 .

2. It is difficult to handle and position the slip gauges.

3. The sine bar is physically clumsy to hold in position.

4. The application is limited for a fixed center distance

between two rollers.

5. Slight errors of the sine bar cause larger angular errors.


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• Bevel protractors is a type of protractor which is used as an

angular measuring instruments.

• Types of bevel protractors:

1. Vernier Bevel Protractor or Universal Protractor

2. Optical Protractor

2. BEVEL PROTRACTOR


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It has a base plate or stock whose

surface has a high degree of flatness

and surface finish and it is placed on

the workpiece whose angle is to be

measured.

An adjustable blade attached to a

circular dial is made to coincide with

the angular surface.

It can be swiveled to the required

angle and locked into position to

facilitate accurate reading of the

circular scale that is mounted on the

dial.

The main scale on the dial is

graduated in degrees and rotates with

the rotation of the adjustable blade.

1. Vernier or Universal Bevel Protractor


A stationary vernier scale mounted close to the dial, enables measurements to

a least count of 5’ or less.

An acute angle attachment is provided for the measurement of acute angles. 58

LC of Universal Bevel Protractor

• The main scale on the dial is divided into four quadrants, each measuring

90°. Each division on this scale reads 1°.

• The Vernier scale has 12 Divisions each side of the centre zero.

• The 12 divisions are denoted as 60 min on the vernier scale (Like this 15,

30, 45, 60). That means 12 division = 60 minutes.

• One division= 60/12 = 5 minutes


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• The total reading =the main scale reading + the number of

the division at which it exactly coincides with any division

on the main scale × least count of the vernier scale.

• In the above case, The main scale reading = 10°

• Vernier scale reading (the number of the division at which it

exactly coincides with any division on the main scale) = 3rd

division

• Least count of the vernier Bevel protractor = 5 Minutes

• The total reading = 10°+15 minutes = 10°

2. Optical Bevel Protractor

• A recent development of

Vernier bevel protector is

optical bevel protector.

• In this instrument, a circular

glass plate is divided at 10

minutes intervals throughout

the whole 360º are fitted inside

the main body.

• A small microscope is fitted

through which the circular

graduations can be viewed.

• The readings are taken against

a Vernier scale with the help of

a microscope.

• With the help of microscope it

is possible to read about 2

minutes.


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3. AUTOCOLLIMATOR


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Auto-collimator is an optical instrument 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.

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

rejected 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, x = 2.fWhere, f = Focul length of the lens

= Tilted angle of reflecting mirror/plane

WORKING OF AUTOCOLLIMATOR


APPLICATIONS OF AUTOCOLLIMATOR

1) Measuring the difference in height of length standards.

2) Checking the flatness and straightness of surfaces.

3) Checking squareness of two surfaces.

4) Checking alignment or parallelism.

5) Comparative measurement using master angles.

6) For machine tool adjustment testing.


4. ANGLE DEKKOR


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ANGLE DEKKOR


• This is also a type of auto-collimator.

• This instrument is essentially used as a comparator and measures the

change in angular position of the reflector in two planes.

• It has an illuminated scale, which receives light directed through a

prism.

• The light beam carrying the image of the illuminated scale passes

through the collimating lens and falls onto the reflecting surface of the

workpiece.

• After getting reflected from the workpiece, it is refocused by the lens in

field view of the eyepiece.

• While doing so, the image of the illuminated scale would have undergone

a rotation of 90° with respect to the optical axis.

• Now, the light beam will pass through the datum scale fixed across the

path of the light beam.

• When viewed through the eyepiece, the reading on the illuminated scale

measures angular deviations from one axis at 90° to the optical axis, and

the reading on the fixed datum scale measures the deviation about an axis

mutually perpendicular to this.

APPLICATIONS OF ANGLE DEKKOR

1. Measurement of sloping angle of V-blocks

2. Calibration of taper gauges

3. Measurement of angles of conical parts

4. Measurement of angles of work part surfaces, which are

simultaneously inclined in two planes

5. Determination of a precise angular setting for machining

operations, for example, milling a slot at some precise angle to a

previously machined datum surface.


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