UNIT-II LINEAR & ANGULAR MEASUREMENT.pptx

ME5552 - METROLOGY AND
MEASUREMENTS
R.VEERAPANDIAN,
Teaching Fellow,
CEG Campus, Anna University
Chennai-25

UNIT II MEASUREMENT OF LINEAR, ANGULAR DIMENSIONS AND ASSEMBLY AND
TRANSMISSION ELEMENTS
Linear Measuring Instruments – Vernier caliper, Micrometer,
Vernier height gauge, Depth Micrometer, Bore gauge, Telescoping
gauge; Gauge blocks – Use and precautions, Comparators –
Working and advantages; Opto-mechanical measurements using
measuring microscope and Profile projector - Angular measuring
instruments – Bevel protractor, Clinometer, Angle gauges,
Precision level, Sine bar, Autocollimator, Angle dekkor,
Alignment telescope.
Measurement of Screw threads - Single element measurements –
Pitch Diameter, Lead, Pitch. Measurement of Gears – purpose –
Analytical measurement – Runout, Pitch variation, Tooth profile,
Tooth thickness, Lead – Functional checking – Rolling gear test.

Surface plates are flat and
plane surface used as a
horizontal reference space
for dimensional
measurement, it's a base for
inspection, toolmaking,
gauging, spotting, marking,
and layout. They can be made
from granite, metal, cast iron,
or glass

Fig. 4.19, where a calliper is shown transferring the outer
diameter of a job on to a graduated
steel rule, to read the dimension accurately and
conveniently. The outer diameter of a job is to
be measured (Step a). Aligning the ends of the
two legs of the calliper to a feature of the part
being measured, like the one shown in Fig. 4.19,
is accomplished quite easily (Step b) because
the calliper provides for easy flexing of the two
legs and a means of locking them into position
whenever required. Now, simply laying the ends
of the calliper on a steel rule facilitates easy measurement
of the dimension in question (Step
c). Thus, as the definition stated earlier mentions, physical
duplication of the separation of
reference and measured points is accomplished with a high
degree of accuracy.

Callipers are available in various types and sizes. The two major types are the firm joint
calliper and the spring calliper. A firm joint calliper, as the name itself suggests, can hold
the position of two legs opened out to a particular degree unless moved by a certain force.
This is possible because of higher friction developed at the joint between the two legs of the
calliper. They are adjusted closely for size by gentle tapping of a leg. A locknut is needed
to lock the calliper in a particular position. On the other hand, a spring calliper can hold a
particular position due to the spring pressure acting against an adjusting nut. This permits
a very careful control, and no lock is needed. Figure 4.20 illustrates the classification
of callipers. Callipers are manufactured in a large number of sizes. They are designated
not by their measurement ranges, but by the length of their legs,which range from 50 to
500 mm.

The proper use of the inside and outside callipers depends to a
large extent on the skill of the
person taking measurements. Measuring with a calliper consists
of adjusting the opening so that
its reference points duplicate the features
of the job being measured. In other words,
there is no other provision in a calliper that
helps in its alignment than the reference
points. As illustrated in Fig. 4.22, the
greatest accuracy is achieved in case of
callipers when the line of measurement
coincides with a plane perpendicular to the
job. The divider provides the best accuracy
when the measurements are taken from
well-marked lines, as shown in Fig. 4.22.
Many a time measurements need to be
taken between edges, in which case care
must be exercised in ascertaining the
proper way of taking measurements.

Type A
•This is made with only one scale on the front of
the beam for direct reading.
•It has jaws on both sides for external and internal
measurements.
•It is also having a blade for depth measurements.
•The calipers are made of good quality steel and
the measuring faces hardened to 650 HV.
minimum.
Type B
•It is made only one scale on the front of the beam for
direct reading.
•It is provided with jaws on one side for external and
internal measurement.
Type C
•It is made only one scale of the front of the beam for
direct reading.
•It has jaws on both sides for making the
measurements and for marking operations.

Least count = 1 MSD/N = 1 mm/10 = 0.1 mm
Therefore, total reading = 1 + (4 × 0.1) = 1.4 mm

The following guidelines are useful for the proper use of a vernier calliper:
1. Clean the vernier calliper and the job being measured thoroughly. Ensure that there are no burrs attached to the job, which
could have resulted from a previous machining operation.
2. When a calliper’s jaws are fully closed, it should indicate zero. If it does not, it must be recalibrated or repaired.
3. Loosen the clamping screw and slide the movable jaw until the opening between the jaws is slightly more than the feature
to be measured.
4. Place the fixed jaw in contact with the reference point of the feature being measured and align the beam of the calliper
approximately with the line of measurement.
5. Slide the movable jaw closer to the feature and operate the fine adjustment screw to establish a light contact between the
jaws and the job.
6. Tighten the clamp screw on the movable jaw without disturbing the light contact between the calliper and the job.
7. Remove the calliper and note down the reading in a comfortable position, holding the graduations on the scale
perpendicular to the line of sight.
8. Repeat the measurement a couple of times to ensure an accurate measurement.
9. After completing the reading, loosen the clamping screw, open out the jaws, and clean and lubricate them.
10. Always store the calliper in the instrument box provided by the supplier. Avoid keeping the vernier calliper in the open
for long durations, since it may get damaged by other objects or contaminants.
11. Strictly adhere to the schedule of periodic calibration of the vernier calliper.

Dial Calliper
A vernier calliper is useful for accurate linear measurements.
However, it demands basic mathematical skill on the part of the
user. One should be able to do simple calculations involving
MSD, vernier coinciding division, and least count, in order to
compute the measured value of a dimension. In addition,
considerable care should be exercised in identifying the
coinciding vernier division. These problems can be offset by
using a dial calliper (Fig. 4.27).
Electronic Digital Calliper
An electronic digital calliper is a battery-operated
instrument that displays the reading on a liquid
crystal display (LCD) screen. The digital display
eliminates the need for calculations and provides an
easier way of taking readings. Figure 4.28 illustrates
the main parts of an electronic digital calliper.

Vernier Height Gauge
In a vernier height gauge, as illustrated in Fig. 4.30, the graduated scale or bar is held in a vertical position by a
finely ground and lapped base. A precision ground surface plate is mandatory while using a height gauge. The
feature of the job to be measured is held between the base and the measuring jaw. The measuring jaw is mounted
on a slider that moves up and down, but can be held in place by tightening of a nut. A fine adjustment clamp is
provided to ensure very fine movement of the slide in order to make a delicate contact with the job. Unlike in
depth gauge, the main scale in a height gauge is stationary while the slider moves up and down. The vernier scale
mounted on the slider gives readings up to an accuracy of 0.01 mm. Vernier height gauges are available in sizes
ranging from 150 to 500 mm for precision tool room applications. Some models have quick adjustment screw
release on the movable jaw, making it possible to directly move to any point within the approximate range, which
can then be properly set using the fine adjustment mechanism. Vernier height gauges find applications in tool
rooms and inspection departments. Modern variants of height gauges such as optical and electronic height gauges
are also becoming increasingly popular.

Abbe’s principle, which states that ‘maximum accuracy may be obtained only when the standard is in
line with the axis of the part being measured’. Figure 4.31 illustrates the relevance of Abbe’s law for
micrometers and vernier callipers.
In case of a micrometer, the axis of the job being measured is in line with the line of measurement of
the instrument, as illustrated in Fig. 4.31(a). In case of a vernier calliper, for the reading to be accurate,
the beam would have to be perfectly straight and the two jaws perfectly at 90° to it. We can therefore
conclude that the degree to which an instrument conforms to Abbe’s law determines its inherent
accuracy

In this example, the main scale reading is 8.5 mm, which is the division
immediately preceding the position of the thimble on the main scale. As
already pointed out, let us assume the least count of the instrument to be 0.01
mm. The 22nd division on the thimble is coinciding with the reference line of
the main scale. Therefore, the reading is as follows:
8.5 + 22 (0.01) mm = 8.72 mm

LINEAR MEASURING INSTRUMENTS
Micrometers:
A micrometer sometimes known as a micrometer screw gauge, is a device incorporating a calibrated screw widely used for
accurate measurement of components in mechanical engineering and machining as well as most mechanical trades, along
with other metrological instruments such as dial, vernier, and digital calipers.
Types of micrometers:
1. Outside micrometer
2. Inside micrometer
3. Differential screw thread micrometer
4. Depth micrometer
1. Outside micrometer:

A micrometer is composed of:
Frame
The C-shaped body that holds the anvil and barrel in constant relation to each other. It is thick because it needs to minimize
flexion, expansion, and contraction, which would distort the measurement. The frame is heavy and consequently has a high
thermal mass, to prevent substantial heating up by the holding hand/fingers. It is often covered by insulating plastic plates
which further reduce heat transference.
Anvil
The shiny part that the spindle moves toward, and that the sample rests against.
Sleeve / barrel / stock
The stationary round component with the linear scale on it, sometimes with vernier markings. In some instruments the scale
is marked on a tight-fitting but movable cylindrical sleeve fitting over the internal fixed barrel.
Lock nut / lock-ring / thimble lock
The knurled component (or lever) that one can tighten to hold the spindle stationary, such as when momentarily holding a
measurement.
Screw
The heart of the micrometer, as explained under "Operating principles". It is inside the barrel.
Spindle
The shiny cylindrical component that the thimble causes to move toward the anvil.
Thimble
The component that one's thumb turns. Graduated markings
Ratchet stop
Device on end of handle that limits applied pressure by slipping at a calibrated torque.

Slip Gauges:
Slip gauges are often called Johannes gauges also, as Johannes originated them. These are rectangular blocks of steel having a
cross- section of about 30 by 10 mm. these are first hardened to resist wear and carefully stabilized so that they are independent
of any subsequent variation in size or shape. The longer gauges in the set and length bars are hardened only locally at their
measuring ends. After being hardened, blocks are carefully finished on the measuring faces to such a fine degree of finish,
flatness and accuracy that any two such faces when perfectly clean may be 'wrung' together. This is accomplished by pressing
the faces into contact (keeping them perpendicular) and then imparting a small twisting motion whilst maintaining the contact
pressure. The contact pressure is just sufficient in order to hold the two slip gauges in contact and additional intentional
pressure.
As regards grades or classes of slip gauges, these could also be designed in five grades as under:
Grade 2:
This is the workshop grade. Typical uses include setting up machine tools, positioning milling cutters and checking mechanical
width.
Grade 1:
Used for more precise work, such as that carried out in a good-class tool room. Typical uses include setting up sine bars and
sine tables, checking gap gauges and setting dial test indicators to zero.
Grade 0:
This is more commonly known as the Inspection grade, and its use is confined to tool room or machine shop inspection. This
means that it is the Inspection Department only who have access to this grade of slips. In this way it is not possible for these
slip gauges to be damaged or abused by the rough usage to be expected on the shop floor.
Grade 00:
This grade would be kept in the Standard Room and would be kept for work of the highest precision only. A typical example
would be the determination of any errors present in the workshop or Grade 2 slips, occasioned by rough or continual usage.

Calibration grade:
This is a special grade, with the actual sizes of slips stated or calibrated on a special chart supplied with the set. This
chart must be consulted when making up a dimension, and because these slips are not specific or set tolerances, they are
not as expensive as the Grade 00.

COMPARATOR
On the other hand, in certain devices the standards are separated
from the instrument. It compares the unknown length with the
standard. Such measurement is known as comparison
measurement and the instrument, which provides such a
comparison, is called a comparator
Figure 6.1 illustrates the difference between direct and
comparison measurements. As can be seen in the figure, a
calibrated standard directly gives the measured value in case of
direct measurement. On the other hand, 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 deviation
can be read or recorded by means of a display or recording unit,
respectively. Accuracy of direct measurement depends on four
factors: accuracy of the standard, accuracy of scale, least count
of the scale, and accuracy of reading the scale. The last factor is
the human element, which depends on the efficiency with which
the scales are read and the accurate interpretation of the
readings.

CLASSIFICATION OF COMPARATORS
We can classify comparators into mechanical device and electrical device on the basis of
the means used for comparison. In recent times, engineers prefer to classify comparators
as low and high-amplification comparators, which also reflect the sophistication of the
technology that is behind these devices. Accordingly, we can draw the following
classification. With respect to the principle used for amplifying and recording
measurements, comparators are classified as follows:
1. Mechanical comparators
2. Optical comparators
3. Electrical and electronic comparators
4. Pneumatic comparators

Universal Bevel Protractor
The universal bevel protractor with a 5' accuracy is commonly
found in all tool rooms and metrology laboratories. Figure 5.1
illustrates the construction of a universal bevel protractor. It has
a base plate or stock whose surface has a high degree of flatness
and surface finish. The stock 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 swivelled 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. A
stationary vernier scale mounted close to the dial, as shown in
Fig. 5.1, enables measurements to a least count of 5’ or less. An
acute angle attachment is provided for the measurement of acute
angles.

The main scale on the dial is divided into four quadrants, each measuring 90°. Each division on this scale reads 1°. The
degrees are numbered from 0 to 90 on either side of the zeroth division. The vernier scale has 24 divisions, which correspond
to 46 divisions on the main scale. However, the divisions on the vernier scale are numbered from 0 to 60 on either side of the
zeroth division, as shown in Fig. 5.2.
Calculation of Least Count
Value of one main scale division = 1°
24 vernier divisions correspond to 46 main scale divisions. From Fig. 5.2, it is clear that one vernier division equals 1/12th of
23°. Let us assume that the zeroth division on both the main and the vernier scales are lined up to coincide with each other.
Now, as the dial rotates, a vernier division, starting from the fifth minute up to the 60th minute, progressively coincides with
a main scale division until the zeroth division on the vernier scale moves over the main scale by 2°. Therefore, the least count
is the difference between one vernier division and two main scale divisions, which is 1/12° or 5’.
Reading Vernier Scales
Consider the situation shown in Fig. 5.3. The zeroth division of the vernier scale is just past the 10° division on the main
scale. The seventh division, marked as the 35' division, on the lefthand side of the vernier scale coincides with a division on
the main scale. Therefore, the reading in this case is 10°35'.

A bevel protractor is a precision angle-measuring instrument. To ensure an accurate measurement, one should
follow these guidelines:
1. The instrument should be thoroughly cleaned before use. It is not recommended to use compressed
air for cleaning, as it can drive particles into the instrument.
2. It is important to understand that the universal bevel protractor does not essentially measure
the angle on the work part. It measures the angle between its own parts, that is, the angle
between the base plate and the adjustable blade. Therefore, one should ensure proper and
intimate contact between the protractor and the features of the part.
3. An easy method to determine if the blade is in contact with the work part is to place a light
behind it and adjust the blade so that no light leaks between the two.
4. It should always be ensured that the instrument is in a plane parallel to the plane of the angle.
In the absence of this condition, the angle measured will be erroneous.
5. The accuracy of measurement also depends on the surface quality of the work part. Burrs
and excessive surface roughness interfere with the intimate contact between the bevel protractor
and the work part, leading to erroneous measurements.
6. One should be careful to not slide the instrument over hard or abrasive surfaces, and not
over-tighten clamps.
7. Before replacing the instrument in its case, it has to be wiped with a clean and dry cloth, a
thin rust-preventing coating has to be applied, and moving parts need to be lubricated.

Clinometer
A clinometers can be used for much larger angles. It comprises a level mounted on a frame so that the frame may be
turned to any desired angle with respect to a horizontal reference. Clinometers are used to determine straightness and
flatness of surfaces. They are also used for setting inclinable tables on jig boring machines and angular jobs on surface
grinding machines. They provide superior accuracy compared to ordinary spirit levels.
To measure with clinometers, the base is kept on the surface of the
workpiece. The lock nut is loosened, and the dial comprising the circular
scale is gently rotated until the bubble in the spirit level is approximately at
the centre. Now, the lock nut is tightened and the fine adjustment nut is
operated until the bubble is exactly at the centre of the vial scale. The
reading is then viewed through the eyepiece. Most clinometers in a
metrology laboratory provide readings up to an accuracy of 1'. Precision
clinometers can be used if the accuracy requirement is up to 1".
A recent advancement in clinometers is the electronic clinometer. It consists
of a pendulum whose displacement is converted into electrical signals by a
linear voltage differential transformer. This provides the advantage of
electronic amplification. It is powered by an electronic chip that has a
provision for recording and data analysis. Electronic clinometers have a
sensitivity of 1". A major advantage of these clinometers is that the readings
settle down within 1 second in contrast to the mechanical type, which
requires a couple of seconds for the reading to settle down.

ANGLE GAUGES
Angle gauges, which are made of high-grade wear-resistant steel, work on a principle similar to slip gauges. While slip gauges
can be built to give linear dimensions, angle gauges can be built to give the required angle. The gauges come in a standard set
of angle blocks that can be wrung together in a suitable combination to build an angle. C.E. Johansson, who developed slip
gauges, is also credited with the invention of angle gauge blocks.
At the outset, it seems improbable that a set of 10 gauges is sufficient to build so many angles. However, angle blocks have a
special feature that is impossible in slip gauges—the former can be subtracted as well as added. This fact is illustrated in Fig.
5.14. This illustration shows the way in which two gauge blocks can be used in combination to generate two different angles. If
a 5° angle block is used along with a 30° angle block, as shown in Fig. 5.14(a), the resulting angle is 35°. If the 5° angle block
is reversed and combined with the 30° angle block, as shown in Fig. 5.14(b), the resulting angle is 25°. Reversal of an angle
block subtracts itself from the total angle generated by combining other angle blocks. This provides the scope for creating
various combinations of angle gauges in order to generate angles that are spread over a wide range by using a minimum
number of gauges.

The illustrations in Fig. 5.15 show how angle gauges can be
combined to provide the required angles. It may be noted that
each angle gauge is engraved with the symbol ‘<’, which
indicates the direction of the included angle. Obviously, when
the angles of the gauges need to be added up, the symbol < of
all gauges should be in line. On the other hand, whenever an
angle gauge is required to be subtracted from the combination,
the gauge should be wrung such that the symbol < is in the other
direction.
Let us consider an angle 42°35′20'', which is to be built using
the 16-gauge set. Starting from degrees, the angle of 42° can be
built by subtracting a 3° block from a 45° block. The angle of
35' can be obtained by combining a 30' gauge with a 5' gauge. A
20" gauge is readily available. The resulting combination is
shown in Fig. 5.15.

Autocollimator
It is a special form of telescope that is used to measure small angles with a high degree of resolution. It is used for
various applications such as precision alignment, verification of angle standards, and detection of angular movement,
among others. It projects a beam of collimated light onto a reflector, which is deflected by a small angle about the
vertical plane. The light reflected is magnified and focused on to an eyepiece or a photo detector. The deflection between
the beam and the reflected beam is a measure of the angular tilt of the reflector. Figure 5.22 illustrates the working
principle of an autocollimator.
The reticle is an illuminated target with a cross-hair pattern, which is positioned in the focal plane of an objective lens.
A plane mirror perpendicular to the optical axis serves the purpose of reflecting an image of the pattern back on to the
observation point. A viewing system is required to observe the relative position of the image of the cross-wires. This is
done in most of the autocollimators by means of a simple eyepiece. If rotation of the plane reflector by an angle q
results in the displacement of the image by an amount d, then, d = 2fq, where f is the focal length of the objective lens.

5.6.3 Angle Dekkor
An angle dekkor is a small variation of the autocollimator. 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,
as shown in Fig. 5.26, 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, as shown in Fig. 5.26. 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.

The view through the eyepiece, which gives the point of intersection of the two scales, is shown in Fig. 5.27. The
scales usually measure up to an accuracy of 1'. This reading actually indicates changes in angular position of the
reflector in two planes. In other words, the initial reading of the angle dekkor corresponds to the reading on the
two scales before shifting the position of the reflector. After the reflector undergoes an angular tilt, the second
reading is noted down by recording the point of intersection on both scales. The difference in readings on the two
scales indicates the tilt of the reflector in two planes at 90° to each other.
Some of the typical applications are as follows:
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.

UNIT-II LINEAR & ANGULAR MEASUREMENT.pptx

More Related Content

Similar to UNIT-II LINEAR & ANGULAR MEASUREMENT.pptx (20)

Recently uploaded (20)

UNIT-II LINEAR & ANGULAR MEASUREMENT.pptx