Engineering Metrology Linear-and-Angular-measuremen

Introduction to Metrology, Linear and Angular Measurement
Metrology & Measurements

WUMS 110 L Metrology & Measurements

4
Slip Gauge
 Slip gauges were first developed
by Johnson, and sometimes also
called as ‘Johnson Gauge Blocks’.
These are rectangular blocks of high
grade hardened steel.
 It is having a cross-section of about
9 mm x 30 mm for size upto 10 mm
and 9 mm x 35 mm for larger sizes.
These blocks are hardened to resist
wear.
 After hardening they are
carefully finished by high grade
lapping to a high degree of finish,
flatness and accuracy.
 The slip gauge is classified
according to their accuracy:
AA for Master slip gauges
A for reference purpose
B for working slip gauges

5
Indian Standard specifications for slip gauges
1. Reference Grade : Used as Standards by manufacturers.
2. Calibration grade : Used where highest level of accuracy is required in
normal engineering practice.
3. Grade-OO : These are placed in the standard room and used for
highest
precision work as checking other lower grade slip gauges ( Grade I and II )
4. Grade-O : These slip gauges are used for inspection of jobs in quality
control department where high precision is required.
5. Grade-I : These slip gauges are used for general purpose manufacturing
gauges
in applications like tool, gauges and component production.
6. Grade-II : These slip gauges are used for rough setting purposes and
checking of components having wide tolerances. These are also known as
workshop grade.

6
Available Sets of Slip Gauges
1. Normal Set ( M-
45 )
2. Special Set ( M-87 )
3. Set M 112
4. Set E 28

7
Material for Gauge Blocks
 The material used for gauge blocks must have excellent wear resistance, size stability and
ability to take extremely fine surface finish.
 Tool steel, chrome plated steel, stainless steel, tungsten carbide, chrome carbide and Cervit
are some of the materials used for gauges. Of these, tungsten carbide, chrome carbide, and
Cervit are the most interesting cases.
 Depending upon the material used the slip gauges may be heat treated to obtain size
stability and required degree of hardness. The surface is lapped to obtain the desired
smoothness and accuracy.
 The carbide block are very hard and therefore does not scratch easily. The finish of
the gauging surfaces is as good as steel, and the lengths appear to be at least as stable as
steel, perhaps even more stable.
 Tungsten carbide has a very low expansion coefficient and because of the high density the
blocks are heavy.
 Chrome carbide has an intermediate thermal expansion coefficient and is roughly the
same density as steel.
 Carbide blocks have become very popular as master blocks because of their durability
and because in a controlled laboratory environment the thermal expansion difference
between carbide and steel is easily manageable.
 Cervit is a glassy ceramic that was designed to have nearly zero thermal expansion
coefficient. The drawbacks are that the material is softer than steel, making scratches a
danger, and by nature the ceramic is brittle.

8
Manufacture of Slip Gauges
 The following operations are carried out to obtain required qualities in
slip gauges during manufacture.
Step -1: The approximate size of slip gauges is made by preliminary operations.
Step -2: The blocks are hardened and wear resistant by a special heat treatment
process.
Step -3: For stabilization of the whole life of blocks, seasoning process is carried
out.
Step -4: The approximate required dimension is done by a final grinding process.
Step -5: Lapping operation is carried out to get the exact size of slip gauges.
Step -6: Comparison is made with grand master sets.

9
Slip Gauges accessories
 The slip gauges can be used for many purpose without help of any accessories,
however, the application of slip gauges can be increased by providing
accessories to the slip gauges.
The following various accessories are used with slip
gauges:
1. Measuring jaw: It is available in two designs specially made for internal and
external features.
2. Scriber and Centre point: It is mainly formed for marking purpose.
3. Holder and base: Holder is nothing but a holding device used to hold
combination of slip gauges. Base is designed for mounting the holder rigidly
on its top surface. It is made of robust construction and designed such that it
remains stable when used with the longest size holder.

10
Wringing of Slip Gauges
 If two slip gauge blocks are wrung together to each other as shown in Fig.
and considerable pull is required to break the wring.
 This phenomenon of wringing occurs due to molecular adhesion between
a liquid film (not more than 6 to 7 microns thick) and the mating surfaces.
This wringing process is used to build up desired dimensions over a range of
sizes in specific increments.
 The success of the wringing operation depends upon the surface finish
and flatness of the blocks used and absence of dirt, grease, burrs and scratches.
When the slip gauges are correctly wrung together, the error in the total
length is negligible.

11
Applications of Slip Gauges
1.They are used to check the accuracyof vernier,
micrometers and other measuring devices.
2. They are used to set the comparator to a specific dimension.
3. They are used for direct precise measurement where the accuracy of work piece
is important.
4. They are frequently used with sine bar to measure angle of work piece.
5. They can be used to check gap between parallel locations.

12
Calibration of Slip Gauges
 The slip gauges are liable to show signs of wear after appreciable period of
use due to handling in the laboratory or inspection room. Hence they
should be checked or recalibrated at regular intervals.
 Workshop and inspection grade gauges are calibrated by direct
comparison against calibration grade gauges with help of a comparator.
A variety of comparators are available such as mechanical, optical
and pneumatic comparators.
 Eden Rolt millionth comparator and Brook level comparator have been
specially designed for slip gauges.
 Various forms of interferometers and optical flat are applicable to
measuring gauge block flatness. Interferometers are optical instruments used for
measuring flatness and determining the length of the slip gauges by direct
reference to the wavelength of light.
 Parallelism between the faces of a gauge block can be measured in two
ways; with interferometry or with an electro-mechanical gauge block
comparator.

14
Sine Bar
 Sine bar is a precision angle measuring instrument used along with slip
gauges. It is used to measure the angles very accurately and or to locate the
work to a given angle.

15
Sine Bar : Construction
 Sine bars are made from high carbon, high chromium, corrosion resistant
steel, suitably hardened, precision ground and stabilized. Two cylinders of
equal diameters are attached at the ends.
 The axes of these two cylinders are mutually parallel to each other and
also parallel to and at exact distance from the upper surface of the sine bar.
The center to center distance between the rollers or plugs is available for
fixed distance i.e. L= 100 mm, 200 mm, 250 mm, 300 mm.
 The diameter of the plugs or roller must be of the same size and the
center distance between them is accurate. The important condition for the sine
bar is that the surface of sine bar must be parallel to the center lines of the roller.
 Some holes are drilled in the body of the sine bar to reduce the weight and
to facilitate handling.

Sine Bar : Working principle
 The principle of operation of the sine bar relies upon the application
of trigonometry. One roller of the bar is placed on the surface plate and
the combination of slip gauges is inserted under the second roller for setting a
given angle. If h’ is the height of the combination of slip gauges and 'L' the
distance between the rollers centres. Then,
Thus the angle to be measured or to be set is determined by indirect method as a
function of sine, for this reason, the device is called a 'sine bar'.
Accuracy requirements of a sine bar:
1. The rollers must be of equal diameter and true geometric cylinders.
2. The distance between the roller axes must be precise and known, and these
axes must be mutually parallel.
3. The upper surface of the bar must be flat and parallel with the roller axes, and
equidistant from each other.

Use of sine bar
1 Locating any work to a given angle:
 As we have discussed in the working principle of sine bar,
Sin  = ℎ
𝑙
Where, h be the height of slip gauge combination, L is the distance between the centre of the
rollers, and  is angle to be set.
Thus knowing , h can be found out and any work could be set at this angle; as the top face of
the sine bar is inclined at angle  to the surface plate. For better results, both the rollers
could also be placed on slip gauges of height h1 and h2 respectively.
2 Checking or measuring unknown angles:
a. When component is of small size:
 Fig. shows how the sine bar is used to check
small components that may be mounted upon
it. The dial gauge is mounted upon a suitable
stand then set at one end of the work and
moved along the upper surface of
the
component.
 If there is a variation in parallelism of the
upper surface of the component and
the
surface plate, it is indicated by the dial gauge.
The combination of the slip gauges is
so
adjusted that the upper surface of
the
component is truly parallel with the surface
plate:
 The angle of the component is then calculated

18
Use of sine bar
b. When the component is of large size:
 When the component is too large to be mounted on the sine-bar, the sine-bar
can often be mounted on the component as shown in Fig.

19
…to be continue
 = Sin-1
(ℎ±𝑑ℎ
)
𝐿
It is impractical to use sine bar for angle above 45°, as beyond
this angle the errors due to the centre distance of rollers, and
gauge blocks, being in error, are much magnified.
The height over the rollers can then be measured by a vernier height gauge; using a dial test
gauge mounted on the anvil of height gauge to ensure constant measuring pressure. This is
achieved by adjusting the height gauge until the dial gauge shows the same zero reading each
time.
The difference of the two height gauge readings being the rise of the sine-bar as shown and Sin
 =
R1−R2
L
Another arrangement of determining angle of large size part is shown in Fig.
The component is placed over a surface plate and the sine bar
is setup at approximate angle on the component so that
its surface is nearly parallel to the surface plate. A
dial gauge is moved along the top surface of the
sine bar to note the variation in parallelism.
If' h' is height of the combination of the slip gauges and 'dh'
the variation in parallelism over distance 'L' then

20
Sources of errors:
 The establishment of angle by the sine principle is essentially a
length measuring process. The following are the various possible sources of
errors using sine bar:
1. Error in measurement of centre distance of two precision rollers.
2. Error in equality of size of rollers and cylindrical accuracy in the form of the
rollers.
3. Error in geometrical condition of measurement like, flatness of the upper
surface of the bar, parallelism of roller axes with each other, parallelism
between the gauging surface and plane of roller axes, etc.
4. Error in slip gauge combination used for angle setting.

21
Advantages and Disadvantages of sine bar
Advantages:
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 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.

22
SINE CENTRE
 Sine centre is basically a sine bar with block holding centers which can
be adjusted and rigidly clamped in any position. These are used for the testing
of conical work, centered at each end as shown in Fig.
 These are extremely useful since the alignment accuracy of the centers
ensures that the correct line of measurement is made along the work piece.
The centers can also be adjusted depending on the length of the conical work
piece, to be hold between centers.

23
SINE CENTRE
The procedure for its setting is the same as that for sin bar. Fig. shows sine
table,
 Which is the most convenient and accurate design for heavy work-piece.
It consists of a self-contained sine bar, hinged at one roller and mounted on
its datum surface. The work being held axially between centers, the angle
of inclination will be half the included angle of the work. The necessary
adjustment is made in the slip gauge height and the angle is calculated as
𝑙
 = Sin-1 (ℎ
)

24
ANGLE GAUGES
The first set of combination of angle gauges was developed by Dr. Tomlinson of
N.P.L in 1941. The slip gauges are built up to give a linear dimension, same way as
the angle gauges can be built up to give a required angle.
 These gauges enable any angle to be set to the nearest 3'' These are pieces
of hardened and stabilized steel. The measuring faces are lapped and polished to a
high degree of accuracy and flatness.
These gauges are about 76 mm long and 16 mm wide and are available in two sets.
 One set consists of 12 pieces and a square block, in three series of values of
angle viz,
1°, 3° , 9°,27° and 41°
1', 3', 9' and 27', and
6'', 18'', and 30''
Another set contains 13 pieces and a square block.
1°, 3°, 9°,27° and 41°
1', 3', 9' and 27', and
3'', 6’’, 18'' and 30''

25
ANGLE GAUGES
 All these angle gauges in combination can be added or subtracted as shown
in Fig. Thus, making a large number of combinations is possible. Each angle
gauge is accurate to within one second and is marked with engraved V which
indicates the direction of the inclined angle.

26
ANGLE GAUGES
Applications:
1. Angle gauges have been widely used in engineering industries for the quick
measurement of angles between two surfaces. A frequent use of these gauges
is to check whether the components is within its off angle tolerance.
2. Where the angle to be measured between the two surfaces exceeds 90°, the
use of precision square becomes essential. The reflective properties of their
lapped surfaces make them particularly suitable for use with collimating type
of instruments.
Limitations:
3. The block formed by the wringing (combination) of number of these gauges
become bulky and cannot always be conveniently applied to work, so they are
more suitable for reference along with other angle measuring devices.
4. Errors are easily compounded when they are wrung in combination.

AUTO-COLLIMATOR
 Auto-collimator is an optical instrument used for the measurement of
small angular differences. For small angular measurements, autocollimator
provides a very sensitive and accurate approach.
Fig. Principle of auto-collimator

AUTO-COLLIMATOR
Working principle:
 Auto-collimator is essentially
an infinity telescope and a
collimator combined into one
instrument. If a light source is
placed in the focus of a collimating
lens, it is projected as a parallel
beam of light.
 If this beam now strikes a plane reflector which is normal to the optical
axis, it will be reflected back along its own path and focused at the same point 0.
 If the plane reflector be now tilted through a small angle 9 as shown in Fig.,
then parallel beam will be deflected through twice this angle, and will be
brought to focus at 0' in the same plane at a distance from O. Obviously OO'
= 𝑥 = 2𝑓𝜃
 Where f= the focal length of the lens, 𝜃 = angle of inclination of
reflecting mirror.

29
AUTO-COLLIMATOR
Construction:
 An autocollimator consists of three parts viz, micrometer microscope,
lighting unit and collimating lens. A line diagram of injected graticule
autocollimator is shown in Fig. have the graticule situated to one side of the
instrument on an axis at right angles to the main axis.

30
AUTO-COLLIMATOR
Construction:
 A 45° transparent beam splitter, similar to the original illuminated reflector
but further down the main axis, reflects the light from the graticule towards the
objective and thus no direct image is formed by the microscope.
 The image seen after reflection in the external reflector, whose angular variations
are being measured, is formed by the light from the objective which passes through
the 45° beam splitter and this image is picked up by the microscope. In this
instrument also, a micrometer is fitted to the target graticule, optically at right
angles to that on the eyepiece. Thus simultaneous measurements can be made in
two planes at right angles.
Applications:
1. Checking of an internal tight-angle.
2. Comparative measurement using master angles.
3. Measuring straightness and flatness of the surfaces.
4. Measuring small linear dimensions.
5. Assessment of squareness and parallelism of components.
6. For precise angular indexing in conjunction with polygons etc.

32
Auto collimator
The basic principle of an autocollimator is simple: one directs a
collimated beam, which by definition has a small beam
divergence, to a flat reflecting object (a mirror) and detects the
angular position of the reflected light, which typically needs to be
close to direct back-reflection

33
Auto collimator
They are typically used to align components and measure
deflections in optical or mechanical systems. An autocollimator
works by projecting an image onto a target mirror and
measuring the deflection of the returned image against a scale,
either visually or by means of an electronic detector
The basic principle of an
autocollimator is simple: one directs
a collimated beam, which by
definition has a small beam
divergence, to a flat reflecting object
(a mirror) and detects the angular
position of the reflected light, which
typically needs to be close to direct
back-reflection

34
Auto collimator
Applications:
1. Checking of an internal tight-angle.
2. Comparative measurement using master angles.
3. Measuring straightness and flatness of the surfaces.
4. Measuring small linear dimensions.
5. Assessment of squareness and parallelism of components.
6. For precise angular indexing in conjunction with polygons etc.

35
ANGLE DEKKOR
 Angle dekkor works on the same principle as that of auto-collimator. It
consists of microscope, collimating lens and two scales engraved on a glass
screen which is placed in the focal plane of the objective lens.

36
ANGLE DEKKOR
 The screen, which lies at the focal plane of the lens, has two
mutually perpendicular scales marked on it which are graduated in
minutes enabling estimations to about 0.2 minutes to be made.
 The essential function of the instrument is to transmit an image of one of
the scales to a reflecting surface which returns the image through the lens
to be superimposed on to the other scale which is fixed.
 Thus the reading on 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 the other two.
 Thus, the changes in angular position of the reflector in two planes are
indicated by changes in the point of intersection of the two scales. Readings
from scale are read direct to 1' without the use of a micrometer.
 Although the angle dekkor is not as sensitive as the auto-collimator, it
is extremely useful for a wide range of angular measurements at short
distances.

37
ANGLE DEKKOR
 The whole optical system as shown in Fig. is enclosed in a tube which
is mounted on an adjustable bracket. The adjustable bracket is attached to a
flat lapped reflective base as shown in Fig.
Applications:
1. Measuring the angle of a component.
2. Checking the sloping angle of a v-block.
3. Measuring the angle of a cone or taper gauges.
4. Precise angular settings for machining operations.

38
Angle Dekkor
This is also a type of auto -collimator.
There is an illuminated scale in the focal
plane of the collimating lens.
This illuminated scale is projected as a
parallel beam by the collimating lens which
after striking a reflector below the
instrument is refocused by the lens in the
field of view of the eyepiece.
In the field of view of microscope, there is another datum scale
fixed across the center of screen.

39
Angle Dekkor
Uses of Angle Dekkor
Measuring angle of a component
Angle dekkor is capable of measuring small variations in angular setting i.e.
determining angular tilt. Angle dekkor is used in combination with angle gauge.
First the angle gauge combination is set up to the nearest known angle of the
component.
Now the angle dekkor is set to zero reading on the illuminated scale. The angle
gauge build up is then removed and replaced by the component under test.
Usually a straightedge being used to ensure that there is no change in lateral
positions. The new position of the reflected scale with respect to the fixed scale
gives the angular tilt of the component from the set angle

40
Angle Dekkor
Checking the slope angle of a V-block
Figure shows the setup for checking the
sloping angle of V block. Initially, a
polished reflector or slip gauge is
attached in close contact with the work
surface.
By using angle gauge zero reading is
obtained in the angle dekkor.
Then the angle may be calculated by
comparing the reading obtained from
the angle dekkor and angle gauge

41
Angle Dekkor
To measure the angle of cone or Taper gauge
Initially, the angle dekkor is set for the nominal angle of
cone by using angle gauge or sine bar. The cone is then placed
in position with its base resting on the surface plate.
A slip gauge or reflector is attached on the cone since no
reflection can be obtained from the curved surface.
Any deviation from the set angle will be noted by the angle
dekkor in the eye piece and indicated by the shifting of the
image of illuminated scale.

Engineering Metrology Linear-and-Angular-measuremen

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