mechanical measurements & metrology...

Sridhara.T Asst. professor, Dept. of Mechanical Engg., SDMIT, Ujire – 574 240 Unit 1

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MECHANICAL MEASUREMENTS

& METROLOGY

10ME42B

Faculty:

SRIDHARA T B.E.,M.Tech.,

Asst. Professor,

Dept. of Mechanical Engineering,

SDMIT, Ujire – 574 240

E-mail: [email protected]

Contact No: +91 8971195657


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CONTENTS

PART –A

METROLOGY

UNIT 1

Standards of Measurements 1. Definition & Objectives of Metrology

2. Engineering & Industrial application

3. Role of Standards

4. Standards of Length:

4.1 Imperial Standard Yard

4.2 International Prototype Meter

4.3 Airy Points

4.4 Wavelength Standard

5. Disadvantages of Material length Standards

6. Advantages of using Wavelength (light) standard as basic unit to define primary

standards.

7. Meter as of Today.

8. Subdivisions of Standards.

9. Line Standards

Characteristics of Line standards

10. End standards

Characteristics of End standards

11. Transfer from Line Standard to End standard or NPL Method of deriving

End Standard from Line Standard

12. Calibration of End Bars.

13. Numerical Problems on Calibration of End Bars.

14. Slip Gauges (Johannson Gauges)

14.1 Basic forms of Slip Gauges.

14.2 Major requirements for Slip gauges.

15. Indian Standard on Slip Gauges (IS: 2984-1966)

16. Set of Gauges.

17. Wringing Phenomena.

18. Manufacture of Slip Gauges.

19. Numerical Problem on Building of Slip Gauges.


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Definition of Metrology:

Metrology: Metrology is the science of pure measurement.

Measurement: The Measurement is the process of comparing quantitatively an unknown

magnitude with a predefined standard.

Application of Metrology in Engineering:

Metrology is mainly concerned with the establishment of units of measurements,

reproducing these units in the form of standards.

The science of metrology is applied to a limited extent before First World War.

However considerable progress has been made in the application of scientific control

of engineering products.

It is also concerned with the development of methods, execution and estimation of

accuracy of measurements and inspectors.

Dynamic metrology refers to a group of techniques for measuring small variations of a

continuous nature.

A legal metrology deals with the units of measurements, methods of measurements

and the measuring instruments.

Lord Kelvin classic statement concerning metrology:

“when you can measure what you are speaking about and express it in numbers, you know

something about it; and when you cannot measure it, when you cannot express it in numbers,

your knowledge is of a meager(deficient in fullness) and unsatisfactory kind. It may be the

beginning of knowledge, but you have scarcely (hardly) in your thought advanced to the

stage of a science”.

Objective of Metrology:

The basic objective of metrology is to determine whether a component has been

manufactured to the required specification.

With advance in metrology, the mass production of modern ultra-precise apparatus

was possible.

Metrology is essential part in advancement of technology.


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Objectives:

1. To provide required accuracy at minimum cost.

2. Through evaluation of newly developed products, and to ensure that components are

within the specified dimensions.

3. To reduce the cost of rejections and rework by applying statistical quality control

techniques.

4. To standardize measuring methods by using proper inspection methods at the

development stage itself.

5. To reduce the cost of inspection by effective and efficient utilization of available

facilities.

6. To determine the process capabilities.

7. To prepare designs for gauges and special inspection fixtures.

8. To maintain the accuracies of measurement through periodical calibration of the

measuring instruments.

Definition of Standards: Standard is defined as “something that is set up and established by authority as a rule for the

measurement of a quantity, weight, value or quality “.

Example: A meter is standard established by an S.I (System International) organization for

measure length.

A measurement system is based on few fundamental units. All the physical quantities can

be expressed in terms of those fundamental units.

Following are the systems of measurements are use in different countries:

a) F.P.S System:

In this system unit of length is yard, unit of mass is pound, unit of time is second.

b) Metric system: In this system unit of length is meter, unit of mass is kg, unit of weight/force is kgf unit of

time is second

c) S.I system: The basic seven (7) units, meter, kg, second, kelvin, ampere, candela, mole.

Role of Standards: The role of standard to achieve, uniform, consistent and repeatable measurements and to

support the system which make such measurements possible throughout the world.

Development of material Standard for measurement of Length:

The earliest standard of length was established in terms of human parts.

The Egyptian unit was called a CUBIT. It was equal to the length of forearm (from the

elbow to the tip of the middle figure).


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Rapid development made in engineering during the 19th century ere due to improved

materials available and more accurate measuring techniques developed.

It was not until 1855 that first accurate standard was made in England. It was known

as Imperial standard Yard.

Other one is International Prototype Meter. These two are material standard.

In contrast to these two wavelength standards adopted as length standard later on.

Imperial standard Yard: (British Standard of Length):

This standard was made in England in the year 1855.

This is made of 1” square cross section Bronze bar (82% copper, 13%tin,

5%zinc) of 38” long.

The bar has two ½ inch diameter X ½ inch deep holes.

Each hole is fitted with 1/10th

inch (0.10”) diameter gold plug.

The top surface of gold plug is lie on the neutral axis of the bronze bar.

The purpose of keeping gold plug lines at neutral axis has the following advantages.

Due to bending of beam the neutral axis remain unaffected.

The plug is protected from accidental damages

The top surface of the gold plugs is highly polished and contains three

lines engraved transversely and two lines longitudinally.

The yard is defined as “The distance between two central transverse lines on the

gold plugs when the temperature of the bar at 620

F and the bar is supported on

rollers in a specified manner”.

38"

36" ( at 62vF)

Neutral axis

Gold plug

1 i

nch

1 inch

1 i

nchBronze bar composition

(82% Cu, 13%Tin, 5%Zn)

Enlarged view of a gold plug showing engraving.

Figure: Imperial Standard Yard.

1/2

in

ch


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International Prototype Meter:

This standard was established originally by international bureau of weights and

measure in the year 1875.

This is made of platinum-irredium alloy (90% platinum and10% irredium).

The upper surface of the web is highly polished and has fine lines engraved over it.

It is inoxidisable and can have a good finish required for ruling good quality of lines.

According this standard, the length of the meter is defined as the distance between the

center portion of two lines engraved on web section of a bar at 0o C of pure platinum-

irredium alloy (90% platinum and 10% iridium) of 102 cm total length and having

web cross section as shown fig.

Disadvantages of Material Length Standard:

The material standards are influenced by effects of variation of environmental

conditions like temperature, pressure, humidity and ageing etc., and thus its changes in

length.

These standards are required to be stored under security to prevent their damage or

destruction.

These are not easily reproducible.

The exact replicas of material length standard were not available for use somewhere

else.

Conversion factor has to be used for changing over to metric system.

The yard length is equal to 0.9144m.

Airy Points:

Neutarl Axis

Engraved lines

Platinum-irredium alloy

1020 mm (102cm)

1 meter ( at 0vC )

16

mm

16 mm

web

engraved lines

Figure: Internatinal Prototype Meter

Tresca cross section

L

SUPPORTS.577L Figure: airy points


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When straight bar above 125-200mm length are supported horizontally for

measurements by two supports at its end, they will sag in the middle.

If the supports are provided towards the centre, then the ends will bend down.

Both these extremes causes error in measurements

This error can be minimized by providing the two supports at such a distance that

slope at the ends is zero and the end faces of the bar are mutually parallel.

Sir G.B. Airy showed that this condition was obtained when the distance between the

supports is,

Where: L = length of the bar,

n = number of supports.

For, simply supported beam, the expression becomes

These points of supports are known as Airy Points.

Hence Airy Points are achieved when the distance between the supports is

0.577 X Length of the bar. for prototype meter airy points are marked at a distance of 58.9cm

For minimum central deflection, the distance between the supports is 0.554 X L apart.

WAVELENGTH STANDARD:

The major drawback with material standards (meter and yard) is that their length

changes slightly with time.

Secondly, considerable difficulty is expressed while comparing and verifying the sizes

of the gauges by using material standards.

Hence Jacques Babinet a French philosopher suggested that wavelength of

monochromatic light can be used as natural and invariant unit of length.

In the 7th General Conference of Weights and Measures in1927 has approved, the

definition of standard of length relative to the meter is expressed in terms of

wavelength of red cadmium as an alternative to the International Prototype Meter.

Later in 11th General Conference of Weights and Measures in 1960, Orange radiation

of isotope krypton-86 was chosen for new definition for Length has approved.

According to this standard Meter as defined as equal to 1650763.73 Wavelength of the

red orange radiation of isotope krypton 86 gas.

0.577L


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1 yard = 0.9144 meter

= 0.9144 X 1650763.73 wavelengths

= 1509458.3 wavelengths.

This standard as now defined can be reproduced to an accuracy of about 1 part in 109

ADVANTAGES OF WAVELENGTH STANDARD:

1. It is not material standard and hence is not influenced by effects of variation of

environmental conditions like temperature, pressure, humidity and ageing.

2. It is need not be preserved or stored under security and thus there is no fear of being

destroyed as in case of yard and meter.

3. It is not subjected to destruction by wear and tear.

4. This standard is easily available to all standardizing laboratories and industries.

5. There is no problem of transferring this standard to other standards meter and yard.

6. The error of reproduction is only of the order of 3 parts in 1011

.

SUBDIVISON OF STANDARDS:

The standards are subdivided into four grades; these are:

1. Primary standards

2. Secondary standards

3. Tertiary standards

4. Working standards.

1. Primary standards: These standards are preserved under careful conditions.

International Prototype meter and Imperial standard Yard are the example of Primary

standards.

Primary standards are used at rare intervals (say after 10 to 20 years) for comparison

with secondary standards.

These standards are not used for general purposes.

2. Secondary standards: Secondary standards are made as nearly as possible exactly similar to primary

standards as regards design, material and length.

They are compared with primary standards after long intervals and records of

deviation are noted.

These standards are kept at number of places for safe custody. (NPL)

They are used occasional comparison with tertiary standards whenever required.


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3. Tertiary standards: Tertiary standards are first standard to be used for reference purposes in laboratories

and workshops.

They are made as true copy of the secondary standards.

They are used for comparison at intervals with working standard.

4. Working standards: These standards are used more frequently in laboratories and workshops.

They are usually made of low grade of material as compared to primary,

secondary and tertiary standards.

Both Line and end working standards are used.

LINE & END Measurement: A Length is measured as the distance between the centers of two engraved lines or two

parallel faces. So the instruments for direct measurement of linear dimension fall into two

categories.

1. Line Standards.

2. End Standards.

1. Line Standards: When the length is measure as the distance between the centers of two

engraved lines is called Line standards.

Example: Both Yard and Prototype Meter are Line standards.

The most common example of Line measurement is the rule with divisions marked on it.

Characteristics of Line Standards: 1. A scale is a quick and easy to use

2. The scale markings are subjected to wear. However, the leading ends are subjected to

wear and this may lead to undersize measurements.

3. The engraved lines themselves possess thickness and it is not possible to take

measurement with high accuracy limited to +0.2 mm.

4. Scales are subjected to parallax error(Reading error).

5. Hence it is requires assistance of magnifying glass or microscope to achieve sufficient

accuracy.

6. A scale does not possess “built in” datum. Therefore it is not possible to align the scale

with the axis of measurement.

2. End Standards: When length is expressed as the distance between two flat parallel faces,

it is known as end standard.

Example: Measurement by Slip gauges, ends of micrometer anvils, varnier calipers, and end

bars.


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Characteristics of End Standards: 1. They require more time for measurement and measure only one dimension at a time.

2. They are subjected to wear on their measuring faces.

3. These standards are highly accurate for measurement of close tolerance upto + 0.001

mm.

4. They are not subjected to parallax error (reading error).

5. End standards have “built in” datum. Hence can be easily aligned with the axis of

measurement.

6. Group of slip gauges can be wrung together to build up a given size; fault wringing

and careless use may lead to inaccurate result.

Differentiate between Line and End Standards:

Sl no Characteristics Line Standard End Standard

1. Principle Length is expressed as

distance between 2 lines

Length is expressed

as distance between 2

ends

2. Accuracy Ltd. To ± 0.2mm. Highly accurate of

closed tolerances to

±0.001mm

3. Ease Quick and easy Time consuming and

requires skill

4. Effect of wear Wear at only the ends wear at measuring

surfaces

5. Alignment Cannot be easily

aligned

easily aligned

6. Cost low cost high cost

7. Parallax Effect Subjected to parallax

effect

not subjected to

parallax effect


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Transfer from line standard to End standard (NPL Method):

Line standard is an example of primary standard used for measurement of length and it is cleared that it is

inconvenient form for general measurement application because it possess parallax error hence its required

microscope or lenses to determine the position of the line.

Sine line standard is defined first hence it is important to transfer this standard to End standard it has been

widely accepted for measurement of length is engineering applications. The end standards are produced

highest accuracy in relation with line standard.

The two possible errors are present in end standards that we will eliminate by using this conversion. They

are the misplacing of the line at the mid-position of the end faces of ½” end blocks and other in the length of

35½” end standard.

x1 x2

lba c d

36" LINE STANDARD

Mean Diffrence d = x1 - x2

35 1/2" END STANDARD

1/2 " end block 1/2 " end block

figure (1)

In order to transfer the line standard to end standard, an instrument called, LINE STANDARD

COMPARATOR IS USED.

It consists of two microscopes mounted about a yard apart over a table.

From the figure (1),

Let us take a gauge of length 35 ½” with end faces are flat and mutually parallel. Whose length be l.

Then this 35 ½” gauge is wrung both side by using ½” end block.

The distance between the two engraved lines on line standard is 36”.


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On these ½” end block approximately at center a fine lines has been engraved. Then the distance

between these two engraved lines on ½” end block wrung with 35 ½” gauge is 36”.

When these two standards are wrung on a surface plate and see through the microscope have

accurate micrometer screw controlled eyepiece, we will get following reading. One position reading

has shown in figure.

The difference of readings between the lines on line standard and the lines on end standard are noted

every time. If the differences are d1,d2,d3 and d4 respectively, then for the successive position of ½”

inch blocks, we have,

l+b+c = 36 + d1

l+b+d = 36 + d2

l+a+c = 36 + d3

l+a+d = 36 +d4

Take the mean of it (add all 4 readings and divided by 4),

𝐥 +𝟏

𝟐 𝐚 + 𝐛 + 𝐜 + 𝐝 = 𝟑𝟔 +

𝒅

𝟒 (1)

In the above equation it may be noted that the error due to the possible misplacing of the lines between the

end faces of the ½” blocks are eliminated

2nd

stage:

From the Brooks Level comparator

LD

1 ba

35 1

/2"

36" End bar being calibrated

1/2" End Block

Take a line standard of length L, is wrung to surface plate. Then take 35½” gauge for which wrung a one ½”

end block and combination of these two is wrung to surface place adjacent to line standard as shown in

figure.


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From the microscope obtaining following readings :

l+a+b = L + D1

l+c+d = L + D2

Take the mean of it (add all 2 readings and divided by 2),

𝐥 +𝟏

𝟐 𝐚 + 𝐛 + 𝐜 + 𝐝 = 𝐋 +

𝑫

𝟐 (2)

compare equation (1) & (2)

𝟑𝟔 + 𝒅

𝟒 = 𝐋 +

𝑫

𝟐

It shows that there is no error in the 35½” gauge block.

Calibration of End Bars:

x1

L

A

B

1 Meterlength bar

x2

LB

LA

surface platefigure (a) figure (b)

The following procedure may be adopted for calibrating two end bars of each 500 mm basic lengths.

Let us take the calibrated end bar of 1 meter length (1000 mm) say L of length and wrung it to a surface

plate.

Let us take two end bars A & B of same basic length say of 500 mm length( length of is LA and length be is

LB) , wrung together to form a basic length of 1 meter and wrung to a surface plate adjacent to the meter bar

as shown in the figure (a).

The difference in height x1 is noted.

From figure (a), we get

L + x1 = LA + LB (1)


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(Say LA+LB which is longer or shorter than L)

x1 = difference in height between one meter length and the combined length of bars A and B.

Then comparison is made between two 500 mm length bars A and B to determine the difference in the

length x2 as shown in figure (b)

From figure (b), we get

LB = LA + x2 (2)

(Say LB which is longer or shorter than LA)

x2 = difference in height between length of bar A and bar B.

Substitute equation (2) in equation (1)

L + x1 = LA + LA + x2

L + x1 = 2 LA + x2

LA = 𝐋 + 𝐱𝟏+ 𝐱𝟐

𝟐 from this equation we know the length of end bar A.

Substitute this value in equation (2) and obtain the length of end bar B.

The above procedure can be used for calibrating any other number of length standards of the same basic

size.

OTHER METHOD USED FOR TRANSFER FROM LINE STANDARD TO END

STANDARD SLIP GAUGES (JOHANSSEN GAUGES) or GAUGE BLOCKS: Slip gauges are rectangular blocks made of high grade steel of having cross section 30 by 10. i.e.,

face length is 30 mm, face width is 10 mm and slip gauge length (L) is distance between two

measuring parallel faces.

Slip gauges are hardened first to resist wear.

Slip gauges were developed by johanssen, a sweedish engineer so these are also called as “johanssen

gauges”.

Slip gauges are universally accepted End standards and widely used in engineering applications.

Slip gauges are made of high grade steel or tungsten carbide.

Figure shows the Slip gauge:

L

Measuring Face

Face Length

Face Width


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BASIC FORMS OF SLIP GAUGES: Slip gauges are available in three basic forms. Namely:

1. Rectangular blocks: These are rectangular in shape & less expensive hence widely used.

These are used where space is limited.

2. Square Blocks: These are square in shape & high expensive hence are used in certain applications.

Due to their large surface area they adhere better to each other when wrung to build long lengths.

3. Square with centre hole Blocks: These are square in shape with centre in hole.

These gauges are inserted on to the tie rod to ensure that the wrung stocks do not fall apart while

handling.

Wringing Phenomenon of Slip Gauges: Wringing: Wringing is defined as the property of adhering a measuring faces of a gauge block by sliding or pressing

the gauge against the measuring faces of other gauge blocks without the use of any extraneous means.

The gap between two wrung slip gauges is only of the order of 0.00635 microns, which is negligible.

The slip gauges are wrung together by hand by a combined sliding and twisting motion as shown in

figure.

Procedure:

1. Before using, the slip gauges are cleaned by using a lint free cloth or cleansing tissue

2. One slip gauge is then oscillated slightly over the other slip gauge with a light pressure.

3. One gauge is then raised at 90 degrees, to the other, and by using light pressure

it is rotated until the blocks are in line.

4. Similarly, for separating the two wrung slip gauges, combined sliding and twisting motion should be

used.

Indian Standard on Slip Gauge (IS: 2984-1966): According to IS standards, Slip gauges are graded according to their accuracy as Grade 00, Grade 0, Grade I

and Grade II.

Grade 00: These are placed in the standard room and used for highest precision work

Grade 0: is used in Laboratories and tool room which serves as standard for periodically checking the

accuracy of Grade I & grade II gauges.

Grade I: It is of higher accuracy and used in inspection departments.

Grade II: These are used in workshops during actual production of components, tools and gauges.

Generally, two sets of slip gauges are used namely:

1. Normal set

2. Special set

SLIDE TWIST


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Normal set is consists of following set gauges: M 45 and M 87 are the examples for normal set slip gauges.

M 45 Slip Gauge Set:

Range (mm) Steps (mm) No. of Pieces

1.001 to 1.009 0.001 9

1.01 to 1.09 0.01 9

1.1 to 1.9 0.1 9

1 to 9 1 9

10 to 90 10 9

TOTAL 45



1.001 to 1.009 0.001 9

1.01 to 1.49 0.01 49

0.5 to 9.5 0.5 19

10 to 90 10 9

1.0005 - 1

TOTAL 87

A Special set is consists of following set gauges: M 112. M 105, M 50, M 33 and M 27 are the examples for Special set slip gauges.



1.001 to 1.009 0.001 9

1.01 to 1.49 0.01 49

0.5 to 24.5 0.5 49

25, 50, 75, 100 25 4

1.0005 - 1

TOTAL 112


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Protector Blocks:

These are 2 additional 1.5mm/ 2 mm /2.5 mm slip gauges with a letter P on measuring faces and are

provided with high grade sets of gauge blocks.

These are accommodated at each other at each end of a combination slip gauge set so that all the

wear occurs on them.

These are made from tungsten carbide.

Procedure for build up gauge blocks for required dimension (Selection of Slip Gauges for required dimension): Let us assume that the dimensions to be build up is 58.975 mm. using M87 set slip gauge.

Always start with the last decimal place.

e.g., here it is 0.005 mm and for this 1.005 mm slip gauge is selected.

Now dimension is left is 58.975 – 1.005 = 57.97 mm.

Then next take second decimal place; and for it select 1.47 mm slip gauge.

Therefore, remainder is 57.97 – 1.47 = 56.50 mm.

[Note: one could have select 1.07 mm piece also, but that way we could have been left with 56.900 and for

it we need another 1.4 mm piece. Our aim should be to choose minimum number of slip gauges for a given

dimension].

Next for third decimal place, select 6.5 mm piece

Now 56.50 -6.50 mm = 50. 00 mm.

Finally, we choose 50 mm slip gauge.

50.000 – 50.000 = 50.000 mm

Thus, we have 50.000 + 6.500 + 1.470 + 1.005 = 58.975 mm.

All these slip gauges are wrung properly to get required dimension.

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