Introduction to Mechanical Measurements and Metrology

Department of Mechanical Engineering
JSS Academy of Technical Education, Bangalore-560060
MECHANICAL MEASUREMENTS AND METROLOGY
(Course Code:18ME36B)

TEXT BOOKS
• Mechanical Measurements, Beckwith Marangoni and Lienhard, Pearson Education, 6th Ed., 2006.
• Instrumentation, Measurement and Analysis, B C Nakra, K K Chaudhry, 4th Edition, McGraw Hill.
• Engineering Metrology, R.K. Jain, Khanna Publishers, Delhi, 2009
REFERENCE BOOKS:
• Engineering Metrology and Measurements, N.V.Raghavendra and L.Krishnamurthy, Oxford
University Press..
Further Reference:
 National Programme on Technology Enhanced Learning (NPTEL)
http://nptel.ac.in/courses/112104121/1

• To understand the concept of metrology and standards of measurement.
• To equip with knowledge of limits, fits, tolerances and gauging.
• To acquire knowledge of linear and Angular measurements, Screw thread and gear
measurement & comparators.
• To understand the knowledge of measurement systems and methods with emphasis
on different Transducers, intermediate modifying and terminating devices.
• To understand the measurement of Force, Torque, Pressure, Temperature and Strain.
Learning Objectives

• Understand the objectives of metrology, methods of measurement, standards of
measurement & various measurement parameters.
• Explain tolerance, limits of size, fits, geometric and position tolerances, gauges and their
design and also understand the working principle of different types of Comparators
• Describe measurement of major & minor diameter, pitch, angle and effective diameter of
screw threads & understand advanced metrology concepts.
• Explain measurement systems, transducers, intermediate modifying devices and terminating
devices
• Describe functioning of force, torque, pressure, strain and temperature measuring devices.
Outcomes

MECHANICAL MEASUREMENTS AND METROLOGY
CHAPTER 1: Introduction to Metrology

Module 1
Introduction to Metrology: Definition, objectives of metrology, Material Standards, Wavelength
Standards, Classification of standards, Line and End standards, Calibration of End bars. Numerical
examples.
Linear and angular measurements: Slip gauges-Indian standards on slip gauges, Adjustable slip
gauges, Wringing of slip gauges, Problems on building of slip gauges (M87, M112), Measurement of
angle-sine bar, Sine centre, Angle gauges, Optical instruments for angular measurements.
Autocollimator-Applications for measuring straightness and squareness.

INTRODUCTION
Metrology: Metrology literally means science of measurements.
• In practical applications, it is the enforcement, verification, and validation of
predefined standards.
Also concerned with;
• Industrial inspection and its various techniques
• Units of measurements and their reproduction in the form of standards
• Ascertaining the uniformity of measurements
• Developing methods of measurement
• Analyzing the accuracy of methods of measurement
• Establishing uncertainty of measurement
• Investigating the causes of measuring errors and subsequently eliminating them.

INTRODUCTION
Metrology: Derived from the Greek word ‘metrologia’, which means measure
NEED FOR INSPECTION
• Ascertain that the part, material, or component conforms to the established
standard.
• Accomplish interchangeability of manufacture.
• Sustain customer goodwill by ensuring that no defective product reaches the
customers.
• Provide the means of finding out inadequacies in manufacture.
• Purchase good-quality raw materials, tools, and equipment that govern the
quality of the finished products.

INTRODUCTION
• Coordinate the functions of quality control, production, purchasing, and other
departments of the organizations.
• Take the decision to perform rework on defective parts, that is, to assess the
possibility of making some of these parts acceptable after minor repairs.
• Promote competition, leading to the manufacture of quality products in bulk by
eliminating bottlenecks and adopting better production techniques.
NEED FOR INSPECTION

INTRODUCTION
Terminologies
• Accuracy is the degree of agreement of the measured dimension with its
true magnitude.
• The maximum amount by which the result differs from the true value.
• The nearness of the measured value to its true value.
• Expressed as a percentage.
Accuracy

INTRODUCTION
Terminologies
• Precision is the degree of repetitiveness of the measuring process.
• Precision is the repeatability of the measuring process.
• Precision refers to the consistent reproducibility of a measurement.
• If an instrument is not precise, it would give different results for the same
dimension for repeated readings.
• In most measurements, precision assumes more significance than accuracy.
Precision

INTRODUCTION
Terminologies
• The ability of the measuring instrument to repeat the same results during the
act of measurements for the same quantity is known as repeatability.
• Random in nature and, by itself, does not assure accuracy, though it is a
desirable characteristic.
Repeatability

INTRODUCTION
Terminologies
Reproducibility is normally specified in terms of a scale reading over a given
period of time
Reproducibility

INTRODUCTION
Terminologies
Difference between Precision and Accuracy
(a) Precise but not accurate (b) Accurate but not precise (c) Precise and accurate (d) Not precise and not accurate

INTRODUCTION
Terminologies
• Difference between the indicated value and the true value of the quantity
measured.
Error
E = Error
Vm = Measured value
Vt = True value
E is also known as the absolute error

INTRODUCTION
Terminologies
• known as relative error
% Error
• Accuracy of an instrument can also be expressed as % error.
• Accuracy of an instrument is always assessed in terms of error.

INTRODUCTION
Terminologies
Factors affecting the Accuracy
• Two terms are associated with accuracy in measuring equipment:
• Sensitivity
• Consistency.
• The ratio of the change of instrument indication to the change of quantity being
measured.
• the ability of the measuring equipment to detect small variations in the quantity
being measured
Sensitivity:

INTRODUCTION
Terminologies
Factors affecting the Accuracy
• Two terms are associated with accuracy in measuring equipment:
• Sensitivity
• Consistency.
• The successive readings of the measured quantity obtained from the
measuring instrument are same all the time, the equipment is said to be
consistent
Consistency

INTRODUCTION
Terminologies
Range
Range is defined as the difference between the lower and higher values that an
instrument is able to measure.
E.g. If an instrument has a scale reading of 0.01–100 mm, then the range of the
instrument is 0.01–100 mm (the difference between the maximum and the
minimum value).

INTRODUCTION
Terminologies
Accuracy and Cost
Relationship of accuracy with cost

INTRODUCTION
OBJECTIVES OF METROLOGY AND MEASUREMENTS
• To ascertain, the newly developed components are comprehensively evaluated
and designed within the process, and that facilities possessing measuring
capabilities are available in the plant.
• To ensure uniformity of measurements.
• To carry out process capability studies to achieve better component tolerances
• To assess the adequacy of measuring instrument capabilities to carry out their
respective measurements
• To ensure cost-effective inspection and optimal use of available facilities
• To adopt quality control techniques to minimize scrap rate and rework

INTRODUCTION
OBJECTIVES OF METROLOGY AND MEASUREMENTS
• To establish inspection procedures from the design stage itself, so that the
measuring methods are standardized
• To calibrate measuring instruments regularly in order to maintain accuracy in
measurement
• To resolve the measurement problems that might arise in the shop floor
• To design gauges and special fixtures required to carry out inspection
• To investigate and eliminate different sources of measuring errors

Standards of Measurement
Introduction
• Today, almost all manufacturing units practise the principle of interchangeability
of manufacture.
• In order to accomplish complete interchangeability of manufacture in
industries, it is essential to a have a measurement system.
• Interchangeability can refer to: Interchangeable parts, the ability to select
components for assembly at random and fit them together within proper
tolerances.

Standards of Measurement
STANDARDS AND THEIR ROLES
• A standard is defined as the fundamental value of any known physical
quantity, as established by national and international organizations of authority,
which can be reproduced.
• Standards play a vital role for manufacturers across the world in achieving
consistency, accuracy, precision, and repeatability in measurements and in
supporting the system.

NATIONAL PHYSICAL LABORATORY
• The National Physical Laboratory (NPL) was established in UK in 1900.
• It is a public institution for standardizing and verifying instruments, testing
materials, and determining physical constants.
• NPL India (NPLI) was established in 1947 in New Delhi under the Council of
Scientific and Industrial Research (CSIR).

• NPL India (NPLI) Roles
• To reinforce and carry out research and development activities in the areas of
physical sciences and key physics-based technologies.
• Maintaining national standards and ensuring that they conform to international
standards.
• To support industries (National and private) in their research and development
activities, by carrying out calibration and testing, precision measurements, and
development of processes and devices.

• NPL India (NPLI) Roles
• It ascertains that the national standards of measurements are traceable to the
international standards.
• Shoulders the responsibility of assisting in research and development activities
in the fields of material development, radio and atmospheric sciences,
superconductivity and cryogenics, etc.

Material Standard
Two standard systems for linear measurement that have been accepted and
adopted worldwide are English and metric (yard and metre) systems
• Yard or metre is defined as the distance between two scribed lines on a bar
of metal maintained under certain conditions of temperature and support.

Material Standard
• Yard or metre is defined as the distance between two scribed lines on a bar of
metal maintained under certain conditions of temperature and support.
Yard or Metre
• The imperial standard yard is a bronze bar 1 sq. inch in cross-section and 38
inches in length, having a composition of 82% Cu, 13% tin, and 5% Zn.

Material Standard
Yard or Metre
The purpose of the placing the gold plug lines
at neutral axis has the following advantages.
• Due to bending of beam the neutral axis
remains unaffected
• The plug remains protected from
accidental damage.
• The top surface of the gold plugs is highly
polished and contains three lines engraved
transversely and two lines longitudinally.
• The temperature of the bar is constant at 62°F
• The bar is supported on rollers in a specified
manner to prevent flexure

Material Standard
Metre
• Also known as international prototype metre, which was established in 1875.
• It is defined as the distance between the centre positions of the two lines
engraved on the highly polished surface of a 102 cm bar of pure platinum–iridium
alloy (90% platinum and 10% iridium) maintained at 0 °C under normal
atmospheric pressure and having the cross-section

Material Standard
Metre • The top surface of the web contains graduations coinciding with
the neutral axis of the section.
The web-shaped section offers two major advantages.
• The section is uniform and has graduations on the neutral axis,
it allows the whole surface to be graduated.
• This cross-section provides greater rigidity
• The bar is in oxidizable
• It is supported by two rollers having at least 1 cm diameter,
which are symmetrically located in the same horizontal plane at
a distance of 751 mm from each other.

Material Standard
Disadvantages of Material Standards
 Material standards are affected by changes in environmental conditions such as
temperature, pressure, humidity, and ageing, resulting in variations in length.
 Preservation of these standards is difficult because they must have appropriate
security to prevent their damage or destruction.
 Replicas of material standards are not available for use at other places.
 They cannot be easily reproduced.
 Comparison and verification of the sizes of gauges pose considerable difficulty.
 While changing to the metric system, a conversion factor is necessary.

WAVELENGTH STANDARD
In the 11th General Conference of Weights and Measures, held in Paris in 1960,
recommended a new standard of length, known as wavelength standard.
• Measured in terms of wavelengths of the red–orange radiation of the krypton 86
isotope gas.
Using wavelengths of a monochromatic light as a natural and invariable unit of
length, the dependency of the working standard on the physical standard can be
eliminated.

WAVELENGTH STANDARD
In the 11th General Conference of Weights and Measures, held in Paris in 1960,
recommended a new standard of length, known as wavelength standard.
According to this standard;
Metre is defined as 1,650,763.73 × wavelengths of the red–orange radiation of a
krypton 86 atom in vacuum.

Classification of standards
Hierarchical classification of standards
Classification of standards based on purpose

Primary standards
• For defining the unit precisely, there shall be one and only one material
standard.
• Preserved carefully and maintained under standard atmospheric conditions so
that they do not change their values.
• Have no direct application to a measuring problem encountered in engineering.
• Used only for comparing with secondary standards.
E.g. International yard and international metre are examples of standard units of
length.

Secondary standards
• Derived from primary standards and resemble closely with respect to design,
material, and length.
• Any error existing in these bars is recorded by comparison with primary standards
after long intervals.
• Kept at different locations under strict supervision
• Used for comparison with tertiary standards (only when it is absolutely essential).
• These safeguard against the loss or destruction of primary standards.

Tertiary standards
• Primary and secondary standards are the ultimate controls for standards.
• Used only for reference purposes and that too at rare intervals.
• Tertiary standards are reference standards employed by NPL.
• Used as the first standards for reference in laboratories and workshops.
• These standards are replicas of secondary standards.
• Used as references for working standards.

Working standards
• Used more frequently in workshops and laboratories.
• The materials used to make these standards are of a lower grade and cost.
• Derived from fundamental standards
• Suffer from loss of instrumental accuracy due to subsequent comparison at each
level in the hierarchical chain.
• Working standards include both line and end standards.

LINE AND END MEASUREMENTS
• The distance between two engraved lines is used to measure the length, it is
called line standard or line measurement.
• E.g. yard and metre.
• The rule with divisions marked with lines is widely used.

LINE AND END MEASUREMENTS
• The distance between two flat parallel surfaces is used to measure the length, it
is known as end standard or end measurement.
• The end faces of the end standards are hardened to reduce wear and lapped
flat and parallel to a very high degree of accuracy.
• Extensively used for precision measurement in workshops and laboratories.
E.g. slip gauges, end bars, ends of micrometer anvils, Vernier calipers, etc.

Comparison of line and end standards

CALIBRATION OF END BARS
• To calibrate two bars having a basic length of 500 mm with the help of a one piece
metre bar.
• The following procedure is adopted

1. The metre bar to be calibrated is wrung to a surface
plate.
2. The two 500 mm bars to be calibrated are wrung
together to form a bar of length of 1 m, in turn is
wrung to the surface plate beside the metre bar, as
shown in Fig. (a).
3. The difference in height e1 is obtained.
4. The two 500 mm bars are then compared to
determine the difference in length, as shown in
Fig.(b).

• Let LX and LY be the lengths of the two 500 mm bars.
• Let e1 be the difference in height between the
calibrated metre bar and the combined lengths of X
and Y.
• Let the difference between the lengths of X and Y be
e2.
• Let L be the actual length of the metre bar.
• Then the first measurement gives a length of
L ± e1 = LX + LY, depending on whether the
combined length of LX and LY is longer or shorter than L.

• The second measurement yields a length of LX ± e2
= LY again depending on whether X is longer or
shorter than Y.
• Then substituting the value of LY from the second
measurement in the first measurement, we get
Or
Therefore,

1. A calibrated metre end bar, which has an actual length of 1000.0005 mm, is to
be used in the calibration of two bars X and Y, each having a basic length of
500 mm. When compared with the metre bar, the sum of LX and LY is found to
be shorter by 0.0003 mm. When X and Y are compared, it is observed that X
is 0.0004 mm longer than Y. Determine the actual length of X and Y.
Numerical examples

The arrangement of gauges is as shown in Fig.
From first principles, we have
L – e1 = LX + LY
However, LX = LY + e2
Therefore, L − e1 = 2LY + e2
Or, LY = (L − e1 − e2)/2
Substituting the values for L, e1, and e2, we get
LY = (1000.0005 − 0.0003 − 0.0004) / 2
LY = 999.9998 / 2 mm
i.e., LY = 499.9999 mm
We have LX = LY + e2
LX = 499.9999 + 0.0004 = 500.0003 mm
Solution

Numerical examples
2. It is required to obtain a metre standard from a calibrated line standard using a composite
line standard. The actual length of the calibrated line standard is 1000.015 mm. The
composite line standard comprises a length bar having a basic length of 950 mm and two
end blocks, (a +b) and (c + d), each having a basic length of 50 mm. Each end block
contains an engraved line at the centre.
Four different measurements were obtained when comparisons were made between the
calibrated line standard and the composite bar using all combinations of end blocks:
L1 = 1000.0035 mm, L2 = 1000.0030 mm, L3 = 1000.0020 mm, and L4 = 1000.0015 mm.
Determine the actual length of the metre bar.
Block (a + b) was found to be 0.001 mm greater than block (c + d) when two end blocks
were compared with each other.

Introduction to Mechanical Measurements and Metrology

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