Metrology Rajesh ME Dept. Syllabus Consists of 5 Units : 1. Concept of measurement 2. Limits, Fits and tolerances 3. Linear measuring instruments and.

Metrology

Rajesh ME Dept

Syllabus• Consists of • 5 Units : 1. Concept of measurement 2. Limits , Fits and tolerances 3. Linear measuring instruments and Angular measuring instrument 4. Form measurement and interferometry 5.Laser and Advances in Metrology• 5 Credits

METROLOGY

• Metrology word is derived from two Greek words such as metro = measurement and logy = science

• science of measurement which includes all aspects both theoretical and practical with reference to measurements

Measurement and Calibration?• process of numerical evaluation of a dimension• Said as an act , or the result of quantitative comparison

between a predetermined standard and an unknown magnitude.

• Set of operations having the objective of determining a value of a quantity

• The basic aim of measurement in industries is to check whether a component has been manufactured to the requirement of a specification or not.

• Calibration is a procedure and apparatus employed for obtaining a comparison

• Measurements provides means for describing various phenomena in a quantitative terms

Measurand

• A physical quantity or the characteristic condition which is the object of interest for measurement in an instrumentation system is termed as “measurand” or “measurement variable” or “process variable”

• Measurand may be

Fundamental quantity: mass, length

Derived quantity : Speed, velocity, acceleration

• Word measurand is used to specify a particular quantity which is to be quantified

• Input quantity to measuring process, this act of measuring process produces result.

Process of comparison (measurement )

Measurand (Quantity to be measured )

Standard (known quantity)

Result

Fundamental measuring process

Input signal Measurement system Output signal

Measurand Measurement

Basic requirements for meaningful results of measurement

• Standards employed must be accurate and universally acceptable.

• Standard must be of same character as the measurand• The apparatus used and methods adopted for

comparison purpose must be provable.

Why we need to measure?

• To generate data for designing • To generate data to validate or propose a theory

Engineers design physical systems in forms of machines to serve some specified functions

The behavior of parts of the machine during the operations of machine needs to be examined or analyzed or designed such that it functions reliably

Such an activity needs data regarding the machine parts in terms of “material properties” which are obtained by performing measurements in laboratory

Significance of Measurements

• It plays an important role in every branch of scientific research and engineering processes

Which includes Control systems Process instrumentation Data reduction

Measurement categories

1. Primary quantity 2. Derived quantity 3. Intrusive – Probe method 4. Non-intrusive

1. Primary quantity:Single quantity that is directly measurable. measurement of

the diameter of a cylindrical Specimen. directly measured using an instrument such as vernier calipers

2. Derived quantity

when a quantity of interest is not directly measurable by a single measurement process. The quantity of interest needs to be estimated by using an appropriate relation involving several measured primary quantities

3. Probe or intrusive method: measurement of a physical quantity uses a probe that is

placed inside the system. Since a probe invariably affects the measured quantity the measurement process is referred to as an intrusive type of measurement.

4. Non-intrusive method:

When the measurement process does not involve insertion of a probe into the system the method is referred to as being non-intrusive . A typical example for such a process is the use of laser Doppler velocimeter (LDV) to measure the velocity of a flowing fluid.

Schematic of a general measurement system

Methods of Measurements

l. Direct method 2. Indirect method 3. Absolute or Fundamental method 4. Comparative method 5. Transposition method 6. Coincidence method 7. Deflection method 8.Complementary method 9. Contact method 10. Contact less method

Direct method of measurement :

value of the quantity to be measured is obtained directly without any calculations

eg : scales, vernier callipers, micrometers Indirect method of measurement :

value of quantity to be measured is obtained by measuring other quantities which are functionally related to the required value

eg : angle measurement by sine bar Absolute or Fundamental method :

based on the measurement of the base quantities used to define the quantity

Comparative method: the value of the quantity to be measured is compared with known value of the same quantity or other quantity practically related to it

• Transposition method: Method of measurement by direct comparison in which the

value of the quantity measured is first balanced by an initial known value A of the same quantity, then the value of the quantity measured is put in place of this known value and is

balanced again by another known value B. If the position of the element indicating equilibrium is the same in both cases, the value of the quantity to be measured is AB

Eg: determination of a mass by means of a balance and known weights

Coincidence method: a differential method of measurement in which a very small difference between the value of the quantity to be measured and the reference is determined by the observation of the coincidence of certain lines or signals

Eg: measurement by vernier calliper, micrometer.

Deflection method:

value of the quantity to be measured is directly indicated by a deflection of a pointer on a calibrated scale.

Complementary method:

value of the quantity to be measured is combined with a known value of the same quantity. The combination is so adjusted that the sum of these two values is equal to predetermined comparison value

Eg: determination of the volume of a solid by liquid displacement Method of measurement by substitution:

It is a method of direct comparison in which the value of a quantity to be measured is replaced by a known value of the same quantity, so selected that the effects produced in the indicating device by these two values are the same

Objectives of Metrology

• Complete evaluation of newly developed products.• Determination of the process capabilities and ensure that these

are better than the relevant component tolerances.• Determination of the measuring instrument capabilities and

ensure that they are quite sufficient for their respective measurements.

• Minimizing the cost of inspection by effective and efficient use of available facilities

• Reducing the cost of rejects and rework through application of Statistical Quality Control Techniques

• To standardize the measuring methods:• To maintain the accuracies of measurement.• To prepare designs for all gauges and special inspection fixtures

Generalized Measurement System and Standards

• Term standard is used to denote universally accepted specifications for devices.

• Components or processes which ensure conformity and interchangeability throughout a particular industry

• A standard provides a reference for assigning a numerical value to a measured quantity

• The national institute of standards and technology (NIST) formerly called National Bureau of Standards (NBS), it was established in1901

standards in the national measurement system

• Calibration standards• Metrology standards• National standards

Calibration standards: Working standards of industrial or governmental laboratories.

Metrology standards: Reference standards of industrial or Governmental laboratories

National standards: It includes prototype and natural phenomenon of Sl (Systems International), the world wide system of weight and measures standards. A standard provides a reference or datum for assigning a numerical value to a measured quantity.

The two standard systems of linear measurements are yard (English) and meter (metric).

For linear measurements various standards are used

Types of Measurement standards

1) Line standard

2) End Standard

3) Wavelength standard

 Standards of Measurements

The different types of standards of length are

1.Material Standards

(a)Line Standard – When length is measured as the distance between centers of two engraved lines. (b)End Standard – When length is measured as the distance between to flat parallel faces.

Line Standard:-

The Imperial Standard yard :-Established in 1855 served till 1960.Construction :- Cross section – 1 Inch Square.Material – Bronze (82%cu,13%tin,5%zinc)Length – 38 Inch.

Definition of Yard:- The Imperial standard was equal to the distance

between two lines engraved on a one inch square section bronze bar. The lines were engraved on two gold plugs let into walls near the ends of the bar so that the lines were in neutral plane.

Yard redefined as equal to 0.9144 meters.

Figure

• 38’’

• 36’’

• Magnified view

• Imperial Yard

• Gold Plug

International Standard prototype Meter

• The unit of length is the meter expressed as the distance at 0o C between the axes of the two median lines engraved on the platinum iridium bar known as international prototype meter. – Line standard. (See figure below) .

• sectional shape gives better rigidity for the amount of  metal involved and is therefore economic in use for an expensive metal

• The meter is defined as 1650763.73 wavelengths of the orange radiation in vacuum of the krypton 86 isotope – 1960

• The meter equals the length of the path travelled by light in a vacuum during a time interval of 1/299792458 of a second

Figure :-• 16 mm

• 16 mm

• Neutral Axis

• International Prototype Meter

Characteristics of Line Standards Scale can be accurately embalmed, but the engraved lines posses

thickness and it is not possible to accurately measure

Scale is used over a wide range Scale markings are not subjected to wear. However the ends are

subjected to wear and this leads to undersize measurements Scale does not posses built in datum. Therefore it is not possible

to align the scale with the axis of measurement Scales are subjected to parallax errors Assistance of magnifying glass or microscope is required

Wavelength Standards An alternative to the line and end standards is to

use the wavelength of monochromatic light as a natural and invariable unit of length. This was demonstrated by A.A.Michelson, an American scientist, using an interferometer. A schematic diagram of the Michelson’s interferometer is shown below.

Figure

LaserS ource

P hoto D etector

M oving

F ixed

AB

C

D

EF

S em i-re flector

Princip le of M ichelson Interferom eter

• A major drawback with the material standards, that their length changes with time, secondly, considerable difficult is expressed while comparing the sizes of the gauges by using material standards

• Jacques Babinet suggested that wavelength of a mano chromatic light can be used as a natural and invariable unit of length approved the definition of standard of length relative to meter

• Orange radiation of isotope Krypton-86 was chosen for the new definition of length in 1960, Krypton-86 and that it should be used in hot cathode discharge lamp, maintained at a temperature of 63K

• According to this standard meter was defined as equal to 165763.73 wavelengths of orange radiation in vacuum of krypton-86 isotope atoms excited at triple point of nitrogen

Advantages Not a material standard and hence it is not influenced

by effects of variation of environmental conditions like temperature, pressure

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

It is not subjected to destruction by wear and tear It gives the unit of length which can be produced

consistently at alltimes. Can be used for making comparative measurements of

very high accuracy

End standards

Distance between two parallel end faces . They are in two forms

1) End/Length bars

2) Slip Gauges

End/length Bars

END BARS

• Primary end standards usually consist of bars of carbon steel about 20 mm in diameter and made in sizes varying from 10 mm to 1200 mm. These are hardened at the ends only. They are used for the measurement of work of larger sizes.

Slip gauges

• These were invented, by C.E. Johanson of Sweden• These are rectangular blocks of steel having a cross-

section of about 30 by 10 mm• These are made of high-grade cast steel and are

hardened throughout.• with the set of slip gauges, combination of slip gauge

enables measurements to be made in the range of 0.0025 to 100 mm

• but in combinations with end/length bars measurement range up to 1200 mm is possible.

Slip gauges are used to provide end standards of specific length by temporarily combining several individual elements- each representing a standard dimension- into a single gauge bar

The success of system depends on formation of a bar of reasonable cohesion between individual elements and its actual dimension truly representing within specific limits, the desired nominal dimension

Generally two sets of slip gauges (normal set and specials set) are used.

The normal set is made up of the following blocks: (all dimensions in mm)

Range Step Pieces

1.001 to 1.0091.01 to 1.09

1.1 to 1.91 to 9

10 to 90

0.0010.010.11

10

99999

Total 45

The Special set is made up of the following blocks: (all dimensions in mm)

• Commonly used slip gauges have following dimensions

Normal size                                 Cross- sectional area

                                                  (w × d) in mm

Upto 10 mm                                    30    × 9

Above 10 mm                                  35    × 9

Range Step Pieces

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 85

Wringing and Enforced Adhesion

• 'wringing' refers to the conditions of intimate and complete contact and of permanent adhesion between measuring faces which is brought about by wringing together the surfaces.

• It is believed that the phenomenon of wringing is due to molecular adhesion between a liquid film and the mating surfaces of the flat surfaces.

• the success of precision measurement by slip gauges depends on the phenomenon of wringing

• Wringing: is thus defined as the property of measuring faces of a gauge block of adhering, by sliding or pressing the gauge against the measuring faces of other gauge blocks or the reference faces of datum surfaces, without the use of any extraneous means

• The recommended sets in the metric units are M112, M105, M87, M50, M33 and M27.

• The normal set of M112 is made up of blocks as given below:Range mm Steps mm Pieces

1.01  to 1.0091.010 to 1.4900.50 to 24.50

25, 50, 75, 1001.0005

0.00010.0100.050

25-

9494941

Total 112

Characteristics of End Standards Highly accurate and used for measurement of  closed

tolerances in precision engineering as well as standard laboratories, tool rooms, inspection departments.

They require more time for measurement and measure only one dimension.

They wear at their measuring faces They are not subjected to parallax error.

Differentiate between Line and End Standards

Sl No Characteristics Line Standard End Standard

1 Principal Length is expressed as distance b/w 2 lines

Length is expressed as distance b/w 2

ends

2 Accuracy Ltd to +/- 0.2mmHighly accurate of closed tolerance to

+/- 0.001 mm

3 Ease Quick and easy Time consuming and requires skill

4 Effect of wear wear at only the ends wears at measuring surface

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

Classification of Standards

• The accuracy of National Standards is transferred to working standards through a chain of intermediate standards in a manner given below

• National Standards • National Reference Standards • Working Standards • Plant Laboratory Reference Standards • Plant Laboratory Working Standards • Shop Floor Standards

here is degradation of accuracy in passing from the defining standards to the shop floor standards. The accuracy of particular standard depends on a combination of the number of times it has been compared with a standard in a higher echelon, the frequency of such comparisons, the care with which it was done, and the stability of the particular standards itself

Accuracy of Measurements

• Purpose of measurement is to determine the true dimensions of a part

• But no measurement can be made absolutely accurate There is always some error

• The amount of error depends upon the following factors

• The accuracy and design of the measuring instrument • The skill of the operator • Method adopted for measurement • Temperature variations • Elastic deformation of the part or instrument etc• Thus, the true dimension of the part cannot be

determined, but can only by approximate.

The agreement of the measured value with the true value of the measured quantity is called accuracy.

If the measurement of dimensions of a part approximates very closely to the true value of that dimension, it is said to be accurate

Precision

• Precision is the repeatability of the measuring process

• It refers to the group of measurements for the same characteristics taken under identical conditions

• It indicates to what extent the identically performed measurements agree with each other

• If the instrument is not precise it will give different (widely varying) results for the same dimension when measured again and again

Factors affecting the accuracy of the measuring system

Basic components of an accuracy evaluation are the five elements of a measuring system:

• Factors affecting the calibration standards. • Factors affecting the work piece. • Factors affecting the inherent characteristics of

the instrument. • Factors affecting the person, who carries out the

measurements, • Factors affecting the environment

Factors affecting the Standard• coefficient of thermal expansion• stability with time, • elastic properties, • geometric compatibility

Factors affecting the Work piece:• cleanliness, surface finish, waviness, scratch, surface

defects etc• adequate datum on the work piece• arrangement of supporting work piece,• thermal equalization etc.

Factors affecting the inherent characteristics of Instrument:

• scale error, • effect of friction• mechanical parts (slides, guide ways or moving

elements),• repeatability and readability

Factors affecting person:• training, skill, • sense of precision appreciation, • ability to select measuring instruments and standards

Factors affecting Environment

• temperature, humidity etc., • clean surrounding and minimum vibration enhance

precision, • adequate illumination, • temperature equalization between standard, work

piece, and instrument

Static characteristics and dynamic Characteristics

• Static characteristics pertains to system where the quantities being measured are constants or vary slowly with time.

• Dynamic characteristics – performance criteria are based on dynamic relations (involves rapidly varying quantities) constant dynamic characteristics.

Purely sinusoidal inputs like A.C voltage with frequency

Range and Span

• Range :- the difference between the largest and the smallest reading of the instrument is called range of instrument.

• Span: the algebraic difference between the upper and lower range values of instruments.

Example –

1)Range :2 KN/m2 to 50 KN/m2

Span : 50-2 = 48KN/m2

2) Range : -5˚C to 90˚C

Span: 90-(-5)=95˚C

Readability• Readability refers to the case with which the readings of a

measuring Instrument can be read• It is the ability of a measuring device to have its indications

converted into meaningful number• Fine and widely spaced graduation lines ordinarily improve

the readability• Readability can also be improved by using magnifying devices

Poor Readability Better Readability

Repeatability

• The ability of the measuring instrument to repeat the same results for the measurements for the same quantity, when the measurement are carried out

• by the same observer,• with the same instrument,• under the same conditions,• without any change in location,• without change in the method of measurement• and the measurements are carried out in short

intervals of time

Resolution

• Smallest increment in the input signal which can be satisfactorily detected by measuring instruments. In other words it is the least count of measuring instrument.

• The resolution of the instrument is high even if it can measure a smallest change in the instrument.

• Sometimes when the input is slowly increased from some arbitrary(non-zero) input value, it is observed that output doesn’t change at all until a certain increment is exceeded, this increment is called as resolution.

Sensitivity

• Sensitivity may be defined as the rate of displacement of the indicating device of an instrument, with respect to the measured quantity

• sensitivity of an instrument is the ratio of the scale spacing to the scale division value

For example: if on a dial indicator,

the scale spacing is 1.0 mm and

the scale division value is 0.01 mm,

then sensitivity is 100.

sensitivity at any value of y =dy/dx

dx and dy are increments of x and y.

Sensitivity

• The sensitivity may be constant or variable along the scale

• For Constant sensitivity we get a linear curve.• Sensitivity refers to the ability of measuring device to

detect small differences in a quantity being measured.• High sensitivity instruments may lead to drifts due to

thermal or other effects, and indications may be less.

change in outputSentivity

change in input

Linearity

• The ability to reproduce the input characteristics symmetrically is called Linearity.

• Linearity is simply a measure of maximum deviation of any point from the straight line.

• Every manufacturer tries to design and manufacture the instrument such that the output is a linear function of input.

• If x is the input and y is the output for a measuring instrument

then y= mx

where m- is the slope of straight line

However it is never possible to achieve complete linearity. Some deviation is always there which is represented by linearity deviation on the measuring instrument

Linearity

Percentage Linearity =Max Deviation /Full scale Reading x 100

Hysteresis

• According laws of thermodynamics , no Process can be exactly reversible .

• Similarly the measuring instruments may give one output when the input is being increased slowly upto the peak value and another output for same input, when it is decreased back to zero value.

• Hysteresis error can be minimized by taking output reading both for ascending and descending values of input and than taking an average.

Errors in measurements

• The error may be inherent in the measurement process or it may be induced due to variations in the way the experiment is conducted

• The errors may be classified as:• Gross errors• Systematic errors• Random errors

Gross errors

• Occur due to human mistakes in reading instruments and recording and calculating results of measurement

• Mathematical analysis of gross error is impossible since these may occur in different amounts

These errors are avoided by adopting two means • Immense care should be taken while taking reading of

data• Two, three or even more readings should be taken for

quantity being measured.

Systematic errors

• Can be divided as

1.Instrumental error

2.Environmental error

3.Observational error