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Unit 1Concept of Measurement

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Syllabus

General concept Generalized measurement

system-Units and standards-measuring

instruments- sensitivity, readability, range of

accuracy, precision-static and dynamic response

repeatability- systematic and random errors-

correction, calibration, interchangeability

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Definition

Metrology is the name given to the science ofpure measurement.

Engineering Metrology is restricted tomeasurements of length & angle

Measurement is defined as the process ofnumerical evaluation of a dimension or theprocess of comparison with standardmeasuring instruments

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Why measure things?

Check quality? Check tolerances?

Allow statistical process control (SPC)?

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Need of Measurement

Establish standard Interchange ability

Customer Satisfaction Validate the design Physical parameter into meaningful number

True dimension Evaluate the Performance

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Methods of Measurement

Direct method Indirect method

Comparative method Coincidence method Contact method

Deflection method Complementary method

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Direct method

Measurements are directly obtained Ex: Vernier Caliper, Scales

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Indirect method

Obtained by measuring other quantities Ex : Weight = Length x Breadth x Height x Density

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Comparative Method

Its compared with other known value Ex: Comparators

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Coincidence method Measurements coincide with certain lines and

signalsFundamental method Measuring a quantity directly in related with

the definition of that quantityContact method Sensor/Measuring tip touch the surface area

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Complementary method The value of quantity to be measured is

combined with known value of the samequantity Ex:Volume determination by liquid displacement

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Deflection method

The value to be measured is directly indicatedby a deflection of pointer Ex: Pressure Measurement

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Common elements of system

Primary sensing element Variable conversion element

Variable manipulation element Data transmission element Data processing element

Data presentation element

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Primary sensingelement

Variable conversionelement

Variablemanipulation element

Data transmissionelement

Data processingelement

Data presentationelement

Temperature

Observer

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Units and standards

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SI: fundamental Units

Physical Quantity Unit ame Symbol

length meter m

mass kilogram kgtime second s

electric current ampere A

temperature Kelvin Kamount of substance mole mol

luminous intensity candela cd

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SI: Derived Units

Physical Quantity Unit ame Symbol

area square meter m 2

volume cubic meter m3

speed meter persecond m/s

acceleration meter persecond squared m/s2

weight, force newton N

pressure pascal Pa

energy, work joule J

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Supplementary units

Physical Quantity Unit Name Symbol

Plane angle Radian rad

Solid angle Steradian sr

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Standards

International standards

Primary standards

Secondary standards

Working standards

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International

International Organization of Legal Metrology, ParisInternational Bureau of Weights and Measures at

Sevres, France

India National Physical LaboratoryDr. K.S. Krishnan MargNew Delhi - 110012IndiaPhone: 91-11-45609212Fax: 91-11-45609310Email: root@nplindia.org or root@nplindia.ernet.in

mailto:root@nplindia.orgmailto:root@mail.nplindia.ernet.inmailto:root@mail.nplindia.ernet.inmailto:root@nplindia.org

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Measuring Instruments

Deflection and null type instruments Analog and digital instruments Active and passive instruments Automatic and manually operated

instruments Contacting and non contacting instruments Absolute and secondary instruments Intelligent instruments.

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DEFLECTION AND NULL TYPE Physical effect generated by the measuring

quantity Equivalent opposing effect to nullify the physical

effect caused by the quantity

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ANALOG AND DIGITALINSTRUMENTS

Physical variables of interest in the form ofcontinuous or stepless variations

Physical variables are represented by digitalquantities

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ACTIVE AND PASSIVE INSTRUMENTS

Instruments are those that require some sourceof auxiliary power

The energy requirements of the instruments aremet entirely from the input signal

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Automatic and manually operated

Manually operated requires the service ofhuman operator

Automated doesn't requires human

operator

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Contacting And Non Contacting Instruments

A contacting with measuring medium Measure the desired input even though they

are not in close contact with the measuringmedium

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Absolute and Secondary Instruments

These instruments give the value of the electricalquantity in terms of absolute quantities

Deflection of the instruments can read directly

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Intelligent instruments

Microprocessors are incorporated withmeasuring instruments

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Help topics

http://www.tresnainstrument.com/education.html

http://www.tresnainstrument.com/education.htmlhttp://www.tresnainstrument.com/education.htmlhttp://www.tresnainstrument.com/education.htmlhttp://www.tresnainstrument.com/education.html

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Characteristics of Measuring Instrument

Sensitivity

Readability

Range of accuracy

Precision

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Definition

Sensitivity- Sensitivity is defined as the ratio of

the magnitude of response (output signal) to the

magnitude of the quantity being measured

(input signal)

Readability- Readability is defined as thecloseness with which the scale of the analog

instrument can be read

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Definition

Range of accuracy- Accuracy of a measuring

system is defined as the closeness of the

instrument output to the true value of themeasured quantity

Precision- Precision is defined as the ability of theinstrument to reproduce a certain set of readings

within a given accuracy

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Sensitivity If the calibration curve is liner, as shown, the sensitivity

of the instrument is the slope of the calibration curve. If the calibration curve is not linear as shown, then the

sensitivity varies with the input.

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Sensitivity

This is the relationship between a change in theoutput reading for a given change of the input.(This relationship may be linear or non-linear.)

Sensitivity is often known as scale factor orinstrument magnification and an instrument with alarge sensitivity (scale factor) will indicate a largemovement of the indicator for a small inputchange.

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Load Cell

Force, F

Output, V o

Output, V o (V)

Input, F i (kN)

Slope = 5 V/kN

K

Input, F (kN) Output, V o (V)

Sensitivity, K = 5 V/kN

Block Diagram:

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Example

(1) A 0.01 W /A meter with 5 A fsd,Rm = W /A x A

= 0.01 x 5 = 0.05 W V max across the Meter will be

= 5 A x 0.05 W = 0.25 V for fsd.

(2) A 0.1 W /A meter with 5 A fsd,will drop 2.5 V(i.e., it is 10 times less sensitive), which may biasthe results

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Readability

Readability is defined as the ease with which

readings may be taken with an instrument. Readability difficulties may often occur due to

parallax errors when an observer is noting the

position of a pointer on a calibrated scale

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Readability

What is the value ?

What is the value ?

What is the value ?

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Accuracy

Accuracy = the extent to which a measuredvalue agrees with a true value

The difference between the measured value &the true value is known as Error ofmeasurement

Accuracy is the quality of conformity

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Example: Accuracy

Who is more accurate when measuring a book thathas a true length of 17.0 cm?

A :

17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm

B ::

15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

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Precision

The precision of a measurement depends on theinstrument used to measure it.

For example, how long is this block?

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How big is the beetle?

Measure between the headand the tail!

Between 1.5 and 1.6 in

Measured length: 1.54 in

The 1 and 5 are known withcertainty

The last digit (4) is estimatedbetween the two nearest finedivision marks.

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Example: Precision

Who is more precise when measuring the same 17.0cm book?

A:17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm

B ::

15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

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Accuracy vs. Precision

High AccuracyHigh Precision

High PrecisionLow Accuracy

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Three targetswith threearrows each to

shoot.

The person hit the bull's-eye?

Bothaccurateand precise

Precise butnotaccurate

Neitheraccuratenor precise

How do theycompare?

Can you define accuracy vs. precision?

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Uncertainty

The word uncertainty casts a doubt about the

exactness of the measurement results

True value = Estimated value + Uncertainty

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Why Is There Uncertainty?

Measurements are performed with instruments ,and no instrument can read to an infinite number ofdecimal places

Which of the instruments below has the greatestuncertainty in measurement?

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Reading a Meterstick

. l2. . . . I . . . . I 3 . . . .I . . . . I 4. . cm

First digit (known) = 2 2.?? cmSecond digit (known) = 0.7 2.7? cm

Third digit (estimated) between 0.05- 0.08 cm

Length reported = 2.77 cmor 2.76 cm

or 2.78 cm

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Known + Estimated Digits

In 2.77 cm

Known digits 2 and 7 are 100% certain

The third digit 7 is estimated (uncertain)

In the reported length, all three digits(2.77 cm) are significant including theestimated one

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Performance of Instruments

All instrumentation systems are characterizedby the system characteristics or systemresponse

There are two basic characteristics ofMeasuring instruments, they are Static character

Dynamic character

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Static Characteristics

The instruments, which are used to measure

the quantities which are slowly varying with

time or mostly constant, i.e., do not vary with

time, is called static characteristics .

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STATIC CHARACTERISTICS OF AN INSTRUMENTS

Accuracy Precision

Sensitivity

Resolution

Threshold

Drift

Error

Repeatability

Reproducibility

Dead zone Backlash

True value

Hysteresis

Linearity

Range or Span

Bias

Tolerance

Stability

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Resolution

This is defined as the smallest input incrementchange that gives some small but definitenumerical change in the output.

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Threshold

This minimum value of input below which nooutput can be appeared is known as thresholdof the instrument.

input

Output

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DriftDrift or Zero drift is variation in the output ofan instrument which is not caused by anychange in the input; it is commonly caused byinternal temperature changes and componentinstability.

Sensitivity drift defines the amount by whichinstruments sensitivity varies as ambientconditions change.

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input

Output

zerodrift

input

Output

sensitivity drift

input

Output sensitivity drift

zerodrift

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Error The deviation of the true value from

the desired value is called Error

Repeatability It is the closeness value of

same output for same input under same

operating condition

Reproducibility - It is the closeness value of

same output for same input under same

operating condition over a period of time

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Range

The Range is the total range of values which

an instrument is capable of measuring.

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Hysteresis

This is the algebraic difference between the averageerrors at corresponding points of measurementwhen approached from opposite directions, i.e.increasing as opposed to decreasing values of theinput.

Actual/ InputValue

MeasuredValue Ideal

Hysteresis iscaused byenergystorage/dissipation inthe system.

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Zero stability

The ability of the instrument to return to

zero reading after the measured has returned to

zero

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Dead band

This is the range of different input values overwhich there is no change in output value.

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Linearity- The ability to reproduce the inputcharacteristics symmetrically and linearly

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Backlash Lost motion or free play of

mechanical elements are known as backlash

True value The errorless value of measured

variable is known as true value

Bias The Constant Error

Tolerance- Maximum Allowable error in

Measurement

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Dynamic Characteristics

The set of criteria defined for the

instruments, which are changes rapidly with

time, is called dynamic characteristics .

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Dynamic Characteristics

Steady state periodic

Transient

Speed of response

Measuring lag

Fidelity

Dynamic error

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Steady state periodic Magnitude has a

definite repeating time cycle

Transient Magnitude whose output does not

have definite repeating time cycle

Speed of response- System responds to

changes in the measured quantity

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Measuring lag Retardation type :Begins immediately after the

change in measured quantity Time delay lag : Begins after a dead time after the

application of the input

Fidelity- The degree to which a measurementsystem indicates changes in the measuredquantity without error

Dynamic error- Difference between the truevalue of the quantity changing with time &the value indicated by the measurementsystem

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Errors in Instruments

Error = True value Measured value

or

Error = Measured value - True value

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Types of Errors

Error of Measurement

Instrumental error

Error of observation

Based on nature of errors

Based on control

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Error of Measurement

Systematic error -Predictable way in

accordance due to conditions change

Random error - Unpredictable manner

Parasitic error - Incorrect execution of

measurement

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Instrumental error

Error of a physical measure

Error of a measuring mechanism

Error of indication of a measuring instrument

Error due to temperature

Error due to friction

Error due to inertia

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Error of observation

Reading error

Parallax error

Interpolation error

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Nature of Errors

Systematic error

Random error

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Based on control

Controllable errors Calibration errors Environmental (Ambient /Atmospheric Condition)

Errors Stylus pressure errors Avoidable errors

Non - Controllable errors

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Correction

Correction is defined as a value which is addedalgebraically to the uncorrected result of themeasurement to compensate to an assumed

systematic error. Ex : Vernier Caliper, Micrometer

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Calibration

Calibration is the process of determining andadjusting an instruments accuracy to makesure its accuracy is with in manufacturing

specifications.

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Interchangeability

A part which can be substituted for thecomponent manufactured to the small shapeand dimensions is known a interchangeable

part. The operation of substituting the part for

similar manufactured components of the

shape and dimensions is known asinterchangeability.

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Compiled by

D.Vasanth Kumar

Assistant Professor

Department of Mechanical Engineering

Jansons Institute of Technology