Unit 1 Concept of Measurement

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

Definition

• Metrology is the name given to the science of pure measurement.

• Engineering Metrology is restricted to measurements of length & angle

• Measurement is defined as the process of numerical evaluation of a dimension or the process of comparison with standard measuring instruments

Why measure things?

• Check quality?• Check tolerances?• Allow statistical process control (SPC)?

Need of Measurement

• Establish standard• Interchange ability• Customer Satisfaction • Validate the design • Physical parameter into meaningful number• True dimension • Evaluate the Performance

Methods of Measurement

• Direct method • Indirect method • Comparative method • Coincidence method • Contact method • Deflection method• Complementary method

Direct method

• Measurements are directly obtained– Ex: Vernier Caliper, Scales

Indirect method

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

Comparative Method

• It’s compared with other known value– Ex: Comparators

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

Complementary method • The value of quantity to be measured is

combined with known value of the same quantity– Ex:Volume determination by liquid displacement

Deflection method

• The value to be measured is directly indicated by a deflection of pointer– Ex: Pressure Measurement

GENERALIZED MEASURING SYSTEM

Common elements of system

• Primary sensing element• Variable conversion element• Variable manipulation element • Data transmission element • Data processing element• Data presentation element

Primary sensing element

Variable conversion element

Variable manipulation element

Data transmission element

Data processing element

Data presentation element

Temperature

Observer

Units and standards

SI: fundamental Units

Physical Quantity Unit Name Symbol

length meter m

mass kilogram kg

time second s

electric current ampere A

temperature Kelvin K

amount of substance mole mol

luminous intensity candela cd

SI: Derived Units

Physical Quantity Unit Name Symbol

area square meter m2

volume cubic meter m3

speed meter persecond

m/s

accelerationmeter per

second squaredm/s2

weight, force newton N

pressure pascal Pa

energy, work joule J

Supplementary units

Physical Quantity Unit Name Symbol

Plane angle Radian rad

Solid angle Steradian sr

Standards

• International standards

• Primary standards

• Secondary standards

• Working standards

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

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.

DEFLECTION AND NULL TYPE• Physical effect generated by the measuring

quantity• Equivalent opposing effect to nullify the physical

effect caused by the quantity

ANALOG AND DIGITAL INSTRUMENTS

• Physical variables of interest in the form of continuous or stepless variations

• Physical variables are represented by digital quantities

ACTIVE AND PASSIVE INSTRUMENTS

• Instruments are those that require some source of auxiliary power

• The energy requirements of the instruments are met entirely from the input signal

Automatic and manually operated• Manually operated – requires the service of

human operator• Automated – doesn't requires human

operator

Contacting And Non Contacting Instruments

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

are not in close contact with the measuring medium

Absolute and Secondary Instruments

• These instruments give the value of the electrical quantity in terms of absolute quantities

• Deflection of the instruments can read directly

Intelligent instruments

• Microprocessors are incorporated with measuring instruments

Help topics

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

Characteristics of Measuring Instrument

• Sensitivity

• Readability

• Range of accuracy

• Precision

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 the closeness with

which the scale of the analog instrument can be read

Definition • Range of accuracy- Accuracy of a measuring

system is defined as the closeness of the

instrument output to the true value of the

measured quantity

• Precision- Precision is defined as the ability of the

instrument to reproduce a certain set of readings

within a given accuracy

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.

Sensitivity

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

Sensitivity is often known as scale factor or instrument magnification and an instrument with a large sensitivity (scale factor) will indicate a large movement of the indicator for a small input change.

Load Cell

Force, F

Output, Vo

Output, Vo (V)

Input, Fi (kN)

Slope = 5 V/kN

K

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

Sensitivity, K = 5 V/kN

Block Diagram:

Example

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

= 0.01 x 5 = 0.05 Vmax across the Meter will be

= 5 A x 0.05 = 0.25 V for fsd.

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

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

Readability

What is the value ?

What is the value ?

What is the value ?

Accuracy

• Accuracy = the extent to which a measured value agrees with a true value

• The difference between the measured value & the true value is known as ‘Error of measurement’

• Accuracy is the quality of conformity

Example: Accuracy

• Who is more accurate when measuring a book that has 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

Precision

• The precision of a measurement depends on the instrument used to measure it.

• For example, how long is this block?

How big is the beetle?

Measure between the head and the tail!

Between 1.5 and 1.6 in

Measured length: 1.54 in

The 1 and 5 are known with certainty

The last digit (4) is estimated between the two nearest fine division marks.

Example: Precision

Who is more precise when measuring the same 17.0 cm 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

Accuracy vs. Precision

High AccuracyHigh Precision

High PrecisionLow Accuracy

Three targets with three arrows each to shoot.

The person hit the bull's-eye?

Both accurate and precise

Precise but not accurate

Neither accurate nor precise

How do they compare?

Can you define accuracy vs. precision?Can you define accuracy vs. precision?

Uncertainty

• The word uncertainty casts a doubt about the

exactness of the measurement results

• True value = Estimated value + Uncertainty

Why Is There Uncertainty?

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

•Which of the instruments below has the greatest uncertainty in measurement?

Reading a Meterstick

. l2. . . . I . . . . I3 . . . .I . . . . I4. . cm

First digit (known) = 2 2.?? cm

Second digit (known) = 0.7 2.7? cm

Third digit (estimated) between 0.05- 0.08 cm

Length reported = 2.77 cm

or 2.76 cm

or 2.78 cm

Known + Estimated Digits

In 2.77 cm…

• Known digits Known digits 2 2 and and 77 are 100% certain are 100% certain

• The third digit The third digit 77 is estimated (uncertain) is estimated (uncertain)

• In the reported length, all In the reported length, all threethree digits digits (2.77 cm) are significant including the (2.77 cm) are significant including the estimated oneestimated one

Performance of Instruments

• All instrumentation systems are characterized by the system characteristics or system response

• There are two basic characteristics of Measuring instruments, they are – Static character – Dynamic character

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’.

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

Resolution

This is defined as the smallest input increment change that gives some small but definite numerical change in the output.

Threshold

This minimum value of input below which no output can be appeared is known as threshold of the instrument.

input

Output

Drift

Drift or Zero drift is variation in the output of an instrument which is not caused by any change in the input; it is commonly caused by internal temperature changes and component instability.

Sensitivity drift defines the amount by which instrument’s sensitivity varies as ambient conditions change.

input

Output

zero drift

input

Output

sensitivity drift

input

Outputsensitivity drift

zero drift

• 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

Range

• The ‘Range’ is the total range of values which

an instrument is capable of measuring.

Hysteresis

This is the algebraic difference between the average errors at corresponding points of measurement when approached from opposite directions, i.e. increasing as opposed to decreasing values of the input.

Actual/ Input Value

Measured Value Ideal

Hysteresis is caused by energy storage/ dissipation in the system.

Zero stability

The ability of the instrument to return to

zero reading after the measured has returned to

zero

Dead band

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

Linearity- The ability to reproduce the input characteristics symmetrically and linearly

• 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

Dynamic Characteristics

• The set of criteria defined for the

instruments, which are changes rapidly with

time, is called ‘dynamic characteristics’.

Dynamic Characteristics

• Steady state periodic

• Transient

• Speed of response

• Measuring lag

• Fidelity

• Dynamic error

• 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

• 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 measurement system indicates changes in the measured quantity without error

• Dynamic error- Difference between the true value of the quantity changing with time & the value indicated by the measurement system

Errors in Instruments

• Error = True value – Measured value

or

• Error = Measured value - True value

Types of Errors

• Error of Measurement

• Instrumental error

• Error of observation

• Based on nature of errors

• Based on control

Error of Measurement

• Systematic error -Predictable way in

accordance due to conditions change

• Random error - Unpredictable manner

• Parasitic error - Incorrect execution of

measurement

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

Error of observation

• Reading error

• Parallax error

• Interpolation error

Nature of Errors

• Systematic error

• Random error

Based on control

• Controllable errors– Calibration errors – Environmental (Ambient /Atmospheric Condition)

Errors – Stylus pressure errors – Avoidable errors

• Non - Controllable errors

Correction

• Correction is defined as a value which is added algebraically to the uncorrected result of the measurement to compensate to an assumed systematic error.

• Ex : Vernier Caliper, Micrometer

Calibration

• Calibration is the process of determining and adjusting an instruments accuracy to make sure its accuracy is with in manufacturing specifications.

Interchangeability

• A part which can be substituted for the component manufactured to the small shape and dimensions is known a interchangeable part.

• The operation of substituting the part for similar manufactured components of the shape and dimensions is known as interchangeability.

Compiled by

D.Vasanth Kumar D.Vasanth Kumar Assistant ProfessorDepartment of Mechanical EngineeringJansons Institute of Technology