1. Introduction of Metrology

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TOPICS OF METROLOGY COVERED IN THIS COURSE

1. Introduction to Metrology

2. Dynamic characteristics of measurement

3. Geometric Specifications

4. Length Metrology

5. Angle Metrology

6. Form and Surface Metrology

7. Screw Thread & Gear Metrology

8. CMM & Machine Tools Metrology

9. Uncertainty analysis and Quality control

10. Lab. Section


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PERTANYAAN

Apakah pengukuran itu?

Mengapa kita harus mengukur?


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Reasons for measuring ? :

To KNOW : weight, length, area etceveryday life

To measure Quality of the measured object for inspection

To meet design specifications to improvequality the manufactured parts asfeedback for manufacturing process

etc

METROLOGY: SCIENCE OF MEASUREMENT OF THE GEOMETRICAL SPECIFICATION DIMENSION, POSITION, FORM & SURFACE

Geometrical Metrology

Measuring : process by which numbers or symbols are assigned toattributes of entities to describe them according to clearly definedrules


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COMPONENTS OF MEASUREMENT SYSTEMS

Measurement systems

Gauges(measurementinstruments)

Workpiece

(temperature,cleanliness,

fixturing, etc)

Calibration/

Traceability(units, date, time,

etc)

Operator(skill level)

Environment

(temperature,

cleanliness,vibration, etc)

Procedures

(methods, agreed

units & standards)

Successful

measurement !

(sufficient correctnessand accuracy forparticular need)


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PERTANYAAN

Jelaskan komponen2 dalam pengukuran


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COMPONENTS OF MEASUREMENT INSTRUMENTS (GAUGES)

In General, they can be devided into three parts :

1. Stage I Detector-Transducer or Sensor stage (INPUT)2. Stage II Intermediate stage : signal conditioning

3. Stage III Terminating or Read-Out stage (OUTPUT)

Stage I

Stage II & III

Input

Output

Estimation

of real value !


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PERTANYAAN

Apa beda akurasi dan presisi?


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PRECISION AND ACCURACY

Precision :

The repeatability of a measuring processes

Or Relates to the quality of an operationbywhich a result is obtained

Accuracy :

The agreement of the result of a measurementwiththe true value of measured quantities

Or Relates to the quality of a result, and isdistinguished from precision, which relates to thequality of the operation by which the result isobtained

Do we get the taget ? NO ERROR

Are we close to each other ?

! In most measurements it is only Precision that is needed !


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PRECISION AND ACCURACY(CONTD)

ERROR: The differencebetween the mean of set of readings on somecomponent and the true value (target).

Less is the ERROR, More Accurate is the instrument

TRUE VALUE is NEVER known UNCERTAINTY creeps in themagnitude of ERROR must be ESTIMATED !

Depends upon : Components of Measurement Systems (explainedbefore)

Accuracy with precision Precision with blunder Accuracy with blunder

No measurement can be absulutely correct there is always some ERROR


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ACCURACY

Highly accurate instrumentpossesses both great sensitivity and

consistency. Sensitivity the ratio of the change of inst. indication to the

change of quantity being measured. Consistency readings are the sameall the time.

VS

Sensitive and Consitent instrument need not necessarily beAccurate,

because the standard from which its scale is calibrated may be wrong

Errors will be constant at any given reading (possible to calibrate)

Notes that !!! :

An instrument can not be more accurate than its degree ofsensitiveness !

Degree of sensitivity not necessarily the same for all over its rangeof readings !

Highly sensitive instr. Is not necessarily consistent in its readings


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ACCURACY(CONTD)

ACCURATE measuring instrument should :

1. It shouldpossess the requisite and constant accuracy

2. As far as possible, the errors should be capable of elimination by

adjusment contained within the instrument itself

3. Every important source of inaccuracy should be known

4. When an error cant be eliminated, it should be made as small as

possible and capable of measurement by the instrument itself

Greater accuracy == greater source of errors to be controlled


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ACCURACY AND COST

The Metrology : should provide the required accuracy capability at the

most economical cost !!!

Six factors influencing ACCURACY(as explained before) :

1. Calibration (C) : methods, quality of the standards, etc

2. Operator (O) : skill level, training, sense of precision and accuracy

appreciation, attitude

3. Workpiece (W) : ambient influences, cleanliness, elastic properties, etc4. Procedures (P) : ambient influences (thermal expansion), stability with

time, standards, methods, etc

5. Instrument (I) : hysteresis, backlash, friction, deformation, etc

6. Environment (E) : temperature heat radiation from light, heating of

components by sunlight or people, vibration, sounds, etc


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ACCURACY AND COST (CONTD)

Selection of measuring instruments involves proper analysis of cost-to-

accuracy consideration

COST rises Exponentially with ACCURACY

Accuracy

Cost

Accuracy should be 10% ofTolerance !


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MANUFACTURING PROCESSES, ACCURACY AND MEASURING

INSTRUMENTS


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Semilog Plot of Trends in Limiting Values of Tolerances in Normal, Precision

and Ultraprecision Regimes with Examples of State-of-the Art

MANUFACTURED PARTS AND STATE-OF-THE ART OF

TOLERANCE


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PERTANYAAN

Apakah error itu?


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ERRORS

Measurement error : The difference between the indicated and the actual values

of the measurand Level ofAccuracy of instruments

Expressed either as an absolute error OR on a relative scale

Contributed by one or more Components of Measurement systems

Must be examined in order to :

get causes, meaning and interpretations of the errors

obtain methods for reducing or circumventing the errors

Four types of (Source of) ERRORS in measurement :

1. Systematic errors (controllable errors) not susceptible to statisticalanalysis : calibration errors, error of technique, uncorrected loading errors,limits of resolutions, ambient conditions, misalignment of workpiece andinstr. location errors, etc. repeated consistently.

2. Random errors (accidental errors) lack of consistency : enviromentalvariations, certain types of human errors, etc.magnitude and sign can notbe predicted.

3. Illegitimate errors should not exist : blunder or mistake (carelessness,

improper training, emotions, etc), computational errors, etc.4. Static errorsresult from intrinsic imperfections or limitations in

hardware and apparatus compared to ideal instruments.


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1 2 3... nx x x xx

n

ERRORS (CONTD)

Arithmatic mean

Standard deviation (mean of the mean)

2

ix x

n

Statistical parameters are used to assess Random Errors to achieveconsistency (precision) of values and not their accuracy (approach to thetruth value) !!! :

Error Distribution = Gaussian Distribution : most of theexamples in a set of data are close to the "average," while relatively few examplestend to one extreme or the other.

Probability distribution of random errors

Probability density

error


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Error Accumulation can be measured interm ofroot-mean-square

X1 X2

2 2

2

/ 2

1

11 2

2

x

x

x

P x x x e dx

ERROS (CONTD)

Probability that X (error value) lies within the interval X1 dan X2

Total static errors = linearity errors (LE) + reading errors (RE)+ characteristic error (CE) + environmental errors (EF)

2 2 2 2 2

1 2 1 2... ...LE LE RE CE EF EF

Characteristic error deviation of the output of a measuring instr.from the predicted (nominal) performance specification


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Large variance !

Small variance !

ERRORS (CONTD)

Variance of Error Distributionmeasure of error distribution

2 2

1

1 n

i

i

xn


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What is Gauge (instrument) R&R? It is a statistical approach of determining if a instrument (gauge or a

gauging system) is suitable for the process under measurement.

Purpose : Measurement is an integral part of any manufacturing unit and is useful in

predicting the quality of the manufacturing process .

The technique is very useful in predicting the inherent variation in theprocess, if any, as too much in-process variations can cause seriousproblems.

BIAS, REPEATABILITY AND REPRODUCIBILITY(R&R)

Type of Measurement Variation :

1. Bias

2. Repeatability

3. Reproducibility


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(CONTD)

Bias :

the difference between the observed average of measurement andthe reference value.

It is the systematic error that is an indication of a measuringinstrument.

The reference value is determined by averaging severalmeasurements using standard measuring equipment.

Bias

Observed average

value

Reference

value


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(CONTD)

Consider the following ten measurements by an appraiser. The reference

value determined by layout inspection equipment is 0.80 mm

X1 = 0.75 X6 = 0.80

X2 = 0.75 X7 = 0.75

X3 = 0.80 X8 = 0.75

X4 = 0.80 X9 = 0.75

X5 = 0.65 X10 = 0.70

The observed average is the sum of the measurements divided by 10.

Bias = Observed AverageReference Value

Bias = 0.75

0.80 = - 0.05

Example :


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BIAS, REPEATABILITYAND REPRODUCIBILITY(R&R)

(CONTD)

Repeatability :

Thevariation in measurements obtained with one measurementinstrumentwhen used several times by an appraiserwhile measuring theidentical characteristic on the same part.

It is also commonly known as equipment variation.

In the above figure, the repeatability of Gage A is more than that of Gage B as shown by

theirprobability density functions.

Gage A

Gage B

( & )


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(CONTD)

Reproducibility :

Thevariation in the average of measurements made by differentappraisers using the same instrumentwhen measuring the identicalcharacteristic on the same part.

It is commonly known as appraiser variation.

Operator A

Operator C

Operator B

B R R


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+

=

Repeatability

Reproducibility

BIAS, REPEATABILITY AND REPRODUCIBILITY

(R&R) (CONTD)


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Stability :

1. The total variation in the measurements obtained with a

measurement system on the same master or partswhenmeasuring a single characteristic over an extended time period.

2. Sometimes referred to as drift.

Stability

Time 1

Time 2

STABILITY

L


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Reference

value

Reference

value

Smaller bias

value

Larger bias

value

Observed Average

value

Observed Average

value

(Lower part of Range)(Higher part of Range)

LINEARITY Maximum deviation of the output of the measuring system from a

specified stright line applied to a plot of data points on curve of

measured values vs. the measurand input values

Reference line :1. Terminal line : drawn from origin to the data point at full scale output2. End point line : drawn between the end points of the data plot

3. Best fit line : the mid-way line of two parallel lines enclosing all data points4. Least square line : sum of the square of deviations of data points from the

line is minimized

PART VARIATION


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The Part Variation is essentially a measure of the variation of the process. Ifa large number of parts made by a process are measured, 99%(5.15 s) of theparts would be within the variation limits.

The Part Variation is always less than or equal to the total variation. In mostindustrial processes the part variation is large compared to the gage variationand so the assumption that the observed standard deviation is approximatelyequal to the total population standard deviation holds good.

PART VARIATION

METHODS TO DETERMINE REPEATABILITY AND


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There are three basic and widely used methods for determining the Instr. R&R :

Range method

Average and Range methodAnalysis of Variance method (ANOVA)

Average and Range method

The Average and Range method is a statistical method that provides an estimateof the following components.

Part Variation

Repeatability

Reproducibility

R&R

Total Variation

This method computes the total measurement system variability, which can beseparated into components like repeatability, reproducibility and part variation.

METHODS TO DETERMINE REPEATABILITYAND

REPRODUCIBILITY(R&R)

AVERAGE RANGE METHOD


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TheAverage and Range method requires multiple parts, appraisers and

trials to quantify the repeatability and reproducibility. The following is a

typical Data sheet used in industries.

AVERAGE RANGE METHOD

AVERAGE RANGE METHOD (CONTD)


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Assumes the following example : (Taken from Measurement System Analysis

Reference Manual)

No. of Appraisers = 2

No. of Trials = 3

No. of parts = 5

AVERAGE RANGE METHOD (CONT D)



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RepeatabilityEquipment Variation (EV) :

= 2.5 x 3.00

= 7.5

Note:

All calculations are based upon predicting 5.15 (99% area under the normal curve)

K1 = 5.15/d2 where d2 depends on the no. of trials (m) and the number of parts times the no. ofappraisers (g). The value of d2 is obtained from Table 1.

In this case m = 3 and g = 2 x 5 = 10. Looking up Table 1 we get d2 = 1.72.

Therefore K1 = 5.15/1.72 = 3.00.

Reproducibility

Appraiser Variation (AV) :

Note:

If a negative value is calculated under the square root sign, the value AV defaults to zero.

n = No.of parts and r = No.of Trials

K2 = 5.15/d2 where d2 depends on the no. of appraisers (m) and g is 1, since there is only one

range calculation.

In this case m = 2. Looking up Table 1 we get d2 = 1.41

Therefore K2 = 5.15/1.41 = 3.65.

1*KREV

)/()*(22

2 nrEVKXAV DIFF

0461.1

)3*5/5.7()65.3*6.0(22




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All the points are within limits(UCLR

and LCLR

) and so the

measurement process is under control and is said to be consistent.




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Repeatability and Reproducibility (R&R) :

Part Variation (PV) :

Note:

K3 = 5.15/d2 where d2 is dependent on the no.of parts (m) and g = 1,since there is only one range calculation.

In this case m = 5 and g = 1. Looking up Table 1 we get d2 = 2.48.

Therefore K3 = 5.15/2.48 = 2.08.

22& AVEVRR

57.7

0461.15.722

3* KRPV p

79.12

08.2*15.6




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There are three points that fall outside the limits and so the measurement

process is not adequate to detect part-to-part variations.

RAXUCLX 2 RAXLCLX 2

For constant A2 look up Table 2.


AVERAGE RANGE OF METHOD (CONTD)


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Total Variation (TV) :

Summary :

22)()&( PVRRTV

86.14

79.1257.722

AVERAGE RANGE OF METHOD (CONT D)



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Table 2. Control Chart constants


1. Introduction of Metrology

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