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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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BIAS, REPEATABILITY AND REPRODUCIBILITY(R&R)
(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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BIAS, REPEATABILITY AND REPRODUCIBILITY(R&R)
(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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BIAS, REPEATABILITY AND REPRODUCIBILITY(R&R)
(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)
AVERAGE RANGE METHOD (CONTD)
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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
AVERAGE RANGE METHOD (CONT D)
AVERAGE RANGE METHOD (CONTD)
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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.
AVERAGE RANGE METHOD (CONT D)
AVERAGE RANGE METHOD (CONTD)
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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
AVERAGE RANGE METHOD (CONT D)
AVERAGE RANGE METHOD (CONTD)
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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 METHOD (CONT D)
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)
AVERAGE RANGE METHOD (CONTD)
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AVERAGE RANGE METHOD (CONT D)
AVERAGE RANGE METHOD (CONTD)
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Table 2. Control Chart constants
AVERAGE RANGE METHOD (CONT D)