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Introduction metrology

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									Industrial Metrology
                Instructor and references
•                Sugeng S
    Instructor : S             d ST.,MS-Eng
                         Supriadi, ST S
•   Office : Manufacturing Laboratory, Dept. of Mechanical Eng. UI
•                    ext
    Phone : 7270032 ext. 222
•   E-mail : priadi_007@yahoo.com
•   References :
        Groover, Mikell P., “Fundamentals of Modern Manufacturing”, Wiley 2nd
        edition, 1999.
        Kalpakjian, “Manufacturing Engineering and Technology, McGraw Hill 4th
        edition, 2001.
        Jain, RK, “Engineering Metrology”, Khanna Publishers, 1979.
        Dotson, Connie, “Fundamental of Dimensional Metrology”, 4th ed.,
        Thomson, 2003.
        Th          2003
                Course E l ti
                C      Evaluation
Course evaluation :
Group Work (Assignment, Lab section) 20%
Mid Test                             20%
Quiz (2 times x 5 %)                 10%
Final Test                           50%

Grade Scale
G d S l :
A/A-                       80 - 100
B+/B/B-                    70 - 79
C+/C/C-                    55 - 69
D+/D/D-                    30 - 54
THE PURPOSE OF THIS COURSE

 1.          y            p            gy
      To study basic concept of metrology

 2.   To understand the application of metrology on
      manufacturing process
                       Topics covered in this course
Week   Topics

                              gy
       Introduction to Metrology

       Dynamic characteristics of measurement
       Geometric Specifications
       G    t i S ifi ti

       Length Metrology

       Angle Metrology

       Form and Surface Metrology
       Screw Thread & Gear Metrology
       CMM & Machine Tools Metrology
       Uncertainty analysis and Quality control

       Lab. Section
           Metrology : science of measurement of the Geometrical specification
                            Dimension, Position
                            Dimension Position, Form & Surface



                                 Geometrical Metrology
                                 G      i l       l

Reasons for measuring ? :
•   To KNOW … : weight, length, area etc
    everyday life
•   To measure Quality of the measured object
      for inspection
•   To meet design specifications to improve
    quality the manufactured parts as
    feedback for      f
    f db k f manufacturing process
•   etc

Measuring : process by which numbers or symbols are assigned to
attributes of entities to describe them according to clearly defined
rules
Components of Measurement Systems

 Measurement systems
                    Gauges
                (measurement
                 instruments)
                                                            Successful
 Procedures                 Environment
 (methods, agreed                   (temperature,
                                                         measurement !
 units & standards)                    cleanliness,
                                       cleanliness
                                    vibration, etc)     (sufficient correctness
                                                        ( ffi i
                                                        and      accuracy   for
  Workpiece                 Calibration/                particular need)
      (temperature,
      (temperature          Traceability
         cleanliness,
                                 (units, date, time,
      fixturing, etc)                            etc)

               Operator
                 (skill level)
Components of Measurement Instruments (gauges

   In General, they can be devided into three parts :
   1.
   1     Stage I
         St              D t t r Tr n d    r rS n r t
                         Detector-Transducer or Sensor stage      (INPUT)
   2.    Stage II        Intermediate stage : signal conditioning
   3.    Stage III
            g            Terminating or Read-Out stage
                                   g                g        (      )
                                                             (OUTPUT)
                                                                          Stage II & III


                                                         Output
 Input



                                                        Estimation
                                                        of real value !
                                                                      Stage I
                Precision and Accuracy
Precision :
•The repeatability of a measuring processes
•Or Relates to the quality of an operation by
which a result is obtained                         A we close t each other ?
                                                   Are   l    to   h th
Accuracy :
•The agreement of the result of a measurement with
 The
the true value of measured quantities
                   q     y            ,
•Or Relates to the quality of a result, and is
distinguished from precision, which relates to the
quality of the operation by which the result is
obtained
                                                   Do we get the taget ? NO    ERR

       ! In most measurements it is only Precision that is needed !
          Precision and Accuracy (cont’d)




Accuracy with precision   Precision with blunder   Accuracy with blunder


No measurement can be absulutely correct   there is always some ERROR
ERROR : The difference between the mean of set of readings on some
component and the true value (target).
•Less is the ERROR, More Accurate is the instrument
•TRUE VALUE is NEVER known UNCERTAINTY creeps in             the
   g
magnitude of ERROR must be ESTIMATED !
•Depends upon : Components of Measurement Systems (explained
before)
                              Accuracy
Highly accurate instrument possesses both great sensitivity and
consistency. Sensitivity the ratio of the change of inst. indication to the
                         measured
change of quantity being measured. Consistency readings are the same
all the time.
                                    VS
Sensitive and Consitent instrument need not necessarily be Accurate,
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 !!! :
                                                    g
• An instrument can not be more accurate than its degree of
  sensitiveness !
• Degree of sensitivity not necessarily the same for all over its range
           g
  of readings !
• Highly sensitive instr. Is not necessarily consistent in its readings
                                             (cont d)
                                    Accuracy (cont’d)

Greater accuracy == greater source of errors to be controlled


ACCURATE measuring instrument should :
1. It should possess 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
                      Accuracy and Cost
The Metrology : should provide the required accuracy capability at the
most economical cost !!!

Six factors influencing ACCURACY (as explained before) :
1.               ( )            quality of the standards, etc
     Calibration (C) : methods, q     y
2.   Operator (O) : skill level, training, sense of precision and accuracy
     appreciation, attitude
3.
3                            influences cleanliness,         properties
     Workpiece (W) : ambient influences, cleanliness elastic properties, etc
4.   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
        p        y       g     p p ,            ,       ,
     components by sunlight or people, vibration, sounds, etc
                 Accuracy and Cost (cont’d)
Selection of measuring instruments involves proper analysis of cost-to-
     accuracy consideration

 COST rises Exponentially with ACCURACY
          Cost
             t




                           Accuracy


 Accuracy should be 10% of Tolerance !
Manufacturing Processes, Accuracy and Measuring
                  Instruments
anufactured parts and state-of-the art of Tolerance




    Semilog Plot of Trends in Limiting Values of Tolerances in Normal, Precision
           and Ultraprecision Regimes with Examples of State-of-the Art
                     p           g                p
                                       Errors
Measurement error : The difference between the indicated and the actual values
of the measurand Level of Accuracy of instruments
 Expressed
•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 :
                         ea g a d te p etat o s o          e os
           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 statistical
 1
     analysis : calibration errors, error of technique, uncorrected loading errors,
     limits of resolutions, ambient conditions, misalignment of workpiece and
     instr. location errors, etc. repeated consistently.
     Random errors (
 2. R d                       id t l            ) lack f       i t         i
                         (accidental errors) l k of consistency : enviromental     t l
     variations, certain types of human errors, etc. magnitude and sign can not
     be predicted.
 3       g                                                            (
 3. Illegitimate errors should not exist : blunder or mistake (carelessness,        ,
     improper training, emotions, etc), computational errors, etc.
 4. Static errors result from intrinsic imperfections or limitations in
     hardware and apparatus compared to ideal instruments.
                             Errors (cont’d)
Statistical parameters are used to assess Random Errors to achieve
consistency (precision) of values and not their accuracy (approach to th
            )
truth value) !!! :
                                       x1 + x2 + x3 + ... + xn
•Arithmatic mean                  x=
                                                 n
                                                                           (        )
                                                                                        2
                                                                         Σ xi − x
•Standard deviation (mean of the mean)                             σ=
                                                                               n

• Error Distribution =           Gaussian Distribution : most of the
                                                               f h
 examples in a set of data are close to the "average," while relatively few examples
 tend to one extreme or the other.




                             error
   Probability density

 Probability distribution of random errors
                                     Erros (cont’d)

                                                            x2
                                                1
                         P ( x1 < x < x 2 ) =
                                                                     2
                                                                         / 2σ 2

                                              σ 2π          ∫
                                                            x1
                                                              e− x                dx




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

•Error Accumulation         can be measured interm of root-mean-square
                               y        (LE)        g        (  )
 Total static errors = linearity errors ( ) + reading errors (RE)
 + characteristic error (CE) + environmental errors (EF)

                       ( LE1 + LE2 + ...)
                                            2
                   =                            + RE 2 + CE 2 + EF12 + EF22 + ...

 Characteristic error deviation of the output of a measuring instr.
 from the predicted (nominal) performance specification
                            Errors (cont’d)
• Variance of Error Distribution       1 n 2
    measure of error distribution   σ = ∑ xi
                                     2

                                       n i =1


                                         Large variance !




                                         Small variance !
    Bias, Repeatability and Reproducibility (R&
 What is Gauge (instrument) R&R ?
     It is a statistical approach of determining if a instrument (gauge or a
                                                          measurement.
     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 the
     process, if any, as too much in-process variations can cause serious
     problems.


Type of Measurement Variation :
1. Bias
2. Repeatability
3. Reproducibility
          Bias, Repeatability and Reproducibility (R&R
                             (cont d)
                             (cont’d)
Bias :
    th diff         between the observed average of measurement and
    the difference b t       th b         d           f            t d
    the reference value.
    It is the systematic error that is an indication of a measuring
    instrument.
    instrument
    The reference value is determined by averaging several
    measurements using standard measuring equipment.

                               Bias




                   Reference
                     value


                                      Observed average
                                           value
    Bias, Repeatability and Reproducibility (R&R)
                       (cont d)
                       (cont’d)
Example :

Consider the following ten measurements by an appraiser. The reference
value determined by layout inspection equipment is 0.80 mm
                        0 75
                   X1 = 0.75               0 80
                                     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
                                                                10
The observed average is the sum of the measurements divided by 10.

                  Bias = Observed Average – Reference Value
                        Bias = 0.75 – 0.80 = - 0.05
     Bias, Repeatability and Reproducibility (R&R)
                        (cont d)
                        (cont’d)
Repeatability :
    The variation in measurements obtained with one measurement
    instrument when used several times by an appraiser while measuring the
    identical characteristic on the same part.
                       y             q p
    It is also commonly known as equipment variation.



                                                 Gage A




                                                       Gage B




    In the above figure, the repeatability of Gage A is more than that of Gage B as shown by
    their probability density functions.
    Bias, Repeatability and Reproducibility (R&R)
                       (cont d)
                       (cont’d)
Reproducibility :
    The variation in the average of measurements made by different
    appraisers using the same instrument when measuring the identical
    characteristic on the same part.
    It is commonly known as appraiser variation.

                                         Operator B




                                                      Operator C

                            Operator A
Bias, Repeatability and Reproducibility (R&R)
                   (cont d)
                   (cont’d)


                                Repeatability



                     +


                               Reproducibility



                     =
                           Stability
Stability :
1. The total variation in the measurements obtained with a
                              h
    measurement system on the same master or parts when h
    measuring a single characteristic over an extended time period.
2. Sometimes referred to as drift.


                            Stability


                  Time 2

                                           Time 1
                                       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                   Reference
                    value                       value
                               Smaller bias                        Larger bias
                                 value                               value




                    Observed Average                      Observed Average
                          value                                 value
                                                          ( g     part    g )
                                                          (Higher p of Range)
                  (Lower part of Range)
                  (L        t fR      )

Reference line :
1. Terminal line : drawn from origin to the data point at full scale output
2. 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 poin
4. Least square line : sum of the square of deviations of data points from th
    line is minimized
                                  Part Variation
The Part Variation is essentially a measure of the variation of the process. If
a large number of parts made by a process are measured, 99%(5.15 s) of the
                                     limits.
parts would be within the variation limits
The Part Variation is always less than or equal to the total variation. In most
industrial processes the part variation is large compared to the gage variation
 nd the         mpti n th t th b r d t nd rd d i ti n i ppr im t l
and so th assumption that the observed standard deviation is approximately
equal to the total population standard deviation holds good.
     Methods to determine Repeatability and Reproducibi
                            (R&R)
There are three basic and widely used methods for determining the Instr. R&R
 Range method
     g
 Average and Range method
 Analysis of Variance method (ANOVA)

Average and Range method
The Average and Range method is a statistical method that provides an estimat
of the following components.
        Part Variation
        Repeatability
        Reproducibility
        R&R
        Total Variation
Thi method computes the total measurement system variability, which can be
This m th d mp t th t t l m           r m nt      t m ri bilit     hi h n b
separated into components like repeatability, reproducibility and part variation.
                                        Average Range Method

he Average and Range method
q           p parts, appraisers and
quires multiple p       pp
als to quantify the repeatability and
producibility. The following is a
pical Data sheet used in industries.
                       Average Range Method (cont’d)
Assumes the following example : (Taken from Measurement System Analysis
Reference Manual)




     No. of Appraisers = 2
     No of Trials
     No.              =3
     No. of parts     =5
                                Average Range Method (cont’d)
 Repeatability – Equipment Variation (EV) :
EV = R * K 1
    = 2.5 x 3.00
     =757.5
Note:
  All calculations are based upon predicting 5.15σ (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. of
 pp i e (g).            l e     is obt ined from Table 1
appraisers (g) The value of d2 i obtained f om T ble 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) :
  AV =      (X   DIFF   * K 2 ) 2 − ( EV         2
                                                     / nr )
       =   ( 0 . 6 * 3 . 65 ) 2 − ( 7 . 5 2 / 5 * 3 )
       = 1 . 0461
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.
            Average Range Method (cont’d)




     h    i         i hi limits(UCL    d           d    h
All the points are within li i (UCLR and LCLR) and so the
measurement process is under control and is said to be consistent.
                  Average Range Method (cont’d)
Repeatability and Reproducibility (R&R) :
                        R & R = EV 2 + AV 2
                             = 7.5 2 + 1.04612
                             = 7.57

Part Variation (PV) :     PV = R p * K 3
                             = 6.15 * 2.08
                             = 12.79

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.
                            1.                               2.48.
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.
                  Average Range Method (cont’d)




There are three points that fall outside the limits and so the measurement
process is not adequate to detect part-to-part variations.
                    UCL   X
                              = X + A2 R      LCL   X
                                                        = X − A2 R

For constant A2 look up Table 2.
               Average Range of Method (cont’d)
Total Variation (TV) :   TV = ( R & R ) 2 + ( PV ) 2

                            = 7.57 2 + 12.79 2
                            = 14.86

Summary :
Average Range Method
       (cont d)
       (cont’d)
Average Range Method
       (cont d)
       (cont’d)
 Table 2. Control Chart constants

								
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