The document discusses critical factors affecting measurement uncertainty in coordinate measuring machines (CMMs) within the context of reverse engineering aerospace products. It details sources of error, including hardware, workpiece characteristics, and environmental factors, while also outlining a methodology for quantifying and calculating uncertainty budgets. The conclusions emphasize that reducing volumetric length and probing errors, alongside appropriate filter selection, can significantly enhance measurement accuracy.

2. DIAGNOSTIC OF CRITICAL FACTORS IN
UNCERTAINTY MEASUREMENT OF COORDINATE
MEASURING MACHINE IN REVERSE ENGINEERING
OF AEROSPACE PRODUCTS
HASSAN HABIB & MUHAMMAD TASLEEM

3. TABLE OF CONTENTS
• Introduction
• Process of Coordinate Measurement Regarding RE
• Sources of Error in CMMs
• Factors Undertaken for the Calculation of Task Specific Uncertainty of
CMM
• Calculation of Uncertainty Budget (GUM Methodology)
• Conclusions

4. INTRODUCTION

5. INTRODUCTION
Terms and Definitions
• Coordinate Measuring Machine
• Measurement Uncertainty
• Guide to the Expression of Uncertainty in Measurement (GUM)
• Geometrical Dimensioning and Tolerancing (GD&T)
• Volumetric Length Measuring Error (VLME)
• Volumetric Probing Error (VPE)
• Reverse Engineering

6. INTRODUCTION
Terms and Definitions
• Coordinate Measuring Machine
“The primary function of a CMM is to measure the actual shape of a work piece,
compare it against the desired shape, and evaluate the metrological information
such as size, form, location, and orientation.”

7. INTRODUCTION
Terms and Definitions
• Measurement Uncertainty
• It defines the quality of a measurement
• In its broadest meanings it is the possible “doubt” in the measurement
• The universally accepted definition is:
“Parameter, associated with the result of a measurement, that characterizes the
dispersion of the values that could reasonably be attributed to the measurand
(characteristic being measured)”

8. INTRODUCTION
Terms and Definitions
• Guide to the Expression of Uncertainty in Measurement (GUM)
• The guide is meant to stipulate general rules and criterion to evaluate and express
uncertainty in measurement of a physical quantity – the measurand – that can be
expressed by a unique value.
• It also encompasses uncertainties associated with conceptual design and
theoretical analysis of experiments
• The guide has been written and developed by BIPM in coordination with ISO, IEC,
IFCC, ILAC, IUPAC, IUPAP, and OIML
• It was first published in 1995

9. INTRODUCTION
Terms and Definitions
• Geometrical Dimensioning and Tolerancing
• Geometric Dimensioning and Tolerancing (GD&T) is a system for defining and
communicating engineering tolerances. It uses a symbolic language on engineering
drawings and computer-generated three-dimensional solid models that explicitly
describes nominal geometry and its allowable variation.

10. INTRODUCTION
Terms and Definitions
• Volumetric Length Measuring Error (VLME)
• It defines the linear component of errors in CMM measurements
• It is calculated by taking linear repeated measurements of standard gauge blocks

11. INTRODUCTION
Terms and Definitions
• Volumetric Probing Error (VPE)
• It defines the radial component of errors in CMM measurements
• It is measured by taking several repeated points on a sphere

12. INTRODUCTION
Terms and Definitions
• Reverse Engineering
• It is a process regenerating digitized data of physical component involving different
measurement and modeling techniques

13. PROCESS OF COORDINATE
MEASUREMENT REGARDING
RE

14. Acclimatizat
ion of Part
to CMM
Environmen
t
Calibration of
Probe Stylus
Thermal
Compens
ation
Alignment of
Machine to
Part
Coordinates
Measurements
Data
Analysis
(Through
Filters)
Conversion
of CMM Data
to Universal
File Format
(IGES)
CAD
Modelling
PROCESS OF COORDINATE
MEASUREMENT REGARDING RE
Reverse Engineering Process

15. SOURCES OF ERROR IN CMMS

16. SOURCES OF ERROR IN CMMS
• Some of the major contributing errors in CMM measurements are:
• CMM Hardware
• Workpiece Errors
• Sampling Strategy
• Algorithms
• Temperature Gradient

17. SOURCES OF ERROR IN CMMS
• Probing Systems of CMM are designed with precision and accuracy,
however, when readings matter in microns there is an uncertainty
involved in the process.
• Rigid Body Errors of the machine during dynamic measurements
impart many errors during the measurement process.
• Vibration Errors of CMM also play a part and are usually evaluated
by regularly performing E&R Test on machines
CMM Hardware

18. SOURCES OF ERROR IN CMMS
• Form Errors - of parts are major contributors of uncertainty in measurements. If there
are form errors then fitting will erroneous.
• Surface Finish also effects the measurements. This effect is on a very small scale as it
involves variations of crests and troughs of surface waviness
• Fixturing can also effect the workpiece geometry.
Workpiece Errors

19. SOURCES OF ERROR IN CMMS
• Samples of the points taken to measure a feature are very critical in determinig their
size, and its crucial to plan the best approach for sampling of data points.
Sampling Strategy

20. SOURCES OF ERROR IN CMMS
• Data fitting of measured sampled points imparts another component in the
measurement uncertainty.
• These errors depend on the users discretion of selecting the best algorithm. The
choice of algorithms is based on the fitment criterion and other applicable
requirements of the concerned part.
Fitting Algorithms

21. SOURCES OF ERROR IN CMMS
• Temperature gradient drastically effects the CMM measurements. The coefficient of
thermal expansion compensations are now available in modern
• As this compensation is also included in PCDMIS 2010, for the sake of research this
factor is taken as a constant.
Temperature

22. FACTORS UNDERTAKEN FOR
THE CALCULATION OF TASK
SPECIFIC UNCERTAINTY OF
CMM

23. FACTORS UNDERTAKEN FOR THE
CALCULATION OF TASK SPECIFIC
UNCERTAINTY OF CMM
Workpiece Characteristics
Sr. # Process Characteristic
1. Material 17-4 PH
2. Rough turning Turning Center
3. Heat treatment H925
4. Cylindrical grinding Grain size 80
5. Measured features Circle, Plane and Line

24. FACTORS UNDERTAKEN FOR THE
CALCULATION OF TASK SPECIFIC
UNCERTAINTY OF CMM
This factor represents the rigid body errors of
Machine for linear measurements.
Uncertainty Factors
01
02
03
04
05
06
07
08
Volumetric Length
Measurement Error
Volumetric Probing
Error
Resolution
Datum Uncertainty
Workpiece Errors
Sampling Strategy
Probing Force
Filters
This factor compensates the probing system errors.
This is the uncertainty induced due to the
reading of last digit after decimal place.
Uncertainty induced in the reading due to the
feature measurement errors.
Uncertainty due to form errors of the workpiece
This is the uncertainty induced to the sampling
points
Uncertainty induced due to the change in probing force
Uncertainty induced due to the filtering strategy
(B)
(B)
(B)
(A)
(A)
(A)
(A)
(A)

25. FACTORS UNDERTAKEN FOR THE
CALCULATION OF TASK SPECIFIC
UNCERTAINTY OF CMM
Uncertainty Factors
01
Volumetric Length
Measurement Error
• Volumetric Length Measurement Error (VLME) is error in the
measurements generated due to inaccuracy of the CMM to take linear
measurements.
• It is considered to be Type B Uncertainty which means that it is
calculated based on OEM measurements. In our case we have taken it
to be the result of E-Test that has been performed by according ISO
10360-2.
• It is given by:
• UL=EL,MPE=2.2 μm.
(B) This factor represents the rigid body errors of
machine for linear measurements.

26. FACTORS UNDERTAKEN FOR THE
CALCULATION OF TASK SPECIFIC
UNCERTAINTY OF CMM
Uncertainty Factors
02
Volumetric Probing
Error
This factor compensates the probing system errors.
• Volumetric Probing Error is error in the measurements generated
due to inaccuracy of the CMM to take radial measurements.
• It is considered to be Type B Uncertainty which means that it is
calculated based on OEM measurements. In our case we have taken it
to be the result of R-Test.
• It is given by:
• 𝑈 𝑃 = 𝑃𝐹𝑇𝑈,𝑀𝑃𝐸 = 1.5 𝜇𝑚.
(B)

27. FACTORS UNDERTAKEN FOR THE
CALCULATION OF TASK SPECIFIC
UNCERTAINTY OF CMM
Uncertainty Factors
03 Resolution
• Resolution is the uncertainty induced in the measurements due to
the last readable digit after decimal place.
• It is considered to be Type B Uncertainty and it’s distribution is
considered to be rectangular. It is calculated according to the guide of
NPL and is given by:
• UR=
0.1
12
=0.029 μm
(B) This is the uncertainty induced due to the
reading of last digit after decimal place.

28. FACTORS UNDERTAKEN FOR THE
CALCULATION OF TASK SPECIFIC
UNCERTAINTY OF CMM
Uncertainty Factors
04 Datum Uncertainty
• Datum Uncertainty is the error that might occur in measuring a
feature after the datum features have been defined. This will result in
deviated results.
• It is considered to be Type A Uncertainty which means that it’s value
can be calculated based on experiments and statistical techniques,
it’s distribution is considered to be normal.
• It is calculated based on the formula provided by Paulo H. Pereira and
Robert J. Hocken and is given by:
• UD=
3
6
Uprimary
2+
2
6
Usecondary
2+
2
6
Utertiary
2
• Where, Uprimary=Usecondary=Utertiary=
σpc
n−x
• σpc= σPFTU,MPE
2
• The value comes out to be UD=0.72 μm
(A) Uncertainty induced in the reading due to the
feature measurement errors.

29. FACTORS UNDERTAKEN FOR THE
CALCULATION OF TASK SPECIFIC
UNCERTAINTY OF CMM
Uncertainty Factors
05 Workpiece Errors
• As elaborated earlier the workpiece form errors effects the
calculations of the measurements taken on the CMM.
• These errors are treated to be Type A uncertainties. These are
measured based on the standard deviation of the surface roughness
(Ra value) calculations and are given by:
• UW=
σ
n
σ = 0.285
n = 28
• UW=0.054 μm
(A) Uncertainty due to form errors of the workpiece

30. FACTORS UNDERTAKEN FOR THE
CALCULATION OF TASK SPECIFIC
UNCERTAINTY OF CMM
Uncertainty Factors
06 Sampling Strategy
• Sampling strategy has been adopted to compensate the uncertainty
induced due to this factor.
• It is considered to be Type A Uncertainty. It is based on repeated
measurement taken on the workpiece in DCC mode at the same
without change in any of the other factors.
• It is calculated as:
• US=
σ
n
σ = 0.0005
n = 10
• US=0.0002 μm
(A) This is the uncertainty induced to the sampling
points

31. FACTORS UNDERTAKEN FOR THE
CALCULATION OF TASK SPECIFIC
UNCERTAINTY OF CMM
Uncertainty Factors
07 Probing Force
• Probing force can induce uncertainty in the calculations as it induces
elastic elongations in the shank of the probe, which might disturb
position vectors.
• It is considered to be Type A Uncertainty and is measured by taking
standard deviation of several measurements after varying probing
forces.
• It is calculated as:
• UPF=
σ
n
σ = 0.0003
n = 20
• UPF=0.00007 μm
(A) Uncertainty induced due to the change in probing force

32. FACTORS UNDERTAKEN FOR THE
CALCULATION OF TASK SPECIFIC
UNCERTAINTY OF CMM
Uncertainty Factors
08 Filters
• Filters used to fit the measurement data can also induce
uncertainties which might cause erroneous measurements to be
recorded.
• It is considered to be Type A Uncertainty and is measured by taking
standard deviations of several measurements taken through three
filters namely least-square, maximum inscribed, and minimum
circumscribed.
• Least square=σLS = 0.6 μm
• Maximum inscribed=σMI = 0.5 μm
• Minimum circumscribed=σMC = 5.8 μm
• UF=
max (σLS,σMI,σMC)
n
• UF=1.8 μm
(A) Uncertainty induced due to the filtering strategy

33. FACTORS UNDERTAKEN FOR THE
CALCULATION OF TASK SPECIFIC
UNCERTAINTY OF CMM
(A)
• Combined uncertainty is the result of combining all the uncertainties whether Type
A or Type B by usual method of combining standard deviations.
• For our purpose it has been done in the following way:
• UC= UL
2+UP
2+UR
2+UD
2+UW
2+US
2+UPF
2+UF
2
• UC=3.29 μm
Combined Uncertainty

34. FACTORS UNDERTAKEN FOR THE
CALCULATION OF TASK SPECIFIC
UNCERTAINTY OF CMM
(A)
• In order to get an uncertainty interval it is necessary to define a confidence level that
defines a band in which any measurement taken may lie.
• To achieve this end, combined uncertainty calculated in the previous step is
multiplied a coverage factor, thereby giving the expanded uncertainty of the
measurement.
• Usually, coverage factor of k=2 is taken in order to define the interval at 95.45%.
• The expanded uncertainty in our case comes out to be:
• U=kUC
• U = 2 x 3.29 = 6.589 μm
Expanded Uncertainty

35. CALCULATION OF
UNCERTAINTY BUDGET (GUM
METHODOLOGY)

36. CALCULATION OF UNCERTAINTY
BUDGET (GUM METHODOLOGY)
Sr. # Uncertainty Type Distribution Value (in μm )
1. Volumetric length error (UL) B Normal 2.2
2. Volumetric probing error(UP) B Normal 1.5
3. Resolution (UR) B Rectangular 0.029
4. Datum uncertainty (UD) A Normal 0.72
5. Work piece form uncertainty (UW) A Normal 0.054
6. Sampling strategy (US) A Normal 0.0002
7. Probing force (UPF) A Normal 0.00007
8. Filters(UF) A Normal 1.8
9. Combined uncertainty (UC) 3.29
10. Expanded uncertainty (U) 6.589
Uncertainty Budget

37. CALCULATION OF UNCERTAINTY
BUDGET (GUM METHODOLOGY)
Uncertainty Budget
2.2
1.5
0.029
0.72
0.054 0.0002
0.00007
1.8
3.294
6.589
0
1
2
3
4
5
6
7
UL UP UR UD UW US UPF UF UC U
Uncertainityinμm
Uncertainities
Uncertainty Budget Plot

38. CONCLUSIONS &
RECOMMENDATIONS

39. CONCLUSIONS & RECOMMENDATIONS
• As it can be seen from the uncertainty budget the maximum contributors are:
• Volumetric Length Error (VLE)
• Volumetric Probing Error
• Filters Utilized
• Reduction of these factors can enhance the uncertainty of the results of CMM
• 21 parametric errors must be removed
• Filters used must be appropriate

40. THANKS