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DIAGNOSTIC OF CRITICAL FACTORS IN UNCERTAINTY MEASUREMENT OF COORDINATE
MEASURING MACHINE IN REVERSE ENGINEERING OF AEROSPACE PRODUCTS
HASSAN HABIB & MUHAMMAD TASLEEM
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
INTRODUCTION
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
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.”
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)”
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
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.
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
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
INTRODUCTION
Terms and Definitions
• Reverse Engineering• It is a process regenerating digitized data of physical component involving different
measurement and modeling techniques
PROCESS OF COORDINATE MEASUREMENT REGARDING
RE
Acclimatization 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
SOURCES OF ERROR IN CMMS
SOURCES OF ERROR IN CMMS
• Some of the major contributing errors in CMM measurements are:• CMM Hardware
• Workpiece Errors
• Sampling Strategy
• Algorithms
• Temperature Gradient
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
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
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
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
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
FACTORS UNDERTAKEN FOR THE CALCULATION OF TASK SPECIFIC UNCERTAINTY OF
CMM
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
FACTORS UNDERTAKEN FOR THE CALCULATION OF TASK SPECIFIC
UNCERTAINTY OF CMM
This factor represents the rigid body errors ofMachine for linear measurements.
Uncertainty Factors
0102030405060708
Volumetric Length Measurement ErrorVolumetric 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 samplingpoints
Uncertainty induced due to the change in probing force
Uncertainty induced due to the filtering strategy
(B)
(B)
(B)
(A)
(A)
(A)
(A)
(A)
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:
(B) This factor represents the rigid body errors of machine for linear measurements.
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:
(B)
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:
(B) This is the uncertainty induced due to the reading of last digit after decimal place.
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:
• Where,
• The value comes out to be
(A) Uncertainty induced in the reading due to the feature measurement errors.
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:
= 0.285σn = 28
(A)Uncertainty due to form errors of the workpiece
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:
= 0.0005σn = 10
(A)This is the uncertainty induced to the samplingpoints
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:
= 0.0003σn = 20
(A)Uncertainty induced due to the change in probing force
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.
(A)Uncertainty induced due to the filtering strategy
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:
Combined Uncertainty
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 = 2 x 3.29 = 6.589
Expanded Uncertainty
CALCULATION OF UNCERTAINTY BUDGET (GUM
METHODOLOGY)
CALCULATION OF UNCERTAINTY BUDGET (GUM METHODOLOGY)
Sr. # Uncertainty Type Distribution Value (in m )μ
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
CALCULATION OF UNCERTAINTY BUDGET (GUM METHODOLOGY)
Uncertainty Budget
UL UP UR UD UW US UPF UF UC U0
1
2
3
4
5
6
7
2.2
1.5
0.029
0.72
0.054 0.0002
0.00007
1.8
3.29426122900113
6.58852245800225
Uncertainty Budget Plot
Uncertainities
Unc
erta
init
y in
mμ
CONCLUSIONS & RECOMMENDATIONS
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
THANKS