uncertainty of coordinate measuring machines

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


• 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


• 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


• 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


• 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


• 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


• 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


• 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


• Some of the major contributing errors in CMM measurements are:• CMM Hardware

• Workpiece Errors

• Sampling Strategy

• Algorithms

• Temperature Gradient


• 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


• 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


• 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


• 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


• 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


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)


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.


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)


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.


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.


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


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


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


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


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


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