iigdt - gd&t & measurement uncertainty - measurement uncertainty.pdf · © iigdt –...

© IIGDT – GD&T: Advanced Applications & Analysis – June 25, 2006

International Institute of GD&TInternational Institute of GD&T

2 Loring Road, Hopkins, MN 553052 Loring Road, Hopkins, MN 55305

www.iigdt.comwww.iigdt.com

GD&T & Measurement Uncertainty

International Institute of GD&TInternational Institute of GD&T

IIGDT


Global Simplification of GD&T

ÂÂÂÂ

‰‰‰‰

Profile of a

Surface

Profile of a

Line

3D Surface

Control

2D Surface

Control

Axis Control

ÍÍÍÍPosition

····Flatness

ÈÈÈÈËËËËÁÁÁÁAngularity

Perpendicularity

Parallelism

ÈÈÈÈËËËËÁÁÁÁAngularity

Perpendicularity

Parallelism

‡‡‡‡Straightness

‡‡‡‡Straightness

‚‚‚‚Circularity

„„„„Cylindricity

ÏÏÏÏCircular Runout

ÌÌÌÌTotal Runout

ÓÓÓÓSymmetry

ÓÓÓÓSymmetry

ÎÎÎÎConcentricity

ÎÎÎÎConcentricity

IIGDT IIGDT


Measurement

Eyeball: L=Lest ± 1 inch

Tape: L=Lest ± 1/16 inch

Micrometer: L=Lest ± 0.001inch

Gage block comparator: L=Lest ± 1 microinch

Uncertainty

Cost of metrology

Profit

Target U

Dollars


Coordinate Measuring Machines


•Correlating Physical Measurements to Functional Parameters

-Input for FEA Models and Experimental Validation

•3D Characterization of Tooling & Product Components

-Standardized Software for Programming Efficiency & Analysis)

-Extraction of Surface Roughness, Waviness, Form

•Maintaining Commodity Plans with Key Measurement Suppliers

•CMMs, Vision Systems, Laser Sensors

Fly Height

Uc

Pitch Torque

2

++

2Roll

Torque

2TotalGramVar

2Slider's

ABSVar+

+P-SA P-StiffxGram Var(2)

POffsetxR-SA R-Stiffx +

Gram Var(2)

R Offsetx

P-LPtCust. SBO+R-LPt

CustSBO+

GramVar(1)

Cust.ZHV

SpringRate x +( ( () ) ) ) )( (

DriveDyn

Functional

Etched Tower Formed DimplePhysical-

Suspension

Physical-

Tooling

U1=Mat'l Thickness at bend area

U2=Width at bend area

U3=Length at bend area

U1=Datums

U2=Clamp Force

U3=Clamp Reference Location

U4=B.P. position at assembly

U5=B.P. edge break

U6=B.P. Flatness

U7=B.P. Squareness

U1=Tongue Flantess

U2=Loadbeam Profile

U3=Welding

U4=Heat Treat

U5=Dimple Location

U6=Dimple Height

U1=Flexure Mat'l Thickness

U2=Arm Length

U3=Arm WidthU1=Loadbeam profile under load

U2=Diameter

U3=Position of Tower

U4=Datums

U1=Loadbeam profile under load

U2=Apex Location

U3=Apex Shape

U1 + U2 + U3

2 22U1 + U2 + ... + U7

2 22

U1 + U2 + ... + U62 22

U1 + U2 + U3

2 22

U1 + U2 + ... + U42 22

U1 + U2 + U3

2 22

U1=Datums

U2=Dimple Punch Location

U3=Dimple Punch Shape

U1 + U2 + U3

2 22

FHSTG

2FHSRT

2FHPT

2

12 Contact

CMMs170 Non-Contact

Coordinate Meas. Systems

15+ Other Meas. Systems

(Orbotech, Cognex VM)Micro-Scale CMM

(Contact)

Micro-Scale CMM

(Non-Contact)

Open-Loop Scanning

Geometric Error Analysis

Thermal Modeling

Surface Analysis

3D Analysis

Non-Contact CMM’s

Other Meas. Systems

3D Measurement

Worcester Polytechnic Institute

Center for Holographic Studies and Laser micro-mechaTronics

LOAD BEAM DYNAMICSLOAD BEAM DYNAMICSOEH AND FEM RESULTS OEH AND FEM RESULTS -- MODE 2 AT 2,582 Hz MODE 2 AT 2,582 Hz

Contact

CMM’s

Physical to Functional Characteristic Hierarchy


ASME B89 Committee on “Metrology”

Comprised of “7” Divisions:

• B89.1 – Length

• B89.2 – Angles

• B89.3 – Geometry

• B89.4 – Coordinate Measuring Technology

• B89.5 – General Principles and Definitions

• B89.6 – Environment

• B89.7 – Measurement Uncertainty


B89.7 – Measurement Uncertainty

“Motivations”

• Need for a uniform approach (GUM) to the treatment of

uncertainty in ASME B89 document

• Need for simplified guidance documents as GUM moves into

industrial arena

• General dissatisfaction with quality of existing written

standards produced by ISO

Design

MeasurementMfg

GD&T

&

Uncertainty

ASME Y14.5M–1994 GUMASME Y14.5.1M–1994


ASME B89.7 Committee

“Measurement Uncertainty”

• B89.7.1 - Guidelines for B89 Doc’s

• B89.7.2 - Inspection Planning

• B89.7.3 - Decision Rules

• B89.7.4 - General Principles

• B89.7.5 - Communications

• B89.7.6 - Uncertainty Considerations in Tolerancing

• B89.7.7 - Advanced Uncertainty Concepts

• B89.7.8 - Traceability


expansion

bending

temperature

systematic effects

r

φ

∆r

random effects

probingprocess

long term stabilitykinematic anddynamic effects

∆x

x

measurement task

& strategy

basic axis geometry

x

z

y

∑ ∑∑= +=

−

= ∂∂

∂∂

+

∂∂

=N

i

ji

j

N

ij i

N

i

i

i

c xxux

f

x

fxu

x

fu

1 1

1

1

2

2

2 ),(2)(

Variances Covariances

software forevaluation ofmeasurement

[ ]∑ −⋅= 2(),( xxaaxJi

Objective Function:

)(),,()( xxaaxxdxdd iiii −⋅===Distance Equation:

Uncertainty

Management

Physical-to-

Functional

Hierarchies

Dimensional

Management

Design of

Experiments

Reliability

Analysis

Regression

AnalysisHistograms

Fishbone

Diagrams

Repeatability

Gage R&R

ANOVA

Control

Charts

Cp, Cpk

Scientific Approach

Current Approach

HTI Chassis Arm Model

Phase 3 HTI_p3.vsl, May 16, 2000

Session: 20000517-141912

sae14_r 5000 samples

-> Slider/Bond Pad SAE Assembly Method [A|F|0.12] deg

Nominal : 0.645211

Mean : 0.634629

Standard Deviation : 1.660454

Lower Spec Limit : N/A

Upper Spec Limit : 0.050000

Cp : N/A

Cpk : -0.126553

Distribution : Tested Normal

Sample Est Sample Est*

% < Low Limit N/A N/A Low -5.426040 -4.346695

% > High Limit 63.780000 63.761454 High 6.822226 5.615953

% Out of Spec 63.780000 63.761454 Range 12.248265 9.962649

95% C.I. for % Out of Spec : 62.447744 to 65.112256 * Est Range : 99.7300%

F

R

E

Q

0

100

200

300

400

500

600

700

-5.500000 2.500000

USL

-3S +3S

Nominal at Median : 0.645211 HLM Study

HLM Variance : 3.748766

Tolerance Effect

weld_base_p3_FEAT_44_GTP 39.90%-> Comp: weld_base_p3 Feat: weld_base_p3_FEAT_44-> (BONUS 0.00) CompPos(DIA) 0.1270(M)[A|B|C]

load_beam_st_FEAT_1_GTL 15.55%-> Comp: load_beam_st Feat: load_beam_st_FEAT_1-> Position(DIA) 0.0800[A|P]

slider_FEAT_2_GTS 15.55%-> Comp: slider Feat: slider_FEAT_2-> Size +- 0.0400

flex_cu_up___hti_p3_GM4 8.27%-> flex_cu_up___hti_p3 assembleop float

load_beam_st_FEAT_4_GTL 3.89%-> Comp: load_beam_st Feat: load_beam_st_FEAT_4-> Position(DIA) 0.0200(S)[A|B|C]

slider_pos_err 3.89%-> Slider Position Error zone 0.020

weld_base_p3_FEAT_12_GTL 3.82%-> Comp: weld_base_p3 Feat: weld_base_p3_FEAT_12-> (BONUS 0.00) Position(DIA) 0.0076(M)[A|D]

load_beam_st_FEAT_26_GTL 2.78%-> Comp: load_beam_st Feat: load_beam_st_FEAT_26-> Position(DIA) 0.0500[A|B|C]

weld_base_p3_FEAT_7_GTL 2.75%-> Comp: weld_base_p3 Feat: weld_base_p3_FEAT_7-> (BONUS 0.00) Position(DIA) 0.0076(M)[A|D]

96.41%

1 additional contributor(s) <= 2.75% each (Not Displayed) 1.64%

13 additional contributor(s) < 1.00% each 1.95%

“Quality Transformation”

Fly Height

Uc

Pitch Torque

2

++

2Roll

Torque

2TotalGramVar

2Slider'sABSVar+

+P-SA P-StiffxGram Var(2)

POffsetxR-SA R-Stiffx +

Gram Var(2)

R Offsetx

P-LPtCust. SBO+R-LPt

CustSBO+

GramVar(1)

Cust.ZHV

SpringRate x +( ( () ) ) ) )( (

DriveDyn

Functional

Etched Tower Formed DimplePhysical-

Suspension

Physical-

Tooling

U1=Mat'l Thickness at bend area

U2=Width at bend area

U3=Length at bend area

U1=Datums

U2=Clamp Force

U3=Clamp Reference Location

U4=B.P. position at assembly

U5=B.P. edge break

U6=B.P. Flatness

U7=B.P. Squareness

U1=Tongue Flantess

U2=Loadbeam Profile

U3=Welding

U4=Heat Treat

U5=Dimple Location

U6=Dimple Height

U1=Flexure Mat'l Thickness

U2=Arm Length

U3=Arm WidthU1=Loadbeam profile under load

U2=Diameter

U3=Position of Tower

U4=Datums

U1=Loadbeam profile under load

U2=Apex Location

U3=Apex Shape

U1 + U2 + U3

2 22U1 + U2 + ... + U7

2 22

U1 + U2 + ... + U62 22

U1 + U2 + U3

2 22

U1 + U2 + ... + U42 22

U1 + U2 + U32 22

U1=Datums

U2=Dimple Punch Location

U3=Dimple Punch Shape

U1 + U2 + U3

2 22

FHSTG

2FHSRT

2FHPT

2


expansion

bending

temperature

systematic effects

r

φ

∆r

random effects

probingprocess

long term stabilitykinematic anddynamic effects

∆x

x

measurement task

& strategy

basic axis geometry

x

z

y

∑ ∑∑= +=

−

= ∂∂

∂∂

+

∂∂

=N

i

ji

j

N

ij i

N

i

i

i

c xxux

f

x

fxu

x

fu

1 1

1

1

2

2

2 ),(2)(

Variances Covariances

software forevaluation ofmeasurement

[ ]∑ −⋅= 2(),( xxaaxJ i

Objective Function:

)(),,()( xxaaxxdxdd iiii −⋅===Distance Equation:

Analytic Solutions

Graphic courtesy of Dr. Trapet - PTB


U95 Estimates Distribution of Multiple

Measurement Systems Over a Period of Time


1. Environment

2. Reference Element for Measurement Equipment

3. Measurement Equipment

4. Measurement Setup

5. Software & Calculations

6. Metrologist / Operator

7. Measurement Object

8. Definition of the Characteristic

9. Measuring Procedure

10.Physical Constants & Conversion Factors

Sources of Error / Contributors toMeasurement Uncertainty


1. Environment for the measurement

• Temperature: absolute temperature, time variance, spatial variance

• Vibration/noise

• Humidity

• Contamination

• Illumination

• Ambient pressure

• Air composition

• Air flow

• Gravity

• Transients in the power supply

• Pressured air (e.g. air bearings)

• Heat radiation

Sources of Error…


2. Reference element of measurement equipment

• Uncertainty of the calibration

• Stability

• Scale mark quality

• Temperature expansion coefficient

• Physical principle: line scale, optical digital scale, magnetic digital

scale, spindle, rack & pinion, interferometer

Sources of Error…

+

+

+

+

+

+

++

+

+

+

++

+

+

+

+

+

+

+

+

+

+

++

+

+

+

++

+

+

+

++

True Center of

Sphere

Incorrect

Center of

Sphere

+++++

+

+

+ +

+

++

+

+

+

+

x+

True Center of

Sphere

Incorrect

Center of

Sphere

+++++

+

+

+ +

+

++

+

+

+

+

x


3. Measurement equipment

• Interpretation system

• Magnification-electrical or mechanical - error wavelength!!

• Zero-point stability

• Force stability/absolute force

• Hysteresis

• Guides/slide-ways

• Temperature expansion

• Parallaxes

• Time since last calibration

• Responds characteristic

• Interpolation system - error wavelength

• Interpolation resolution

Sources of Error…


4. Measurement setup (excl. the placement and clamping

of the workpiece)

• Cosine errors

• Abbe principle

• Temperature sensitivity

• Stiffness/rigidity

• Tip radius

• Form deviation of tip

• Stiffness of the probe system

• Optical aperture

• Interaction between workpiece and setup

• Warming up

Sources of Error…


5. Software and calculations

• Rounding/Quantification

• Algorithms

• Implementation of algorithms

• Number of significant digits in the computation

• Sampling

• Filtering

• Correction of algorithm/Certification of algorithm

• Interpolation extrapolation

Sources of Error…


6. Metrologist –operator

• Education

• Experience

• Training

• Physical disadvantages/ability

• Knowledge

• Honest

Sources of Error…


7. Measurement Workpiece or Measuring Instrument

• Surface Roughness, Waviness, & Form

• Temperature expansion coefficient

• Weight

• Size

• Shape

• Magnetism

• Cleanliness

• Internal stress

• Creep characteristics

Sources of Error…

0

0.5

1

1.5

2

2.5

3

3.5

0

0.5

1

1.5

2

2.5

3

3.5

-10

0

10

X axis (mm)

Original Surface

Y axis (mm)

Z a

xis

(um

)

0

0.5

1

1.5

2

2.5

3

0

1

2

3

-10

0

10

X axis (mm)

Roughness

Y axis (mm)

Z a

xis

(um

)

0

0.5

1

1.5

2

2.5

3

0

0.5

1

1.5

2

2.5

3

-5

0

5

X axis (mm)

Waviness

Y axis (mm)

Z a

xis

(um

)


8. Definition of the Characteristic

• Toleranced feature

• Reference system

• Degree of freedom

• Distance

• Angle

Sources of Error…


9. Measuring procedure

• Number of measurements

• Order of measurements

• Duration of measurements

• Choice of principle of measurement

• Reference standard

• Alignment

• Clamping

• Fixturing

• Number of points

• Probing principle

• Drift check

Sources of Error…


10. Physical constants and conversion factors

• Lacking knowledge of the correct physical values of e.g. material

properties (workpiece, measuring instrument, ambient air, etc.)

Sources of Error.


Business Drivers to Support a Decision to

Invest into Aggressive GD&T Training

1. Increased Business due to Increased Capability

2. Increased Profit with Reduced or Eliminated Returns

3. Increased Recognition as a Leading Edge Supplier/Customer

4. Increased Customer Satisfaction Based on Improved Conditions

5. Increased Yield / Reduced Inspection (reduced scrap and rework)

6. Unambiguous and Understood Engineering Requirements

7. Better ability to predict and control processes

iigdt - gd&t & measurement uncertainty - measurement uncertainty.pdf · © iigdt –...

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