DATA GATHERING AND ANALYSIS - Faculty of …taminmn/pdf-files/ULP 0010.pdf · · 2009-05-15DATA...

DATA GATHERING AND ANALYSIS

MOHD NASIR BIN TAMIN(Ph.D. Mechanical Engineering and Applied Mechanics)

ProfessorDepartment of Applied Mechanics

1

Department of Applied MechanicsFaculty of Mechanical Engineering, UTM

ULP 0010 - Research Methodology

29th January 2009

RESEARCH – a process

Identify researcharea

Literature review

ProblemIdentification

Theoretical

2

TheoreticalFramework

MethodologyResearch Design

Data Collection & Analysis

Conclusions

A COURSE ON RESEARCH METHODOLOGY- A Typical Outline

Philosophy and Overview of Research

Literature Review

Problem Formulation

Research Design

Data Gathering, Instrumentation and Measurement

3

Data Gathering, Instrumentation and Measurement

Sampling

Techniques of Data Analysis

Academic Writing

Thesis Presentation

OBJECTIVES

To identify methods and techniques in gatheringexperimental data.

To describe issues related to the working principles of devices associated with instrumentation.

To illustrate the principles and procedures involved in sampling and measuringphysical quantities.

4

in sampling and measuringphysical quantities.

To review general considerations in analysisof experimental data.

To illustrate the use of statistical techniques and physical reasoning in describing, analyzingand comparing experimental data.

Data Gathering Instrumentation

Measurement

Sampling

OUTLINE

Data Analysis

5

Servo-hydraulic universal testing machine with furnace for high-temperature test.

Data Analysis

Types and nature of measured data

Considerations in data analysis

Statistical considerations

Regression analysis

The physical aspects of measured data

DATA GATHERING (EXPERIMENTAL)

Activities of acquiring (measuring, observing, surveying) physical quantities of selected samples employing specific technique and instrument.

6

Collecting published data.

Material: AISI 4340 SteelEXAMPLE 1 - MECHANICAL (TENSION) TEST

PTHE MACHINE / INSTRUMENT

7

P

Lo+∆LLo

Ao

Elongation, ∆L (in.)

Load

, P(lb

f)

THE SAMPLE

THE MEASUREMENTS

DATA GATHERING (EXPERIMENTAL)

WHAT is the data.

HOW to collect the data Direct measurement

Observation / Survey

Published data / Database

- SAMPLING

- INSTRUMENTATION

- MEASUREMENT

8

WHEN to collect data / measure

WHY need data collection.

Force

Indenter

SampleIndentation

EXAMPLE 2 – INDENTATION HARDNESS TEST


Measurement

Sampling

9

OBJECTIVE

To determine the hardness number for a material by measurements of surface indention

INSTRUMENTATION

Working/ Test Principle

Machine/ System Characteristics

Calibration

10Micro-hardness tester

TEST PRINCIPLE

Hardness is determined by forcing a hardened indentor under a known load into the surface of a material and measuring the size of the indentation left after the test.

Select a suitable indentor

Apply known force(1 to 1000g)

Measure size of indentafter load removal

BRINELL HARDNESS TEST

11

indentor

eg. 10-mm sphere

(1 to 1000g) after load removal

dD

Smaller indent reflectsgreater hardness

−=

2d2D-DDπ

P2BHN

d2

VICKERS HARDNESS TEST

TEST PRINCIPLE (Cont.)

12

Square-Based Diamond Pyramid d1

HV = 1854.4L/d2

L is the load in gfd is the mean diagonal in µm

MACHINE / SYSTEM CHARACTERISTICS

Repeatability and Reproducibility

Sensitivity

Zero-setting

Shake-down

13

Shake-down

Automatic features

SAFETY

REPEATABILITY(Hardness Test)

For each standardized block, let d1, d2 ..., d5 be the diagonal lengths of the indentations, arranged in increasing order of magnitude.

14

The repeatability of the machine is expressed by the quantity (d5 - d1)/ davg, where davg is the average of d1

to d5.

REPEATABILITY

Ability of the measuring instrument to produce identical readings repeatedly.

Hardness Test

15

SENSITIVITY

When a small increment of input (excitation) causes a large change in the response (read-out) of the instrument.

600

16Terikan

0.0 0.1 0.2 0.3 0.4 0.5

Teg

asan

( M

Pa)

0

200

400

Ujikaji AUjikaji B

E = 200x103 MPaRequires sensitive strain measuring device

BUILT-IN SYSTEM RESPONSE

17

440C at 62.7 HRC

Universal testing machine

Load cell

ZERO-SETTING

FORCE DISP.

18

Specimen

Load cell

Specimen grips

Crosshead

Data acquisition system

Extensometer

SHAKE-DOWN

Application of repetitive small load magnitude to set-in the load train and avoid lag or back-lash.

19

AUTOMATIC FEATURES

On-line data processing software provides a quick glance of the quality of collected test data.

20

SAFETY

The operator (YOU)

People around test set-up

Machine and devices

While Working in the Lab:

21

Close Calls

1

10

600

30

Disabling injury

Minor injuries

Property damage incidents

Report all:

Accidents

Injuries

Fires

Spills

Close calls

Adopted from W. Wood, McGill University

CALIBRATION

Setting/ tuning of measuring devices so as to output actual/ true quantity being measured.

0.3

0.35

0.4

0.45

Ap

plie

d S

trai

n (

mm

/mm

) [R

ead

ing

s fr

om

mic

rom

eter

]

Tru

e/ r

efer

ence

d q

uan

tity

22

Extensometer calibration curve for Instron 4206+8801Gauge Length = 25 mm

Travel Length = 12.5 mm22-02-2006

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Measured Strain (mm/mm) [readings from console/PC]

Ap

plie

d S

trai

n (

mm

/mm

) [R

ead

ing

s fr

om

mic

rom

eter

]

MeasuredStrain (Instron 8801)

MeasuredStrain (Instron 4206)

Measured quantity

Tru

e/ r

efer

ence

d q

uan

tity

What and How to measure

How many measurements are sufficient

Accuracy, Precision and Bias

Uncertainty

MEASUREMENT

23

Error


Measurement

Sampling


d2

MEASUREMENT – VICKERS HARDNESS, HV

24


HV = 1854.4L/d2

L is the load in gfd is the mean diagonal in µm

HOW TO MEASURE

(MEASUREMENT OF LENGTH)

25

Learn how to read vernier sacles, dial gages and estimate of uncertainties.

Flame Hardened 8660 Gear

FREQUENCY OF DATA COLLECTION

How many Hardness measurements are sufficient?

26

Near SurfaceMicrocracks

Case Structure Core

2% Nital

Depth

Automated MHT HV Traverse FREQUENCY OF DATA COLLECTION

27Flame Hardened 8660 Alloy Steel Gear

Accuracy – the degree to which the measurements deviate from the true value.

Precision – ability to give

Accuracy

ACCURACY, PRECISION AND BIAS

28

Precision – ability to give multiple estimates that are near to each other.

Bias - a systematic deviation of values from the true value.

Precisio

n

Instrument Factors

(Hardness Test)

Accuracy of applied load Inertia effects, speed of loading Lateral indenter movement

FACTORS AFFECTING PRECISION AND BIAS

29

Lateral indenter movement Indentation time Indenter shape deviations Damage to the indenter (plus films) Insufficient spacing between indents and from edges

Measurement Factors

(Hardness Test)

Calibration of measurement system Resolution of the optics Magnification


30

Magnification Operator bias in sizing indents Inadequate image quality Non-uniform illumination

Material (Specimen) Factors

(Hardness Test)

Heterogeneity in composition and microstructure Crystallographic texture Quality of specimen preparation


31

Quality of specimen preparation Low reflectivity or transparency

UNCERTAINTY ESTIMATION

Report: Pressure, p = 100 kN/m2 ± 1 kN/m2

For a set of n experimental measurements x1, x2, x3,…,xn

with uncertainty w1, w2, w3,…,wn

The uncertainty, w , in the desired result, R = R(x, x , x ,…,x) is

32

The uncertainty, wR, in the desired result, R = R(x1, x2, x3,…,xn) is

2/122

22

2

11

...

∂∂++

∂∂+

∂∂= n

nR w

x

Rw

x

Rw

x

Rw

Ref: Kline, S.J. and F.A. McClintock, “Describing Uncertainties in Single-Sample Experiment”, Mech. Eng., pp. 3, Jan. 1953

Example 3:

The resistance of a certain size of copper wire is given as:

R = Ro [1 + α (T – 20)]

Where

33

Ro = 6Ω ± 0.3 pct. at 20 oC

α = 0.004 /oC ± 1 pct.

T = 30 oC ± 1 oC

Calculate the resistance of the wire and its uncertainty

Solution 3:Nominal value of the resistance:

R = Ro [1 + α (T – 20)] = 6 [1 + (0.004) (30 – 20)] = 6.24 ΩUncertainties:

= 1 + α (T – 20) = 1 + (0.004) (30-20) = 1.04

= Ro (T-20) = 6 (30-20) = 60

oR

R

∂∂

α∂∂R

34

= Ro α = 6 (0.004) = 0,024

α∂

oR

R

∂∂

wRo = 6 (0.003) = 0.018 Ω

wα = (0.004) (0.01) = 4x10-5 /oC

wT = 1 oC

wR = [(1.04)2 (0.018)2 + (60)2 (4x10-5)2 + (0.024)2 (1)2 ] 1/2 = 0.0305 Ω or 0.49 pct.

ERROR(Hardness Test)

• The error of the machine is expressed by the quantity dstd - davg, where davg is the average of the indentation diagonals and dstd is the value provided on the test block certification.

35

provided on the test block certification.

• The average observed diagonal shall not differ from the certificate diagonal by more than 2% or 0.5 µm, whichever is greater.

INACCURACY OF MEASUREMENTS

Instrument Calibration

Instrument Reproducibility

The purpose of measurements is to describe some physical properties of an object / material / system quantitatively

Sources of Error

36

Instrument Reproducibility

Measuring arrangement

Work piece

Environmental Conditions

Observer’s Skill

SCATTER OF MEASURED DATA

37

SCATTER OF EXPERIMENTAL DATA

We should be able to handle the analysis of this data.

38

this data.

SAMPLING DESIGN

Materials:• Virgin• Retired

Example 4:

Creep-fatigue interaction effects on high-strength steels

39

Location of cut for retired samples

Direction of cutfor specimen

Shape, size and numberof specimens


Measurement

Sampling

Ref. : ASTM E370

SAMPLING PROCEDURES

Unrestricted Random SamplingRandom sample selection from the population as a whole.

Stratified Random SamplingPartition the population into known meaningful strata. Random selection is made within each stratum, making sure

To obtain a representative sample with maximum randomness.

40

Random selection is made within each stratum, making sure all strata are represented.

Optimum-allocation-of-strata Random SamplingIf information about the population strata and the way they will be used is available, optimum sample selection is made to give the most representative information about the population.

FATIGUE TEST PROCEDURES

∆P, R = -1

Completely reversed axial fatigue

(This test is commonly done in reversed bending cycles)

Raw data:

Stress(MPa)

Nf

(cycles)

SAMPLING

How many test samples are sufficient?

41

Str

ess

Time

(MPa) (cycles)

1 pair of data per specimen

0

STRESS-LIFE (S-N) DIAGRAM

Fat

igue

str

engt

h, S

f(M

Pa)

600

800

1000

Cr-Mo steel, normalized

SUT = 800 MPa

Se = 338 MPa

DESIRED RESULTS

42

1 10 102 103 104 105 106 107 108

Number of stress cycles, N

Fat

igue

str

engt

h, S

300

400

500

600

Ref: Shigley, J.E., Mechanical Engineering Design, First Metric Edition, McGraw-Hill, 1986

Fatigue limit


Measurement

Sampling

OUTLINE (re-visit)

Data Analysis

43

Data Analysis

Types and nature of measured data

Considerations in data analysis

Statistical considerations

Regression analysis

The physical aspects of measured data

ROADMAP OF DATA ANALYSIS

MEASURED DATA

Curve-fitting

Verification & Validation

Physical Aspects

44

fitting

Numerical & Analytical

Models

(Extract model Parameters)

Validation

Reliability Analysis

Aspects

Information / Knowledge

(Interpret & Establish)

(Comparative Study)

TYPES OF DATA

Generated data

Measured data

Single reading

Random measurements

Time-dependent data

45

Others (micrographs)

Composition of steel (wt. %)

NATURE OF MEASURED DATA

Consistency

Uncertainty

Scatter

Outliers

46

Trends

Physical-based content

Evolution / history

CONSIDERATIONS IN DATA ANALYSIS

Anticipate the results from theory

Examine the data for consistency

Reduce the data

Perform a statistical analysis of data

where appropriate

47

Estimate the uncertainties in the

results

Correlate the data

Interpret and extract information

TOOLS / METHODS FOR DATA ANALYSIS

Data reduction

Uncertainty analysis

Statistical analysis

Regression analysis / Correlation

Mechanism-based interpretation

48

Simulation

V = 180 m/min

t = 0.125 mm/rev0

100

200

300

0.0 0.2 0.4 0.6 0.8 1.0Tool Advancement (mm)

Cut

ting

For

ce (

N)

STATISTICAL CONSIDERATION

Influence of the distribution of variables

(e.g. Stress and strength, household expenditure and income)

49

Pf = P( Stress ≥ Strength)

R = 1 - Pf

QUALITY versus

RELIABILITY

STATISTICS – BASIC DEFINITIONS

Population (or Universe)

a collection of objects having some common (fixed) characteristics.The characteristics of a population are called parameters.

Sample

any sub-collection of objects drawn from a population.

50

any sub-collection of objects drawn from a population.The characteristics of samples are called statistics.

Population parameters are usually estimatedon the basis of statisticscalculated for representative sample.

Procedures used to select samples and determine appropriate sample size are often called statistical design of experiment.

All sample types have in common some element of randomness.

DESCRIPTIVE STATISTICSSome useful statistics used in estimating population parameters.

51

IMPORTANT SAMPLING DISTRIBUTIONS

Gaussian or Normal

Chi-squared distribution

Student’s t-distribution

Snedcor distribution

52

Weibull distribution

-often used for representation of life data

SAMPLING DISTRIBUTION

- a three-parameter distribution (Na, No, b)

- A family of probability density functions, each can be written as:

Weibull Distribution

b

oa

o

NN

NNb

oa

o

oa

eNN

NN

NN

bNf

−−

−−

−−

−=

1

)(

N = spec. life, cycles

53

Shape parameter:

b = 1 simple exponential

b = 2 Rayleigh

b = 3.57 Appx. Gaussian

N = spec. life, cycles

No ≥ 0 , minimum life parameter

Na = characteristic life parameter at 63.2 pct. failed

WEIBULL DISTRIBUTION

Two-parameter Weibull distribution is widely

used for life data analysis

Weibull cumulative probability distribution

−−=B

n

tF(t) exp1

F(t) = Fraction failingt = time

Failure distribution type:

B<1.0 (Infant mortality)

54

t = timen = characteristic life B = slope or shape parameter

Weibull distribution uses existing service experience data. It does not predict future service experience using first engineering principles

B=1.0 (Random failure, independent of usage)

1.0< B<4.0 (Early wear out failure)

B>4.0 (Old age/ rapid wear out failure)

WEIBULL DISTRIBUTION

99

90

8070

Delta T&Stress

Delta T=150; dwell=29.5min


Delta T=150; dwell=1min

Probability Plot for Start

Arbitrary Censoring - LSXY Estimates

Weibull

Effect of dwell (hold) time at peak temperature on thermal shock tests of microelectronic chips.

Per

cent

of c

ompo

nent

fai

led

55

Start

Percent

100001000

70605040

30

20

10

5

3

2

1

Table of Statistics

1.000

6.35594 591.43 1.000

Shape Scale C orr

6.35594 1747.47 0.947

6.35594 7658.47


Cycles to Failure, Nf

Per

cent

of c

ompo

nent

fai

led

ACCELERATION FACTOR

REGRESSION / CURVE FITTING

Regression is a process used by statisticians to obtain a curve which best fit a set of data points.

(But you are not a statistician!)

To plot curves of experimental data and extract various significant facts from these curves

56

(Must understand physical phenomena involved in the experiment)

Correlation of experimental data is desired in terms of an analytical expression between variables that were measured in the experiment.

METHOD OF LEAST SQUARES

For a set of n observations x1, x2, x3,…,xn

the sum of the squares of their deviations from some mean value is

( )∑=

−=n

imi xxS

1

2

To minimize Swith respect to xm

57

( )∑ ∑= =

−−=−−==∂∂ n

i

n

imimi

m

nxxxxx

S

1 1

220

∑=

=n

iim x

nx

1

1 is the arithmetic mean value which minimizes the sum of the squares of the deviations

LINEAR REGRESSION

Equation of a straight line:

y = mx + c

Slope, and y-intercept, ( )

∑∑−

∑∑ ∑−

=

N

xx

N

yxxy

m 22

N

xmyb

∑ ∑−=

58

Correlation coefficient, ( -1 ≤ r ≤ 1)

N

y

x

s

msr =

r = 0 : no correlation

r = 1 : perfect correlation

Fuel Consumption Data

Example 5 – Curve fitting

Car Weight

(1000 lbs)

Fuel consumption

(gal/100 miles)

AMC Concorde 3.4 5.5

Chevy Caprice 3.8 5.9

Ford Wagon 4.1 6.5

59

Ford Wagon 4.1 6.5

Chevette 2.2 3.3

Toyota Corona 2.6 3.6

Ford Mustang Ghia 2.9 4.6

Mazda GLC 2.0 2.9

AMC Sprint 2.7 3.6

VW Rabbit 1.9 3.1

Buick Century 3.4 4.9

DEMO

Fuel Consumption Data


Fue

l Con

sum

ptio

n (g

al/1

00 m

iles)

5

6

7

- W ↑ , Consmp ↑

- extrapolation

60

Weight (kips)

1 2 3 4 5

Fue

l Con

sum

ptio

n (g

al/1

00 m

iles)

2

3

4

y = 0.0518 + 1.3055x + 0.0613x2 r2 = 0.9806

- zero-intercept

- validity of extracted information

-

Material: AISI 4340 Steel

MECHANICAL (TENSION) TEST

P

61

P

Lo+∆LLo

Ao

Elongation, ∆L (in.)

Load

, P(lb

f)

DEMO

ST

RE

SS

, σ (

MP

a)

200

400

600

800


150

200

Non-linear /Power-law

σ = K(εp)n

62

STRAIN, ε(%)

0.0 0.1 0.2 0.3 0.4 0.5 0.60

200

ALYAWS RELATE EXPERIMENTAL DATA TO THE PHYSICS OF THE PHENOMENON

STRAIN, ε(%)

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010S

TR

ES

S, σ

(M

Pa)

0

50

100

σ = EεLinear σ = Eε

ST

RE

SS

, σ (

MP

a)

100

200

300

400

500

600

700

(M

Pa)

1000

63

PLASTIC STRAIN, εp

0.0 0.1 0.2 0.3 0.4 0.5 0.60

PLASTIC STRAIN, εp

0.01 0.1 1

ST

RE

SS

, σ (

MP

a)

100

σ = Kεn

log K = 2.8735n = 0.1992r2 = 0.9772

199.03.747 pεσ =

ALYAWS RELATE EXPERIMENTAL DATA TO THE PHYSICS OF THE PHENOMENON

Fatigue crack growth rate data for TiAl intermetallic alloy

Example 7 – Physical Mechanisms

64


65


We should be able to describe the physical mechanism

66

physical mechanism of observed phenomenon

• American Standard for Testing and Materials (ASTM)ASTM E139 – 00 Standard Test Method for Conducting Creep, Creep-Rupture,

and Stress-Rupture Tests of Metallic Materials

• International Standard (ISO)ISO 6892:1998(E) Metallic Materials – Tensile Testing at Ambient Temperature

TESTING STANDARDS

STANDARDS AND GUIDELINES

67

• European Standard (EN), British Standard (BS)EN ISO 7500-2:1999 E Metallic Materials – Verification of Static Uniaxial Testing

Machines – Part 2: Tension Creep Testing Machines – Verification of the Applied Load

• Japanese Industrial Standard (JIS)JIS Z 2271:1999 (E) Method of Creep and Creep Rupture Test for Metallic Materials

• Malaysian Standard (MS)MS ISO 1352:1998 Steel – Torsional Stress Fatigue Testing

LEVEL OF EXACTNESS

FACTS

KNOWLEDGE

Le

vel o

f e

xact

ness

of

sta

tistic

al m

ode

l

WISDOM

68

DATA

INFORMATION

Level of improvements in decision making

Le

vel o

f e

xact

ness

of

sta

tistic

al m

ode

l

Q & A SESSION

69

Q & A SESSION

DATA GATHERING AND ANALYSIS - Faculty of …taminmn/pdf-files/ULP 0010.pdf · · 2009-05-15DATA...

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