„RECENT ISSUES IN THE CALIBRATION OF MATERIAL TESTING MACHINES“

(Future Developmentsfrom Static to Dynamic Forces,

from Single to Multicomponent Forcesand from Large to Small Forces

in respect to Applications like in the Fieldof Material Testing, ....)

Rolf Kumme

Physikalisch-Technische Bundesanstalt, Germany

WG 1.21 + WG 1.23

Applications of Force Measurement

metrology in medicine

1 N10 N

100 N1 kN

10 kN100 kN

1 MN10 MN

100 MN

aircraft industry

open cut mining

space industry

off-shore industry

materials testing / safety technique

automobile industry

automation technology

(Atomic Force Microscopes)

103Force in Newton

10-9 10-6 10-5 10-4 10-3 10-2 10-1 100 101

Coordinate measuringmach.

Hardness measuring devices

102

AFM

Stylus systems

Typical Applications

New Facility

FSM of PTB

Needs for extension of PTB´s FSM to smallforces

Microsystem and nanotechnology

demand of traceability of smallforces

Calibration of Material Testing MachinesThe verification and calibration of the tension/compression testing machineis in general performed on site at the place of installation of the testingmachine, according to the procedure described in ISO 7500-1. The standard specifies the criteria for the classification of the testingmachine by way of the on-site calibration of its force-measuring system. The class of the transfer standard (force-proving instrument, specified in ISO 376) shall be equal to or better than the class for which the testingmachine is to be classified. Conformity with respect to the classification of a testing machineaccording to ISO 7500-1 thus implies that the uncertainties of forcesassociated with the transfer standard have been taken into account.

=> „UNCERTAINTY OF MEASUREMENT IN THE VERIFICATION AND CALIBRATION OF THE FORCE-MEASURING SYSTEMS OF TESTING MACHINES“ by Amritlal Sawla, PTBIn: PROCEEDINGS OF THE ASIA-PACIFIC SYMPOSIUM ON MEASUREMENT OF FORCE, MASS AND TORQUE (APMF 2000) TSUKUBA, JAPAN - NOVEMBER, 2000.

Acrobat-Dokument

Force Standard Machines of PTB20 kN

5 MN

1 MN200 N

2 kN100 kN

2 MN16,5 MN

Set-Up based on a compensation balance

Piezoelectricaladjustment device

Force transducer(to be investigated)

Electrodynamic force compensation balance

Levermecha-

nismCoil

Magnet

Positionsensor

16,5-MN-hydraulic amplification-FSM

Fg

A1 A2

oil pressure p

m

F1 F2

force transduceroiloil

loadframe

piston piston

1

2 3

5

4

6 7 8

11

10

9

12

13

14

15

16

17

18

19

PTB‘s „new“ 2 MN Deadweight FSM

Measurement Uncertainty of 2 MN Deadweight Force Standard Machine

m mass of deadweightsgloc local gravity at the position of deadweightρm density of the deadweightsρL density of air∆1 relative deviation due to magnetic forces∆2 relative deviation due to influences of the compensation lever∆3 relative deviation due to other effects like force introduction

(verified by ideal force transducers)

( ) ( ) ( ) ( ) ( )∑=

∆+

+

−++=

3

1

222

22

22)(i

imm

LL

m

Lloc wwwgwmwFw ρ

ρρρ

ρρ

( )∏=

∆−⋅−⋅⋅=3

1

1)1(i

im

LlocgmF

ρρ

=> Rel. Uncertainty: W <= 2*10-5 (k=2)

Comparison of stack 5 (10 x 100 kN) with stack combination 4, 3, 2, 1 by using a 2 MN force transducer.

-2

-1

0

1

2

1 2 3 4 5 6 7 8 9 10 11 12

No. of measurement

Rel

. dev

iatio

n in

10-6

Stack

No.5 10x

100kN

No.410x

50kN

No.310x

20kN

No.210x

20kN

No.110x

10kN

Stack 4,3,2,1 Stack 4,3,2,1Stack 5 Stack 5

2 MN Transducer1050 kN Force

Rotation effect in the 2 MN force standard machine measuredin 2 rotations according key comparison procedure.

-8

-6

-4

-2

0

2

4

6

8

0 60 120 180 240 300 360 420 480 540 600 660 720Position in degree

Rel.

devi

atio

n in

10-6

500 kN1 MN

1 preload +1 measurementcycle in position60° 60°120° 120°180° 180°240° 240°300° 300°360°/0° 360°1.rotation 2.rotation

1.

0 6 12 18 24 30 60 90 120 150

2. 3.preload preloadmeasurements

2. 3.1. measure-

ment3 preloads0 degree 0 degree 60 degree

time in min.

F2

F1

Inluences on the Uncertainty of Force CalibrationThe Measurement Uncertainty is determinded by: - Force Calibration Machine Wbmc- Calibration Procedure- Force Transducer to be calibrated Wtra

MU is calculated as follows:

EA10/04 describes the calculation only for ISO 376 and for the Force Measuring Device (Transducer+Indicator)

New Uncertainty Annex for ISO 376 under discussion.

The relative expanded uncertainty of calibration W will be determined by considering the best measurement capability of the force calibration machine as follows:

22bmctra wwkW +⋅=

Contibution for fixed loading profile (Key Comparison)

0

500

1000

1500

0 6 12 18

time in minutes

forc

e in

kN

start of rotationmeasurement

measurement

measurement

measurement

222222revresinprotrepzertra wwwwwww +++++=

Calibration Procedures of Force Measuring Devices

1. Key ComparisonComparison of Force Standard Machines with rel. Uncertainties of < 0,002% (Deadweight)

2. Traceability of Accreditatied Laboratories forCalibration of Force Measuring Devices

DKD Procedure to verify the Traceability of Force Calibration Machines with rel. Uncertainties down to 0,005% (Deadweight)

3. Procedure according IS0 376 for Calibration of Material Testing Machines

4. Simplified Procedures according DKD 3-3

5. Continous Procedures according DKD 3-9

6. Special Procedures which have to be evaluated.

Influences in the calibration of force transducersMU according EA10/04 :

Comments to MU:

- MU components of indicator has to be taken intoaccount if indicator is changed.

- MU according loading procedure is missing.

- MU valid only for parts of force introduction used in calibration.

=> User has to take additional influences into account.

222222revresinprotrepzertra wwwwwww +++++=

Contibutions according EA10/04 Table 7.1: Probability distributions assumed for the different input quantities(a: relative half-width of the maximum deviation of the input quantity)

Uncertainty contributions Probability distribution Estimated relative(input quantities) variance

zero deviation rectangular distribution 32

32zer

20

2

==f

aw

reproducibility without rotation rectangular distribution 32'

32rep

2

2

==b

aw

reproducibility with rotation U-shaped distribution 22

22rot

2

2

==b

aw

interpolation deviation triangular distribution 62

62inp

2

2

==cf

aw

resolution rectangular distribution 32/

32res

2

2

==Fr

aw

reversibility (hysteresis) rectangular distribution 32

32rev

2

2

==ν

aw

Probable changes in ISO 376 New ISO 376 Annex prepared by ISO/TC 164/SC 1 WG3:

1. The Annex will be independent off EA10/04.

2. The uncertainty should be independent of the classification.

3. The uncertainty for increasing and decreasing forces should becalculated seperately.

For example:

Case 1

Case 2

222222revresinprotrepzertra wwwwwww +++++=

22222resinprotrepzertra wwwwww ++++=

Table 9.2: Limits for the expanded relative uncertainty fordifferent classes of (EN 10002-3) ISO 376

min. max.Class 00 Wbmc 0,06 %Class 0.5 0,06 % 0,12 %Class 1 0,12 % 0,24 %Class 2 0,20 % 0,45 %

Static sensitivity of force transducers.

-0,15

-0,10

-0,05

0,00

0,05

0,10

0,15

-2000 -1000 0 1000 2000

force in N

rel.

inte

rpol

atio

n er

ror

in %

Summary Measurement Uncertainty Force

1. MU is depending on the Procedure.

2. MU is only valid for the calibration result.

3. The user has to take additional contributionsinto account.

Needs for extension of PTB´s FSM and methods to dynamic forces

1. Material Testing Machines

- sinusoidal testing

- impact testing

2. Crash tests in automobile industry

- collision forces

- dummy forces

3. Modal analysis

- sinusoidal excitation

- impact excitation

4. Dynamic weighing

- different loading times and sequences

How can we use dynamic force calibrationin materials testing machines ?

1. force measuring devices of good dynamic properties

2. interaction with materials testing machine

=> analysis of application, resonance effects

3. Compensation of systematic dynamic influences

Compensation of mass forces.

F S U m x bk

S Ut f0 f t tf

ff0 f= ⋅ + ⋅ + ⋅ ⋅− −1 1&& &

bttffffft xmFrkrbrm &&&&& ⋅−=⋅+⋅+⋅

Amplitude response of the force transducer

0.1

1.0

10.0

100.0

1000.0

0 1 2 3frequency ratio

ampl

ifica

tion

func

tion

D=0,001

0,01

0,10,51,0

( ) { }tjeFtFtFrkrbrm ⋅⋅=+⋅⋅==⋅+⋅+⋅ ωϕω ˆRe)cos(ˆFtffffft &&&

bttffffft xmFrkrbrm &&&&& ⋅−=⋅+⋅+⋅

Phase response of the force transducer.

-180

-90

0

0 1 2 3frequency ratio

phas

e in

deg

ree

D=0,001 0,010,1

0,51,0

bttffffft xmFrkrbrm &&&&& ⋅−=⋅+⋅+⋅

( ) { }tjeFtFtFrkrbrm ⋅⋅=+⋅⋅==⋅+⋅+⋅ ωϕω ˆRe)cos(ˆFtffffft &&&

Resonance behaviour of a force transducer.

0.1

1.0

10.0

100.0

1000.0

0 1 2 3frequency ratio

ampl

ifica

tion

func

tion

D=0,001

0,01

0,10,51,0

-180

-90

0

0 1 2 3frequency ratio

phas

e in

deg

ree

D=0,001 0,010,1

0,51,0

2

0

2

22

0

f

0

41

1ˆ

ˆ,

+

−

=⋅

=

ωω

ωω

ωω

DFrkDV ϕ ϕ ϕ

ωω

ωω

rF r F= − = −

−

arctan2

1

0

0

2

D

amplification function matching phase curve

f f Dr = −021 2 f f f k

m mr = = = ⋅+d 0f

ti ta

12π

resonance frequency fr , eigenfrequency fd , characteristic frequency f0

fundamental eigenfrequency f0g ti

f0g 2

1mkf ⋅=

π

small damping factor 0<D<0,01 =>

Abrupt unloading of a force transducer.

-1.0

-0.5

0.0

0.5

1.0

0 5 10 15 20norm. time

r f/r

0

0,01

0,1

D=0,5

bttffffft xmFrkrbrm &&&&& ⋅−=⋅+⋅+⋅

( ) 0210

f

0ff

0f2

0

===+⋅+⋅ rkFrrDr &&&

ωω

Abrupt loading of a force transducer.

0.0

0.5

1.0

1.5

2.0

2.5

0 5 10 15 20norm. time

r f/r

0

0,01

0,1

D=0,5

( )1 2

02 0

00

ω ω⋅ + ⋅ + = =&& &r D r r F

krf f f

f

bttffffft xmFrkrbrm &&&&& ⋅−=⋅+⋅+⋅

Dynamic properties of force measuringdevices.

=> Model description of the force measuring device.

mechanical influences: electrical influences:

Stain gauge force measuring devices.

=> Multiplication of frequency responses:

Tfu=Tfb·Tbu

Signal flow piezoelectric force measuring device.

=> Multiplication of frequency responses:

Tfu=Tfq·Tqu

Principle of the comparison calibrationwith equivalent model.

Force ratio of upper to lower transducerand inertance measurement.

0,1

1

10

100

0 200 400 600 800 1000

frequency in Hz

forc

e ra

tio

0,0

0,5

1,0

1,5

iner

tanc

e in

1/k

g

13 kg 7 kg

inertance

Compensation of inertia forces.

Practical techniques to improvedynamic force measurement in

applications.

1. Rotation effect in dynamic measurements.

2. Multicomponent acceleration measurements.

3. Methods for error compensation:- electronic circuits for error compensation

- different software techniques

offline, online, realtime depending on the application

F S U m x bk

S Ut f0 f t tf

ff0 f= ⋅ + ⋅ + ⋅ ⋅− −1 1&& &

bttffffft xmFrkrbrm &&&&& ⋅−=⋅+⋅+⋅

Conclusion for dynamic force measurementin practical applications.

- Method is depending on the practical application:

- Compensation of mass forces=> force measurement

+ acceleration measurement

- Consideration of resonance behaviour

=> force measurement

+ transducer resonance

(+ acceleration measurement)

Dynamic force measurementin future.

1. Extension of the force range to the needs of practical applications.

2. Development of dynamic force transfer standards for material testing machines.

3. Development of force measuring devices

with compensation techniques forspecial applications.

4. Reduction of the measurement uncertaintyby interferometric measurement techniques.

Principle of dynamic force calibration.

S UFf

f=

F m xt m= ⋅ &&

( )F m m x= + ⋅e m&&

( )Ux

S m mf

mf e&&

= ⋅ +

( )S U

m m xff

e m=

+ ⋅ &&

xm

xb

me

m

Fs

forcetransducer

loadmass

dynamic sensitivity:

end mass known:

end mass unknown:

Uf

Principle of the facility for dynamic forces up to 10 kN.

computerand signalanalyser

control and measuring system

poweramplifier

electro-dynamicshaker

Necessary is:1. Theory for determination of dynamic force:

2. Accelerationmeasuring system=> acceleration transducersor laser interferometer

3. Axial force generation

=> air bearingsor other methods for thegeneration of axial forces.

4. Force excition forlarge dynamic forcessine: 17,8 kNhalf sine: 40 kN

( )F u x t dVV

= ⋅ ⋅∫ ρ && ,amF rr⋅=

Combination of the 17,8 kN shaker system with laser vibrometer.

Extension of the calibration to large dynamic forces with the comparison method.

Forc

e

Load cycle time tc=1000 s

a) Stepwise Load Cycle

Forc

e

Load cycle time tc=10 s

b) Continuous Load Cycle

Forc

etc=1....0,0001 s

c) Sinusoidal Load CycleControlsystem

Amplifier

Amplifier

Up to 100 kN

Servohydraulicforce generation

FT

FT

Conclusion: Calibration of force transducers.

- Different calibration procedures are possible:

static (continous or stepwise)

dynamic (sinusoidal, impact, ....)

- Different influences have to be taken into account:

static and quasistatic influences:

nonlinearity, hysteresis, creep...

=> sensitivity

dynamic influences:

frequency response of amplifier, force transducer, coupling of load mass to transducer

=> dynamic sensitivity

Conclusion for dynamicapplications.

1. Static and dynamic calibration of the force sensorDeviations between the static sensitivity determined bystepwise calibration methods and the dynamic sensitivityindicate the limits of the use of static sensitivity.

2. Analysis of the mechanical applicationAnalysis of the vibration behaviour

3. Compensation of systematic influencesCompensation of inertia forces and consideration of theresonance behaviour.

Future developments in force measurementin

respect to applications and material testing.1. Investigation and calibration of force measuringdevices with static, quasistatic, coninuous, periodical and impact forces.

2. Extension of the range of force standardsaccording the needs in industry like in the field of material testing machines.

3. Development and investigation of transferstandards for dynamic forces, multicomponent measurements and small forces.

=> Additional Procedures for Calibration of Material Testing Machines.

=> Uncertainty Analysis depending on Application.