Procedures of force transducer calibrationwith periodical forces in the low and high

frequency

Rolf Kumme

EURAMET Bucharest 2008

Devision 1 „Mechanics and Acoustics“

1.21Force

Realization

1.22Torque

Realization

1.23Periodical

Force

Department 1.2„Solid Mechanics“

From DKD Laboratories „Force“ and „Material TestingMachines“ required procedures for force calibration

TypicalForce calibrations

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

e

tc=1....0,0001 s

c) Sinusoidal Load Cycleperiodical

continous

staticForce

Calibration

- static

- dynamic- continousDKD-R 3-9

- periodical - impact

DIN EN ISO 376

DKD-R 3-3DIN xxxLoading Facilities

Realization and Dissemination of the Unit Force (dynamic).

F m xa ta t= ⋅ &&

( )F m m x= + ⋅ta e t&&

xt

xb

me

mta

Fs

Kraft-aufnehmer

Zusatz-masse

Uf

F(t) = m · a(t)1 N = 1 kg · 1 m/s2

F(t) ~ σ (t)σ (t) = ε(t)· E(f) ε(t) = ∆l / l

Definition DisseminationDynamic Force Transfer Standards(force transducers and amplifierwith well known dynamicproperties)

Realization

shaker

Metrology of Dynamic Force

Realization of dynamic forces with dyn. force measuring facilitiesMatrological Basics

FDyn = (m+m)el. a

calibrated

calibrated

force transcucer and

force transducer

Acceleration transducer as a reference

As a reference

1

5

.

.

10

10

-3

-4

≤

≤

U

U

≤

≤

5

5

.

.

10

10

-2

-3

5

10 Hz

10 Hz

0 Hz

.10-3 ≤

≤

≤

≤

U

f

f

f

≤

≤

≤

≤

5.10

1000 Hz

1000 Hz

100 Hz

-2

Principle

Acceleration of load mass

Reference transducer+ acceleration transducer

Reference transducer

Typ. Uncertainty ( =2)kTyp. Frequency Range

100 kN Dynamic Force Measuring Facility Frequency Range: 0 Hz - 100 Hz

Hydraulic Power Station

Controller

Measuring amplifier

Reference transducer

Device under test

Mounting device

Hydraulic zylinderWith servo valve

Oil supply

Bending momentsReference signal

Transducer signal

⇒Investigation and Calibration of Dynamic Force Transfer Standards

Static und quasistatic properties of force transducers

Force transducer curve Force transducer creep

-0,20%

-0,15%

-0,10%

-0,05%

0,00%

0,05%

-16 -12 -8 -4 0 4 8 12 16

force in kN

rel.

linea

rity

devi

atio

n

100 % load50 % load25 % load

Kraftverlauf(Eingangsgröße)

t5t2t1t0

tB tB

t4 t6 t7

S

t

S0

S2

S3

t∆ F t∆ F

t3

S6

S7

tAtA

Messsignalverlauf(Ausgangsgröße)

Forcerange

Time

force transducersignal

Results with periodical forces up to 100 kN.

-1,0E-03

-5,0E-04

0,0E+00

5,0E-04

1,0E-03

0,1 1 10Frequency in Hz

Rel

ativ

e de

viat

ion

Investigations with periodical forces up to 100 kN in low frequency range < 10 Hz.

⇒In low frequency range with selected linear transducers with small hysteresis relative deviations in the order of 10-4 is possible.

⇒Requirements for force transfer standards for low frequency range:

Good linearity, small hysteresis, small creep effect

Dynamic properties of force measuring devices.

mechanical influences: electrical influences:

=> Model description of the force measuring device.

Simplified model of force transducer

bfkf

mba

mbi

mti

mta

xb

xtFt

Fb

Uf

mt

mb

Force transducer

m x F k x x b x xt t t f t b f t b⋅ = − ⋅ − − ⋅ −&& ( ) ( & & )

m x F k x x b x xb b b f t b f t b⋅ = + ⋅ − + ⋅ −&& ( ) ( & & )

r x xf t b= −

m r b r k r F m xt f f f f f t t b⋅ + ⋅ + ⋅ = − ⋅&& & &&

m r b r k r F m xb f f f f f b b t⋅ + ⋅ + ⋅ = − + ⋅&& & &&

DE-System:

relative displacement:

static sensitivity:

linear dependency:

Dynamic calibration:

2. Determination of dynamic sensitivity.1. Verification of transducer model.

S UFf0

f

t

= ∆∆

k r S Uf f f0 f⋅ = ⋅−1

Description by a simpified force transducer model.

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

10 kN Dynamic Force Measuring FacilityFrequeny range: 20 Hz – 1000 Hz (set-up dependent)

( )F u x t dVV

= ⋅ ⋅∫ ρ && ,

1

7654

23

Laser

Detector

S1

T S2E2

E +E1 2

l2

l1E1

Fixed

s t s t( ) $ cos= ⋅ ⋅ω

λ

U

$ /s Z= ⋅ λ 8$ $a s= ⋅ω 2

Interferometric measuring facility for dynamic forces up to 100 N, Frequency range: 20 Hz - 1000 Hz

=> Investigation and calibration of force transducers with forces < 100 N

Force transducer investigation

frequency / Hz

dyn.

sens

itivi

ty /

mV

/N

4.52

4.54

4.56

4.58

4.60

4.62

4.64

0 200 400 600 800 1000

F

s tr a ing a u g e

reso

nanc

e fr

eque

ncy

/ Hz

load mass / kg

0

200

400

600

800

1000

1200

0 2 4 6 8 10 12

Summary and Outlook

- New measuring facilities for dynamic forces:

- shaker systems (Principle with accelerated load mass)force range: 1 N - 10 kNfrequency range: 20 Hz - 1000 Hz

- Servohydraulic facilities(Comparison calibration)force range: 0 N - 100 kNfrequency range: 0 Hz - 100 Hz

- Aim and outlook: - Traceablity chain for dynamic forces- Dynamic force transfer standards

Summary and outlook

- Different calibration procedures are necessary:

static (force steps)

continous (ramp)

dynamic (periodical, impact, ....)

- Different influences have to be taken into account:

Static and quasistatic influences:

nonlinearities, hysteresis, creep, ...

=> sensitivity

Dynamic influences:

Frequency response of amplifier, force transducer, coupling

=> dynamic sensitivity