procedures of force transducer calibration with periodical...
TRANSCRIPT
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