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Dynamic calibration of force transducers based on the determination of inertia forces with interferometric calibrated acceleration transducers

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Industrial research and development

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Nombre de lectures 9
Langue English
Poids de l'ouvrage 2 Mo

Commission of the European Communities
OC Γ iOTOF ΙΊΠοιΙΟΓΐ
APPLIED METROLOGY
Development of methods
for dynamic force calibration
Part 1
Dynamic calibration of force transducers
based on the determination
of inertia forces with interferometric calibrated
acceleration transducers Commission of the European Communities
ber information
APPLIED METROLOGY
Development of methods
for dynamic force calibration
Part 1
Dynamic calibration of force transducers
based on the determination
of inertia forces with interferometric calibrated
acceleration transducers
R. Kumme, G. Lauer, M. Peters, A. Sawla
Physikalisch-Technische Bundesanstalt
Bundesallee 100
D-3300 Braunschweig
Contract No 3313/1 /0/118/86/10-BCR-D(30)
Synthesis report
PARI. H.'ROP. Bíblica.
Directorate-General
N.C./COM;Ì>5-£55" Science, Research and Development
CLEUR 12933/1 EN j 1990
fW^O ^S ^l· 5 %S Published by the
COMMISSION OF THE EUROPEAN COMMUNITIES
Directorate-General
Telecommunications, Information Industries and Innovation
L-2920 Luxembourg
LEGAL NOTICE
Neither the Commission of the European Communities nor any person acting on
behalf of the Commission is responsible for the use which might be made of the
following information
ISBN 92-826-1730-0 (Volume 2)
ISBN 92-826-1728-9 (Volumes 1 and 2)
Cataloguing data can be found at the end of this publication
·* - Luxembourg: Office for Official Publications of the European Communities, 1990
ISBN 92-826-1729-7 Catalogue number: CD-NA-12933-EN-C
k
__ - - ©ECSC-EEC-EAEC, Brussels · Luxembourg, 1990
' Printed in Belgium Preface
In recent years, considerable progress has been made in the
field of force measurement, which has resulted from a large
number of innovations in the construction of force transducers,
in the development of measuring amplifiers and compensators, and
in the field of force standard machines. This progress has
allowed the uncertainties of measurement for the realization and
transfer of the force scale to be reduced to some 10"s. To
achieve this, it has been necessary to develop new measuring
methods which take quasi-static influences such as time depen­
dence of the loading process of the force standard machines and
creep of the force transducers into account. This methods permit
purely static calibrations with the smallest possible uncer­
tainty of measurement, but they do not take the dynamic proper­
ties of the force measuring devices into consideration. In many
applications, however, force transducers whose characteristic
values have been determined by static methods must be used for
measuring dynamic forces, whereby the information on their
dynamic behaviour remains unknown.
In the field of material testing machines, the most different
force signals are applied, e.g. sinusoidal, random noise or
shock loads, the frequencies extending into the kHz range. In
crash tests carried out by car industry, and in the case of
forging hammers used in metal working, high force peak occur in
addition to high frequencies of some kHz. In structure analysis,
the development of frequency analyzers has resulted in modal
analysis increasingly gaining in importance. Here, too, stati­
cally calibrated force transducers are used for measuring time-
dependent forces.
A. Sawla's Ph.D. thesis HI published in 1979 already allowed
the conclusion to be drawn that considerable measurement errors
of several percent may occur in the applications referred to
above. Force transducers based on different design principles
may exhibit a basically different dynamic behaviour. Moreover,
when a force transducer is installed in a mechanical structure,
the interaction between structure and transducer must be taken
into account. In systems which are not very rigid, and when
great masses are concerned, resonance phenomena may occur
already at very low frequencies.
Ill — To reduce the uncertainties of the measurement in the above-
mentioned cases of application, the force transducers used
should be dynamically calibrated. At the PTB, a project entitled
"Development of methods for dynamic force calibration" was
therefore carried out.
When force transducers for higher forces (mainly based on strain
gauge .applications) are calibrated, the influences of the
transverse forces are stronger than in the calibration of force
transducers for lower forces (mainly based on piezoelectric
principles). Therefore two different procedures were performed
for the dynamic force calibration, depending upon the principle
of the force transducers. Accordingly, the report is divided
into two parts. The first part describes the dynamic calibration
of force transducers using interferometrically calibrated
acceleration transducers; the second part refers to the dynamic
calibration of force transducers by direct interferometric
methods.
Abstract
Development of methods for dynamic force calibration, Part 1
R. Kumme, G. Lauer, M. Peters, A. Sawla
A dynamic calibration and testing facility for forces up to 1.5
kN was built-up to investigate the dynamic properties of force
transducers. The dynamic calibration procedure is based on the
generation of inertia forces. For the calculation of inertia
forces according to Newton's law the acting mass and the
corresponding acceleration is measured.
It was shown, that force transducers of similar static
calibration results can show considerable differences in the
dynamic case. Consequently a static calibration of force
transducers is not sufficient for dynamic applications.
The reproducibility of the dynamic calibration can be increased
by performing series of measurements in different angular in­
stallation positions. Since this procedure is very time consum­
ing in an other method the acceleration is measured simulta­
neously at different angular positions. In both procedures the
mean values ot the measurements are used for the calibration.
— IV — CONTENTS
Page
Preface III
Table of symbols VI
INTRODUCTION 3
THEORETICAL DESCRIPTION 4
2.1. Force definition
2.2.e measurement and calibration of force transducers 4
2.3. Static calibration 5
2.4. Selection of a set-up for the dynamic calibration
of force transducers 6
2.5. Description of the calibration set-up 7
2.6. Force transducer model 8
2.7. The calibration set-up 10
by R. Kumme
2.8. Simplified description of the calibration set-up 11
by R. Kumme
2.9. Influence of the load mass fixing or a non-rigid
load mass5
by R. Kumme
2.10. Influence of the force transducer fixing on the
shaker 17
by R. Kumme
2.11. Influence of the shaker head suspension 19
by R. Kumme
2.12. Sensitivity of the force transducer 21
by R. Kumme
2.13. Conclusions for a calibration5
CALIBRATION OF TESTING FACILITY FOR THE DYNAMIC
INVESTIGATION AND CALIBRATION OF FORCE TRANSDUCERS
UP TO 1.5 kN 26
3.1. The electrodynamic shaker 2
3.2 The mechanical calibration set-up 27
3.3.e force measuring chain8
by R. Kumme
3.4. The reference bridge9
3.5. The acceleration measuring chain
3.6. Electronic evaluation with computer system 31
by R. Kumme
— V — 4. RESULTS OF THE MEASUREMENTS 32
4.1. Static calibration of force transducers 3
4.2. Measurements for the dynamic investigation and
calibration of force transducers3
4.2.1. Determination of sensitivity and dynamic
end mass
by R. Kumme
4.2.2. Influences exerted by side forces 36
4.2.3. Improvement of the measuring method by
rotational measurements 37
by R. Kumme
4.2.4. Improvement of the measuring method by
multi-channel acceleration measurement 38
4.2.5. Investigations into the linearity9
by R. Kumme
5. CONCLUSION 41
6. REFERENCES PART 12
7. FIGURES AND TABLES TO PART 15
— VI-Table of symbols
a acceleration
Ao constant in the equation of a straight line
Ai slope of a straight line
bb damping constant between force transducer and"shaker
bfgt of the forcer
bg damping of the shaker connection to the foundation
beg of ther head suspension
bt damping constant of the connection between force transducer
and load mass
E elasticity modulus (in general: elasticity tensor)
E complex elasticity modulus
F force vector
Foe amplitude
F» force generated by the shaker
F«e of inertia
g acceleration due to gravity
gioc local acceleration due to gravity
H(ur) complex frequency response H(u>0:= rt/x.t
kb spring stiffness between force transducer and shaker
kfgs of the forcer
kg spring stiffness of the shaker connection to the foundation
k«gs of ther head suspension
kt spring stiffness of the force transducer connection to the
load mass
Lb distance between the coordinates Xbi and Xb2 of the force
transducer base and of the shaker head at rest
Lf distance between thes xt1 and Xbi of the top and
base masses of the force transducer at rest
Lg distance between the coordinates xs and xg of the shaker
body and of the foundation at rest
Ls distance between thes Xb2 and xs of the shaker
head and the shaker body at rest
Lt distance between the coordinates xt 1 and xt2 of the force
transducer top mass and the load mass at rest
m mass in generali or total mass of the force transducer
nib base mass mb=mbi+rrib2
— VII — mt top mass mt=mti+mt2
nibi base mass of the force transducer
rm>2 mass of the shaker head
me mass of the shaker body
mti top mass of the force transducer
mt2 load mass screwed on the force transducer
mt2i different load masses with i=l to Ν
Ν number of load masses
rb relative coordinate rb:= (Xbi-Xb2)-Lb
fb l.time derivative of rb
r'b 2. time e of rb
Rb amplitude of the relative coordinate rb
rt relative coordinate rt : = (xt-Xb)-Lt
rt l.time derivative of rt
'rt 2.time e of rt
Rt amplitude of the relative coordinate rt
rt relative coordinate rt:= (xt2-xti)-Lt
rt l.time derivative of rt
rt 2.time e of rt
Rt amplitude of the relative coordinate rt
Sf sensitivity of the force transducer
t time
TAD frequency response function of the acceleration measuring
chain
TAQ frequency response function of the accelerometer
TQU y e n of the charge amplifier
TFU frequency response function of the force measuring chain
TFD y e n of the force transducer
TDD frequency response function of the amplifier in the
force measuring chain
Ua acceleration transducer signal
Ut signal of the force measuring chain
Uti signal of the force g chain for the mass mt2i
Xb coordinate of the base mass
#
Xb l.time derivative of Xb
Xb 2.time e of Xb
Xbi coordinate of the force transducer base
Xbι l.time derivative of Xbi
Xbι 2.time derivative of Xbι
— VIII —