Absolute calibration of piezoelectric force transducers by laser interferometry

European Union

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Industrial research and development

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• Sciences et techniques

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• Publié par: EUROPEAN-UNION
• Nombre de lectures: 75
• Langue: English
• Poids de l'ouvrage: 2 Mo

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Commission of the European Communities
ber information
APPLIED METROLOGY
Development of methods
for dynamic force calibration
Part 2
Absolute calibration of piezoelectric
force transducers by laser interferometry Commission of the European Communities
ber information
APPLIED METROLOGY
Development of methods
for dynamic force calibration
Part 2
Absolute calibration of piezoelectric
force transducers by laser interferometry
G. Lauer
Physikalisch-Technische Bundesanstalt
Bundesallee 100
D-3300 Braunschweig
Contract No 3313/1/0/118/86/10-BCR-D(30)
Final report
PARI ri!K0P. BibtirA
Directorate-General
N.C./C0M3SSSS Science, Research and Development
1990 CLEUR 12933/2 EN
A**>5W 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 then is responsible for the use which might be made of the
following information
ISBN 92-826-1729-7 (Volume 1)
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
_ 'I
ISBN 92-826-1730-0 Catalogue number: CD-NB-12933-EN-C
» —
© ECSC-EEC-EAEC, Brussels • Luxembourg, 1990
Printed in Belgium Abstract
An absolute method for the calibration of piezoelectric force transducers
using sinusoidally varying forces is described. The method is based on
Newton's second law: known masses are screwed onto the force transducer
and the accelerations of the masses are determined by interferometry
("fringe counting method"). A linear least squares fit is used to calculate
the sensitivity and the "end mass" of the force transducer.
The method used requires that the stiffness of the load masses and the
mounting stiffness are high enough to prevent relative motion. To prove
this assumption, i.e. to determine the frequency range where it is valid, two
Interferometrical methods were used. One set-up is able to measure
frequency responses of the sensor load assembly up to 100 kHz, the other
measures the relative motion with a double beam interferometer. Applying a
simple theoretical model, the mounting stiffness is estimated and used to
calculate the error contribution.
One of the greatest error sources is the transverse force sensitivity of the
force transducer in combination with thee motion of the vibration
exciter. This calibration error is reduced considerably by a special
measurement technique.
For the application of force sensors it is important to estimate the error
induced by transverse forces. A method was therefore developed to
determine the maximum transverse sensitivity of force transducers. For all
transducers tested the bending momenty dominates.
It is shown that the sensitivity of piezoelectric force transducers can be
determined in the frequency range from 10 Hz to 1000 Hz with a total
relative uncertainty of less than 0,6% (confidence level: 95%).
— Ill — CONTENTS
Page
Abstract III
List of symbols VI
1. INTRODUCTION 3
2. DESCRIPTION OF THE CALIBRATION PROCEDURE 4
2.1. Calibration principle
2.2. Frequency response measurements 6
2.3. Principle of the interferometric measurement of
vibrational displacement amplitudes 10
2.4. Description of the measuring system4
2.5. Carrying-out of the calibration measurements7
3. LIMITATIONS TO AND ERROR SOURCES OF THE CALIBRATION
METHOD USED 2
3.1. Frequency limitations caused by the finite mounting
stiffness of the load4
3.1.1. Introduction
3.1.2. Heterodyne interferometer with two-mode laser
for measuring the frequency response of force
transducers7
3.1.3. Frequency response measurements for estimating
the relation motion 35
3.1.4. Precision measurement of relative motion to
estimate the mounting stiffness of the load
mass 40
3.1.5. Frequency limitations caused by finite rigidity
of the load masses3
3.2. Influence of transverse sensitivity of the force
transducer ande movement of the vibration
generators 51
3.2.1. Introduction
3.2.2. Transverse acceleration of the calibration
shakers
3.2.3. Determination of the transverse sensitivity
of force transducers 55
— V — 3.2.4. Method for reducing the influence of transverse
motion and transverse sensitivity of the force
transducer 65
3.3. Other sources of errors that influence the calibration
uncertainty7
4. EVALUATION OF THE MEASUREMENTS : CALCULATION OF SENSITIVITY,
END MASS AND CALIBRATION UNCERTAINTY8
5. CONCLUSIONS 7
Bibliography of Part 29
Annex A : Measurement results for force transducer BO 83
Annex B :t results for forcer Bl 101
Annex C : Measurement results for force transducer Kl 11
— VI — List of frequently used symbols
a acceleration of the load mass m
af transverse acceleration
b damping coefficient
f vibration frequency
h distance
Ji Bessel function of first kind and i-th order
k spring stiffness
m, mi load masses
mt end mass of force transducer
Q.Qi output charges
rm calculated uncertainty of end mass mj
r-rdy of sensitivity S
R magnitude of frequency response
RAe ofye with mass set A
RHe of frequency response with mass set B
s displacement
S sensitivity (magnitude) of force transducer
Sq transverse sensitivity
T ratio Q/a
Tn normalized T
Tr reference value for normalizing T
x complex displacement of load mass
xtxt of end mass
Xj.xt amplitude of load mass
X complex displacemente of end mass
z number of fringes
X laser wavelength
vy total uncertainty of Qi/aj
w angular frequency of vibration
ory
f displacement amplitude
— VII —