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AUTOMATED TESTING OF
ACCELEROMETER TRANSVERSE SENSITIVITY
Jeffrey J. Dosch David M. LallyR&D Group Leader Engineering
Vice President
PCB PiezotronicsDepew NY 14043
ABSTRACT
A new system for automated testing of accelerometertransverse
sensitivity has been designed and implementedat PCB Piezotronics.
This paper describes the transversetest system theory,
construction, and operation. Transversesensitivities obtained from
the automated system andsensitivities obtained by the manual method
described inISO 5347-11:1993 were found to agree to within the
stateduncertainty of 0.3%.
NOMENCLATURE
ia linear acceleration [g]
i rotational acceleration [radian/s2]
iS linear sensitivity [mV/g]
i rotational acceleration [mV/rad/ s2]
SUT sensor under test
ov SUT output [Volts]
Interferometer phase [radian]
S sensitivity [mV/g]g acceleration constant [9.80665 m/s
2]
c excitation frequency [radian/s]
Re( ) real part of ( )Im( ) imaginary part of ( )( )* complex
conjugate of ( )subscripts:
x,y,z coordinate axes
t transverse direction
INTRODUCTION
A number of final calibration tests are performed by
anaccelerometer manufacturer to ensure the quality andaccuracy of
the sensor used by the test engineer. Finalcalibration of an
accelerometer for test and measurementapplications may include
testing of sensor sensitivity,frequency response, time constant,
resonant frequency,and transverse sensitivity.
The trend in modal testing is for increasingly large
channelcounts and the consequent demand for lower cost sensors.The
challenge to the sensor manufacturer is to reduce thesensor cost
without sacrificing quality and sensor accuracy.Because of the
costs involved in final calibration, ratherthan testing on a 100%
basis, some sensor manufacturershave addressed the cost challenge
by statistical sampling ofsome of their final tests. Where
feasible, PCB Piezotronicshas addressed the challenge in a
different way and that isto automate the final calibration testing,
and thus allow cost-effective final calibration of each sensor
manufactured.
This paper describes a new automated system for testing
ofaccelerometer transverse sensitivity. The system uses a
resonant beam to generate uniform motion in the transverseplane.
The beam motion is controlled and data is acquiredvia
computer-based acquisition and control. Compared tothe manual
method used previously, the new approach hasbeen found to provide
more accurate and consistentcalibration in the production
environment.
THEORY
Ideally, an accelerometer will respond only to motion alongits
sensing axis. In the non-ideal world an accelerometermay respond to
axial acceleration in a directionperpendicular to the main sensing
axis and to rotationalacceleration. Consider the accelerometer with
the desiredsensing axis oriented in the z direction (Figure 1)
and
subject to both linear and rotational acceleration. Outputfrom
the sensor will be equal to:
[ ]
=
z
y
x
z
y
x
zyxzyxo
a
a
a
SSSv
(1)
Where ia and i are the linear and rotational acceleration
componentsiS and i are the accelerometers sensitivity
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to these accelerations. For most piezoelectric
accelerometers the rotational sensitivity, i , is small andcan
be ignored. In such instances, only linear accelerationcomponents
contribute to sensor output:
[ ]
=
z
y
x
zyxo
a
a
a
SSSv
(2)
For the sensor with sensing oriented along the z-axis, the
maximum transverse sensitivity has a magnitude equal to
St(Figure 1):
22
yxt SSS += (3)
The transverse sensitivity is usually expressed as apercentage
of the main axis sensitivity:
z
t
S
STranverse =100(%) (4)
Typical values of transverse sensitivity are: less than 2%
forpiezoelectric quartz accelerometers and less than 5%
forpiezoceramic accelerometers.
The calibrator described in this paper generates rectilinear
acceleration in the x-y plane at a frequency c . The
motion is controlled such that acceleration componentsalong the
x and y axis are in phase quadrature (shifted inphase by 90
degrees):
)sin()( tXta cx = (5))cos()( tYta cy = (6)
In the general case equations (5) and (6) describe
ellipticalmotion in x-y plane; if X = Y, then a circle is
described. In
the automated test system, acceleration components xa
and ya are measured with reference accelerometers.
Acceleration magnitude and direction determined at any
time tis:
22)( yxt aata += (7)
=
x
y
a
at 1tan)( (8)
Maximum transverse sensitivity of the sensor under test
(SUT) is then determined from the SUT output, )(tvo , and
Eq (7):
=
)(
)(max
ta
tvS
t
o
t (9)
Eq (9) describes a time domain method for calculating themaximum
transverse sensitivity and assumes phase
quadrature of the x and y reference accelerometers.
Improved signal resolution can be obtained by using
Fourierdomain signal processing. The improved resolution
isespecially useful when testing accelerometers with lowsensitivity
such as shock accelerometers that may havemain axis sensitivities
as small as 0.05 mV/g.
A digital Fourier transform is applied to the acquired
signals.The spectral components of the SUT and x-y reference
sensors evaluated at the excitation frequency c are the
complex quantities:
( )c
taFFTjA xcx == )()(
(10)
c
taFFTjA ycy == )()( (11)
( )c
tvFFTjV oco == )()( (12)
The SUT output that is in-phase with the x and the yreference
accelerometers is respectively:
=
x
x
oxA
AVV Re (13)
=
y
y
oyA
AVV Re (14)
The cross sensitivities in the x and the y directions are:
x
x
xA
VS = (15)
y
y
yA
V
S = (16)
Given the above cross sensitivities in the x and y
directions,the maximum transverse sensitivity magnitude and
directionis calculated:
22
yxt SSS += (17)
x
y
tS
S1
tan = (18)
AUTOMATED TRANSVERSE TESTER
The automated transverse test system consists of aresonant beam,
x and y reference accelerometers,independent x and y exciters to
generate acceleration in thex-y plane, and personal computer based
acquisition andcontrol (Figures 2 and 3). The computer acquires the
SUTand x and y reference signals. The computer also controlsthe
motion in the x-y plane, generating near circular motion
according to equations (5) and (6) with X =Y, whilemaintaining
phase quadrature. Transverse sensitivity iscalculated from the
acquired signals using Eqs. (10)through (18).
The resonant beam was designed to provide rectilinear
motion in the x-y plane, with negligible motion in the
zdirection and minimal rotational acceleration. The
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