acceleration-velocity-position outline -accelerometers -velocity -position + misc!! material from...
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Acceleration-velocity-position
Outline- Accelerometers- Velocity- Position + Misc!!
Material from• Fraden chap. 7• Fraden chap. 8• Wikipedia• Web
– Analog Devices– MEMSIC
• SINTEF
Position – velocity - acceleration
Oscillatory motion
• Position
• Velocity
• Acceleration
)cos(,)( 00 txextx tj
)sin(,)( 000 txexjexdt
dtv tjtj
)cos(,)( 02
02
02
2
txexexdt
dta tjtj
f 2
Consequence 1:
low frequency -> measure position or velocity
high frequency -> measure acceleration
Consequence 2
• Plotting position amplitude emphasizes low frequencies
• Plotting acceleration emphasizes high frequencies
Fig 3: Bearing damage
Fig 2: Misalignment
Vel
ocity
Frequency
Acc
eler
atio
n
Frequency
Velocity is the usual compromise
Acceleration -> Position
• Acceleration is independent of inertial system
• Can be measured without reference
• Can be measured in a closed container
Position can be found by integrating twice:
dtdttatx )()(
BUT
errorsother2
1)(
errors)other)(()()(
2
toffsettx
dtdtoffsettadtdttatx
true
truemeasuredmeasured
=> Measure position if you can
Or, get a grip on your errors
Accelerometer approaches
Fma
Measure F• Compression• Bending
Stress/force based
kxF
Piezoelectric
Piezoresistive
Measure x
Capacitive
(Optical)
(Magnetic)
AC
DC
FP
Thermal
Parallell plateComb
Measure v
Inductive
Cantilever
Fiberdt
dxv
Piezoresistivt akselerometer 2
10 100 1 103 1 10
4 1 105
1 104
1 103
0.01
0.1
1
Frequency (Hz)
Out
put V
/g
Triangulering - GPS
Wikipedia
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