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(,)( 0

2

0

2

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

Velo

city

Frequency

Accele

ration

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

kxF

Piezoelectric

Piezoresistive

Measure x

Capacitive

(Optical)

(Magnetic)

AC

DC

FP

Thermal

Parallell plateComb

Measure v

Inductive

Cantilever

Fiber

dt

dxv

Capacitive spring based

Capacitive finger

Analog Devices

Piezoresistive accelerometer

Piezoresistivt akselerometer 2

10 100 1 103

1 104

1 105

1 104

1 103

0.01

0.1

1

Frequency (Hz)

Outp

ut V

/g

Termisk masse (luft)

http://www.memsic.com/memsic/products/technology.html

Magnetic velocity measurement

Potentiometric level sensor

Tilt sensors

2D tilt sensor

Linear variable differential

transformer LVDT

Eddy current sensor

Permanant magnet - Hall sensor

Permanent field 1

Permanent field 2

Position sensitive detector

Linear -> Rotary

Position encoders

Ultrasound time of flight

7.42

Impedance matching

Triangulering - GPS

Wikipedia

Optisk mus

+ billedanalyse