Pressure transducers and accelerometers Lecture 6

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Pressure transducers and accelerometersLecture
6

• Oct. 30, 2006

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Objectives

• (1) Calibrate pressure transducer
• Compare calibration with published data
• (2) Calibrate accelerometer
• Static mode
• (3) Compare spring constant values calculated
  from
• Static method
• F kx and
• Dynamic method (using accelerometer)
• ? (k/m)1/2

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Uses of pressure transducers

• To monitor
• Air bag systems
• Air speed
• Brake pressure
• Coolant, fuel and oil pressure
• Steering system pressure
• Sports

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Variation of pressure with depth

• Hydrostatic pressure increases with increasing
  submersion depth
• Weight of the column W mg rAgh
• r density of fluid
• Weight is supported by the net pressure (P-Po)A
• Then P Po rgh
• Pressure increases with depth
• All points at a given depth are
• at the same pressure

PoA
h
PA
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Strain gages - introduction

• The resistance of a metal changes with a change
  in length (strain)
• Hookes law states
• E s/ e
• Where E elastic modulus (constant for a given
  material), s stress and e strain
• Strain e D ? / ? o
• D ? / ? o is the proportional change in length

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Strain gages - introduction

• Resistance R of a metal given by
• R C(? /A)
• C material constant
• A cross-sectional area
• ? length
• The dR/R d?/ ?
• DR CoD ? / ? o Coe
• Strain gages can be used to measure small
  displacements

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Strain gage pressure transducer

• Pressure increases length of wire
• Change in resistance
• Measured and correlated with pressure

Deflection of diaphragm sensed with strain gages
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Piezoelectric pressure transducers

• Piezo (pressure) electric materials
• Dielectric material
• Alternating and - charge
• Deformation causes charge to build up on metal
  plates

Charge dxF d dielectric constant of the
material
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Piezoelectric pressure transducers

• The piezoelectric material is diffused onto a
  silicon diaphragm
• 100X more sensitive than wire strain gage
  transducers
• As diaphragm flexes resistance changes, measured
  by a bridge circuit

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(1) In lab - pressure calibration

• Record voltage for Dh 0 to 100 cm

amp
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In lab - pressure calibration
Do not include gain when calculating
sensitivity Take data every 5 cm
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In lab - pressure calibration
GAIN 100 red jumper
pressure transducer
Output (DMM)
Amplifier is used because signal small
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In lab - pressure calibration - electrical
connections
power to pressure transducer
DMM
GAIN 100
DMM
signal from pressure transducer
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Calibration curve

• Sensitivity volts/cm-H2O
• Plot volts vs cm H2O
• Compare experimental data with data available on
  the web
• You are using an Omega PX36 pressure transducer

volts



Dh, cm
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In lab - measure hysteresis

• Determine the hysteresis for your set-up
• Plot volts vs. cm-H2O steadily increasing and
  then decreasing the height
• Or vice versa

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Accelerometers

• An accelerometer is a device for measuring the
  change in velocity of an object (acceleration).
• An accelerometer inherently measures its own
  motion

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Some measures of acceleration

• Good cars can decelerate at 1 g
• 100 km/hr - 0 in 3s
• Race cars can accelerate at 4 g's
• 0 - 100 km/hr in under a second.
• A truck hitting the gravel of a runaway truck
  ramp
• decelerate at 3 g's
• A car hitting a set of sand barrels
• decelerate at 5 g's
• Fighter pilots
• withstand 5 gs without blacking out

1 g 9.8 m/sec2
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Applications for accelerometers

• Car air bags
• Inertial guidance systems
• Vibration sensing
• Footpods
• Runner feedback pace, distance, etc.
• Recently Ipod nano can give audio feedback
• Detection if a laptop is falling
• Automatically moves read/write head away from
  inner drive - protect data
• Measurement of gravitational force
• Anti-theft devices

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How to measure acceleration - simple harmonic
motion
k spring constant m mass
Acceleration d2y/dt2 -w2y Acceleration a
linear function of displacement
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How to measure acceleration - pendulum motion
Fnet -mgsinq ma -mgsinq a -gsinq
Two simple motions spring pendulum show
that the displacement of an object can be used to
determine acceleration
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Types of accelerometers

• Strain gage
• Lowest cost, least sensitive
• Piezoelectric
• MEMs
• Micro electrical mechanical system
• This is the accelerometer you will use in the lab

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Strain gage accelerometers

• Acceleration detected by bending of the
  cantilever beam
• Displacement measured by strain gages
• Wheatstone bridge formed with other gages
• Applications for
• Steady acceleration
• Low cost alternative

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Piezoelectric accelerometers

• Same principle as with piezoelectric pressure
  transducers
• Pressure causes material to deform
• Voltage proportional to charge on surface of
  metal plates

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MEMs accelerometer

• A typical MEMS accelerometer uses a silicon mass
  suspended by a silicon beam.
• Mechanically equivalent to a spring mass damper
  of a traditional mechanical accelerometer.
• Capacitive sensing is used to measure the motion
  of the mass.

hair 80µm
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Lab accelerometer (MEMs device)
2.5 cm
This accelerometer has a built in amplifier
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(2) In lab - static calibration of accelerometer

• Accelerometer connected to a plate that can sweep
  out 0-90
• The force on the accelerometer depends on the
  angle

• Wires are connected to a Wheatstone bridge
  circuit

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In lab - static calibration of accelerometer
to DMM
Take data for increasing and decreasing
angles Plot Volts vs. cosq
volts
q
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(3) Determination of spring constant
N kgm/s2

• Mass on pan connected to spring
• Use Hookes law
• F kx
• k spring constant (N/m)
• Want k in mks units only

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In lab - spring constant static method
Use 3 different weights to calculate k
NOTE To convert mass to force in N, multiply
the weight (in kg) by 9.8 m2/sec
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In lab - spring constant dynamic method

• (k/m)1/2 ? 2?/T
• k ?2m (2?/T)2m
• 50 N/m

w 810 gms
The period, T, measured directly from graph T
changes with different weight
T 0.8 sec
Use 3 different weights to calculate k
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Next week

• Using strain gages on an aluminum alloy
  cantilever beam
• Determine deflection under a load
• Calculate elastic modulus (E)
• Calculate Poissons ratio (n)
• Compare to published values
• Aluminum alloy composition and heat treatment is
  2024-T4