Experiment 5 continued

1
Experiment 5 (continued)

• Part A Review Bridge Circuit, Cantilever Beam
• Part B Oscillating Circuits
• Part C Oscillator Applications
• Project 2 Overview

2
Agenda

• Review
• Bridge, Strain Gauge, Cantilever Beam, Thevenin
  equivalent
• Oscillating Circuits
• Comparison to Spring-Mass
• Conservation of Energy
• Oscillator Applications
• Project 2 Overview (velocity measurement)

3
What you will know

• (Review) How the Bridge, Strain, Gauge and
  Cantilever Beam relate
• Why the Thevenin equivalent is important
• Similarities in concept between a spring-mass and
  electronics
• Dynamics of Oscillating circuits
• Technology using these concepts
• Detail about Project 2 (due Oct 29th)

4
Applications

• Bridge circuits are used to measure ________
  resistances.
• What other types of sensors that change
  resistance in an environment are there?
• What are some applications for strain gauges?
  http//www.hitecorp.com/oemts.cfm

unknown
5
Review
Question Why use two strain gauges instead of
one?
http//www.allaboutcircuits.com/vol_1/chpt_9/7.htm
l
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Why is the Thevenin equivalent important?

• Macromodel used to model electronic sources
• Reduces the level of complexity
• To predict the behavior under a load for a
  non-ideal source

7
Thevenin Method
A
B

• Find Vth (open circuit voltage)
• Remove load if there is one so that load is open
• Open circuit means infinite resistance
• Find voltage across the open load
• Find Rth (Thevenin resistance)
• Set voltage sources to zero (current sources to
  open) in effect, shut off the sources (goes to
  zero) and what is left is Rth
• Short circuit meaning resistance is zero
• Find equivalent resistance from A to B

8
Practice Thevenin equivalent

• Find the Thevenin voltage of the circuit
• Find the Thevenin Resistance
• If you place a load resistor of 2K between A and
  B, what would be the voltage at point A?

V16 V, R150O, R2500O, R3800O, R43000O
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Why is Thevenins method important to this
experiment?

• When a bridge circuit is unbalanced you get a
  voltage output rather than zero.
• Thevenins method allow for easy prediction of
  what is happening across a load
• The result of these non-zero voltage fluctuations
  for a cantilever beam is.

10
Modeling Damped Oscillations

• v(t) A sin(?t) Be-at Ce-atsin(?t)

What causes the dampening? Why doesnt it
oscillate forever?
11
Examples of Harmonic Oscillators

• Spring-mass combination
• Violin string
• Wind instrument
• Clock pendulum
• Playground swing
• LC or RLC circuits
• Others?

12
Harmonic Oscillator

• Equation
• Solution x Asin(?t)
• x is the displacement of the oscillator while A
  is the amplitude of the displacement

13
Spring

• Spring Force
• F ma -kx
• Oscillation Frequency
• This expression for frequency holds for a
  massless spring with a mass at the end, as shown
  in the diagram.

14
Spring vs. Circuits

• From your basic physics book the conservation of
  energy
• WPotential energy Kinetic Energy
• If you pull a spring it gains potential energy
• When released you gain kinetic energy at the
  expense of potential energy then it builds
  potential again as the spring compresses
• A circuit with a capacitor and inductor does the
  same thing!

15
Oscillating Circuits

• Energy Stored in a Capacitor
• CE ½CV²
• (like potential energy)
• Energy stored in an Inductor
• LE ½LI²
• (like kinetic energy)
• An Oscillating Circuit transfers energy between
  the capacitor and the inductor.
• http//www.walter-fendt.de/ph11e/osccirc.htm

16
Voltage and Current

• Note that the circuit is in series,
• so the current through the
• capacitor and the inductor are the same.
• Also, there are only two elements in the
  circuit, so, by Kirchoffs Voltage Law, the
  voltage across the capacitor and the inductor
  must be the same.

17
Transfer of Energy

• When current is passed through the coils of the
  inductor, a magnetic field is created
• This magnetic field can do work
• WM(1/2) L I2
• When voltage is applied to the capacitor charge
  flows to the plates positive on one side negative
  on the other
• Force is now between the plates, energy is stored
  in the electric field created
• WE(1/2) C V2

18
Transfer of Energy

• Capacitor has been charged to some voltage at
  time t0
• Charge will flow creating a current through the
  inductor (potential to kinetic)
• Charge on capacitor plates is gone and current in
  inductor will reach its maximum (potential0,
  kineticmax)
• Current will then charge capacitor back up and
  process starts over!

19
Oscillator Analysis

• Spring-Mass
• W KE PE
• KE kinetic energy½mv²
• PE potential energy(spring)½kx²
• W ½mv² ½kx²

• Electronics
• W LE CE
• LE inductor energy½LI²
• CE capacitor energy½CV²
• W ½LI² ½CV²

20
Oscillator Analysis

• Take the time derivative

• Take the time derivative

21
Oscillator Analysis

• W is a constant. Therefore,
• Also

• W is a constant. Therefore,
• Also

22
Oscillator Analysis

• Simplify

• Simplify

Harmonic equation for oscillating circuits
23
Oscillator Analysis

• Solution

• Solution

V Asin(?t)
x Asin(?t)
24
Using Conservation Laws

• Please also see the write up for experiment 5 for
  how to use energy conservation to derive the
  equations of motion for the beam and voltage and
  current relationships for inductors and
  capacitors.
• Almost everything useful we know can be derived
  from some kind of conservation law.

25
Large Scale Oscillators
Petronas Tower (452m)
CN Tower (553m)

• Tall buildings are like cantilever beams, they
  all
• have a natural resonating frequency.

26
Deadly Oscillations
The Tacoma Narrows Bridge went into oscillation
when exposed to high winds. The movie shows what
happened. http//www.slcc.edu/schools/hum_sci/phys
ics/tutor/2210/mechanical_oscillations/ In the
1985 Mexico City earthquake, buildings between 5
and 15 stories tall collapsed because they
resonated at the same frequency as the quake.
Taller and shorter buildings survived.
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Controlling Deadly Oscillations
http//www.nd.edu/tkijewsk/Instruction/solution.h
tml
How do you prevent this?

• Active Mass Damper
• Small auxiliary mass on the upper floors of a
  building
• Actuator between mass and structure
• Response and loads are measured at key points and
  sent to a control computer

Actuator reacts by applying inertial forces to
reduce structural response
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Atomic Force Microscopy -AFM

• This is one of the key instruments driving the
  nanotechnology revolution
• Dynamic mode uses frequency to extract force
  information

Note Strain Gage
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AFM on Mars

• Redundancy is built into the AFM so that the tips
  can be replaced remotely.

30
AFM on Mars
Landing projected May 25, 2008

• Soil is scooped up by robot arm and placed on
  sample. Sample wheel rotates to scan head. Scan
  is made and image is stored.

http//www.nasa.gov/mission_pages/phoenix/main/ind
ex.html
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AFM Image of Human Chromosomes

• There are other ways to measure deflection.

32
AFM Optical Pickup

• The movement of the cantilever is measured by
  bouncing a laser beam off the surface of the
  cantilever

33
MEMS Accelerometer
Micro-electro Mechanical Systems
Note Scale

• An array of cantilever beams can be constructed
  at very small scale to act as accelerometers.

Nintendo Wii uses these for measuring movement
and tilt Others?
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Hard Drive Cantilever

• The read-write head is at the end of a
  cantilever. This control problem is a remarkable
  feat of engineering.

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More on Hard Drives

• A great example of Mechatronics.

39
Project 2 Velocity Measurement
40
Project 2 Velocity Measurement

• Cantilever beam sensors

• Position measurement - obtained by strain gauge
• Acceleration measurement - obtained by the
  accelerometer
• What op-amps would you use to get velocity for
  each?

41
Sensor Signals

• The 2 signals
• Position
• Acceleration

42
Basic Steps for Project

• Mount an accelerometer close to the end of the
  beam
• Wire 2.5V, -2.5V, and signal between IOBoard and
  Circuit
• Record acceleration signal
• Reconnect strain gauge circuit
• Calibrate the stain gauge
• Record position signal
• Compare accelerometer and strain gauge signals
• Build an integrator circuit to get velocity from
  the accelerometer sensor
• Build a differentiator circuit to get velocity
  from the strain gauge sensor
• Include all calibration and gain constants and
  compare measurements of velocity

43
The Analog Device Accelerometer

• The AD Accelerometer is an excellent example of a
  MEMS device in which a large number of very, very
  small cantilever beams are used to measure
  acceleration. A simplified view of a beam is
  shown here.

44
Accelerometer

• The AD chip produces a signal proportional to
  acceleration
• 2.5V and -2.5V supplies are on the IOBoard.
• Only 3 wires need to be connected, 2.5V, -2.5V
  and the signal vout.

45
Accelerometer Circuit

• The ADXL150 is surface mounted, so we must use a
  surfboard to connect it to a protoboard

46
Caution

• Please be very careful with the accelerometers.
  While they can stand quite large g forces, they
  are electrically fragile. If you apply the wrong
  voltages to them, they will be ruined. AD is
  generous with these devices (you can obtain
  samples too), but we receive a limited number
  each year.
• Note this model is obsolete, so you cant get
  this one. Others are available.

47
Mount the Accelerometer Near the End of the Beam

• Place the small protoboard as close to the end as
  practical
• The axis of the accelerometer needs to be
  vertical

48
Accelerometer Signal

• The output from the accelerometer circuit is
  38mV per g, where g is the acceleration of
  gravity.
• The equation below includes the units in brackets

49
Amplified Strain Gauge Circuit
50
Position Measurement Using the Strain Gauge

• Set up the amplified strain gauge circuit
• Place a ruler near the end of the beam
• Make several measurements of bridge output
  voltage and beam position
• Find a simple linear relationship between voltage
  and beam position (k1) in V/m.

51
Comparing the accelerometer measurements with the
strain gauge measurements

• The position, x, is calculated from the strain
  gauge signal.
• The acceleration is calculated from the
  accelerometer signal.
• The two signals can be compared, approximately,
  by measuring ? (2pf).

52
Velocity

• One option integrate the acceleration signal
• Build a Miller integrator circuit - exp. 4
• Need a corner frequency below the beam
  oscillation frequency
• Avoid saturation of the op-amp gain isnt too
  big
• Good strong signal gain isnt too small

53
Velocity

• Another option differentiate the strain gauge
  signal.
• Build an op-amp differentiator exp. 4
• Corner frequency higher than the beam oscillation
  frequency
• Avoid saturation but keep the signal strong.
• Strain gauge Differential op amp output is this
  circuits input

54
Velocity

• Be careful to include all gain constants when
  calculating the velocity.
• For the accelerometer
• Constant of sensor (.038V/g) g 9.8m/s2
• Constant for the op-amp integrator (-1/RC)
• For the strain gauge
• The strain gauge sensitivity constant, k1
• Constant for the op-amp differentiator (-RC)

55
MATLAB

• Save the data to a file
• Open the file with MATLAB
• faster
• Handles 65,000 points better than Excel
• Basic instructions are in the project write up

56
Some Questions

• How would you use some of the accelerometer
  signals in your car to enhance your driving
  experience?
• If there are so many accelerometers in present
  day cars, why is acceleration not displayed for
  the driver? (If you find a car with one, let us
  know.)
• If you had a portable accelerometer, what would
  you do with it?

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Passive Differentiator
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Active Differentiator
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Typical Acceleration

• Compare your results with typical acceleration
  values you can experience.

60
Crash Test Data
Ballpark Calc 56.6mph 25.3m/s Stopping in 0.1
s Acceleration is about -253 m/s2 -25.8 g

• Head on crash at 56.6 mph

61
Crash Test Data
Ballpark Calc 112.1mph 50.1 m/s Stopping in
0.1 s Acceleration is about -501 m/s2 -51.1 g

• Head on crash at 112.1 mph

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Crash Test Analysis Software

• Software can be downloaded from NHTSA website
• http//www-nrd.nhtsa.dot.gov/software/

63
Crash Videos

• http//www.arasvo.com/crown_victoria/cv_movies.htm
  

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Airbags

• Several types of accelerometers are used at
  least 2 must sense excessive acceleration to
  trigger the airbag.