Vibration and Engineering Design (Perspective of a Mechanical Engineer working in Vibration related problems) Abhijit Gupta, Ph.D, P.E. Professor, Dept of Mechanical Engineering Northern Illinois University, DeKalb, IL 60115

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Vibration and Engineering Design (Perspective
of a Mechanical Engineer working in Vibration
related problems) Abhijit Gupta, Ph.D, P.E.
Professor, Dept of Mechanical Engineering
Northern Illinois University, DeKalb, IL 60115

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My research interests

• Measurement of Dynamic Modulus (Including
  Damping) of Viscoelastic Materials
• Accelerated Testing
• Bridge vibration
• Electromagnetic Shock Absorber
• Tremor Control

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First some thoughts on engineering in general

• Engineers are tinkerers and problem solvers
•  
• NASA has more engineers than scientists
• Mechanical Engineering is one of the important
• Engineering Discipline
• Mechanical Engineering encompasses many aspects
• Aerospace
• Automotive
• Manufacturing
• Utility Industries
• Biotech

Impossible to name an industry that does not
employ mechanical engineers
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• Mechanical Engineers are involved with
• Conversion of energy (engine, turbine, motor,
  fuel cell, etc.) 
• Conversion of motion (gears, piston-cylinder,
  etc.) 
• Design and Analysis  
• Choosing the correct material
• Manufacturing the product

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Steps in Engineering Design
1. Identify the need
2. Define the problem
3. Search for information (including reverse
engineering)
4. Set Design Criteria and Constraints
5. Consider a number of solutions
6. Analyze the design
7. Make a decision
8. Develop specifications
9. Communicate the design solution
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Examples

• Before we get serious let us see some examples
  of Mechanical Engineering in the field of
  Vibration
• and Acoustics and have some fun
• We will look at human body vibration, machinery
  vibration,
• structural vibration, and vibration issues in
  sports and medical field
• It may be added that when excitation frequency
  equals to natural frequency, it is called
  resonance (and usually should be avoided)

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Linear vs. Oscillatory Motion
Displacement
D
Detroit 35 Miles
Time
Velocity
Speed limit 65 MPH
V
Time
TEST 0-60 MPH in 8.6 second
Acceleration
A
Time
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Mechanical Parameters and Components
Velocity
Displacement
Acceleration
d
v
a
k
c
m
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Undamped free vibration
Displacement
Displacement
d D sin?nt
D
Time
T
Frequency
m
Period, Tn in sec
k
Frequency, fn in Hz 1/sec
k
?n 2 ? fn
m
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• Natural frequency of a simple single degree of
  freedom undamped system is given by the equation
• ?N square root of (stiffness / mass)
• Usually we do not want structures to vibrate in
  resonance (though there are some special cases
  where resonance is desirable)

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Effect of Change in Mass
time
Increasing mass reduces frequency
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Mass, Spring and Damper
time
Increasing damping reduces the amplitude
k
c1 c2
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Human Vibration
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Resonance Frequency Ranges of Human body sections

• Eyeball, Intraocular Structure (20-90 Hz)
• Head (axial mode) (20-30 Hz)
• Shoulder Girdle (4-5 Hz)
• Chest wall (50-100 Hz)
• Arm (5-10 Hz)
• Hand (30-50 Hz)
• Abdominal Mass (4-8 Hz)
• Spinal column (axial mode) (10-12 Hz)
• It may be noted that the abdominal mass mode
  (around 5 Hz)
• makes us nauseating and is avoided in automotive
  design.
• Top gun pilots had problem with a particular
  maneuver when the eyeball
• socket went into resonance.

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Machines and Vibration
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Forces and Vibration
System Response (Mobility)
Input Forces


Vibration


Structural Parameters Mass Stiffness Damping
Vibration Parameters Acceleration Velocity Displa
cement
Forces caused by Imbalance Shock Friction Acoustic
891875
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Machine condition monitored by vibration
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Structural Applications

• Now let us look as some structural vibration
  applications
• 1) vibration of an windmill
• 2) Tacoma Narrows bridge failure
• 3) Vibration of a car

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Windmill Vibration
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Rotating Wind Turbine
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Testing of a small object(Laser Vibrometer)
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Wave Power

• Energy from Ocean Surface Waves
• Wave power is proportional to the wave period and
  to the square of the wave height
• Example Consider moderate ocean swells, in deep
  water, a few kilometers off a coastline, with a
  wave height of 3 meters and a wave period of 8
  seconds. Using the following formula to solve for
  power, we get
• implying that there are 36 kilowatts of
  power potential per meter of coastline.

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Bridge Vibration

• Structural vibration
• Fluid structure interaction
• Damage detection

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Vibration of CABLE STAYED BRIDGES(with
Argonne National Lab)

• 
  

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Tacoma Narrows Bridge Failure

• Tacoma Narrows Bridge collapse
• http//www.youtube.com/watch?vP0Fi1VcbpAI
• http//www.vibrationdata.com/Tacoma.htm
• Minnesota Bridge collapse
• http//www.youtube.com/watch?vnerQhIyOwxMfeature
  related

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Causes of the Tacoma Narrows Bridge Failure
The bridge survived only 4 months (July 1 Nov
7, 1940) Possible causes of Failure
mentioned Resonance (it was not a case of
steady-state excitation, so
resonance was not the cause) Vortex Shedding
(Again not a cause because the frequency observed
(0.2 Hz) and frequency calculated (1 Hz) were not
same Aerodynamic Flutter (due to restricted wind
flow when the architect changed the design
suggested by the engineer). New design addressed
that issue.
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Bridge Vibration and Damage Detection

• Minnesota Bridge Collapse The I-35W
  Mississippi River bridge was an eight-lane,
  1,907 feet steel bridge across the Mississippi
  river in Minneapolis collapsed at 605 pm on Aug
  1, 2007. Thirteen people died and approximately
  one hundred more were injured.
• This raised the whether vibration can be
  used to detect damage in bridges before they
  collapse.
• In the past vibration signature has been used
  for damage detection of aerospace applications
  and military applications.

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Automobile Vibration
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Components of a car

• For comfortable ride in a car requires analysis
  of car frame and many other components, e.g.
  exhaust systems (bellows), shock absorber, tire
  etc.
• We will look into a shock absorber in more detail

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How about Shock absorber

• We know what a typical shock absorber does
• Saves us from unpleasant vibration
• (recall that 5 Hz abdominal mode)
• by dissipating energy
• But why not try to recover the energy?

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Electromagnetic Shock Absorber

• Need for Improved Vehicle Fuel Efficiency

• In traditional Shock Absorber Energy is wasted
  as heat (In a semi-tractor trailer shocks are hot
  within fifteen minutes of driving)

• Information about car/truck available. Also
  information about road profiles are available

• Design criteria is that it should behave
  similar to a conventional shock. There may be
  space and weight constraints

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Let us look at a quarter bus/truck/car model
u road profile input kt tire spring
constant mu unsprung mass xu displacement of
unsprung mass
ks suspension spring constant cs suspension
damping constant ms sprung mass xs
displacement of sprung mass
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• Force on a coil moving inside an electromagnetic
  field is proportional to velocity same as that
  for conventional damper for shock absorber.
• This leads to Electromagnetic shock absorber
• We worked on this concept with Argonne National
  Lab.
• Bose corp also worked on this concept and plan
  to use for a high end Lexus model.

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Lab Testing of EM Shock 1 at NIU Vibration Lab
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Lab Testing of EM Shock 2 at NIU Vibration Lab
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Vehicle Testing(ATV and close up view)

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Energy harvesting as enabling factor for bridge
monitoring

• http//www.intelligent-systems.info/bridge.htm
• Electromagnetic generator to power sensor for
  bridge damage

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Tremor Control

• Intention tremor Multiple Sclerosis
• Essential tremor Inherited and worsen with age
• People affected Quarter million to 1 million
  people
• Available Medication Serious side effects
  including addiction
• Main concern Quality of life (eating, drinking,
  writing, personal care) and even keeping the
  job
• Mechanical issue Low frequency vibration with
  tremor frequency varying from 4.5 to 8 Hz

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Approach

• Principle Active Vibration control
• Tools Matlab Simulink, dSpace
• Hardware Prosthetic arm, Piezo patch and
  amplifier

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Experiment Setup
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ACCELERATED TESTING

• Operating at stresses much higher than normal
• Predict life under normal operating conditions
• Identify design weakness
• Accelerating factor does damping matter ?

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Other issues

• Sine to random
• Random to sine
• SDOF is ok but what about MDOF?
• Equivalent damage
• Driving factor Shaker time (especially big
  shakers)

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Vibration in sports
Golf Clubs, Tennis Racquets, Spring Board diving,
Baseball - all has vibration applications. Even
a traditional sport like Baseball has been
studied for vibration related issues. Solid bats
have only bending modes whereas aluminum bats or
composite bats also have hoop modes with
desirable trampoline effect. More on it later
(depending on performnace of Cubs and Sox)!
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Acoustics

• Sound is caused by vibration, so the science of
  studying sound (acoustics) and vibration are
  related
• If you are into music (and especially so called
  audiophile), you may already have looked at
  vibration response of speakers and decided what
  kind of speakers you want
• Quite often it is the low frequency response that
  drives up the price. Earlier two Mechanical
  Engineering students made a pair of concrete
  enclosure speakers in their final design project
  and the speakers were almost as good as thousand
  dollar worth speakers

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Sound and Human Being(some are music, some are
noise, and some in between)
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Designing a product

• Sometimes products are designed so that vibration
  is minimum and sometimes products are designed so
  that sound is minimum ( or maximum). Eventual
  goal is to either make human being more
  comfortable or make a machine or building last
  longer
• Now may be the time to take apart a product and
  think all engineering aspects of it. Vibration
  and acoustics may be one concern, material and
  manufacturing issues are also of concern and
  sometime there may be interdisciplinary i.e.
  electrical or industrial engineering issues need
  to be addressed.

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Acknowledgement

• CEET Associate Deans office
• Bruel Kjaer
• Argonne National Laboratory
• NASA
• Sandia National Laboratory