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Vibration Control
Topics: Introduction to Vibration Control
Methods of Vibration Control
Vibration Isolation
Rigidly Coupled Viscous Damper
Elastically Coupled Viscous Damper
Undamped Vibration Absorber
Forced Damped Vibration Absorber
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Introduction Vibration Control
There are numerous Sources of Vibration in an Industrial
Environment Presence of Vibration leads to
Excessive wear of bearings,
Formation of cracks,
Loosening of fasteners,Structural and mechanical failures,
Frequent and costly maintenance of machines,
Electronic malfunctions
Exposure of Humans leads to Pain, Discomfort andReduced efficiency.
Hence it is necessary to eliminate or reduce vibration
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Methods of Vibration Control
Avoid Resonance
Balancing / Control of Excitation Forces
Adequate Damping
Vibration Isolation
Vibration Absorber
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http://h/Curriculam%20Development/PG%20Course%20material%20on%20Design%20for%20NVH/TacomaNarrowsBridge%5b1%5d.mpghttp://h/Curriculam%20Development/PG%20Course%20material%20on%20Design%20for%20NVH/TacomaNarrowsBridge%5b1%5d.mpg8/8/2019 Chapter 7 Methods of Vibration Control
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Vibrations of a structure Complex and multiple excitation sources
A number of natural frequencies/modes
are excited.
Modes can not be accurately measured.
In case of real life structures there can be
vagueness in structural parameters Some parameters change with time
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Passive Vibration Control:
dampers, absorbers, stiffeners, structural dynamic
modification.
Active Vibration Control:
piezoelectric, shape memory alloy, Electro-Rheological
fluids, Magneto-strictive materials
Active Vibration Control can not replace PassiveVibration Control, it can compliment it in a big way.
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Vibration IsolationVibration isolation works in two modes
To protect the sensitive equipment from
the vibrations communicated from the
ground
To protect the machine vibratory forces tobe communicated to foundation and to
ground.
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Vibration Control
Topics: Introduction to Vibration Control
Methods of Vibration Control
Vibration Isolation
Rigidly Coupled Viscous Damper
Elastically Coupled Viscous Damper
Undamped Vibration Absorber
Forced Damped Vibration Absorber
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Isolating the structures from vibration is
very important
Accuracy of the machines
Comfort levels of the passengers
Transmission of vibrations to other
nearby equipment
Sound Generated due to the vibration
is to be in limits
Vibration of the buildings due to theequipment present in them
Vibration Isolation
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Transmissibility(a) Force excitation
(1)
Figure 1 Force Excitation Model
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Vibration IsolationVibration isolation works in two modes
To protect the sensitive equipment from
the vibrations communicated from theground
To protect the machine vibratory forces tobe communicated to foundation and to
ground.
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The oscillation magnitude as a function of frequency is :
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(b) Motion excitation
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Larger r (= f/fn) is
better; should be more
than at least 1.414.
In post resonance
region smaller damping
is better but mostly the
machine has to cross
resonance so damping is
desired.
Isolator should be
designed keeping in
view avoidance of
resonance.
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Static Deflection is anotherlimiting factor /st g k =
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A Typical Machine Foundation
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Antivibration Rubber Mounts
Vibro EP
Antivibration PadsFor Wooden Floor
Vibro FM
Antivibration Hangers
Vibro CH-mini
Antivibration Strip
Vibro Strip
Antivibration Spring Mounts
Vibro SM
Ant ivibration Spring Hanger
Vibro CH
Some Typical Anti-vibration Mounts
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Shock Isolation Response to a velocity step
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Shock Isolation
2 2
0
( )
0, 0,2
( )
m
d
m
md Fs d mu
at t d d u which gives
d u Fs d dd
m
+ =
= = =
=
&& &&
&
&
& &
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Vibration IsolationVibration Isolation with Rigidly Coupled Viscous Damper
Periodic Force
Transmitted Force
Phase Angle
sinF t=
Transmissibility
( )
31
22
2tan
1 2
r
r r
= +
Phase Lag
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Vibration IsolationVibration Isolation with Elastically Coupled Viscous Damper
Transmissibility
Phase Lag
Force Transmitted
To Ground
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Vibration IsolationVibration Isolation with Elastically Coupled Viscous Damper
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Vibration Control
Topics: Introduction to Vibration Control
Methods of Vibration Control
Vibration Isolation
Rigidly Coupled Viscous Damper
Elastically Coupled Viscous Damper
Undamped Vibration Absorber
Forced Damped Vibration Absorber
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Vibration Absorber:Takes over theResponse
(9)
Model for the Analysis of Vibration Absorber
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20 2 2
1 2 2 21 2 1 2 2 2
0 22 2 2 2
1 2 1 2 2 2
2 2 1 2 0 2
( )
( )( )
( )( )
/ 0; /
F k mX
k k m k m k
F kXk k m k m k
if k m X X F k
=
+
=+
= = =
This result is used as the Vibration Absorber Principle
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The ratio of amplitudes is given by
Let , and mass ratio, then
`
We note that X=0 at =p
Design the system such that
Then amplitude of vibration of absorber becomes
1 1k m
k m= =
Undamped Vibration Absorber
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It is to be observed that , the vibration of main mass becomes zero at the
condition
This means that the absorber system absorbs all the energy of the parent system;
Hence it is called Dynamic Absorber
The frequency of the combined system is
And the two natural frequencies are
1 1k m
k m= =
Undamped Vibration Absorber
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Natural Frequency variation of dynamically absorbed system
Undamped Vibration Absorber
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Undamped Vibration Absorber
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Practical implementation of dynamic vibration absorber
A beam attached with cantilevers with tunable masses
Tuned absorber system, because the position of mass on the cantileverbeam can be changed
Undamped Vibration Absorber
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Vibration Control
Topics: Introduction to Vibration Control
Methods of Vibration Control
Vibration Isolation
Rigidly Coupled Viscous Damper
Elastically Coupled Viscous Damper Undamped Vibration Absorber
Damped Vibration Absorber
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A forced damped absorber configuration is given below.
The equations of motion are given by
Defining the system
properties
Damped Vibration Absorber
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The solution of X gives
For damping value at 0 the equation reduces to previous undraped case
and at infinity both masses got locked together and become rigid
Damped Vibration Absorber
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Solving the above equation , we get
All Curves with different
Damping pass through points
P and Q
Hence it is possible to find
the optimum Damping value
Damped Vibration Absorber
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The optimum damping value is given by
Which is obtained by differentiating equation with rf
Thus the frequency response of a
tuned absorber is given
Damped Vibration Absorber
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A Transmission line
damper is a fine example
of a vibration absorber
where the vibrations of
the transmission wire are
absorbed in the damper,
which is tuned to the
natural frequency of the
wire.
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Active Vibration Control
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Smart StructuresSensors
Piezoelectric
Magnetostricitive
Strain Guages Electromagnetic
Actuators
Piezoelectric
Electro rheological
Magneto-rheological Magnetostrictive
Shape Memory Alloy
Electromagnetic
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Active Vibration Control of a SDOF System
)()()()()(2
txDHtFtftFKxCDxxMD e ==++
x(t)
Processor
F(t)
K C
M
F(t) x(t)
Amplifier
Actuator
Sensor
fe(t)
- H(D)
+ Plant
21
2)( CDCDCDH o ++=
)()()()()( 212
tFtxCKDxCCxDCM o =+++++
If,
Equation of motion:
We have,
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MODAL SPACE CONTROL
In a number of the complex flexible structures we are interested in
controlling the first few modes only. Transforming the system into
modal space and controlling its individual modes is modal space
control.
Independent Modal Space Control (Mierovitch)
Coupled Modal Control
Modified Independent Space Control (Baz)
Efficient Modal Control
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Independent Modal Space Control Is based on the assumption that the control force required for
controlling a particular mode is independent of the control force required
in any other mode.
A particular mode is controlled by LQR applied to the modal
equation and converting the modal forces to physical forces.
The energy gets transferred to higher or other modes and the
spillover effect is significant sometimes
For controlling multiple modes, the number of actuators required
is equal to the number of modes to be controlled.
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EFFICIENT MODAL CONTROL STRATEGY
Weighting of the control force according to
displacement in each mode
Feedback in mode i: Feedback in mode j : Feedback in mode k
Weighting of the control force according to energy in
each mode and frequency weighting
Feedback in mode i: Feedback in mode j : Feedback in mode k
)(
)(
)(
)(:
)(
)(
)(
)(:1
kfrequency
ifrequency
ienergy
kenergy
jfrequency
ifrequency
ienergy
jenergy=
)(
)(:
)(
)(:1
intdisplaceme
kntdisplaceme
intdisplaceme
jntdisplaceme=
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0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-1.5
-1
-0.5
0
0.5
1
1.5x 10
-3
Time (sec)
Displacementattipofbeam(m
)
Figure 2 Uncontrolled response of beam due to excitation of
first three modes
0 500 1000 1500 2000 2500
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Amplitude
Sampling rate
Figure 3 FFT of the uncontrolled response
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Figure 4 Controlled response at tip of beam due to
feedback force applied according to IMSCFigure 5 Controlled response at tip of beam due to
feedback force applied according to EMC
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Case Study: Fuzzy logic basedcontrol implementation on a
beam structure
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What is Fuzzy Logic?
Fuzzy Logic is all about relative importance of precision:
As Complexity rises, precise statements lose meaning and
meaningful statements lose precision.
---- Lotfi Zadeh (Father of Fuzzy Logic)
How important is it to be exactly right when a roughanswer will do?
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A 1500 Kg mass
is approaching
your head at 45.01 m/sec.Look Out!!
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LOOK
OUT!!
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Simulink Model of Fuzzy logic based Active Vibration
Control of SDOF system.
M
F p
M
1
MF p
Fuzzy Logic
Controller
Multiply Power
Sum x
M
K
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Typical Experimental set-up for structuralvibration control of a continuous system:
Actuator
Accelerometer
ControllerAmplifier
Beam
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Charge amplifier
Fuzzy Logic
Controller
Voltage amplifier
Cantilever beam
Collocated Piezo
sensor/actuator pair.
Schematic diagram of the experimental set-up.
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Why fuzzy logic foractive vibration control:
To take care of vagueness in structure
Fuzzy control has been used mostly in asupervisory mode in AVC. Investigate the
effects of applying fuzzy logic in real time
Less sensitive to changes in structural
parameters
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Velocity.
-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03
Membershipvalue.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
N Z P
(-a,0) (-b,0) (b,0) (a,0)
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Uncontrolled
Controlled
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Uncontrolled
Controlled
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Control off Control on
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Performance of Fuzzy Logic controller vs
Velocity Feedback Controller.
0 10 20 30 40 50 600
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Maxim
umappliedforce
Settling Time, Secs
Velocity feedback
Fuzzy logicCritical Damping
Critical Damping
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Vibrating structure
Elastic constrain layerViscoelastic shear layer
Vibration control by Passive constrained layer
Charge amplifier
Vibrating structureViscoelastic shear layer
Charge Ampli fier Feed Back Control
Piezoelectric layer
Piezoelectric Layer
Vibration control by Active constrained layer
PointSensor
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Vibration Control of Beam w ith Partially Covered Active Constrained Layer
Data Acquisition System
FeedbackAlgorithm
Actuation
Amplifier
Band Pass
Filter
Piezo Sensor amplifier
System
+ -
Battery
PZT Actuator
Viscoelastic Layer
PZT Sensor
Host Beam
Solenoid
Figure : Schematic diagram of the experimental setup.
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Vibration Control of Beam w ith Partially Covered Active Constrained Layer
Controller
PZT ActuatorPartially covered Beam
PZT Sensor
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Vibration Control of Beam w ith Partially Covered Active Constrained Layer
Figure: The variation of the damping ratio for the variablecoverage of active and passive constrained layers w ithdifferent values of the proportional and derivat ive gains.
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Development Of a Semi-activeSuspension for An Automotive Vehicle
using Magnetorheological dampers
Active Isolation
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The ProblemVehicle
Road Disturbances &
Load Disturbances
+
Art of Compromise between
Two conflicting goals, good
Handling and Comfort Ride
Passive Suspension
(Spring parallel with viscous damper)
+
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Passive Suspension Ideal skyhook damper
Performance Analysis of.contd.
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MR damper based quarter car Semi
active Suspension- modeling, control
and performance analysis
Two Degree of Freedom model of suspension
Work presented and reported in the international conferenceorganized by SAE India- Jan 2004
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Full Car Magnetorheological..contd.
Bump Model
DisplacementAcceleration
1( )sz
1( )sz
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Source: www.enme.umd.edu
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Source: www.enme.umd.edu
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Source: www.enme.umd.edu
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Assignment
1
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Assignment
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