Chapter 7 Methods of Vibration Control

8/8/2019 Chapter 7 Methods of Vibration Control

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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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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.mpg


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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



Vibration Isolation






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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



Vibration Isolation






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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= =



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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= =



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Natural Frequency variation of dynamically absorbed system



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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



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Vibration Control



Vibration Isolation


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



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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



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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



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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



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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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Controller

PZT ActuatorPartially covered Beam

PZT Sensor


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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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Assignment

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Assignment

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Documents

Chapter 7 Methods of Vibration Control