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Vibration Analysis onVibration Analysis on
Power PlatePower Plate
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ObjectiveObjective
y To analyze a power plate arrangement
y Come up with a mathematical model
y
Determination of model parametersy Vibration response of the developed
mathematical model
y Simulation of results
y Experimental validation
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About the systemAbout the system
y It is a brand of vibrating platform used as exerciseequipment.
y It consists of a vibrating base, which may vibrate up
and down approximately 1 to 2 mm (1/16") 25 to 50
times per second and large enough to accommodate aperson in deep squat.
y The vibrations cause an involuntary reflex muscle
contraction25-50 times a second compared to once or
twice a second normally.
y Makers claim that using the Power-Plate for 10 minutes
is equivalent to 60 minutes of conventional exercise.
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The SystemThe System
Isolator
Motor
Unbalance
Power plate panel
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ComponentsComponents
y Consists of a panel supported on four
diamond shaped isolators
y Panel bounded by noise absorbers
Filtering of the noises
y Harmonic excitation
Two motors having unbalances
Semicircular discs- 4 nos. on each side
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Mathematical ModelMathematical Model
y Forced VibrationSystem
Single dof model
y The governing equation:
y u is the unbalance in themotor
2
02( )
d x dxM C Kx F Sin t
dt dt [ !
2
0F u[!
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AssumptionsAssumptions
y System is assumed to be symmetric
Single dof modeling
Only bouncing motion for the panel
y Both motors running in phase
y Rigid mounting is assumed for isolators.
y Assuming perfect isolation by isolators.
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ParametersParameters
y
The relevant parameters: Masses
Stiffness
Damping factor
Excitation force
Operating frequency
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EstimationEstimation
y
Mass Mass of the panel assembly, m = 37.5kg
y
Stiffness Force deflection method
Applied wt, f = 15kgf
Deflection, d= 7mm
K= f/d =21021.4 N/m
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ContinueContinue....
y Damping factor
Logarithmic decrement
method
Estimated damping
0
2
1ln 2
1n
X
n X
\T
\
!
.15\ !
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ContinueContinue
y Excitation force Forced excitation due to unbalance
Mass of the semicircular disc, m = 155g
Eccentricity = CG of disc,
Unbalance, u = mrc
= .00329kgm
Low setting
4 discs causing unbalance per motor
High Setting
8 discs causing unbalance per motor
Excitation force,
4
3c
rr
T
!
2
0F u[!
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AnalysisAnalysis
y
Steady state responsey where
y
Time domain result Duhamels integral
2
12 222
1 2
X r
er r\
!
rp
[!
2( )
0
( ) ( ) ( ( ))
t
p t
d
d
u x t Sin e Sin p t d
Mp
\ X[ [X X X !
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ResultsResults
y
The response for various settings of thesystem were obtained
y Sample result
M = 37.5kg
K = 21021.4N/m
u = .00329kgm
w = 40Hz
The Steady state response, X = .726mm
.15\ !
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Results..Results..
30Hz Low setting 50Hz Low setting
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ContinueContinue
30Hz with Human
weight in high setting
30Hz with Human
weight in low setting
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Experimental SetupExperimental Setup
y Objective:
Vibration response measurement
y The apparatus:
Accelerometer
Charge amplifier Oscilloscope
y Charge amplifier setting
Sensitivity = 1.09
100mV = 1 mm
y Accelerometer
Fixed on the panel centre using magnet
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ObservationsObservations
SlNo: Frequency,w(Hz) Response(mV) Response(mm) TheoreticalResponse(mm)
1 30 60.8 .608 .746
2 35 53.6 .536 .734
3 40 50.7 .507 .726
4 50 47.8 .478 .717
Low Setting
High Setting
Sl
No:
Frequency,
w(Hz)
Response
(mV)
Response
(mm)
Theoretical
response(mm)
1 30 176.2 1.762 1.492
2 35 164.3 1.643 1.468
3 40 154.7 1.547 1.452
4 50 146.5 1.465 1.434
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Experimental resultExperimental result
y Sample resulty w = 40Hz
y M = 37.5kg
y
w =40Hz
y M=100kg
2
0 8F u[!
-1.00E-01
-8.00E-02
-6.00E-02
-4.00E-02
-2.00E-02
0.00E+00
2.00E-02
4.00E-02
6.00E-02
8.00E-02
1.00E-01
1.20E-01
Response Volt
Response Volt
2
0 8F u[!
-1.50E-01
-1.00E-01
-5.00E-02
0.00E+00
5.00E-02
1.00E-01
1.50E-01
Response Volt
Response Volt
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ConclusionConclusion
y Experimental results were matching withthe mathematical model.
y The presence of man on the machine causes
asymmetry disrupting the basics of themodel
y Small phase differences in the motors are
not causing considerable change in
response.
y Higher values of the phase lag causes
asymmetry
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ThankThankYouYou
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