PPT Complete

8/6/2019 PPT Complete

1/20

Vibration Analysis onVibration Analysis on

Power PlatePower Plate


2/20

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


3/20

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.


4/20

The SystemThe System

Isolator

Motor

Unbalance

Power plate panel


5/20

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


6/20

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[!


7/20

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.


8/20

ParametersParameters

y

The relevant parameters: Masses

Stiffness

Damping factor

Excitation force

Operating frequency


9/20

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


10/20

ContinueContinue....

y Damping factor

Logarithmic decrement

method

Estimated damping

0

2

1ln 2

1n

X

n X

\T

\

!

.15\ !


11/20

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[!


12/20

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 !


13/20

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\ !


14/20

Results..Results..

30Hz Low setting 50Hz Low setting


15/20

ContinueContinue

30Hz with Human

weight in high setting

30Hz with Human

weight in low setting


16/20

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


17/20

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


18/20

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


19/20

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


20/20

ThankThankYouYou

Documents

PPT Complete