Ketan's Lab Report

8/9/2019 Ketan's Lab Report

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Robert Gordon University

Engineering Analysis 1

Sushil Goswami BEng. Mechanical & Offshore Engineering Page 1

COURSEWORK

ON

TUNED DYNAMIC

ABSORBER

BY

SUSHIL GOSWAMI

0903143

3

RD

YEAR BEng MECHANICAL & OFFSHOREENGINEERING


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Objective: To eliminate the vibrations of a simply supported beam using a tuned

dynamic absorber.

Diagram:

Data Given:

Mass of beam: 2.112 kg

Length of beam: 820 mm between bearings

Beam cross-section (b x h): 25.4 mm x 12.7 mm

Beam material (steel) E: 200 GN/m2

Mass of motor unit: 6.120 kg

Absorber masses: 0.165 kg each

Cantilever dimensions (b x h): 12.7 mm x 0.84mm

Cantilever material E: 200 GN/m2


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Procedure, Calculations & Measurements:

1. Calculate the theoretical natural frequency of the system.

At mid-span, the stiffness of a simply supported beam is given by

K1= where I=

K1=75490.67 N/mEquivalent mass of the beam referred to mid-span is given by

Me=

Me= 1.407 kg

The fundamental natural frequency of the system is given by

n1= n1= 980.53 rpm

2. Starting from about 20% below this value, gradually increase the motor speed

until a resonance condition occurs. Note the resonant frequency and compare

with the calculated value.We start with the angular speed of 784.4 rpm (80% of 980.53 rpm).

Resonance occurs at 950 rpm as against the calculated value of 980.53 rpm.

3. Calculate the position of the absorber masses in order that the absorber is

tuned to the resonant frequency of the motor/beam system.

For the absorber to be tuned to the resonant frequency of the original

motor/beam system, the added system should have a natural frequency equal

to the forcing frequency i.e.

= 4.76cm

4. Fix the absorber and observe its effectiveness at the resonant frequency of

the original system.

We observe that as the masses in the absorber are moved along the

cantilever arms, the amplitude of the frequency of the motor/beam system

changes accordingly. The closer the absorber masses are to the machine, the

higher is the resonance. The further the absorber masses are from themachine, the lesser is the resonance.

5. Tune the absorber by adjusting the position of the masses.

We move the absorber masses along the length of the cantilever arms and

observe the change in vibrations of the motor/beam system . At 4cm, we

observe that there is no resonance in the whole system.


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6. Starting from about 30% below the original resonant frequency, gradually

increase the motor speed and observe the two frequencies at which

resonance occurs, one below and one above the original resonance.

We start at 686.4 rpm (70% of 980.53 rpm) and gradually increase the motor

speed. Resonance occurs in the combined system at 805 rpm and 1110 rpm,

one below and one above the original resonance.

Conclusion:As evident from above, there is discrepancy between calculated and

experimentally determined natural frequencies. The possible sources of error are as

listed below:

y The stiffness of the beam depends upon the second moment of area and the

total length of the beam. As the beam is centra lly loaded, over a period of

time, the effective length of the beam changes and so does the second

moment of area due to sagging as a result of constant and prolonged stress

conditions. This has a direct effect on the stiffness of the beam and hence it

doesnt remain constant at its original value. The calculated value is basedupon the original stiffness of the beam while the observed value is based

upon the current stiffness of the beam.

y As we gradually reach closer to the resonant frequency, the system d oesnt

go into resonance instantaneously. It starts wobbling at motor speeds closer

to the original resonance frequency. Now as the experiment involves user to

observe its resonance frequency, there is a possibility of mistaking a lower or

higher frequency as the original resonance frequency.

A sinusoidal force F0sin w tacts on an undamped main

mass-spring system (without the absorber mass attached). When the forcingfrequency equals the natural frequency of the main mass the response is infinite.

This is called resonance, and it can cause severe problems for vibrating systems.When an absorbing mass-spring system is attached to the main mass and theresonance of the absorber is tuned to match that of the main mass, the motion of themain mass is reduced to zero at its resonance frequency. Thus, the energy of themain mass is apparently "absorbed" by the tuned dynamic absorber. It is interestingto note that the motion of the absorber is finite at this resonance frequency, eventhough there is NO damping in either oscillator. This is because the system haschanged from a 1-DOF system to a 2-DOF system and now has two resonance

frequencies, neither of which equals the original resonance frequency of the main


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mass (and also the absorber). If no damping is present, the response of the 2-DOFsystem is infinite at these new frequencies. While this may not be a problem whenthe machine is running at its natural frequency, an infinite response can causeproblems during start-up and shutdown. A finite amount of damping for both masseswill prevent the motion of either mass from becoming infinite at either of the newresonance frequencies. However if damping is present in either mass-spring

element, the response of the main mass will no longer be zero at the targetfrequency.

The use of tuned absorbers is limited to constant speed applications. As seen above,the combined system now would have two resonant frequencies, one below and oneabove the original resonant frequency. In a non-constant speed application, if themotor speed changes to any of these two frequencies, the system would vibrate inresonance. Hence, the use of tuned absorbers is limited to constant speedapplications.

References:

y http://paws.kettering.edu/~drussell/Demos/absorber/DynamicAbsorber.html

y http://www.mfg.mtu.edu/cyberman/machtool/machtool/vibration/absorb.html

y http://abel.math.harvard.edu/archive/21b_fall_03/tacoma/

y http://ta.twi.tudelft.nl/nw/users/vuik/information/tacoma_eng.html

y Lecture notes by Ketan Pancholi, RGU, Aberdeen.


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Ketan's Lab Report