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8/9/2019 Ketan's Lab Report
1/11
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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Robert Gordon University
Engineering Analysis 1
Sushil Goswami BEng. Mechanical & Offshore Engineering Page 2
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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Engineering Analysis 1
Sushil Goswami BEng. Mechanical & Offshore Engineering Page 3
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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Robert Gordon University
Engineering Analysis 1
Sushil Goswami BEng. Mechanical & Offshore Engineering Page 4
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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Engineering Analysis 1
Sushil Goswami BEng. Mechanical & Offshore Engineering Page 5
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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