1. NONLINEAR HYDRODYNAMIC
FORCES
MANUFACTURE AND TRANSDUCER
SELECTION
By Sachindra Max
2010

2. Overview of the Project
• This experiment is to
understand the fluid
hydrodynamic forces acting
on a floating body.
• This is practically applicable
for borehole oil drilling in
offshore and onshore.
• Properties of Fluids inside
the bore will be able to
measure from this equipment.
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3. Overview of the Project
• My main objective was to manufacture the experiment rig
and select transducers to it.
• Apart form that I compared the experimental results in
different conditions with a theoretically obtained values.
• Methods of multiple scale analysis is used to evaluate the
theoretical values.
Experimental Theoretical
Results Values
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4. About bore hole drilling
• Bore holes may construct for may different purposes.
• In the Oil and Gas industry bore hole drilling is very important.
• Drilling is divided mainly in to 2 categories.
1. Onshore Drilling 2. Offshore Drilling
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5. About bore hole Drilling cont..
• This technology has a history of hundreds years.
• Drilling methods have been developed over the time for
different purposes and environments to increase its efficiency.
• Few main drilling types,
I. Auger drilling
II. Air core drilling
III. Cable tool drilling
IV. Diamond core drilling
V. Hydraulic-rotary drilling
VI. Sonic (vibratory) drilling / Resonance enhanced drilling
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6. Manufacturing of apparatus
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7. Experimental rig – Manufacturing
• The rig is adjusted couple of times to achieve the desired
experimental results.
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8. Transducer Selection

9. Transducer Selection – Linear variable
displacement transducer
• Linear variable displacement transducer (LVDT) is used to
measure the amplitude of the oscillation.
• Change in position vertically of the actuator rod measures the
amplitude of the oscillation.
• This device uses the eddy current principle to get the
measurement.
• Accuracy of the LVDT used is sufficient enough for the
experiment.
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10. Transducer Selection – Accelerometer
• Acceleration of the inner cylinder is measured by using this
device.
• Device is connected to a oscilloscope or to a computer
software to get the experimental results.
• Fixing this unit to the experimental rig is easy and accuracy is
high enough for the experiment.
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11. Transducer Selection – Pressure
Transducer
• Pressure transducer is necessary to fix to the bottom of the
large cylinder to measure the variable fluid pressure due to
the impact of the actuator.
• This can be connected to a oscilloscope or to a computer
software just like the Accelerometer or LVDT.
• Similarly fluid level can be measured by using the basic
hydrostatic pressure equation.
P = hρg
• Suitable transducer for this experiment has a pressure range
of 0 – 6 bar
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12. Transducer Selection – Vibro impactor
• This device creates the vertical sinusoidal force to vibrate the
system.
• The metal bar is placed in a solenoid which creates a magnetic
flux according to the current supplied.
• This is a very simple design and it’s the most appropriate for the
experiment.
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13. Transducer Selection – Motor selection
• Initially experiment rig was supposed to design with a electric
motor instead of a vibro impactor.
• Setup of the motor could be done as shown above.
• Main disadvantage of connecting a motor to the experiment is
that it can create vibration NOT only vertically but also
horizontally.
• Therefore it can create unnecessary friction to the vibrating
system.
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14. Arrangement of the experimental rig
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15. Experimental rig – Signal generation /
inputs
Signal Vibrating
Transformer
Generator system
• A Sinusoidal current is generated from a signal generator and
sent it to the vibro impactor, solenoid of the impactor creates
a sinusoidal magnetic flux in the same frequency as the
current. Therefore the metal bar will vibrates at the same
frequency as the current.
• Amplitude of the sinusoidal motion of the metal bar is varied
by varying the supplied voltage from the transformer.
• Best results of the experiment can be achieved by setting the
vibrating frequency to 6Hz and voltage to 12v.
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16. Experimental rig – Results / data
outputs
Oscilloscope Vibrating
Transducers
/ Computer system
• Output signals from all the transducers are connected either
to a oscilloscope or to a computer.
• Graphical representation of the data can be filtered well only
in the computer software.
• Oscilloscope used to show the general idea of the motion
graphically.
• Experimental data is taken at different conditions such as with
water and without.
• Data is recorded as a function of time from the computer
software and then plotted as shown in next slides. 16

17. Data acquisition for various cycles
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18. Water damped system with the LVDT :
Displacement Vs. Time
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19. Water damped system with the
Accelerometer : Acceleration Vs. Time
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20. Mathematical model for the
experimental results
• Experiment rig can be simplified to a simple spring damper
system as shown above.
• Springs of the rig will act same and water of the system
behave as a damper. 20

21. Transient motion of the system
without water
• Suspended system is lifted up n released manually with a
magnetic system and let the system vibrate freely with no
external forced applied.
• Equation of the acceleration Vs. time graph of the system can
assumed as;
1
• Oscillating Velocity of the system can be obtained by
integrating the equation 1
2
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22. • Graphical representation of the equation 2
Velocity Vs. time – without water
( in a time interval of 0 – 2 seconds )
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23. • Equation 2 can be integrated once and obtained the displacement
Vs. time equation
3
Displacement Vs. time – without water
( In a time interval of 0 – 2 seconds)
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24. Theoretical model for the system
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25. Method of multiple scales
• This is a perturbation method.
• Duffing equation is used to evaluate the theoretical values.
• This equation can be used to this experiment since it’s
amplitude is low and it can be used for water damping
systems.
• Duffing equation :-
• This equation does not contain a damping term. There for its
modified with an additional damping term.
• Duffing equation with damping term :-
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26. Duffing equation
• Substitutions;
• After the substitution coefficients of each power of ϵ is
separated;
• Solutions for u0 , u1 , u2 obtained.
• u is obtained by substituting u0 , u1 , u2
• Where;
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27. Comparison
• Data obtained experimentally and numerically needs to
compared.
• Amplitude of the oscillation will be lower in experiment
values due to the friction acting at contacting points.
• The values can be compared as shown in the next slide.
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28. Graphical comparison
Experimental results Theoretical values 28

29. Conclusion
• Properties of water such as the damping term can be
evaluated by comparing the two methods.
• Accuracy of the system can be increased buy remanufacturing
some parts. And by using proper rigid connections.
• Experiment rig needs to be modified further for real life
applications.
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30. Thank you.
Any Questions ?
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