NONLINEAR HYDRODYNAMIC         FORCESMANUFACTURE AND TRANSDUCER        SELECTION          By Sachindra Max                ...
Overview of the Project• This experiment is to   understand the fluid   hydrodynamic forces acting   on a floating body.• ...
Overview of the Project• My main objective was to manufacture the experiment rig  and select transducers to it.• Apart for...
About bore hole drilling• Bore holes may construct for may different purposes.• In the Oil and Gas industry bore hole dril...
About bore hole Drilling cont..• This technology has a history of hundreds years.• Drilling methods have been developed ov...
Manufacturing of apparatus                             6
Experimental rig – Manufacturing• The rig is adjusted couple of times to achieve the desired  experimental results.       ...
Transducer Selection
Transducer Selection – Linear variable       displacement transducer• Linear variable displacement transducer (LVDT) is us...
Transducer Selection – Accelerometer• Acceleration of the inner cylinder is measured by using this  device.• Device is con...
Transducer Selection – Pressure               Transducer• Pressure transducer is necessary to fix to the bottom of the  la...
Transducer Selection – Vibro impactor• This device creates the vertical sinusoidal force to vibrate the  system.• The meta...
Transducer Selection – Motor selection• Initially experiment rig was supposed to design with a electric  motor instead of ...
Arrangement of the experimental rig                                      14
Experimental rig – Signal generation /                inputs                               Signal        Vibrating        ...
Experimental rig – Results / data                outputs              Oscilloscope                  Vibrating             ...
Data acquisition for various cycles                                      17
Water damped system with the LVDT :       Displacement Vs. Time                                  18
Water damped system with theAccelerometer : Acceleration Vs. Time                                    19
Mathematical model for the           experimental results• Experiment rig can be simplified to a simple spring damper  sys...
Transient motion of the system              without water• Suspended system is lifted up n released manually with a  magne...
• Graphical representation of the equation 2                Velocity Vs. time – without water              ( in a time int...
• Equation 2 can be integrated once and obtained the displacement  Vs. time equation                                      ...
Theoretical model for the system                                   24
Method of multiple scales• This is a perturbation method.• Duffing equation is used to evaluate the theoretical values.• T...
Duffing equation• Substitutions;• After the substitution coefficients of each power of ϵ is  separated;• Solutions for u0 ...
Comparison• Data obtained experimentally and numerically needs to  compared.• Amplitude of the oscillation will be lower i...
Graphical comparisonExperimental results   Theoretical values   28
Conclusion• Properties of water such as the damping term can be  evaluated by comparing the two methods.• Accuracy of the ...
Thank you.Any Questions ?                  30
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Nonlinear hydrodynamic forces - manufacture and transducer selection

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Nonlinear hydrodynamic forces - manufacture and transducer selection

  1. 1. NONLINEAR HYDRODYNAMIC FORCESMANUFACTURE AND TRANSDUCER SELECTION By Sachindra Max 2010
  2. 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. 2
  3. 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 3
  4. 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 4
  5. 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 drillingII. Air core drillingIII. Cable tool drillingIV. Diamond core drillingV. Hydraulic-rotary drillingVI. Sonic (vibratory) drilling / Resonance enhanced drilling 5
  6. 6. Manufacturing of apparatus 6
  7. 7. Experimental rig – Manufacturing• The rig is adjusted couple of times to achieve the desired experimental results. 7
  8. 8. Transducer Selection
  9. 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. 9
  10. 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. 10
  11. 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 11
  12. 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. 12
  13. 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. 13
  14. 14. Arrangement of the experimental rig 14
  15. 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. 15
  16. 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. 17. Data acquisition for various cycles 17
  18. 18. Water damped system with the LVDT : Displacement Vs. Time 18
  19. 19. Water damped system with theAccelerometer : Acceleration Vs. Time 19
  20. 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. 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 21
  22. 22. • Graphical representation of the equation 2 Velocity Vs. time – without water ( in a time interval of 0 – 2 seconds ) 22
  23. 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) 23
  24. 24. Theoretical model for the system 24
  25. 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 :- 25
  26. 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; 26
  27. 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. 27
  28. 28. Graphical comparisonExperimental results Theoretical values 28
  29. 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. 29
  30. 30. Thank you.Any Questions ? 30

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