Thesis presentation2

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Thesis presentation2

  1. 1. BACKWARD PRECESSIONAL WHIP AND WHIRL FOR A TWO-POINT RUBBING CONTACT MODEL OF A RIGID ROTOR SUPPORTED BY AN ELASTICALLY SUPPORTED RIGID STATOR<br />Master’s Thesis<br />By<br />Dhruv D. Kumar<br />
  2. 2. SINGLE POINT AND TWO POINT CONTACT<br />ANALYTIC SINGLE CONTACT MODEL<br />ANALYTIC TWO-CONTACT MODEL<br />Flexible rotor<br />Elastically supported stator <br />One point of contact between rotor-stator.<br />Rigid rotor<br />Elastically supported rigid stator<br />Two points of contact between rotor-stator.<br />Figure cited from-Childs, D. W., and Bhattacharya, A., 2007, “Prediction of Dry-Friction whirl and<br /> whip between a Rotor and a Stator,” ASME J. Vib. Acoust., 129, pp. 355–362. <br />
  3. 3. EVENTS LEADING TO 2 POINT DRY FRICTION INVESTIGATION<br /><ul><li>NRG systems #40 anemometer sensors were exhibiting post calibration slowdown
  4. 4. Faulty sensors had a dominant vibration frequency separate from the rotating speed.
  5. 5. Effected sensors exhibited spiral sort of motion, NRG systems perceived it as self excited vibratory phenomena.
  6. 6. Dr Childs confirmed NRG’s suspicion that the observed phenomenon was dry-friction whip.
  7. 7. Low RCl and friction was the reason of occurrence of dry friction whip.
  8. 8. Anemometer has a rigid shaft with a mass disk at roughly its center, this rotor is supported on 2 Teflon bearings, the rubbing contact. Radius to clearance ratio is of the order of 30</li></ul>“Solidworks model NRG#40 anemometer” by `NRG systems<br />“Solidworks model NRG#40 anemometer” by `NRG systems<br />
  9. 9. <ul><li>Child’s two contact model was extended to incorporate pitch and yaw motion.
  10. 10. Assuming:(i) Contact always occurs at both locations, and (ii) The same radius-to-clearance (RCl) ratio holds at both contact locations Mode1 and Mode 2 solutions were developed.</li></ul>Figure cited from-Kärkkäinen, A., Helfert, M., Aeschlimann, B., Mikkola A., “Dynamic Analysis of Rotor System With Misaligned Retainer Bearings”, ASME J. Tribol. 130, 021102 (2008)<br /><ul><li>Non-Linear simulation model was developed with similar properties to validate the mathematical model</li></ul>Method of Research<br />
  11. 11. <ul><li>Rotor equation of motion derived.
  12. 12. The equations were derived using Lagrange’s Equation
  13. 13. The above equation is in complex form where </li></ul>ROTOR DIAGRAM<br />Analytical model<br />
  14. 14. <ul><li>Stator equation of motion derived
  15. 15. The equation is in complex form, where</li></ul>STATOR DIAGRAM<br /><ul><li>Relations between the rotor and stator displacement vectors at either contact location form geometric constraints.</li></ul>CLEARANCE DIAGRAM<br />Analytical model<br />
  16. 16. <ul><li>Mode 1 solution developed- Assumed planar precessing mode with the normal reaction contact forces in phase at the two contact points.
  17. 17. Mode 2 solution developed- Assumed planar precessing mode with the normal reaction contact forces out of phase at the two contact points.
  18. 18. These solutions were evaluated for three different configurations </li></ul>Disk at center<br />Disk at ¾ location<br />Disk at overhang location<br />Analytical solution<br />
  19. 19. Model Definition<br /><ul><li>The model defined is a purely made up model and is not </li></ul>connected to any piece of Turbomachinery.<br /><ul><li>Friction is required to produce a solution against the BP frequency</li></li></ul><li>MODE 1<br />MODE2<br /><ul><li>Historically it is seen whirling occurs between rotor natural freq. and rotor-stator pinned natural freq., incidentally here rotor frequency is 0Hz.
  20. 20. Whirling solution till 87 Hz (undamped pinned rotor-stator natural frequency)
  21. 21. Practically Whirling till 84.6 Hz as beyond it
  22. 22. Whirl transitions to whip or a loose contact (unpredictable)
  23. 23. Enters whirling solution at 105 Hz (stator Natural frequency).
  24. 24. Whirling solution till 135 Hz (undamped rotor-stator pitch mode frequency)</li></ul>Disk at Center<br />
  25. 25. MODE 1<br />MODE2<br /><ul><li>Whirling solution till 87 Hz (rotor natural frequency)
  26. 26. Practically Whirling till 83 Hz as beyond it
  27. 27. Whirl transitions to whip or a loose contact (unpredictable)
  28. 28. Whirling beyond C, when both contact have positive .Transition to whip at pinned rotor-stator pitch frequency.
  29. 29. Whirling solution till 87 Hz (rotor natural frequency)
  30. 30. Practically Whirling till 83 Hz as beyond it
  31. 31. Whirl transitions to whip or a loose contact (unpredictable)
  32. 32. Enters whirling solution at 105 Hz (stator Natural frequency). But unpredictable beyond pt C.</li></ul>Disk at ¾ location<br />
  33. 33. MODE 1<br />MODE2<br /><ul><li>Whirling extends from 0 to 80Hz
  34. 34. Transitions to whip at 80Hz
  35. 35. No other whirl region.
  36. 36. A positive is seen but the right contact does not reach a min require value of .5 to whirl, hence no whirling.
  37. 37. Only two areas have positive for both contacts simultaneously.
  38. 38. Whirling starts at A and enters whip at B (rotor-stator pinned frequency).
  39. 39. Second region never enters whirl since at all times </li></ul>Disk at overhang position<br />
  40. 40. <ul><li>All the three configurations are simulated using XLTRC2 non linear time transient. Flexible rotor and stator models are used vs rigid rotor and stator models for the analytical solutions.
  41. 41. Cases with different Radius to clearance (RCl) at the two contacts are also explored.
  42. 42. No analytical solution possible for different RCl</li></ul>Simulation Model<br />
  43. 43. Anemometer had a RCl of 30 but to imitate real turbomachinery RCl values of 100 and 125 were chosen. <br />BP frequency=RCl*running speed, hence high RCl will make very large BP frequencies hence it will be impractical<br />Cases Explored<br />
  44. 44. <ul><li> Hunt’s and Crossley’s nonlinear connection model was used.
  45. 45. API imbalance introduced for Disk at center.
  46. 46. Stator support configurations</li></ul>These values are same as used in analytical model<br /><ul><li>Speed up- Rotor given an initial excitation at 20 rpm and simulation run until steady state cycle persisted, followed by running a new simulation with increased rotor speed from the precious state.
  47. 47. Speed down- Rotor given an initial excitation at 252 rpm and simulation run until steady state cycle persisted, followed by running a new simulation with decreased rotor speed from the precious state.</li></ul>Simulation Model<br />
  48. 48. BP freq vs running speed (Speed up)<br />BP freq vs running speed (Speed down)<br /><ul><li>Each of the points plotted is a time transient simulation run and 120 such points have been plotted from 20Hz-252Hz at 2 rpm jumps.
  49. 49. Initial whirling
  50. 50. Whipping at 84.6 Hz.
  51. 51. Investigation of individual contact velocities for the two contact locations agrees with BP predictions for whip and whirl regimes.
  52. 52. Speed down has a different whip-to-whirl jump down frequency and a smaller whip regime as compared to speed up.</li></ul>Contact velocity vs running speed<br />Disk at center RClL= RClR=100<br />
  53. 53. Two sided FFT (speed up) with imbalance<br />Two sided FFT (speed up) <br /><ul><li>Dominance of frequency on negative side suggesting backward whirl
  54. 54. No change in dominant frequencies after introducing imbalance. The max speed is 252 rpm and at these slow speed imbalance is not expected to make a difference.</li></ul>Disk at center RClL= RClR=100<br />
  55. 55. Comparison for Disk at Center<br />Analytical prediction<br />Simulation prediction<br /><ul><li>84.6Hz as the whirl-to-whip transition frequency. Analytical solution agrees with simulation prediction for the first half .
  56. 56. Second jump by analytical model predicted at 109 Hz</li></ul>Second jump by simulation model predicted at 250 Hz. Hence the whip-to-whirl transition is not validated.<br />
  57. 57. BP freq vs running speed (Speed up)<br />BP freq vs running speed (Speed down)<br /><ul><li>Analytical solution does not necessarily apply.
  58. 58. Initial whirling followed by whipping at 84.6 Hz. Smaller whip.
  59. 59. BP graph misleading, investigation of contact velocities shows slipping at both contacts at all conditions. Left slips lesser than right net results imitates whirling.
  60. 60. Speed down has a different whip-to-whirl jump down frequency and a smaller whip regime as compared to speed up</li></ul>Contact velocity vs running speed<br />Disk at center RClL=100, RClR=125<br />
  61. 61. Two sided FFT (speed up) <br /><ul><li>Dominant frequency is on the negative side indicating a backward precessional motion.</li></ul>Disk at center RClL=100, RClR=125<br />
  62. 62. BP freq vs running speed (Speed up)<br />BP freq vs running speed (Speed down)<br /><ul><li>Initial whirling
  63. 63. Whipping at 83 Hz and 84.6Hz
  64. 64. Investigation of individual contact velocities for the two contact locations agrees with BP predictions for whip and whirl regimes.
  65. 65. Speed down has a different whip-to-whirl jump down frequency and a smaller whip regime as compared to speed up</li></ul>Contact velocity vs running speed<br />Disk at ¾ location RClL= RClR=100<br />
  66. 66. Two sided FFT (speed up) <br /><ul><li>Negative dominant frequency shows backward precession.</li></ul>Disk at ¾ location RClL= RClR=100<br />
  67. 67. Comparison for Disk at ¾ location<br />Analytical prediction<br />Simulation prediction<br /><ul><li>83Hz as the whirl-to-whip transition frequency. Analytical solution agrees with simulation prediction for the first half
  68. 68. Second jump by analytical model predicted at 109 Hz</li></ul>Second jump by simulation model predicted at 300 Hz. Hence the whip-to-whirl transition is not validated.<br />
  69. 69. BP freq vs running speed (Speed up)<br />BP freq vs running speed (Speed down)<br /><ul><li>Similar characteristic as with same RCl except for jump frequency (higher freq)
  70. 70. Whipping at 84.6Hz and smaller whip as compared to the above case
  71. 71. BP graph misleading, investigation of contact velocities shows slipping at both contacts at all conditions. Left slips lesser than right net results imitates whirling.
  72. 72. Speed down has a different whip-to-whirl jump down frequency and a smaller whip regime as compared to speed up</li></ul>Contact velocity vs running speed<br />Disk at ¾ location RClL= 100, RClR=125<br />
  73. 73. Two sided FFT (speed up) <br /><ul><li>Negative dominant frequency shows backward precession.</li></ul>Disk at ¾ location RClL= 100, RClR=125<br />
  74. 74. BP freq vs running speed (Speed up)<br />BP freq vs running speed (Speed down)<br /><ul><li>Similar characteristic as with previous two cases except for jump frequency
  75. 75. Whipping at 84.6Hz
  76. 76. BP graph misleading, investigation of contact velocities shows slipping at both contacts at all conditions. Left slips lesser than right net results imitates whirling.
  77. 77. Speed down has a different whip-to-whirl jump down frequency and a smaller whip regime as compared to speed up</li></ul>Contact velocity vs running speed<br />Disk at ¾ location RClL= 125, RClR=100<br />
  78. 78. Two sided FFT (speed up) <br /><ul><li>Negative dominant frequency shows backward precession.</li></ul>Disk at ¾ location RClL= 125, RClR=100<br />
  79. 79. BP freq vs running speed (Speed up)<br />BP freq vs running speed (Speed down)<br /><ul><li>Both whip together briefly at 81 Hz, then left whips at 111 Hz and right at 81Hz.
  80. 80. Right contact has a broader whip (closer to disk)
  81. 81. Both jump to next whirl mode at different conditions
  82. 82. Individual investigations show initial whirling for left contact but slipping for all the other condition for both contacts.
  83. 83. Speed down case has equal whip regimes for both .</li></ul>Contact velocity vs running speed<br />Disk at overhang location RClL=RClR=100<br />
  84. 84. Two sided FFT (speed up) left contact <br />Two sided FFT (speed up) right contact<br />Disk at overhang location RClL=RClR=100<br />
  85. 85. BP freq vs running speed (Speed up)<br />BP freq vs running speed (Speed down)<br /><ul><li>Both whip together at 81 Hz, then left whips at 111 Hz and right at 81Hz.
  86. 86. Right contact has a broader whip (closer to disk) but less than the one where the right contact had RCl=100
  87. 87. Both jump to next whirl mode at different times and follow different paths corresponding to the RCl at the contact.
  88. 88. Contact velocity investigations show slipping for all conditions for both contacts.
  89. 89. Speed down case has equal whip regimes for both. Both contact follow their own whirl paths corresponding to the RCl</li></ul>Contact velocity vs running speed<br />Disk at overhang location RClL=100, RClR=125<br />
  90. 90. Two sided FFT (speed up) left contact <br />Two sided FFT (speed up) right contact<br />Disk at overhang location RClL=100, RClR=125<br />
  91. 91. BP freq vs running speed (Speed up)<br />BP freq vs running speed (Speed down)<br /><ul><li>Right whips at 81 Hz and left continues whirling. Left then whips at 111 Hz when right at 81Hz.
  92. 92. Right contact has a broader whip (closer to disk) even broader than the one where contact had RCl=125
  93. 93. Both jump to next whirl mode at different times and follow different paths corresponding to the RCl at the contact.
  94. 94. Contact velocity investigations show slipping for all conditions for both contacts.
  95. 95. Speed down case has equal whip regimes for both. Both contact follow their own whirl paths corresponding to the RCl</li></ul>Contact velocity vs running speed<br />Disk at overhang location RClL=125, RClR=100<br />
  96. 96. Two sided FFT (speed up) left contact <br />Two sided FFT (speed up) right contact<br />Disk at overhang location RClL=125, RClR=100<br />
  97. 97. Summary & Conclusion<br />For the cases 1) Disk at center 2) Disk at ¾ location and RClL=RClR=100<br />Case 1) Disk at center<br />Analytical model predicts a whirl solution from 0Hz to 84.6Hz beyond which it transitions to a whip regime. It transitions back to a whirl at a frequency of 109 Hz.<br />Simulation model predicts a whirl solution up to 84.6Hz beyond which it transitions to a whip. It whips at 84.6Hz frequency until it transitions back to a whirl regime at 250Hz. For the speed down case this transition happens at 133 HZ<br />Case2) Disk at ¾ location<br />Analytical model predicts a whip solution from 0Hz to 83Hz beyond which it transitions to a whip regime. It transitions back to a whirl at a frequency of 109 Hz. For the speed down case this transition happens at 146 HZ<br />Simulation model predicts a whirl solution up to 84.6Hz beyond which it transitions to a whip. It whips at 84.6Hz frequency until it transitions back to a whirl regime at 300Hz.<br />CONCLUSION<br /><ul><li>There is partial agreement between the analytical model predictions and simulation prediction. The analytical whirl-to-whip transition frequencies are validated by the simulation model.
  98. 98. Neither of the speed up or speed down case agree with the whip-to-whirl transition of the analytical model </li></li></ul><li>Summary & Conclusion<br />For the case 3) Disk at overhang location and RClL=RClR=100<br /><ul><li>Analytical mode 1 predict a small whirl regime from 59 Hz to 80Hz. Beyond this it whips at all frequencies</li></ul>Analytical mode 2 predict a whirl regime from 0Hz to 80 Hz. Beyond this it whips at all frequencies.<br /><ul><li>Simulation results predict the two contacts whip at different frequencies, one at 81 Hz and the other at 111 Hz.</li></ul>Cases with different RCl at the two contacts.<br /><ul><li>Simulation results for these cases show that the BP graph predicts whirling(rolling without slipping) solutions , but when investigated for the individual contact velocities they shows slipping at all conditions. One contact has a higher slipping velocity than the other thereby imitating whirl</li></ul>CONCLUSION<br /><ul><li>Neither of the mode 1 or mode 2 solutions for disk at overhang location have the capability to predict multiple whip regimes for the two contacts. Hence the Analytical model is not validated by the simulation prediction.
  99. 99. For cases with different RCl at the two contact the BP graph imitates whirl but is actually slipping at all conditions</li></li></ul><li>APPLICATION<br />In terms of application if tests or simulation show that you have a tracking super-synchronous result , its does not necessarily imply rolling without slipping as per the classical whirl definition, it can also be an imitation as seen in this thesis.<br />

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