This master's thesis investigates backward precessional whip and whirl for a two-point rubbing contact model of a rigid rotor supported by an elastically supported rigid stator. Analytical models are developed to predict whirl and whip regimes and are validated against non-linear time transient simulations. The simulations show partial agreement with analytical predictions for whirl-to-whip transition frequencies but do not capture whip-to-whirl transitions accurately. Additionally, simulations reveal that cases with different radius-to-clearance ratios at the two contact points can exhibit apparent whirling behavior due to unequal slipping velocities rather than true rolling contact.

1. BACKWARD PRECESSIONAL WHIP AND WHIRL FOR A TWO-POINT RUBBING CONTACT MODEL OF A RIGID ROTOR SUPPORTED BY AN ELASTICALLY SUPPORTED RIGID STATOR Master’s Thesis By Dhruv D. Kumar

2. SINGLE POINT AND TWO POINT CONTACT ANALYTIC SINGLE CONTACT MODEL ANALYTIC TWO-CONTACT MODEL Flexible rotor Elastically supported stator One point of contact between rotor-stator. Rigid rotor Elastically supported rigid stator Two points of contact between rotor-stator. Figure cited from-Childs, D. W., and Bhattacharya, A., 2007, “Prediction of Dry-Friction whirl and whip between a Rotor and a Stator,” ASME J. Vib. Acoust., 129, pp. 355–362.

4. Faulty sensors had a dominant vibration frequency separate from the rotating speed.

5. Effected sensors exhibited spiral sort of motion, NRG systems perceived it as self excited vibratory phenomena.

6. Dr Childs confirmed NRG’s suspicion that the observed phenomenon was dry-friction whip.

7. Low RCl and friction was the reason of occurrence of dry friction whip.

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“Solidworks model NRG#40 anemometer” by `NRG systems “Solidworks model NRG#40 anemometer” by `NRG systems

12. The equations were derived using Lagrange’s Equation

13. The above equation is in complex form where ROTOR DIAGRAM Analytical model

17. Mode 2 solution developed- Assumed planar precessing mode with the normal reaction contact forces out of phase at the two contact points.

18. These solutions were evaluated for three different configurations Disk at center Disk at ¾ location Disk at overhang location Analytical solution

20. Whirling solution till 87 Hz (undamped pinned rotor-stator natural frequency)

21. Practically Whirling till 84.6 Hz as beyond it

22. Whirl transitions to whip or a loose contact (unpredictable)

23. Enters whirling solution at 105 Hz (stator Natural frequency).

24. Whirling solution till 135 Hz (undamped rotor-stator pitch mode frequency)Disk at Center

26. Practically Whirling till 83 Hz as beyond it

27. Whirl transitions to whip or a loose contact (unpredictable)

28. Whirling beyond C, when both contact have positive .Transition to whip at pinned rotor-stator pitch frequency.

29. Whirling solution till 87 Hz (rotor natural frequency)

30. Practically Whirling till 83 Hz as beyond it

31. Whirl transitions to whip or a loose contact (unpredictable)

32. Enters whirling solution at 105 Hz (stator Natural frequency). But unpredictable beyond pt C.Disk at ¾ location

34. Transitions to whip at 80Hz

35. No other whirl region.

36. A positive is seen but the right contact does not reach a min require value of .5 to whirl, hence no whirling.

37. Only two areas have positive for both contacts simultaneously.

38. Whirling starts at A and enters whip at B (rotor-stator pinned frequency).

39. Second region never enters whirl since at all times Disk at overhang position

41. Cases with different Radius to clearance (RCl) at the two contacts are also explored.

42. No analytical solution possible for different RClSimulation Model

43. Anemometer had a RCl of 30 but to imitate real turbomachinery RCl values of 100 and 125 were chosen. BP frequency=RCl*running speed, hence high RCl will make very large BP frequencies hence it will be impractical Cases Explored

45. API imbalance introduced for Disk at center.

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.Simulation Model

49. Initial whirling

50. Whipping at 84.6 Hz.

51. Investigation of individual contact velocities for the two contact locations agrees with BP predictions for whip and whirl regimes.

52. Speed down has a different whip-to-whirl jump down frequency and a smaller whip regime as compared to speed up.Contact velocity vs running speed Disk at center RClL= RClR=100

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.Disk at center RClL= RClR=100

56. Second jump by analytical model predicted at 109 HzSecond jump by simulation model predicted at 250 Hz. Hence the whip-to-whirl transition is not validated.

58. Initial whirling followed by whipping at 84.6 Hz. Smaller whip.

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. Speed down has a different whip-to-whirl jump down frequency and a smaller whip regime as compared to speed upContact velocity vs running speed Disk at center RClL=100, RClR=125

63. Whipping at 83 Hz and 84.6Hz

64. Investigation of individual contact velocities for the two contact locations agrees with BP predictions for whip and whirl regimes.

65. Speed down has a different whip-to-whirl jump down frequency and a smaller whip regime as compared to speed upContact velocity vs running speed Disk at ¾ location RClL= RClR=100

68. Second jump by analytical model predicted at 109 HzSecond jump by simulation model predicted at 300 Hz. Hence the whip-to-whirl transition is not validated.

70. Whipping at 84.6Hz and smaller whip as compared to the above case

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. Speed down has a different whip-to-whirl jump down frequency and a smaller whip regime as compared to speed upContact velocity vs running speed Disk at ¾ location RClL= 100, RClR=125

75. Whipping at 84.6Hz

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. Speed down has a different whip-to-whirl jump down frequency and a smaller whip regime as compared to speed upContact velocity vs running speed Disk at ¾ location RClL= 125, RClR=100

80. Right contact has a broader whip (closer to disk)

81. Both jump to next whirl mode at different conditions

82. Individual investigations show initial whirling for left contact but slipping for all the other condition for both contacts.

83. Speed down case has equal whip regimes for both .Contact velocity vs running speed Disk at overhang location RClL=RClR=100

84. Two sided FFT (speed up) left contact Two sided FFT (speed up) right contact Disk at overhang location RClL=RClR=100

86. Right contact has a broader whip (closer to disk) but less than the one where the right contact had RCl=100

87. Both jump to next whirl mode at different times and follow different paths corresponding to the RCl at the contact.

88. Contact velocity investigations show slipping for all conditions for both contacts.

89. Speed down case has equal whip regimes for both. Both contact follow their own whirl paths corresponding to the RClContact velocity vs running speed Disk at overhang location RClL=100, RClR=125

90. Two sided FFT (speed up) left contact Two sided FFT (speed up) right contact Disk at overhang location RClL=100, RClR=125

92. Right contact has a broader whip (closer to disk) even broader than the one where contact had RCl=125

93. Both jump to next whirl mode at different times and follow different paths corresponding to the RCl at the contact.

94. Contact velocity investigations show slipping for all conditions for both contacts.

95. Speed down case has equal whip regimes for both. Both contact follow their own whirl paths corresponding to the RClContact velocity vs running speed Disk at overhang location RClL=125, RClR=100

96. Two sided FFT (speed up) left contact Two sided FFT (speed up) right contact Disk at overhang location RClL=125, RClR=100