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Cracked Rotors Modeling for Vibration Analysis and Control

Ebrahimi, Ali Reza | 2009

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 40090 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Behzad , Mehdi; Meghdari, Ali
  7. Abstract:
  8. The main aim of this thesis is to develop a mathematical model for vibration analysis of cracked rotors. This model should be a simple and precise model for prediction of the cracked rotor vibration behavior and suitable for vibration control. In order to create such model, the pure bending of a cracked beam is analyzed at first. This analysis is performed for two different orientations of the crack with respect to the beam and the bending vector. In this section a continuous bending model with continuous model for crack is developed which can predict the full deformation of the cracked beam in bending and can estimate the stress distribution in the beam with good approximation. Comparison of the results with those obtained by finite element method shows the validation and good precision of the model. In the next section, a vibration model for the cracked beam is developed based upon the presented bending model. This model can predict the natural frequencies and mode shapes precisely and can give a good approximation for dynamic stress evaluation in such beams. Comparison of the results with those obtained by finite element model and the existing models shows the precision and the profits of this model. In the next step, the equations of motion for a cracked beam are transformed into a rotating coordinate system and the equations of motion for a cracked rotor are extracted. This model is a fully continuous model in which a continuous model for crack is used. The results show that by using this model one can calculate the critical speeds, forced vibration response and perform other useful analyses with appropriate approximation for cracked rotor. In order to verify the model, the results are compared with an experimental test setup results and an excellent agreement is observed. Finally, in the last section of this thesis the presented model for the cracked rotor is upgraded by adding an electromagnetic actuator. Then, two different control algorithms for vibration control of such rotor are suggested. In one of them, the aim is to reduce the overall average vibration amplitude in the rotor. In the other, the aim is to minimize the stress at the crack position. Both of the presented control algorithms show a good performance in vibration control of this rotor.

  9. Keywords:
  10. Cracked Rotor ; Vibrational Analysis ; Vibration Control ; Stress Analysis ; Cracked Beam

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