This course focuses on the whirling vibration of a rigid rotor. Topics include the equations of motion of a rigid rotor in the absolute and rotating coordinate systems, the comparison of two solutions corresponding to these equations of motion, unstable vibration in the case with some damping, critical speed of revolution in the case that the gyro effect is considered, and the whirling vibration of a non-isotropic rotor.
In this course, based on a clear understanding of the relation between the solutions of equations of motion and the actual whirling vibration, students will be able to recognize the relations between the solutions of equations of motion and the actual motion not only for the whirling vibration of a rigid rotor but also for other phenomena.
At end of this course, students will be able to:
1) Derive the equations of motion of a rigid rotor in the absolute and rotating coordinate systems.
2) Explain the critical speed of revolution and the self-balancing effect.
3) Explain the external damping, and internal damping and their effects.
4) Explain the change of a critical speed in the case that the gyro effect is considered.
5) Explain the characteristics of the whirling vibration of a non-isotropic rotor.
Rotor dynamics, whirling vibration, critical speed, external damping, internal damping, gyro effects, 2nd critical speed,
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
At the beginning of each class, the previous class will be briefly reviewed.
Course schedule | Required learning | |
---|---|---|
Class 1 | Introduction of rotor dynamics | Review of vibration characteristics of single degree of freedom system |
Class 2 | Equations of motion of a rigid rotor in a stationary and rotating coordinate systems and a whirling vibration | Understanding of whirling vibration, critical speed, self-balancing, free vibration and degeneration |
Class 3 | Whirling vibration in case with a support with non-isotropic stiffness | Understanding of forward whirling and backward whirling |
Class 4 | Vibration of a rigid rotor in case with some damping, balancing of rotor | Understanding of effects of an external and internal damping, static balancing and dynamic balancing |
Class 5 | Equations of motion in case in the case that a gyro effect is considered | Derivation of equations of motion in case in the case that a gyro effect is considered |
Class 6 | Equations of motion in case in the case that a gyro effect is considered | Understanding of relation between the rotational speed and critical speed |
Class 7 | Whirling vibration of a non-isotropic rotor, 2nd critical speed | Understanding of unstable vibration of non-isotropic rotor and 2nd critical speed |
Class 8 | Summary |
None required.
Handouts will be distributed at beginning of class when necessary.
1 .Students will be assessed on their understanding of critical speed, forward whirling, backward whirling and so on.
2. Student’s course score are based on exercise problems and final exams.
Students must have successfully completed Mechanical Vibrations(MEC.D201.R) or have equivalent knowledge.