Vibration Analysis of Rotors

This text is intended for use as an advanced course in either rotordynamics or vibration at the graduate level. This text has mostly grown out of the research work in my laboratory and the lectures given to graduate students in the Mechanical Engineering Department, KAIST. The text contains a variety of topics not normally found in rotordynamics or vibration textbooks. The text emphasizes the analytical aspects and is thus quite different from conventional rotordynamics texts; potential readers are expected to have a firm background in elementary rotordynamics and vibration. In most previously published rotordynamics texts, the behavior of simple rotors has been of a primary concern, while more realistic, multi-degree-f-freedom or continuous systems are seldom treated in a rigorous way, mostly due to the difficulty of a mathematical treatment of such complicated systems. When one wanted to gain a deep insight into dynamic phenomena of complicated rotor systems, one has, in the past, either had to rely on computational techniques, such as the transfer matrix and finite element methods, or cautiously to extend ideas learned from simple rotors whose analytical solutions are readily available. The former methods are limited in the interpretation of results, since the calculations relate only to the simulated case, not to more general system behavior. Ideas learned from simple rotors can, fortunately, often be extended to many practical rotor systems, but there is of course no guarantee of their validity.

Inhalt
1 Whirl of Simple Rotors.- 1.1 Introduction.- 1.2 Whirling and critical speed of a simple(Jeffcott) rotor.- 1.3 Whirling of a simple rotor in orthotropic bearings.- 1.4 Whirling of a simple rotor in damped isotropic bearings.- 1.5 Isotropic bearings.- 1.6 Whirling of a simple shaft with asymmetric stiffnesses.- 1.7 Whirling of a simple rotor with internal/external damping.- 1.8 Synchronous whirling- Phasor.- 1.9 Whirl orbits(Lissajous figures)- Asynchronous whirling.- 1.10 References.- 2 Gyroscopic Whirling of a Simple Rotor.- 2.1 Introduction.- 2.2 Gyroscopes.- 2.3 Gyroscopic whirling of a simple rotor supported by torsional springs.- 2.4 Gyroscopic whirling of an overhung rotor.- 2.5 Effects of internal/external damping.- 2.6 Stability of a simple rotor with asymmetric inertia.- 2.7 A simple rotor with asymmetric stiffness and asymmetric inertia.- 2.8 A rigid rotor supported by bearings at ends.- 2.9 References.- 3 Fluid Film Bearings.- 3.1 Introduction.- 3.2 Equilibrium position of journal center.- 3.3 Journal bearing coefficients.- 3.4 Instability in journal bearings- Oil whirl and oil whip.- 3.5 Simple rotor instability.- 3.6 Effect of couplings in bearing coefficients matrices.- 3.7 References.- 3.8 Appendix A3.- 4 Lambda Matrices and General Eigenvalue Problems.- 4.1 Introduction.- 4.2 Eigenvalues and vectors.- 4.3 Regular pencils of matrices.- 4.4 Lambda-matrices.- 4.5 References.- 5 Multi-Degree-of-Freedom Rotor-Bearing Systems.- 5.1 Introduction.- 5.2 Equations of motion of rotating machinery.- 5.3 Modal analysis of multi-dof rotor-bearing systems.- 5.4 Complex modal analysis- Discrete isotropic rotors.- 5.5 Modal testing of rotating machinery.- 5.6 Concluding remark.- 5.7 References.- 6 Harmonic Response of Rotor-Bearing Systems.- 6.1 Introduction.- 6.2 Rotorsystems with rotational speed dependent parameters.- 6.3 Harmonic response and critical speed analysis by generalized modal analysis.- 6.4 Balancing using influence coefficients.- 6.5 Generalized modal balancing theory.- 6.6 Concluding remark.- 6.7 References.- 7 Distributed Parameter Rotor-Bearing Systems.- 7.1 Introduction.- 7.2 Equations of motion.- 7.3 Modal analysis.- 7.4 Mode shapes and orthogonality.- 7.5 Frequency equation of a uniform shaft with hinged ends.- 7.6 Modal frequencies and critical speeds of a uniform shaft.- 7.7 Influence of internal/external friction on critical speeds.- 7.8 Steady state and transient responses.- 7.9 References.- 7.10 Appendix A7.- 8 Vibrations of a Rotor under Combined Effects.- 8.1 Introduction.- 8.2 The effect of shear deformation on critical speeds.- 8.3 Unbalanced simple rotor rotating at an uneven speed.- 8.4 Effect of torque on the stability of flexural rotors.- 8.5 Dynamics of a cracked rotor.- 8.6 References.- 8.7 Appendix A8.