Stability of Rotating Machines

Rotating machines as systems for propulsion (turbojet engines...), energy production (windmills, alternators...) or ay system needing to rotate a shaft (pump, gyroscope, centrifuges...) hold an important place in everyday life. These machines obey the laws of dynamics and often evolve in a multiphysical context: fluid-structure interaction, mechatronics. This lesson's purpose is to provide the key elements for such systems modelling, concentrating on stability aspects. Indeed this point is essential because a lot of energy is concentrated in these machines and their stability is major concern for their good functionning as well as for safety.

I/ Reminder of rotating elastic structure equations, modal characterictics in fixed and rotating frame. II/ Linear systems stability analysis: equations with constants coefficients, equations with periodic coefficients. Introduction to non-linear systems stability III/ Rotors stability problems: phenomenological analysis, analysis of structural elements leading to instabilities: • Symmetry, dissipation, buckling in rotating parts • Bearings characteristics • Rotor / stator coupling • Fluid-structure coupling • Non - linear phenomena causing instability (bifurcation...)