Rotordynamics

Abstract

So far in the discussion we have illustrated the methods used for the dynamic analysis of mechanical systems. The main purpose of analysis has always been both to study forced motion and to study the stability of these systems and, therefore, analysis of perturbed motion around the steady-state or rest condition. In describing the various types of system which, we should remember, has been subdivided into dissipative systems and systems subject to force fields, we have included various examples of applications, with the main aim of better highlighting the problem and to better illustrate the methods of analysis used. The subject of rotordynamics which will be addressed in this chapter is now proposed with a dual purpose:• to provide basic knowledge to the engineer who has to handle the design and use of machinery, since rotors are essential and vital organs in any machinery; • to offer this subject, given the multitude of problems that it entails, as a valid example of the use of the techniques illustrated in the previous chapters.

Active learning approach to enhance rotor dynamics understanding: A classroom demonstration

“…A thin disk of mass M is mounted on the rotor centre line, and it is perfectly perpendicular to the rotor axis. 14 A schematic representation of the presented model is shown in Figure 1. From this scheme, it is clear that the disk centre of mass (COM) G is not coincident with the axis of rotation (in S ): this aims to represent the fact that, due to small manufacturing imperfections, the rotor is generally unbalanced.…”

“…From their analytical expression, it can be noticed that when the rotor is rotating at high speed, even small eccentricities can head to high excitation forces. Considering the free motion, which means no inertial forcing terms on the right, and given the symmetry of the shaft cross-section, the system eigenfrequencies: Finally, the frequency response function 14 (FRF) can be expressed according to The expression obtained in (12) is a real quantity, as the damping is assumed to be negligible, and it can be represented by two diagrams: the first one regards the magnitude, while the second refers to its phase. As shown in Figure 3, the former tends to infinity when the excitation frequency is equal to the system eigenfrequency, while the latter reaches the value of −π/2.…”

“…Therefore, to enhance students’ deep understanding of the mathematical equations governing this physical phenomenon, an active learning activity was given during the course of ‘Mechanics of Vibration’, taught in the second semester of the last year of the bachelor's degree in mechanical engineering at Politecnico di Milano. The starting model adopted in this work is the so-called Jeffcott rotor, 14 which is a system commonly used to represent the physics of rotor dynamics. Starting from model equations, an experimental laboratory bench was designed and realised, with the aim of showing main theoretical concepts to students.…”

Teaching by active learning: A laboratory experience on fundamentals of vibrations

“…The assignment given to the students begins with the mathematical modelling of the building, performed utilizing Lagrangian equations. 8 As a first approximation, the system can be easily modelled through a lumped mass approach, given that the mass of each storey is much larger than the mass of laminas. Thus, the dynamic model consists of a series of masses connected by springs.…”

“…One way suggested to them to estimate the damping ratio ξ of the system is to adopt the logarithmic decrement. Given a free-decay of one of the modes of the building the damping ratio can be estimated by evaluating the quantity 8 : Where T is the period of oscillation of the time history and q i (t) is the value of any two successive peaks. The damping ratio of the i-th mode is related to δ i 0.25em through: After evaluating the damping of the system also the Frequency Response Function of the system can be formulated analytically.…”