Rotordynamics

Rotordynamics (or rotor dynamics) is a specialized branch of applied mechanics concerned with the behavior and diagnosis of rotating structures.

Rotating machinery produces vibrations depending upon the structure of the mechanism involved in the process.

Vibration behavior of the machine due to imbalance is one of the main aspects of rotating machinery which must be studied in detail and considered while designing.

When the vibration is in resonance, it creates a destructive energy which should be the main concern when designing a rotating machine.

The objective here should be to avoid operations that are close to the critical and pass safely through them when in acceleration or deceleration.

The equation of motion, in generalized matrix form, for an axially symmetric rotor rotating at a constant spin speed Ω is

The general solution to the above equation involves complex eigenvectors which are spin speed dependent.

An interesting feature of the rotordynamic system of equations are the off-diagonal terms of stiffness, damping, and mass.

When a rotor is unstable, it will typically require immediate shutdown of the machine to avoid catastrophic failure.

The simplest form of the rotor constrains the disk to a plane orthogonal to the axis of rotation.

After calculating the equivalent stiffness, k, of the system, we can create the following second-order linear ordinary differential equation that describes the radial deflection of the disk from the rotor centerline.

Not only does the spin speed influence the amplitude of the forcing function, it can also produce dynamic amplification near the system's natural frequency.

W. J. M. Rankine first performed an analysis of a spinning shaft in 1869, but his model was not adequate and he predicted that supercritical speeds could not be attained.

Henry Jeffcott was commissioned by the Royal Society of London to resolve the conflict between theory and practice.

He published a paper now considered classic in the Philosophical Magazine in 1919 in which he confirmed the existence of stable supercritical speeds.

... Superior algorithms or computer codes will not cure bad models or a lack of engineering judgment."

These codes make it easy to add bearing coefficients, side loads, and many other items only a rotordynamicist would need.

The non-rotor dynamic specific codes are full featured FEA solvers, and have many years of development in their solving techniques.