Rotordynamics

Rotordynamics is the branch of mechanical engineering that studies the dynamic behavior of rotating shafts and their supporting structures, including bearings, seals, and housing. It focuses on how imbalance, bearing forces, gyroscopic effects, and damping interact to influence vibration, stability, and dynamic response.

The motion of a rotor is described by coupled differential equations that incorporate rigid-body modes, disk unbalance, gyroscopic coupling, and bearing forces. In lumped-parameter models, a rotor is simplified as a system of masses connected by flexible elements, producing equations of motion of the form Mx'' + Cx' + Kx = F, with gyroscopic terms that couple horizontal and vertical motions. The Jeffcott rotor is a classical three-degree-of-freedom model used for basic insights into critical speeds and whirling behavior.

Key phenomena in rotordynamics include critical speeds, where the rotor’s natural frequency coincides with operating excitation, and whirling, a lateral motion that can be forward or backward relative to rotation. The Campbell diagram plots natural frequencies as a function of speed to identify potential instabilities. Unbalance, misalignment, bearing nonlinearities, and seals can lead to excessive vibration or instability, requiring design or control measures.

Bearings and supports strongly influence rotor behavior. Hydrodynamic and gas bearings provide stiffness and damping through fluid film forces, while seals, clearances, and misalignments contribute nonlinearities. Modeling approaches range from simple two- or three-degree-of-freedom systems to distributed-parameter and finite-element models, used to predict critical speeds, stability, and response to unbalance, and to guide balancing, detuning, and vibration-control strategies.

Applications span turbines, compressors, flywheels, electric machines, and hard-disk drives, where reliable operation demands understanding and management of rotordynamic phenomena.