Turbomachinery Rotordynamics With Case Studies Pdf -

: Gyroscopic matrix, which scales linearly with rotational speed ( Ωcap omega : Structural stiffness matrix.

Mü(t)+(C+G(Ω))u̇(t)+(K+N(Ω))u(t)=F(t)cap M u double dot open paren t close paren plus open paren cap C plus cap G open paren cap omega close paren close paren u dot open paren t close paren plus open paren cap K plus cap N open paren cap omega close paren close paren u open paren t close paren equals cap F open paren t close paren : Mass matrix (including rotor inertia).

Fluid-film tilting pad or sleeve bearings generate hydrodynamic lift, which introduces non-linear stiffness and cross-coupled damping coefficients.

High-pressure impellers and labyrinth seals generate tangential fluid forces perpendicular to rotor displacement. This cross-coupling acts as a negative damping mechanism, destabilizing the rotor. Torsional Rotordynamics turbomachinery rotordynamics with case studies pdf

If the oil whirl frequency increases to the point where it matches the first rigid-body natural frequency of the rotor, the system locks into resonance. This is called oil whip. Even if shaft speed increases further, the vibration frequency remains locked at the natural frequency, rapidly causing catastrophic damage. Aerodynamic Cross-Coupling (Alford’s Forces)

Case Study 2: Chronic 1X Resonance due to Thermal Shaft Bow in a Steam Turbine Background and Symptoms

The modification stabilized the compressor, raising the logarithmic decrement from -0.15negative 0.15 +0.35positive 0.35 . Subsynchronous vibrations were eliminated. : Gyroscopic matrix, which scales linearly with rotational

The foundational framework for understanding lateral vibrations is the Jeffcott Rotor Model. Developed by Henry Jeffcott in 1919, this simplified model consists of a single, concentrated mass (disk) mounted centrally on a flexible, massless shaft supported by rigid bearings.

Discretizes the rotor into many small elements to account for complex geometries, temperature gradients, and material properties.

The cross-coupled stiffness dropped significantly, stabilizing the machine and allowing it to safely achieve full design pressure. Case Study 2: Oil Whip Destruction in a Main Steam Turbine This is called oil whip

Indicates the severity of the resonance. High damping minimizes AF, allowing machines to pass safely through critical speeds during startup. Synchronous vs. Asynchronous Vibration

A core objective in rotordynamic design is determining a machine’s . A critical speed occurs when the rotational speed matches one of the lateral or torsional natural frequencies of the rotor system.

synchronous vibration levels at its outboard bearing housing whenever load exceeded 85% capacity.

Comprehensive Guide to Turbomachinery Rotordynamics: Principles, Modeling, and Real-World Case Studies