The Campbell Diagram (or Frequency Whirl Speed Map) plots the system’s natural frequencies against the rotor's operating speed. Because gyroscopic moments split natural frequencies into forward whirl (FW) and backward whirl (BW) modes, natural frequencies change with speed. The intersections between the excitation lines (like the 1X running speed line) and the natural frequency curves pinpoint the system's critical speeds. Stability and Subsynchronous Vibration
The standard approach involves dividing the rotor shaft into discrete cylindrical or conical beam elements.
Impellers, turbine wheels, and couplings are modeled as rigid disks possessing mass, polar inertia ( Ipcap I sub p ), and transverse inertia ( Itcap I sub t
Cross-coupled stiffness from seals or impeller shroud forces. Internal Friction: Hysteresis in shrink-fitted parts. 2. Rotordynamic Analysis Methods turbomachinery rotordynamics with case studies pdf
Every rotor has natural frequencies (modes) at which it prefers to vibrate. The rotational speeds at which the excitation frequency (1x RPM) coincides with a natural frequency are termed . Operating near a critical speed without adequate damping can lead to resonant vibrations, high stresses, and failure.
The phase angle of the 1X vibration shifted continuously over time at a constant operating speed.
A graphical representation used to identify the intersections of excitation frequencies (like 1X run speed) with the rotor’s natural frequencies. The Campbell Diagram (or Frequency Whirl Speed Map)
Proximity probe orbits transitioned from a tight, synchronous ellipse into an erratic, wide, forward-whirling circular pattern.
Investigation revealed an internal steam leak past a rotor shaft carbon ring seal. The localized jet of hot steam created an asymmetric temperature distribution across the shaft circumference, inducing a progressive thermal shaft bow (the Morton Effect). Engineering Remediation
: Increased bearing preload and changed lubricant viscosity. Vibration amplitude dropped by 70%. not individual components.
The turbine was shut down, and the defective carbon ring seals were replaced with tighter clearances.
Several authoritative papers and technical reports on turbomachinery rotordynamics include detailed case studies and are available in PDF format. These documents often cover critical speed analysis, stability issues, and real-world troubleshooting for high-speed rotors, compressors, and turbines.
Modern engineering relies on Finite Element Analysis (FEA) and specialized rotordynamic software to build high-fidelity virtual prototypes. Lateral Rotordynamic Analysis
: Balance the entire rotating train, not individual components.