Campbell Diagram¶
A Campbell diagram maps rotating-machine frequencies against spin speed and compares mode branches with excitation-order lines to locate candidate critical speeds.
Core Idea¶
A Campbell diagram places rotation speed on one axis and modal or measured response frequency on the other. Shaft-linked excitation orders such as 1X are overlaid. An intersection marks a candidate critical speed where forcing and a mode coincide; it does not predict amplitude by itself. Excitation strength, damping and operating range determine consequence.[ref-d62070b56eb2][ref-8e491eee046c]
Scope of Application¶
A NASA rotor test-rig model found a first 1X critical near 2610 rpm and a second forward critical near 28153 rpm, outside its intended approximately 10000-rpm operation. Its modeled Bode result showed a first-critical amplitude peak and phase inversion, not independent experimental verification.[^ref-d62070b56eb2] A separate NASA compressor study plotted first bending, first torsion and second bending blade modes against engine-order lines, then measured stresses and damping to assess severity.[^ref-8e491eee046c] The two machines' speeds and modes are not interchangeable.
Clarity¶
At 3000 rpm, 1X is 50 Hz and 2X is 100 Hz. If a mode branch crosses 50 Hz at that speed, it matches synchronous forcing. This is author arithmetic, not a NASA measured point. A crossing outside normal operation or with weak excitation may have little design consequence. Some valid rotor models even have flat mode-frequency branches; the 2003 NASA centered-disk model did for its first translational whirl modes.[^ref-d62070b56eb2]
Manages Complexity¶
The diagram screens many speeds, vibrational modes and periodic forcing orders together. It tells the engineer which coincidences warrant forced-response study. It does not replace amplitude, phase, stress, damping or uncertainty assessment. A single-speed spectrum or a Bode plot answers a different question.
Abstract Reasoning¶
For spin N rpm, order m has frequency mN/60 Hz. Compare it to each mode branch f_j(N) and solve f_j(N)=mN/60. Then ask whether that order exists, couples to the mode, lies in the speed range and produces a significant response. A frequency-equality condition is necessary for one kind of resonance screening, not sufficient for danger.
Knowledge Transfer¶
The speed–frequency/order map transfers from shaft whirl to compressor-blade vibration, but the physical modes and excitation mechanisms change. The diagram is a specialized Visualization Graphics map; Resonance remains a related phenomenon, not its strict parent. A crossing alone does not establish vibration severity. Acoustic-pressure waterfall measurement is another possible variant, but it is not the worked NASA example here.
Relationships to Other Abstractions¶
Current abstraction Campbell Diagram Domain-specific
Parents (1) — more general patterns this builds on
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Campbell Diagram is a kind of Visualization (graphics) Domain-specific
Campbell diagrams are speed-frequency visualizations of rotating systems.
Hierarchy path (1) — routes to 1 parentless root
- Campbell Diagram → Visualization (graphics)
Neighborhood in Abstraction Space¶
Campbell Diagram sits in a sparse region of the domain-specific corpus (78th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (2551 abstractions)
Nearest neighbors
- Sommerfeld effect — 0.86
- Group-Velocity Dispersion — 0.83
- Pyroshock — 0.82
- Circle criterion — 0.82
- Rotating Unbalance — 0.82
Computed from structural-signature embeddings · 2026-10-08
References¶
[^ref-d62070b56eb2]: Gyekenyesi, Andrew L., Jerzy T. Sawicki, and George Y. Baaklini. “Vibration Based Crack Detection in a Rotating Disk Part 1—An Analytical Study.” NASA/TM-2003-212624/PART1, September 2003, especially the rotordynamic analysis and Figures 7–10: https://ntrs.nasa.gov/api/citations/20040000850/downloads/20040000850.pdf . [^ref-8e491eee046c]: Newman, Frederick A. “Experimental Vibration Damping Characteristics of the Third-Stage Rotor of a Three-Stage Transonic Axial-Flow Compressor.” NASA TM-100948 / AIAA-88-3229, 1988, especially pp.2–3 and experimental Campbell results: https://ntrs.nasa.gov/api/citations/19880015258/downloads/19880015258.pdf .