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.

Version: v1 · 2026-10-04 · History
Domain-specific #: 13718
Domain group: Applied Sciences & Engineering
Origin domain: Engineering & Design (beyond software)
Subdomain: Rotordynamics → Engineering & Design (beyond software)

Core Idea¶

A Campbell diagram is a speed–frequency map for a rotating machine. One axis gives shaft speed; the other gives natural or measured vibration frequency. Modal branches are compared with speed-linked forcing frequencies, such as the 1X (once per revolution) line or higher engine orders. Where a branch and an order line meet, their frequencies coincide and the speed is a candidate critical speed. The diagram is a locating tool, not a stand-alone severity prediction: excitation strength, damping, mode participation and measured response determine whether that coincidence produces dangerous vibration.^[1]^[2]

A mode curve need not slope with speed: a NASA Jeffcott-like rotor model had first translational forward/backward modes independent of spin speed because the relevant gyroscopic moments were absent. The 1988 NASA compressor study also states directly that a Campbell crossing does not give vibration level. The map and the amplitude assessment remain separate.^[1]^[2]

Structural Signature¶

Sig role-phrases:

Rotation-speed axis: the operating or run-up range in rpm or angular speed.
Mode or measured-response frequency: a branch for a natural whirl/blade mode or observed spectral peak, flat or changing with speed as the system warrants.
Order excitation line: a rotation-linked periodic forcing line, with 1X equal to shaft rate in cycles per second.
Crossing candidate: the speed where a specified order and modal branch coincide.
Response and damping check: amplitude, phase, stress, forcing and damping evidence needed to judge consequence.^[1]^[2]

The functional chain is speed → mode and forcing frequencies → coincidence → response check. A mode map without an excitation relation cannot by itself identify a synchronous critical. A crossing without the response check can identify a concern but not its severity.

What It Is Not¶

The diagram is not simply a vibration spectrum at one speed, a Bode amplitude/phase plot, or a generic claim that all resonance is harmful. It is also not the resonance phenomenon itself. The prime Resonance describes amplified response at frequency; the Campbell diagram is an engineering map that helps locate where speed-dependent forcing may meet a mode. A crossing can be unimportant if forcing is weak or damping high, while a serious response may require analysis beyond line intersection.^[2]

Nor must every modal frequency change with spin speed. Gyroscopic coupling, bearing properties and stiffening can alter branches, but a particular model may yield horizontal branches. In the NASA 2003 analysis, the first two translational whirl frequencies stayed independent of speed due to absent gyroscopic moments in its centered-disk, Jeffcott-like configuration. Drawing a sloped curve because the textbook says rotating modes shift would contradict the actual model.^[1]

Scope of Application¶

In rotordynamic design, engineers compute natural modes over a range of spin speeds, overlay synchronous or higher-order excitations, and compare crossings with the intended operating and run-up range. The 2003 NASA test-rig analysis identified a first synchronous critical near 2610 rpm and a second forward critical near 28153 rpm; the intended operation was around 10000 rpm (later described as testing up to 8000 rpm). The first is traversed during run-up, while the second is outside intended operation. The analysis's modeled 1X Bode plot showed an amplitude peak and phase inversion around the first crossing, supplying modeled response evidence beyond the map.^[1]

For turbomachinery blades, engine-order forcing can intersect several predicted bending or torsion modes. A 1988 NASA third-stage compressor-rotor study plotted first bending, first torsion and second bending modes against engine-order excitations and also presented measured response/damping evidence. It cautioned that intersections show coincident frequency, not vibration level, and that not all resonances can necessarily be avoided in an operating speed range. Design significance depends on excitation and damping, not merely a red dot at a line crossing.^[2]

Clarity¶

At 3000 rpm, the shaft turns at 50 revolutions per second, so a 1X order is 50 Hz and a 2X order is 100 Hz. This is author arithmetic, not a measured point from the NASA reports. If a natural branch reaches 50 Hz there, the 1X line crosses it; if it reaches 100 Hz, the 2X line crosses. Which forcing mechanism actually exists and couples to the mode remains a separate question. A Campbell diagram makes coincidence legible, not inevitable damage.^[2]

The NASA rotor case makes the distinction concrete. Its modeled 1X line crossed the first branch at 2610 rpm, and the amplitude/phase plot supported a real first critical response. The second forward crossing at 28153 rpm had a very different design role because it lay far above the intended operating regime. A diagram that marked both simply as “bad” would erase the speed-range decision.^[1]

Manages Complexity¶

Rotating machinery presents many speeds, modes and forcing orders. The diagram places them on one coordinate system, enabling an engineer to see which combinations deserve detailed forced-response study. The NASA compressor report used it to screen predicted blade modes against engine orders before examining measured stress and damping. That sequencing is a useful division of labor: the map selects questions; response measurements answer how serious each selected question is.^[2]

But compression into one plot can hide assumptions. Mode tracking across speeds depends on the model; a measured response ridge may reflect forcing as well as an eigenfrequency; damping is not visible in a simple frequency intersection. In the 2003 model, shaft/disk arrangement removed a gyroscopic trend for certain modes; in another rotor, bearing stiffness or coupling could change it. The output is only as good as its mode, order and operating-range definitions.^[1]

Abstract Reasoning¶

Let spin speed be N rpm. The shaft rate is N/60 Hz, so a synchronous order m has f_m(N)=mN/60. Let mode branch f_j(N) be obtained from a specified rotor model or measurement. Solve f_j(N)=f_m(N) to locate a candidate crossing. Then ask whether the excitation has nonzero coupling to that mode, whether damping permits amplification, and whether the speed falls in start-up or steady operation. The equation locates frequency equality; it is not an amplitude formula.^[1]^[2]

For the Jeffcott-like NASA rig, some f_j(N) were nearly constant, yet they still crossed the rising 1X line. A crossing need not be produced by a rising modal branch. Conversely, for compressor blades, several engine orders can meet several mode curves; a designer cannot treat the lowest crossing as the only concern. The analytic sequence is therefore enumerate relevant orders and branches; locate; rank by operating exposure and response evidence.^[1]^[2]

Knowledge Transfer¶

The speed–frequency/order logic transfers from a shaft test rig to compressor blades because both have rotating periodic excitations and vibrational modes. The objects being modeled differ: shaft whirl and blade bending/torsion are not interchangeable mode shapes, and a 1X imbalance line is not every blade-row engine order. The 2610-rpm number from the NASA rig has no meaning for the compressor. Transfer is the plotting/diagnostic scheme, not numeric critical speeds or material safety margins.^[1]^[2]

Acoustic-pressure waterfall plots can be related speed–spectrum views, but neither NASA case here supplies a worked fan/engine-noise waterfall analysis. This entry therefore does not assert an acoustical mapped case or equate every waterfall with a predicted Campbell map. An expansion into that measurement variant would require its own source-located example and a clear distinction between measured response peaks and computed eigenfrequency curves.

Examples¶

NASA rotor test rig: one traversed critical, one outside operation¶

An embedded NASA/TM-2003-212624 analysis in a NASA final report models a centered disk on a flexible shaft. Figure 7 overlays the 1X excitation line and whirl-frequency branches. Their first intersection gives about 2610 rpm. A second forward critical at 28153 rpm is beyond the approximately 10000-rpm intended speed, while the first must be traversed. The report's modeled Bode result shows a first-critical amplitude peak and phase inversion, linking the plotted crossing to a predicted response rather than an independent experimental verification. It also says its first forward/backward translational frequencies are speed-independent because gyroscopic moments are absent for that mode family.^[1]

Mapped back: rpm on the rig is the rotation-speed axis; flat first whirl branches and higher forward branch are the mode frequencies; the 1X line is the order excitation; 2610 and 28153 rpm are distinct crossing candidates; the first Bode peak/phase inversion and the second's location outside operation are the response and damping/operating check. These results belong to the modeled NASA rig, not all turbine rotors.

NASA third-stage compressor rotor blade¶

Newman's 1988 NASA memorandum analyzes a three-stage transonic axial-flow compressor's third-stage rotor blades. Its Campbell plot brings predicted first bending, first torsion and second bending mode frequencies together with engine-order excitations across compressor speed. The paper explicitly says the crossings locate coincidences but do not give vibration levels; it reports experimental Campbell results, blade stress and fitted damping to investigate severity. This is not an invented numeric crossing: the source's substantive outcome is which mode/order pairs require response assessment.^[2]

Mapped back: compressor operating speed is the rotation-speed axis; bending/torsion branches are mode frequencies; engine-order traces are excitation lines; their intersections are crossing candidates; measured stress plus aerodynamic/mechanical damping provide the response check the frequency plot alone lacks. The original study warns that avoiding every operating-range coincidence may be impossible; severity, not intersection count alone, guides design.

Structural Tensions¶

No universal intrinsic two-sided cost of the Campbell diagram is established by these sources. Frequency coincidence versus vibration amplitude is a diagnostic limit, not opposing benefits of the map. A speed-independent branch versus a sloped branch is a model-specific physical difference, not a tradeoff. Likewise a crossing inside or outside the operating range changes relevance without making the diagram itself conflicted. The honest conclusion is that the plot is a first-stage locator and must be followed by forcing, damping and measured-response evidence where risk matters.^[1]^[2]

Structural–Framed Character¶

The map is formal and structural in its axes, curves and intersection rule, but it is framed by engineering choices of model, speed range, excitation orders and acceptable response. Its evaluative weight appears at the design decision: a critical speed in normal operation with high stress is not treated like a remote crossing. Human practice supplies measurements, modal identification and safety margins; the diagram's institutional origin is rotating-machinery design and test, not a generic graph of any two variables. Its vocabulary can travel from shaft whirl to compressor-blade vibration when speed-linked excitation and mode branches can be recognized. Importing “critical” into every line crossing without evidence of forcing or amplitude confuses a candidate condition with a harmful response. Its character: a mathematically legible, model-dependent engineering screening map whose consequences require empirical and operational judgment.^[1]^[2]

Structural Core vs. Domain Accent¶

The skeletal relation is rotation speed → mode-frequency branches and order-forcing lines → coincidences → response/operating-range assessment. The NASA centered disk and transonic compressor blade are accents. The mechanism depends on rotational kinematics, modal dynamics and vibration forcing; reducing it to “two lines cross” would erase why the crossing matters. The named diagram therefore fails the prime bar. Visualization Graphics is its graphical genus; Resonance remains a related phenomenon, not the chart's parent, because a plotted coincidence alone need not be amplified response.

This entry is a kind of Visualization (graphics).

Strict parent: Visualization (graphics). A Campbell diagram graphically maps speed, modal branches and excitation orders; many visualizations lack those axes and their rotating-system interpretation. Resonance remains a related possible outcome, not the diagram's parent. A crossing identifies candidate frequency coincidence, not vibration severity without forcing, damping and response evidence.

Relationships to Other Abstractions¶

Current abstraction Campbell Diagram Domain-specific

Parents (1) — more general patterns this builds on

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 (78^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (2551 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With¶

A Campbell crossing is not a guaranteed dangerous amplitude, and a Bode amplitude peak is not itself a full speed–frequency Campbell map. Mode curves may be flat in a valid special rotor, so “all natural frequencies change with speed” is false. The 1988 blade case concerns engine-order forced response; the 2003 shaft case concerns synchronous whirl criticals. An acoustic waterfall is a possible speed–spectrum measurement variant, not automatically the same as a model's predicted eigenfrequency/order map. Do not transfer the NASA rigs' critical rpm values to another machine.^[1]^[2]

References¶

[1] 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 . registry ↩a ↩b ↩c ↩d ↩e ↩f ↩g ↩h ↩i ↩j ↩k ↩l ↩m ↩n

[2] 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 . registry ↩a ↩b ↩c ↩d ↩e ↩f ↩g ↩h ↩i ↩j ↩k ↩l ↩m ↩n