Technology / Technical guide
Campbell Diagrams: Modal Branches, Rotor Orders & Crossings
A Campbell diagram places frequency information against rotational speed. Modal branches describe the represented system, while order lines describe excitation timing. Their intersections identify relationships to examine, rather than automatically establishing vibration magnitude or an approved operating range.
Name the axes and the type of line first.
The meaning of a crossing depends on which quantities are plotted and how their frequencies are referenced. A mode branch, a prescribed order and a measured spectral ridge can occupy similar positions while representing different information.
01 / Axes
Spin speed and oscillation frequency are separate quantities.
A common diagram uses rotor speed n in rpm horizontally and frequency f in hertz vertically.
A common diagram uses rotor speed n in rpm horizontally and frequency f in hertz vertically. The two axes both relate to time but carry different units and physical meanings. A diagonal line needs a stated conversion rather than an unexplained slope.
Other displays can transpose the axes or use angular-frequency units. A measured magnitude map can also add a colour scale. Those conventions must be identified before interpreting a line as a natural frequency, excitation order or actual response peak.
02 / Modal branches
Natural frequencies can vary with the rotating state.
A modal branch follows a frequency predicted for a model as spin speed changes.
A modal branch follows a frequency predicted for a model as spin speed changes. Gyroscopic effects, prestress and boundary conditions can change those branches. A stationary natural frequency is therefore not automatically a horizontal branch valid at every speed.
Ansys’s rotordynamic guide distinguishes rotational-speed-dependent frequencies and excitation relationships. Branch identity also involves mode shape; two nearby frequency values do not alone establish that they represent the same deformation throughout the speed range.
03 / Order lines
A fixed order maps rotation into a time frequency.
For an excitation with k cycles per mechanical revolution at steady speed, fexc = k n/60 in hertz.
For an excitation with k cycles per mechanical revolution at steady speed, fexc = k n/60 in hertz. A 1x line has k = 1. An electrical order or another reference needs its own conversion; labels cannot silently change their revolution basis.
For a purely hypothetical constant modal frequency of 12 Hz, the 1x line crosses it at 720 rpm and a 3x line at 240 rpm. These are diagram arithmetic, not MARSTON speeds, blade count, natural frequencies or permitted operating points.
04 / Crossing meaning
Frequency coincidence is necessary information, not amplitude.
A crossing identifies where a represented excitation frequency equals a represented modal frequency.
A crossing identifies where a represented excitation frequency equals a represented modal frequency. Response also depends on the excitation’s magnitude and direction, modal participation and damping. An excitation with little participation in a mode may not produce the response suggested by frequency coincidence alone.
The unbalance guide defines one rotating force source. Its magnitude is a different quantity from the position of its order line. Plotting that line does not disclose the actual force or the resulting support displacement.
05 / Different phenomena
Mode intersection does not universally define instability.
Two modal branches can approach or interact under a model, but a frequency plot without growth/decay information does not establish dynamic stability.
Two modal branches can approach or interact under a model, but a frequency plot without growth/decay information does not establish dynamic stability. Damping and coupling retain separate roles. Likewise, a measured ridge can arise from an input rather than a natural mode.
The flutter guide explains why a coupled self-excited instability is different from a positively damped forced resonance. A Campbell line crossing alone should not be relabelled as a flutter boundary or a failure event.
06 / Scope
Keep the complete model and observation conditions.
A free component, a supported assembly and a rotating prestressed model can produce different branches.
A free component, a supported assembly and a rotating prestressed model can produce different branches. Frequency-reference and mode-tracking conventions also matter to comparison. A diagram is an organised representation, not evidence that every omitted component or load has been assessed.
No MARSTON Campbell map, modal branch, order amplitude, critical-speed margin or balance result is supplied here. The page explains how quantities relate without a speed sweep, vibration test, tuning action or a numerical exclusion band for actual equipment.
Related technical guides: Aeroelastic Flutter: Coupling, Self-Excitation & Resonance · Rotor Static Unbalance & Couple Unbalance: Force and Moment · Bearing Stiffness and Damping Coefficients.
General background: Ansys: selected modal/rotational-frequency and Campbell interpretation. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Rotor speed | n in rpm | Horizontal axis in the stated convention. |
| Modal branch | Frequency of the represented system | Can depend on speed and model state. |
| Excitation order | k cycles per mechanical revolution | fexc = k n/60 in Hz. |
| Crossing | Equality of represented frequencies | Does not independently give amplitude. |
| Stability | Growth/decay behaviour | Not established by frequency intersection alone. |
Engineering questions.
Is rotor speed the same as modal frequency?
No. They describe different motion quantities and usually use different units.
Are all modal branches horizontal?
No. Rotation, prestress and coupling can change them.
What does a 3x line mean here?
Three excitation cycles per mechanical revolution at steady speed.
Does every crossing produce the same resonance amplitude?
No. Force, participation, damping and conditions matter.
Is a branch crossing always flutter?
No. Frequency information alone does not establish coupled instability.
Are the 240 and 720 rpm values actual product speeds?
No. They belong to a hypothetical 12 Hz comparison.
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A Campbell diagram places frequency information against rotational speed. Share the model and applicable operating or design information for an engineering discussion.