The Campbell Diagram (also known as an interference diagram or speed-frequency map) is a
three-dimensional representation that displays the frequency spectrum of a rotating machine
as a function of rotational speed. It is the primary tool for identifying critical speeds,
resonance crossings, and speed-dependent noise and vibration phenomena.
Theory
Structure of the Diagram
The Campbell Diagram plots three quantities simultaneously:
Horizontal axis: Rotational speed (RPM) or time during a run-up/coast-down.
Vertical axis: Frequency (Hz) or order number.
Color/intensity: Amplitude of the spectral component (typically in dB).
The diagram is constructed by computing successive FFT or order spectra at regular RPM (or time)
intervals and stacking them side by side. The result is a color map where the spectral evolution
with speed becomes visible at a glance.
Order Lines
Speed-proportional components appear as straight lines through the origin in the RPM-frequency
plane. The slope of each line corresponds to its order:
f = Order × RPM / 60
V-Listen can overlay order lines on the Campbell Diagram for easy identification. For example,
the 1st order line shows where unbalance excitation falls in frequency at each speed, and the
gear mesh order line shows the gear meshing frequency.
Resonance Crossings
Structural resonances appear as horizontal bands of elevated amplitude at fixed frequencies
(independent of speed). When an order line crosses a resonance, the amplitude increases
significantly, producing a bright spot on the diagram. These crossings indicate
critical speeds where forced excitation from the rotating component coincides
with a natural frequency of the structure.
A resonance crossing is identified by the intersection of a diagonal order line with a
horizontal resonance band. The critical speed at which this occurs can be calculated as:
RPMcritical = 60 × fnatural / Order.
Color Mapping
The choice of color map and amplitude range significantly affects the readability of the
Campbell Diagram. V-Listen provides the following options:
Parameter
Options
Description
Color Map
Jet, Viridis, Inferno, Grayscale
Color palette for amplitude mapping.
Amplitude Scale
dB / Linear
Logarithmic (dB) or linear amplitude scaling.
Dynamic Range
20 – 120 dB
Range of amplitudes mapped to the color palette.
Auto Range
On / Off
Automatically adjust the color range to the data.
A dynamic range of 60–80 dB is usually appropriate for most measurements. Setting the
range too wide will wash out low-level features; setting it too narrow will saturate large areas
of the diagram.
Vertical lines: Transient events at a specific speed (e.g., gear engagement,
clutch operation).
Common Patterns
Run-up vs coast-down differences: Thermal effects on resonance frequencies
and speed-dependent damping can cause slight shifts between run-up and coast-down.
Sub-harmonic orders: Fractional orders (0.5×, 1.5×) may indicate
looseness, rub, or other nonlinear behavior.
Sidebands: Modulation patterns around a dominant order (e.g., gear mesh
with sidebands at ±1× shaft speed) indicate modulation effects.
Practical Tips
Use a controlled run-up at a constant acceleration rate for the best quality Campbell Diagram.
Irregular speed changes produce artifacts and uneven RPM coverage.
Select a spectrum size that provides adequate frequency resolution while ensuring enough
averages per RPM step for a smooth result.
Use the cursor tool to read exact frequency, RPM, and amplitude values at any point in
the diagram.
Export order lines data to a table for detailed analysis of each resonance crossing. See
Order Cut for extracting individual orders.
Compare the Campbell Diagram with modal analysis results to correlate observed resonances
with identified mode shapes.
A fast run-up rate may cause the instantaneous RPM to change significantly within a single
FFT block, smearing order lines in the diagram. Reduce the spectrum size or slow the run-up
rate if this occurs.