Understanding the Bode Plot in Vibration Analysis
A Bode plot (pronounced “bo-dee,” after engineer Hendrik Bode) is a specialised graph that shows how a machine’s vibration response changes with rotational speed. It pairs two charts on a shared speed (RPM) axis — an amplitude curve above a phase curve — and is the primary tool for finding a rotor’s critical speeds. Because the most revealing data appears while speed is changing, the Bode plot is almost always built from a controlled run-up ili coast-down.
1. Definition: What is a Bode Plot?
The plot consists of two graphs that share the same horizontal speed axis:
- An amplitude plot (top), showing the magnitude of the 1X — synchronous — vibration as speed varies.
- A phase plot (bottom), showing the phase lag of that 1X vibration relative to a once-per-revolution timing reference on the shaft.
Read together, the two curves give a complete picture of a rotor’s dynamic behaviour. Crucially, the data is filtered to the 1X component only — it isolates the synchronous response (dominated by unbalance) from everything else in the spectrum, which is what makes the resonance signature so clean.
2. Why the Bode Plot Matters
The Bode plot is the definitive way to identify critical speeds. A critical speed is a rotational speed that coincides with one of the rotor’s natural frequencies, driving the machine into resonance and greatly amplifying its vibration. Two classic indicators mark a critical speed:
- A distinct peak in the amplitude plot. As speed sweeps through the natural frequency, amplitude rises to a maximum and then falls away again.
- A 180-degree shift in the phase plot. Passing through the resonance, the phase lag swings through a total of 180 degrees. The critical speed lies precisely where the phase has shifted by 90 degrees — a more reliable locator than the amplitude peak alone, since the phase crossing is sharp even when damping smears the peak.
Knowing exactly where the criticals fall lets engineers keep continuous operating speeds away from them, avoiding the high vibration, accelerated wear and risk of catastrophic failure that running on a critical would bring. The locations can be predicted in advance with a rotor critical speed calculator and visualised across the operating range on a Campbell diagram, then confirmed against the measured Bode plot.
3. Interpreting a Bode Plot
Beyond locating criticals, the plot reveals a great deal more about the rotor system:
- Amplification factor (AF): the sharpness of the resonance peak reflects how much damping the system has. A tall, narrow peak means low damping and a high amplification factor — potentially dangerous — whereas a broad, flat peak indicates a well-damped, more forgiving rotor.
- Split criticals: if a rotor has unequal stiffness in the horizontal and vertical directions (anisotropic support), it can show two closely spaced resonance peaks instead of one, known as a “split critical.”
- System changes: comparing Bode plots recorded over time exposes structural change. A developing shaft crack or loosening foundation bolts shifts the location and reshapes the critical-speed peaks, often before any other symptom appears.
- Balancing information: the plot is essential for multi-speed, multi-plane balancing of flexible rotors, because it shows the rotor’s response at each speed and guides where correction weights must go to tame a specific critical.
4. Data Collection and Instrumentation
Generating a Bode plot requires three things working together:
- A vibration transducer — most often a proximity probe measuring shaft displacement directly, though casing-mounted sensors are also used on many machines.
- A phase-reference sensor — a tachometer or Keyphasor giving one clean pulse per shaft revolution.
- A data-acquisition system able to track the amplitude and phase of the 1X-filtered signal continuously as speed changes.
The data is captured during a controlled startup or coast-down so the machine sweeps through its whole speed range and every critical within it. On general-purpose machinery that does not carry permanent proximity probes, a portable two-channel analyser such as the Balanset-1A performs the same role in the field: triggering from its laser tachometer, it logs synchronised 1X amplitude and phase through a run-up or coast-down so the analyst can plot the response and pinpoint resonances on site, without permanently instrumenting the machine.
5. The Bode Plot and Adjacent Displays
The Bode plot is one of a family of transient-data views and is most powerful when read alongside its relatives. The Nyquist plot presents the same amplitude-and-phase information as a single polar curve, where a resonance traces a clear loop. A cascade (waterfall) plot stacks full spectra against speed, so non-synchronous components — which the 1X-only Bode plot deliberately ignores — also become visible. Choosing the right combination of these views turns a run-up record into a thorough picture of rotor dynamics.
