Understanding the Nyquist Plot (Polar Plot)
ఎ Nyquist plot — widely called a polar plot in vibration work — is a graph that displays a changing vibration vector on a polar coordinate system. Unlike a Bode plot, which spreads amplitude and phase across two separate Cartesian graphs, the Nyquist plot folds both into a single picture. The distance from the origin is the amplitude of the vibration, and the angle around the plot is its phase angle, so every point on the curve is one complete vibration vector.
1. Definition: Amplitude and Phase on One Diagram
The plot traces the path swept by the tip of the 1× (synchronous) vibration vector as the machine’s speed changes, typically through a startup or shutdown. Speed is marked along the curve with changing colours or symbols, so the analyst can read not only the vector’s magnitude and direction but also the RPM at which each point was captured.
- The distance from the origin (centre) represents the amplitude of the vibration — the further out, the larger the response.
- The angle around the plot represents the phase angle of the vibration relative to the tachometer reference.
Because both axes describe a single rotating component, the Nyquist plot is read as the locus of a vector rather than as a pair of trend lines, and that compactness is exactly what makes it so revealing near a resonance.
2. Why is the Nyquist Plot Important?
The Nyquist plot gives a uniquely compact view of a machine’s dynamic response. Its primary purpose, like the Bode plot, is to identify and analyse critical speeds — the resonances of the rotor-bearing system.
The classic indicator of a critical speed on a Nyquist plot is a loop. As speed approaches a natural frequency, the amplitude rises and the curve moves away from the origin. As the speed passes through the critical speed, the phase undergoes a 180-degree shift, sweeping the vector tip around to form a circle or loop. The point of maximum amplitude is the top of the loop, and the critical speed itself sits at the 90-degree phase-shift point on the loop — a far more obvious landmark than the gradual phase ramp on a Bode plot.
3. Interpreting a Nyquist Plot
The shape, size and orientation of the loop carry a great deal of diagnostic information about the rotor’s health and dynamic properties.
- Damping: the diameter of the loop is inversely related to system damping. A large, well-formed circle indicates low damping and high amplification; a small, tight loop indicates a well-damped system.
- Anisotropy (split criticals): if a rotor system has different stiffness in the horizontal and vertical directions, the plot may show two distinct, overlapping loops — a clear “split critical” caused by directional stiffness.
- Heavy-spot location: the orientation of the loop helps locate the rotor’s heavy spot — the unbalance — relative to the phase reference mark on the shaft, which directs where a correction weight should go.
- System changes: comparing Nyquist plots over time reveals shifts in machine condition. A change in loop size or shape signals a change in damping or stiffness, which may point to a cracked rotor, a loose foundation, or evolving bearing characteristics.
- Balancing: the plot is used in advanced flexible-rotor balancing. By observing how the loop moves after a trial weight is added, an analyst derives the influence coefficients needed to compute the balancing solution.
4. Capturing the Data in the Field
A Nyquist plot is only as good as the synchronised amplitude-and-phase data behind it, and that data depends on a clean once-per-revolution phase reference taken through a speed sweep. In the field, a portable two-channel analyser such as the Balanset-1A measures 1× amplitude and phase against its optical-tachometer pulse during a run-up or coast-down, providing the vector-versus-speed record from which a polar plot is drawn. The same amplitude-and-phase measurement underpins field balancing, so one instrument both characterises a resonance and corrects the unbalance that excites it. To check that an order line will actually cross a natural frequency within the operating range, an analyst can sketch the interference first with the Campbell diagram calculator.
5. Nyquist Plot vs Bode Plot
Nyquist and Bode plots display the exact same data — 1× amplitude and phase versus speed — in different formats, and the choice between them often comes down to analyst preference and the feature being emphasised.
- Bode plot: better for reading the precise RPM of the peak amplitude and the exact start and end of the 180-degree phase shift, because its speed axis is linear and easy to scale.
- Nyquist plot: better for taking in the whole dynamic response at once. It excels at showing the amount of damping through loop size and at exposing split criticals as overlapping loops, both more intuitively than a Bode plot can.
A closely related display is the shaft orbit, which plots motion in the bearing plane rather than a single vector versus speed. Most modern vibration analysers can draw all three, and experienced analysts use them together for a comprehensive rotor-dynamics diagnosis.
