Understanding the Nyquist Plot (Polar Plot)

Definition: What is a Nyquist Plot?

A Nyquist plot, also commonly known as a polar plot in the field of vibration analysis, is a graph used to display the changing characteristics of a vibration vector on a polar coordinate system. Unlike a Bode plot, which shows amplitude and phase on two separate Cartesian graphs, the Nyquist plot combines them into a single plot.

• The distance from the origin (center) of the plot represents the amplitude of the vibration.
• The angle around the plot represents the phase angle of the vibration.

The plot traces the path of the 1X (synchronous) vibration vector’s tip as the machine’s speed changes, typically during a startup or shutdown. The speed is often indicated by changing colors or symbols along the plotted line.

Why is the Nyquist Plot Important?

The Nyquist plot provides a unique and powerful visualization of a machine’s dynamic response. Its primary use is, like the Bode plot, to identify and analyze a machine’s critical speeds (resonances).

The classic indicator of a critical speed on a Nyquist plot is a loop. As the machine’s speed approaches a natural frequency, the vibration amplitude increases, causing the plot to move away from the origin. As the speed passes through the critical speed, the phase undergoes a 180-degree shift, which causes the vector’s tip to sweep around and form a circle or loop. The point of maximum amplitude is the top of the loop, and the critical speed itself is at the 90-degree phase shift point on the loop.

Interpreting a Nyquist Plot

The shape, size, and orientation of the loop on a Nyquist plot can reveal detailed information about the rotor’s health and dynamic properties:

• Damping: The diameter of the loop is inversely proportional to the damping in the system. A large, well-formed circle indicates low damping (high amplification), while 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, clearly indicating a “split critical.”
• Heavy Spot Location: The orientation of the loop can help determine the location of the rotor’s heavy spot (unbalance) relative to the phase reference mark on the shaft.
• System Changes: Comparing Nyquist plots over time can reveal changes in the machine’s condition. A change in the size or shape of the loop indicates a change in damping or stiffness, which could be caused by issues like a cracked rotor, loose foundation, or changes in bearing characteristics.
• Balancing: The plot is used in advanced flexible rotor balancing. By observing the change in the plot after adding a trial weight, an analyst can determine the influence coefficients needed to calculate the correct balancing solution.

Nyquist Plot vs. Bode Plot

Nyquist and Bode plots display the exact same data (1X amplitude and phase vs. speed) but in different formats. The choice between them often comes down to analyst preference and the specific feature they want to emphasize.

• Bode Plot: Better for clearly seeing the exact RPM of the peak amplitude and the precise start and end points of the 180-degree phase shift. The speed axis is linear and easy to read.
• Nyquist Plot: Better for visualizing the overall dynamic response in a single view. It excels at showing the amount of damping (loop size) and identifying split criticals (overlapping loops) more intuitively than a Bode plot.

Most modern vibration analysis software can display both plot types, and experienced analysts will often use them together for a comprehensive diagnosis.

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