The Waterfall Plot (Cascade Diagram) in Vibration Analysis

Definition: What is a Waterfall Plot?

A waterfall plot, also known as a cascade diagram, is a three-dimensional graph used to visualize how a vibration spectrum changes over time or with another variable, most commonly machine speed. The plot consists of a series of individual FFT spectra “stacked” one behind the other, creating a 3D surface that resembles a cascading waterfall. This presentation makes it easy to see how the amplitudes of different vibration components change as the machine’s operating conditions vary.

The three axes of a typical waterfall plot are:

• X-axis: Frequency
• Y-axis: Amplitude
• Z-axis: Time or, more commonly, RPM (machine speed)

The Primary Application: Run-up and Coast-down Testing

The most important application of a waterfall plot is for analyzing vibration data collected during a machine’s startup (run-up) or shutdown (coast-down). During these transient events, the machine’s speed sweeps through its entire operating range. The waterfall plot provides a complete and detailed map of the machine’s dynamic response across this full speed range.

This analysis is crucial for:

• Identifying Critical Speeds and Resonances: A resonance is identified as a “ridge” on the waterfall plot that occurs at a fixed *frequency*, regardless of the machine’s speed. As the various running-speed orders (1x, 2x, etc.) sweep across this fixed frequency, their amplitude will increase dramatically, creating a clear peak on the plot.
• Separating Forced Vibration from Resonance: The plot clearly distinguishes between speed-dependent peaks (forced vibrations like unbalance, which follow the order lines) and fixed-frequency peaks (resonances, which form a straight ridge across the speed axis).

– Observing Changes in Rotor Stability: It can be used to see the speed at which sub-synchronous instabilities like oil whirl or whip appear and disappear.

How to Interpret a Waterfall Plot

Analyzing a waterfall plot involves looking for two main features:

1. Order Lines (Diagonal Ridges)

These are the ridges of vibration that are directly tied to the machine’s running speed. They appear as diagonal lines on the plot.

• The most prominent diagonal line is usually the 1st order (1x), which represents the response to rotor unbalance.
• Other diagonal lines can be seen for the 2nd order (2x), which is often related to misalignment, and other harmonics.

2. Resonances (Horizontal Ridges)

These are ridges of high vibration that occur at a constant frequency, independent of the machine’s speed. They appear as horizontal lines running across the plot.

• When an order line (like the 1x unbalance response) intersects with a resonance line, its amplitude will increase significantly, forming a large peak at that specific speed.
• The speed at which this intersection occurs is a critical speed of the system.

Data Acquisition and Display

To create a clear waterfall plot, the data is typically acquired using order tracking. This requires a tachometer signal to ensure that the spectral data is free from “smearing” as the speed changes. While a waterfall plot can be displayed with a fixed frequency axis, it is often more useful to display it as an “order-based” waterfall, where the x-axis is in orders rather than Hz.

In addition to the 3D waterfall view, this same data is also used to create other important run-up/coast-down plots, such as the Bode plot (which plots the amplitude and phase of a single order versus speed) and the Nyquist plot (which plots the real vs. imaginary part of an order’s vector).

The waterfall plot is an indispensable tool for any in-depth rotordynamic analysis, providing a complete picture of a machine’s behavior across its entire speed range.

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