Understanding the Bode Plot in Vibration Analysis

Definition: What is a Bode Plot?

A Bode (pronounced ‘bo-dee’) plot is a specialized graph used in vibration analysis to show how a machine’s vibration response changes with its rotational speed. It consists of two plots displayed on a shared speed (RPM) axis:

• An Amplitude Plot (top), which shows the magnitude of the 1X (synchronous) vibration.
• A Phase Plot (bottom), which shows the phase lag of the 1X vibration relative to a timing reference on the shaft.

This combined plot provides a complete picture of a rotor’s dynamic characteristics and is most commonly used to analyze data captured during machine startup or shutdown (transient conditions).

Why is the Bode Plot Important?

The Bode plot is the primary tool for identifying a machine’s critical speeds. A critical speed is a rotational speed that matches one of the rotor’s natural frequencies, causing the machine to enter a state of resonance where vibration amplitudes are significantly amplified.

The classic indicators of a critical speed on a Bode plot are:

1. A distinct peak in the amplitude plot: As the machine’s speed passes through the natural frequency, the vibration amplitude rises to a maximum and then decreases.
2. A 180-degree shift in the phase plot: As the speed moves through the resonance peak, the phase lag of the vibration signal shifts by a total of 180 degrees. The critical speed is precisely located at the speed where the phase has shifted by 90 degrees.

By identifying these critical speeds, engineers can ensure that the machine does not operate continuously at these resonant speeds, which could lead to high vibration, premature wear, and catastrophic failure.

Interpreting a Bode Plot

Beyond identifying critical speeds, a Bode plot can reveal other important information about a rotor system:

• Amplification Factor (AF): The “sharpness” of the resonance peak indicates the amount of damping in the system. A sharp, high peak means low damping and a high amplification factor, which can be dangerous. A broader, flatter peak indicates a well-damped system.
• Split Criticals: If a rotor has different stiffness in the horizontal and vertical directions (anisotropic stiffness), it may exhibit two closely spaced resonance peaks, known as a “split critical.”
• System Changes: Comparing Bode plots taken over time can reveal changes in the machine’s structure, such as a cracked shaft or loose foundation bolts, which would alter the location and shape of the critical speed peaks.
• Balancing Information: The Bode plot is essential for multi-plane, multi-speed balancing of flexible rotors, as it shows the rotor’s response at different speeds, allowing for the placement of correction weights to counteract the effects of specific critical speeds.

Data Collection

To generate a Bode plot, the following instrumentation is required:

• A vibration transducer (typically a proximity probe) to measure the shaft’s vibration.
• A phase reference sensor (a tachometer or Keyphasor) that provides one pulse per revolution of the shaft.
• A data acquisition system capable of tracking the amplitude and phase of the 1X filtered vibration signal as the machine’s speed changes.

The data is almost always collected during a controlled startup or coast-down of the machine to ensure it passes through its entire speed range.

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