Understanding Harmonics in Vibration Analysis

Definition: What is a Harmonic?

In vibration analysis, a harmonic is a frequency that is an integer multiple of a fundamental frequency. The fundamental frequency is typically the primary driving frequency of a system, such as the rotational speed of a shaft. This fundamental frequency is referred to as the 1st harmonic or 1x. The subsequent harmonics are:

• The 2nd harmonic (2x) is the frequency at exactly two times the fundamental.
• The 3rd harmonic (3x) is the frequency at exactly three times the fundamental.
• And so on (4x, 5x, 6x…).

For example, if a motor is running at 1,800 RPM (30 Hz), its harmonics would appear in the vibration spectrum at 60 Hz (2x), 90 Hz (3x), 120 Hz (4x), and so on.

Why are Harmonics Generated?

In a perfectly linear system with a pure sinusoidal forcing function (like a perfectly balanced rotor), only the 1x fundamental frequency would be generated. However, real-world machinery is not perfectly linear. Harmonics are generated when the motion of a component is distorted or non-sinusoidal. This distortion can be caused by a variety of mechanical and electrical conditions. The presence and amplitude of specific harmonics are therefore powerful diagnostic indicators.

Common Causes and Diagnostic Value of Harmonics

The pattern of harmonics in a vibration spectrum provides valuable clues to the root cause of a machine fault.

High 1x Amplitude (The Fundamental)

A dominant peak at 1x is most commonly associated with unbalance. Eccentricity and bent shafts also produce a strong 1x signal.

High 2x Amplitude (2nd Harmonic)

A strong 2nd harmonic, often comparable in amplitude to the 1x peak, is a classic indicator of shaft misalignment. The misalignment forces the shaft to bend twice during each revolution, producing a strong 2x frequency component. Severe parallel misalignment can also produce 3x and 4x harmonics.

A “Family” of Harmonics (1x, 2x, 3x, 4x, 5x…)

When you see a series of many running speed harmonics, it is the primary signature of mechanical looseness. The impacts and non-linear motion created by loose components (such as a loose bearing in its housing or a loose bolt on a machine foot) distort the vibration signal and generate a rich pattern of harmonics. The more severe the looseness, the more harmonics will be present.

Other Causes of Harmonics

• Overhung Rotors: A bent shaft on a machine with an overhung rotor (like a vertical pump) can generate strong 1x, 2x, and 3x harmonics.
• Reciprocating Machines: The non-sinusoidal motion of pistons and crankshafts in engines and compressors naturally generates a rich spectrum of harmonics.
• Electrical Issues: Problems in AC motors can generate harmonics of the line frequency (e.g., 120 Hz in a 60 Hz system).
• Rubs: A light, partial rub can generate a series of high-order harmonics, sometimes up to 10x, 20x, or even more.

Analysis Considerations

When analyzing harmonics, it is important to consider:

• Which harmonic is dominant? The answer points to different potential faults.
• How many harmonics are present? A large number suggests looseness or severe distortion.
• What is the amplitude trend? An increase in the amplitude of harmonics over time indicates a worsening condition.
• Are they radial or axial? For example, misalignment often shows high axial vibration, while unbalance is primarily radial.

By examining the complete pattern of fundamental and harmonic frequencies, a vibration analyst can diagnose machine problems with a high degree of confidence.

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