Vibration Analysis Fundamentals: Units, Waveform, and Spectrum

What Vibration Analysis Tells You

Every rotating machine vibrates. A perfectly balanced, properly aligned machine vibrates very little. A machine with a developing fault vibrates more, and — critically — it vibrates at predictable frequencies that point directly to the cause. Vibration analysis is the practice of measuring, recording, and interpreting those vibrations before a fault becomes a failure. In industrial and marine settings, catching a bad bearing or an unbalanced impeller early means planned maintenance instead of an unplanned shutdown.

The Three Measurement Parameters

Vibration can be described three ways, and each one is useful for a different part of the frequency range.

Displacement is the peak-to-peak distance the machine surface actually moves. It is measured in mils (thousandths of an inch) in US customary units or micrometers (µm) in SI. Displacement is most sensitive to low-frequency motion and is used when the concern is shaft orbit or overall movement — for example, slow-speed equipment such as large paper-machine rolls.

Velocity is the rate of change of displacement — how fast the surface is moving back and forth. Units are inches per second peak (in/s pk) or millimeters per second RMS (mm/s RMS). ISO 10816 / ISO 20816 vibration severity guidelines express limits in velocity (mm/s RMS), which makes velocity the most widely used parameter for general machinery health screening across the mid-frequency range.

Acceleration is the rate of change of velocity. Units are g (where 1 g = 9.81 m/s²) or in/s². Acceleration emphasizes high-frequency events. Rolling-element bearing defects and gear-mesh problems produce brief, high-frequency impulses; acceleration — especially processed into spike energy or enveloped acceleration — detects these impulses earliest.

The three parameters are mathematically related. For a pure sinusoidal vibration at frequency f (Hz):

• Velocity = 2π × f × Displacement
• Acceleration = 2π × f × Velocity = (2π × f)² × Displacement

Because frequency multiplies displacement to give velocity, and multiplies again to give acceleration, high frequencies favor acceleration measurements while low frequencies favor displacement.

The Time Waveform

A time waveform is a plot of vibration amplitude (y-axis) against time (x-axis). Think of it as the raw signal the sensor sees, scrolling across the screen. The time waveform reveals:

• Periodicity — repeating patterns whose period (seconds per cycle) identifies the source frequency
• Impulsiveness — sharp spikes separated by regular intervals, a classic sign of a rolling-element bearing defect or a cracked gear tooth
• Waveform shape — a clean sine wave suggests simple unbalance; a clipped or distorted wave suggests looseness or rub

Always examine the time waveform first. It shows you what the signal actually looks like and can reveal truncation, noise, or measurement problems that the spectrum might hide.

The FFT Frequency Spectrum

The Fast Fourier Transform (FFT) spectrum — often called simply the spectrum — mathematically decomposes the time waveform into its individual frequency components. The x-axis is frequency (Hz or orders of running speed); the y-axis is amplitude at each frequency. Each peak is a separate vibration source.

Key fault signatures in the spectrum:

| Fault | Dominant spectral peak(s) |

|---|---|

| Mass unbalance | 1× RPM (running speed) |

| Angular misalignment | 1× and 2× RPM; axial component elevated |

| Parallel misalignment | 2× RPM dominant |

| Mechanical looseness | Multiple harmonics of 1× (½× sub-harmonics possible) |

| Rolling-element bearing defect | BPFO or BPFI and their harmonics, often in sidebands |

The spectrum does not replace the waveform — together, they give a complete picture.

Bearing Fault Frequencies

Rolling-element bearings produce defect frequencies that depend on bearing geometry and shaft speed. Two of the most important are:

• BPFO (Ball Pass Frequency, Outer race) — rate at which rolling elements strike a defect on the outer race
• BPFI (Ball Pass Frequency, Inner race) — rate at which rolling elements strike a defect on the inner race

Formulas (with shaft speed in revolutions per second, n = number of rolling elements, Bd = ball diameter, Pd = pitch diameter, θ = contact angle):

> BPFO = (n/2) × shaft_rps × (1 − (Bd/Pd) × cos θ)

>

> BPFI = (n/2) × shaft_rps × (1 + (Bd/Pd) × cos θ)

Worksheets will supply all geometry values. The result is in Hz.

ISO 10816 / ISO 20816 Severity

ISO 10816 (and its successor ISO 20816) categorize machinery into groups by power and mounting, then assign velocity severity zones from Zone A (new machine, acceptable) through Zone D (dangerous, shut down). Always compare your measured velocity RMS value against the correct machine group — a large marine pump and a small bench grinder fall in different categories.

Safety Points

• Do not remove guards to place a sensor. Use a magnetic base on an accessible flat surface or a permanently mounted stud location.
• When working near rotating equipment, keep clothing, cables, and hair clear of shafts and couplings.
• Before connecting the analyzer to any machine, verify that lockout/tagout (LOTO) requirements do not apply — vibration analysis is performed on running equipment, but you must confirm the machine is in a controlled, normal operating state and that no LOTO is in effect by another trade.
• Wear safety glasses and hearing protection as required by the site's PPE program.
• On marine vessels, be aware of deck motion and secure your analyzer and cables so they cannot fall into machinery.