Getting the shakes07 March 2019

Vibration signals can identify the condition of a machine’s balance, lubrication, bearings and gears

Changes in machinery vibration indicate underlying problems that should be corrected before they get worse. Vibration is usually measured using an accelerometer. In most monitoring applications, the acceleration signal is integrated to produce a reading in velocity, as well as acceleration, but vibration can also be measured as a displacement.

For example, consider measuring the radial displacement of a misaligned shaft. This will produce a sinusoidal displacement with frequency ‘f’ equal to the speed of rotation (1 Hz = 1 cycle per second). The amplitude ‘A’ is the maximum displacement from the nominal position for a perfectly-aligned shaft. The final property of the waveform, phase shift (φ), indicates where in the cycle it starts; this becomes relevant when we compare two different vibration sources. Whether an imbalance of displacement, velocity or acceleration, all produce a sinusoidal waveform.

In practice, it would be impossible to use a dial indicator in contact with a shaft for vibration analysis, unless the shaft was turning very slowly. Displacement is sometimes measured using eddy current proximity sensors to detect vibrations in shafts within journal bearings or in cutting tools. Most vibration measurements are, however, made using an accelerometer on the outside of a machine, perhaps with the sensor attached using a magnet.

Andy Mellor, MD of Pragmatic Maintenance and Reliability, offers the following rules of thumb: displacement is a better measurement for low frequencies; velocity is better between 10 Hz to around 2 kHz, and above 2 kHz acceleration is more informative. This makes sense, since the higher the frequency, the higher the acceleration. Faults like unbalance, misalignment and looseness have frequencies at shaft running speed, or a few multiples of it. They’re best detected using velocity. Bearing faults produce higher frequencies and are best trended via acceleration. Smart monitoring will use both velocity and acceleration.


When positioning sensors, it is important to consider the direction of expected vibrations. Accelerometers measure motions in the direction perpendicular to the surface on to which they are attached. Certain types of faults in rotating machinery may be expected to produce radial motion; while others, such as angular misalignment and some bearing faults, produce predominantly axial motion. Signal amplitude is also likely to be greater when the sensor is mounted directly over the source of vibration, especially if the vibration has a high frequency. It may, therefore, be useful to take a number of readings, usually directly over each bearing, to identify which one is causing the most vibration.


Time waveform analysis uses a plot of acceleration against time. Imagine that there are three sources of vibration, each producing a sinusoidal response. Each sinusoidal waveform is characterised by a unique amplitude, frequency and phase shift. The actual observed vibration will be the sum of these.

An important, if often neglected, first step is to consider the resolution of data in the time waveform. This affects the analysis results. The resolution should be sufficient to capture the highest frequencies expected, considering number of gear teeth and the number of rollers in bearings.

There are also cases where the time waveform provides insight about what might be going wrong. Clear spikes or waves in the waveform might indicate a problem. Misalignment may produce ‘M’ or ‘W’ shaped waveforms, while damaged bearings or gear teeth produce periodic impacts.

If the individual sources are known, then it is easy to add these together to give the combined vibration signal – even if the resultappears chaotic and difficult to interpret. Working backwards from the combined signal to obtain the individual waveforms of the sources is not so simple. Luckily, algorithms using the Fast Fourier Transform (FFT) mathematical technique can be used to decompose a complex signal. This process is often referred to as spectrum analysis. The information can then be summarised in a spectral plot that shows each of the underlying waveforms in terms of its frequency and amplitude.


This is the most common way to analyse vibration signals. Using spectrum analysis, it can be quite simple to identify changes in the condition of the machine by looking for changes in the amplitude of vibrations and identifying new sources, which appear as new peaks in the frequency plot.

In spectrum analysis, it is useful to identify the frequency corresponding to the running speed of the shaft. This is normally denoted 1x. Unbalance and angular misalignment will produce vibration at frequency 1x. When this spike has a low amplitude, and all other spikes are smaller, a machine may be running well.

Spikes that are whole number multiples of 1x, such as 2x or 3x, (known as harmonics) may be caused by parallel misalignment, loose bearings, pumps or fans running away from best efficiency points, damaged gears, and so forth. Angular misalignment between shafts generally produces axial vibrations at the running speed, since this creates relative motion between the shafts, in the axial direction, with the distance peaking once per revolution. Parallel misalignment produces radial vibrations that may be at the running speed or a multiple of it, depending on the coupling used. Looseness causes harmonics and, sometimes, an increase in the noise floor, the random noise across all frequencies.

Mellor states: “Vibrations due to electrical faults on motors are often multiples of the supply frequency. On AC motors, 2x can indicate soft foot, distortion of the stator windings or electrical imbalance. On DC motors, 6x the rectifier supply frequency can be a symptom of faulty rectifier control cards.” Soft foot is a condition where mounting feet, typically for a motor, are not aligned with the mounting surface or base plate. This means that, when the mounting bolts are tightened, the feet are distorted and the motor is moved out of alignment. Soft foot can make accurate shaft alignment difficult.

Although some basic rules of thumb can be useful, it is also dangerous to apply them blindly. Instead, a vibration analyst should consider the mechanics of the machine and its failure modes.

Simply by noticing the direction and position at which a particular frequency has its greatest amplitude can provide information. A defect in the bearing casing will produce a shockwave each time one of the rollers passes the defect. Its frequency will depend on running speed, roller numbers, and the time it takes each roller to precess around the casing. This is almost never at an exact multiple of running speed.

This type of defect may have a very high frequency and may initially have a very low amplitude. These properties can mean that it is not detected by a standard spectral analysis. Methods can be used to remove the low frequency, high amplitude vibrations to identify such effects. These methods have names such as Spike Energy, Shock Pulse Method, High-Frequency Demodulation, PeakVue (from Emerson) and enveloping (from Hansford Sensors).

Phase analysis is another tool to diagnose the exact cause. For example, measuring the vibration at each end of a shaft simultaneously indicates whether both ends are going up and down at the same time (in phase) or at different times (out of phase).

Vibration analysis is a powerful method to identify and diagnose faults. Those considering the technique should remember that understanding the machine is key to a successful analysis result.

Jody Muelaner

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