Fundamentals and technology

Harmonic oscillation can be described mathematically using a sinusoidal function. These are some of the variables affecting oscillation:

Period T is the time required to complete a full cycle. The inverse of the period is called the frequency (f = 1/T). At a motor speed of 3,000 revolutions per minute, the rotation is repeated every 20 ms (Period T), which corresponds to a frequency of 50 Hz.

Amplitude A refers to the maximum displacement of the oscillation from the equilibrium position. There are different notions that can be used in connection with the amplitude. Besides the classic peak value (= amplitude, peak), root-mean-square (= RMS value) and vibration amplitude (= 2x amplitude, peak-peak) are two common metrics.

Phase refers to the displacement in time of a periodic phenomenon, e.g. of a sinusoid from a reference point (e.g. pulse of an encoder). In our case, the phase is an important metric for balancing a rotating system in order to determine the position of the counterweight.

In practice, many different harmonic oscillations will overlap, which is why the individual sine functions will usually no longer be identifiable in the time signal.

Time domain

When analysing vibration in the time domain, the complex superimposed vibration signal is plotted on a time axis. Dominant transient signals or patterns that occur in the time signal can be used to draw conclusions about the damage.
For example, bearing damage at an early stage creates needle-like periodic amplitudes in the time signal.

RMS (root-mean-square) and Peak are common condition parameters used in the time domain.
For example, in vibration monitoring, the root-mean-square of the vibration velocity (v-RMS) is used for unbalance, misalignment and loosening, while the root-mean-square of the vibration acceleration (a-RMS) is used for friction or insufficient lubrication in gears or bearings.
A common metric for peak values is the peak value of the vibration acceleration a-peak, which represents transient events, e.g. as a result of bearing damage or a sudden machine crash.

Frequency domain

When analysing vibration in the frequency domain, the complex superimposed time signal is decomposed into its different frequency components and amplitudes using the Fast Fourier Transform (FFT). This makes it possible to quickly and clearly identify dominant frequencies such as the unbalance frequency in the vibration mixture.

A special form of FFT is the envelope curve spectrum (= H-FFT), where the periodic shock pulses (e.g. of rolling bearing damage) that stimulate the natural frequency of the system are demodulated and pre-filtered accordingly. Especially with rolling bearings or complex machine kinematics (e.g. gears), the advantage of H-FFT analyses is that the recurring shock pulse frequencies of the damaging part can be clearly recognised.

Broadband measurement

Broadband measurements record and analyse the entire frequency range of a signal including all frequency components. Measurements are carried out across a broad frequency range (e.g. 2...1000 Hz) and condition parameters (such as the root-mean-square of vibration velocity v-RMS) are calculated from this and transmitted in real time for condition monitoring.

Narrowband measurement

Narrowband measurements are carried out in only a narrow frequency range or in specific frequencies within the overall spectrum. They are often used where there is a particular interest in a specific frequency component (such as the bearing frequencies of a rolling bearing) or in a specific frequency range.

Vibration displacement d

Vibration displacement is the actual distance a measuring point moves away from its original static position. The parameter is used to detect cyclic movements in an application, such as conveyor motion or the state of the damping elements of a vibrating conveyor. Typically, vibration displacement is recorded in a frequency range below 500 Hz.

Vibration velocity v

The vibration velocity, especially the RMS value, is a good indicator of the energy acting on a machine. Unbalance, loosening, misalignment or belt issues in particular can result in an increased v-RMS. These applications typically have a frequency range of 2...1000 Hz (according to ISO 10816-3 or ISO 20816-3).

Vibration acceleration a

High-frequency broadband characteristic values such as a-peak or a-RMS are established indicators of bearing damage, rubbing, friction or cavitation. Especially in the early stages of damage, the high-frequency acceleration peaks are not covered by the ISO 20816 frequency range. Thus, the vibration acceleration is especially useful as an early warning indicator of the short transient shock pulses resulting from incipient bearing damage or gear tooth faults.

Crest factor

A special parameter of vibration acceleration measurements is the crest factor. It is calculated by dividing the peak value by the RMS value:
Crest = a−peak / a−RMS

The crest factor is useful for evaluating bearing damage. Especially during the early stages of bearing damage, rolling elements periodically passing through pitting will cause short vibration shocks. These shock pulses will lead to an increased a-peak. However, in this phase, the a-RMS value will remain relatively small. As the damage progresses, the frequency of pitting and the intensity of the shock pulses will increase, leading to an increased a-RMS. Especially in this initial phase between high a-peak and low a-RMS values, the crest factor is a useful additional indicator for identifying bearing damage early, as the crest factor must also be high in this phase and will gradually fall with increasing a-RMS values.

Single-axis vs. multi-axis measurement

In most applications, uniaxial vibration measurement is sufficient, as the main vibration occurs in a radial direction from the shaft.
However, 3-axis measurements can have decisive advantages in terms of function, flexibility, and costs.

For example, depending on kinematics and machine construction, the stiffness of a machine can be different in intensity and characteristics in the axial, horizontal or vertical direction. 3-axis measurements provide mounting flexibility and capture all three dimensions in a targeted way, taking account of different vibration stimulations.
In addition, certain machine geometries and fault patterns considerably impact the direction of damage evolution. For example, shaft misalignments can be dominant in the axial or radial direction, or unbalance/shocks can have different predominant directions with certain machine geometries.

Natural frequency is a specific frequency of an overall system, which will cause the system to oscillate at high amplitudes even upon slight excitation. Resonance occurs when the excitation frequency, or a multiple of it, coincides with the natural frequency of the system.

An overall system has multiple natural frequencies, which means that multiple resonances can be caused by excitation. For example, an overall system consisting of an electric motor and a vibration sensor has different natural frequencies, so the acceleration signal of the sensor can contain the resonance of the motor, but also its own resonance.
The natural frequency of the system is defined by its mass and stiffness. The damping of a system determines the amplification of the excitation at a natural frequency.