# Vibration analysis - commonly used terms and definitions

May 4, 2021

The following are definitions of terms that appear in a vibration analysis reports and may need further explanation. Many of the definitions have been simplified by confining their meaning to conditions particular to our industry. In some cases, graphics are provided to aid in defining terms. Many of the graphics are exaggerated to illustrate the concepts.

### Acceleration

The rate at which velocity changes with time (dv/dt). Acceleration is usually expressed in gravitation units (G).

### Acceleration Due to Gravity (G)

This acceleration is approximately equal to 386 inches per second squared (386 in/s2).

### Accelerometer

A sensor that measures the acceleration of a structure at the point to which the sensor is attached. Most accelerometers are manufactured from quartz or doped ceramic piezoelectric crystals. A change in pressure on a piezoelectric crystal produces a change in electrical charge in the crystalline lattice, which may be output as a voltage signal. The crystal output has to be amplified to a voltage level detectable by a voltage analyzer.

### Amplitude

The level of voltage or engineering units (e.g.. velocity, acceleration, displacement) measured in terms of zero-to-peak or peak-to-peak of the signal strength. The level reported may be further modified by applying root mean square (rms) or average corrections to it. and is also affected by the time domain window applied to the input signal. The figure illustrates these parameters for a sinusoidal spectrum.

### Axis

Axis refers to one of the principal axes of a component. The principal axes are typically in the horizontal, vertical, and axial directions. Data is most often taken in these directions but need not be confined to these arbitrary axes.

### Balancing

Balancing corrects the vibration associated with the running speed component of a rotating machine by equalizing the distribution of the mass. An unbalanced component does not have its mass uniformly distributed about its axis of rotation. The corrections are generally applied in discrete planes perpendicular to the axis of rotation. A single plane balance may be referred to as static balance. Balancing in two or more planes is referred to as dynamic balancing. Mass adjustment can be accomplished by adding or removing mass.

### Beat

The effect caused by slightly different frequencies coming together so that their amplitudes alternately cancel and reinforce each other.

### Bump test

Impacting a structure to excite and measure its natural frequencies.

### Ball pass inner race frequency (BPI)

The frequency at which the rolling element of an anti-friction bearing passes a given point on the inner race. The presence, amplitude, and harmonics of this frequency are used to evaluate bearing condition.

### Ball pass outer race frequency (BPO)

The frequency at which the rolling element of an anti-friction bearing passes a given point on the outer race. The amplitude of this frequency or its harmonics are used to determine the outer race condition.

### Coast-down

Test Measuring vibration on a machine that has been turned off and is coasting down. This test is used to determine resonances within the measured frequency range.

### Coherence

A measure of the quality of the relationship between a system or component input signal and the measured output signal. Coherence is used to judge the accuracy of a transfer function measurement by comparing the input and output signals. Coherence is a number between 0 and 1, with 1 representing the absolute relationship between two events.

### Critical speed

The rotational speed (frequency) that a shaft or rotor experiences resonance, normally due to imbalance. Subcritical machines operate below their first critical, and supercritical machines operate above their first critical. Subcritical machines are referred to as rigid, and supercritical machines are referred to as flexible.

### Continuous monitoring system

Equipment which provides continuous vibration analysis from various transducers permanently mounted to a machine.

### Cycle

One complete performance of a periodic motion.

### Cycles per minute (CPM)

A unit of frequency representing the number of complete performances of a periodic motion occurring each minute.

### Damping

The dissipation of vibration energies. Damping tends to reduce the magnitude of a vibration. A good example is a shock absorber on a car suspension system.

### Displacement

The change in position of a system or some part of the system from a reference point, usually the equilibrium position.

### Fast Fourier transform (FFT)

A mathematical algorithm that a vibration analyzer uses to convert the time domain data to frequency domain data. For example, an FFT can convert a velocity versus time plot to a velocity versus frequency plot.

### Flexible rotor

A rotor that does not satisfy the conditions of a rigid rotor.

### Flexible supports

A support system consisting of bearing brackets, machine frame, etc. in which the fundamental natural frequency of the system is below operating speed.

### Forced vibration

A condition of vibration where a force is acting on a structure or object causing it to vibrate.

### Forcing function

The energy source that causes a vibration in a component or system.

### Free vibration

A decreasing vibration in a coasting system after all forcing functions have been removed, i.e. a condition of vibration which allows an object or structure to oscillate without the influence of outside forces.

### Frequency

The number of repetitions of a vibration signal in one common unit of time. Frequency is equal to the inverse of the period (F = l/P). Units of frequency are cycles per minute (CPM) or cycles per second (Hz).

### Fundamental train frequency (FTF)

The frequency of rotation of the rolling element cage in an anti-friction bearing.

### Hertz (Hz)

A unit of frequency representing the number of cycles per second.

### Imaginary spectrum

The imaginary spectrum is formed by obtaining a component of the transfer function. If acceleration is used in the response channel. then the imaginary spectrum fill indicate the relative modal position of the measured point. A collection of all the imaginary points can be used to build a modal picture of the "shape" of the item tested. In other words. the relative "shape" of the vibration can be depicted.

### Impact test

Same as the bump test.

### Impulse (I)

The product of a force (F) and the time (T) during which it acts on a mass. Impulse causes a change in momentum (M): I=F x T=VbarM.

### Inertia

A measure of the ability of a system to resist changes in momentum.

### Mils

Displacement expxessed in terms of thousandths of an inch (0.001").

### Modal analysis

The study of the shapes of a system at its natural frequencies. The understanding of the shapes aid in correcting resonance problems.

### Natural frequency

The frequency at which a system shows amplified response to an input forcing function. The frequency that occurs during free vibration.

### Period

The time required for one complete vibration cycle. The period is equal to the inverse of the frequency (P = 1/F).

### Periodic motion

Motion that can be expressed in terms of sine or cosine waves, or by a summation of sine or cosine waves.

### Phase

The angular relationship between the movements of the components of a system, or between movements of systems.

### Portable data collector

A portable, hand-held data collector box used to record vibration measurements at various locations on a regular, repetitive basis.

### Predictive maintenance

Scheduled periodic monitoring of machines to predict when components will fail. This allows replacement of the component during regularly scheduled outages before the component fails and causes an unplanned outage.

### Preventive maintenance

Replacing machine components without knowing the severity of the defect to try to prevent machine failure.

### Real spectrum

The real spectrum is formed by obtaining a component of the transfer function. If the transfer function response data is acceleration, the real spectrum will have a zero line crossing at the center of each natural frequency.

### Real time analyzer

A device that transforms a vibration signal into a readable spectrum so fast that the device is essentially showing the information as it happens. The speed at which an analyzer will take data that has no gaps in it. An FFT analyzer is limited by its digitizer and the speed of its FFT algorithm. A speed of one or two kilohertz (2 kHz) is adequate for most machinery work. The real time rate has very little importance in modal work. Some modem analyzers have RTRs of greater than 10 kHz and some analog analyzers have speeds exceeding 100 kHz.

### Real time rate (RTR)

The coincidence of a forcing function with a system natural frequency. A swing is an example of an oscillating system. If the swing is pushed (the forcing function) at the swing’s natural frequency, then the swing continues to go higher with each push. Likewise, a forcing function acting on a machine component at that component’s natural frequency will cause the intensity of vibrations to increase. If allowed to continue, the amplification of the vibration usually results in fatigue failure.

### Resonance

The coincidence of a forcing function with a system natural frequency. A swing is an example of an oscillating system. If the swing is pushed (the forcing function) at the swing's natural frequency, then the swing continues to go higher with each push. Likewise, a forcing function acting on a machine component at that component’s natural frequency will cause the intensity of vibrations to increase. If allowed to continue, the amplification of the vibration usually results in fatigue failure.

### Rigid rotor

A rotor in which an unbalance can be corrected by attaching balancing weights in any two arbitrarily sclectcd planes. This usually implies that the fundamental natural frequency of the rotor is above the operating speed.

### Rigid supports

A support system consisting of bearing brackets, machine frame, etc. in which the fundamental natural frequency of the system is above operating speed.

### Root mean square (RMS)

The rms value of the amplitude of vibration is obtained by multiplying 0.7071 times the peak amplitude (Arms =0.7071 x Apeak) for a pure sine or cosine signal. A certain amount of energy is associated with any given spectrum peak. Obtaining the rms value of this peak provides the steady state value that would result in an equivalent energy output.

### Shaker test

Using a mechanical vibrator to input a forcing function into a system to determine the system response. The vibrator may input a variety of signals, such as discrete sine waves, sweep sine waves, broad based random waves, shock pulses, or other signal types.

### Signal analyzer

Interprets complex electrical signals and breaks them down into their component parts.

### Spectrum

A graph of signal amplitude on the y-axis versus frequency on the x-axis of an x-y graph.

### Start-up test

Obtaining vibration data on a machine as it comes up to speed to determine if the machine is passing through any critical speeds.

### Station

The location at which data is taken.

### Superposition

Vibratory motion at one point is the sum of vibration forces affecting that point.

### System

A group of interacting bodies or components.

### System response

The ratio of output force within a system to the input force causing that response (Foutput/Finput).

### Transducer

A device that converts mechanical velocity and acceleration (vibration) into an electrical signal that varies in proportion to these physical quantities and that can then be quantified and displayed. (See accelerometer). A linear variable displacement transducer (LVDT) is a measurement device which provides electrical signals proportional to the displacement of an object relative to another object.

### Transfer function

A measure of the response of a system to an input in terms of system gain. A typical hammer impact test measures the amount of acceleration in gravity units caused per input pounds of force (G's/Finput). The phase relationship between the two signals can also be determined, which is important when performing modal analysis.

### Transient

An event that may occur one time or may occur at random.

### Transmissibility

Same as system response: the ratio of output force within a system to the input force causing that response

### Unbalance

When the center of mass for a rotating body does not coincide with the axis of rotation.

### Velocity

The rate of change of displacement with time (ds/dt). Most machinery health measurements are made in terms of velocity since the severity of damage caused by a given velocity is fairly constant across a wide frequency band.

### Velocity transducer

A device which measures the velocity of a structure at the point to which it is attached.

### Velometer

A measurement device that works on the same principle as the accelerometer, but internal circuitry provides an output proportional to the velocity of the structure to which it is mounted.

### Vibration

The time varying movement of a system from a reference point, usually the equilibrium position.

### Vibration baseline survey

Vibration data obtained to establish the condition of a machine at a certain point in time. Generally, the data is obtained just after installation or rebuild of the machine and not taken on a regular basis such as with predictive maintenance.

For assistance with vibration analysis and condition monitoring, contact your Valmet representative.