**Beginner’s Guide to Machine Vibration **

**CONTENTS**

**Page**

**Foreword .vii**

**Chapter 1**

**Why Is Monitoring Vibration Important? . 1**

**What is machine vibration? . 2**

**What causes machine vibration? 4**

**Why monitor machine vibration? 9**

**Summary . 15**

**Chapter 2**

**How Is Machine Vibration Described? . 17**

**How is vibration described? 18**

**What is amplitude? . 19**

**What is frequency? . 22**

**What is a waveform? 23**

**What is a spectrum? . 24**

**Summary . 26**

**Chapter 3**

**How Is Machine Vibration Measured? 27**

**Which machines need monitoring? 28**

**How does the instrument work? . 29**

**How is the accelerometer mounted? 30**

**How are parameters set? . 38**

**How is data collected? 48**

**Summary . 54**

**Appendix A**

**List Of Symbols . 55**

**Appendix B**

**Common Vibration Terms **

**APPENDIX A**

**LIST**

**OF**

**SYMBOLS**

**Symbol Meaning**

**adj. adjective**

**cos x the cosine of x**

**cpm cycles per minute**

**cps cycles per second**

**dB decibel(s)**

**FFT fast Fourier transform**

**f max the maximum frequency value on a spectrum**

**ft foot (or feet)**

**ft/s feet per second**

**ft/s² feet per second per second**

**g acceleration due to gravity (9.80665 m/s²)**

**Hz Hertz**

**in inch(es)**

**in/s inches per second**

**kcpm kilocycles per minute (1000 cpm)**

**kg kilogram**

**kgf kilogram force**

**kHz kiloHertz (1000 Hz)**

**lb pound(s)**

**lbf pound force**

**The following are**

**the symbols, units,**

**and abbreviations**

**used in this bookSymbol Meaning**

**Ibf/in pound force per inch**

**log x the logarithm of x**

**log10 x the base-10 logarithm of x**

**MAS Measurement Analysis Software**

**m meter(s)**

**mil 0.001 inch**

**mm millimeter(s)**

**mm/s millimeters per second**

**m/s meters per second**

**m/s² meters per second per second**

**mV/g milliVolts per g**

**n. noun**

**pref. prefix**

**rad radian(s)**

**rad/s radians per second**

**rms root-mean-square**

**rpm revolutions per minute**

**s second(s)**

**sec second(s)**

**sin x the sine of x**

**t time**

**vb COMMTEST INSTRUMENTS vibration analyzer**

**vdB decibel unit for velocity**

**w.r.t. with reference to**

**x the average value of x**

**x² the square of x (x times x)**

**1X fundamental frequency**

**° degree(s)**

**√x the square root of x**

**θ angle**

**∅ phase angle**

**π the constant pi (roughly equal to 3.14)**

**Σx the sum of x values**

**ω angular frequency (expressed in rad/s)APPENDIX B**

**COMMON**

**VIBRATION**

**TERMS**

**w.r.t. = with**

**reference**

**to**

**adj. = adjective**

**n. = noun**

**pref. = prefixA**

**Acceleration**

**The rate of change of velocity. The acceleration of an object is the rate**

**at which it is gaining or losing speed in a particular direction. The**

**acceleration of an object is proportional to the force causing it to**

**accelerate. Commonly used acceleration units are mm/s2 (metric),**

**m/s2 (SI), in/s2 (imperial), ft/s2 (imperial), and g. See also**

**Accelerometer and Triaxial accelerometer.**

**Acceleration due to gravity**

**See g.**

**Accelerometer**

**A transducer with an electrical output directly proportional to the**

**acceleration of the vibrating point in the direction in which the**

**transducer is attached. The acceleration of a vibrating body is usually**

**measured using an accelerometer. See also Triaxial accelerometer.**

**A/D converter**

**The electronic hardware that converts analog signals to digital values**

**by way of data sampling.**

**Alarm envelope**

**A graph that specifies the maximum allowable amplitude for each**

**frequency value in a spectrum or group of spectra. An alarm envelope**

**is usually based on a reference spectrum that is “ideal” or “normal” for**

**the measurement point.Algorithm**

**The procedure for performing a task e.g. the procedure for calculating**

**a spectrum from a waveform – the Fast Fourier transform – is an**

**algorithm.**

**Aliasing**

**The illusion of high frequency signals appearing as low frequency**

**signals due to the sampling frequency being less than twice the highest**

**frequency component in the signal. Vibration measurement**

**instruments avoid aliasing by filtering out frequency components above**

**the specified f max (by way of a “low pass” or “anti-aliasing” filter) and**

**sampling the filtered signal at a rate at least twice the f max.**

**Alignment**

**The process where the axes of machine components are positioned**

**and orientated correctly and accurately with respect to one another.**

**See also Misalignment.**

**Amplitude**

**The magnitude of a signal or periodic motion e.g. the magnitude of the**

**velocity of a vibrating body. Amplitude can be expressed in a variety of**

**ways, the most common amplitude types being “peak”, “peak-to-peak”,**

**and “root-mean-square” (rms).**

**Amplitude modulation**

**The fluctuation in the amplitude of a signal due to the influence of**

**another signal that is of a different frequency. In rotating machinery,**

**high frequency signals, such as bearing inner race defect signals, are**

**often amplitude-modulated by the lower frequency signal of the rotating**

**shaft, due to the defect passing in and out of the load zone once every**

**revolution. The spectrum corresponding to a sinusoid amplitudemodulated by another is characterized by a peak located at the**

**frequency of the sinusoid, and a sideband on either side of the peak,**

**each sideband distanced from the peak by the frequency of the**

**modulating sinusoid. The term “amplitude modulation” is sometimes**

**abbreviated as “AM”. See also Frequency modulation.Analog (w.r.t. signals)**

**Having a continuous relationship with the physical quantity being**

**measured e.g. an accelerometer outputs an analog signal that bears**

**continuous similarity to the vibration being measured. Due to the**

**continuity with which an analog signal describes the physical quantity**

**being measured, information regarding the physical quantity can be**

**obtained from the analog signal at any instant in time. See also A/D**

**converter and Digital.**

**Analog-to-digital converter**

**See A/D converter.**

**Analysis parameters**

**See Measurement parameters.**

**Analysis software (w.r.t. vibration monitoring)**

**Computer software for the detailed analysis of collected data. See also**

**Measurement Analysis Software.**

**Angular contact bearing**

**A bearing that supports both radial and axial shaft loads. The rolling**

**elements in an angular contact bearing are usually orientated at an**

**angle to the shaft axis. See also Thrust bearing.**

**Angular frequency**

**The oscillation rate of a signal or periodic motion expressed as the**

**angular distance traversed per unit time e.g. an object vibrating at one**

**cycle per second has an angular frequency of 2π radians per second**

**(since one cycle, or an angle of 2π radians, is traversed every second).**

**Angular frequency is usually denoted by the symbol, ω and measured**

**in rad/s (radians per second). See also Frequency and Radian.Angular misalignment**

**See Misalignment.**

**Anti-aliasing filter**

**A low pass filter that removes all signal components of frequencies**

**higher than the specified f max. See also Aliasing.**

**Asynchronous peak**

**See Non-synchronous peak.**

**Attenuation**

**Reduction in the level of a signal. As a vibration signal travels through**

**a mechanical structure, its level decreases. In general, high frequency**

**components decrease in level more than low frequency components.**

**Auto-correlation**

**The level of similarity between two “snapshots” of the same waveform.**

**Two snapshots that are identical have an auto-correlation of one, and if**

**they are entirely different, the auto-correlation is zero.**

**Averaging**

**A mathematical operation aimed at reducing spectral or waveform**

**distortions arising from random noise signals. An “average” spectrum**

**or waveform is derived from a series of individual spectra or timesynchronized waveforms. The amplitude at each frequency or time**

**value of an average spectrum or waveform, is the average of**

**amplitudes of the individual spectra or waveforms at that frequency or**

**time value. The two most common methods of amplitude averaging**

**are linear averaging and exponential averaging. See also Peak hold.Axes**

**Plural of Axis.**

**Axial direction**

**The direction of the centerline of a shaft or rotor.**

**Axial force**

**A force acting in the direction of the centerline of a shaft or rotor. Axial**

**force is sometimes called “thrust”. An overhung rotor vibrates in the**

**axial direction because the moment caused by the weight of the rotor**

**causes an axial excitation force.**

**Axial vibration**

**Vibration in the direction of the centerline of a shaft or rotor. Axial**

**vibration is seen in overhung rotors. See also Radial vibration.**

**Axis (w.r.t. graphs)**

**See x-axis and y-axis.**

**Axis (w.r.t. motion)**

**An imaginary line around or along which motion takes place e.g. the**

**lengthwise centerline of a shaft is the axis of rotation of the shaft.**

**Axis (w.r.t. the vb instrument)**

**A data group in the vb instrument data structure, namely, a data group**

**for grouping recordings taken in the same orientation at a particular**

**measurement point. See also Data structure.Axis (w.r.t. vibration measurements)**

**The orientation or direction in which the accelerometer is mounted**

**when a vibration measurement is taken. The accelerometer is usually**

**mounted in the axial, radial, horizontal, vertical, or tangential direction**

**of a rotating part.B**

**Background noise**

**See Noise.**

**Backlash**

**A condition where a machine part can move independently of the part**

**driving it e.g. a gear that can rotate freely a slight distance without**

**being obstructed by the pinion, or a pulley that can rotate slightly to**

**take up slackness in a belt. Backlash is caused by looseness in a drive**

**train and leads to motion inaccuracy.**

**Balanced**

**The condition where the axis of rotation and mass centerline of a**

**rotating part are coincident. See also Unbalance.**

**Balancing**

**The adjustment of the mass distribution in a rotating part so that the**

**axis of rotation and mass centerline of the rotating part are coincident.**

**See also Correction weights and Unbalance.**

**Balance weights**

**See Correction weights.**

**Ball pass frequency**

**The speed at which bearing rolling elements pass a certain point on the**

**inner or outer race of the bearing. The ball pass frequencies for the**

**inner and outer races are often abbreviated as “BPFI” and “BPFO”**

**respectively. The vibration spectrum of a defective bearing often has**

**peaks at the BPFI and BPFO frequencies. The BPFI is usually about**

**0.6 times the operating speed multiplied by the number of rolling**

**elements, and the BPFO is usually about 0.4 times the same quantity.Ball spin frequency**

**The speed at which a rolling element revolves around its own axis in a**

**bearing. The term “ball spin frequency” is often abbreviated as “BSF”.**

**The vibration spectrum of a defective bearing often has a peak at the**

**ball spin frequency. The ball spin frequency is usually not a whole**

**number multiple of the fundamental frequency.**

**Band pass filter**

**A filter that allows only signal components of frequencies between two**

**cut-off frequency values to pass through. Band pass filters are used**

**when only a certain frequency range is of interest.**

**Bandwidth**

**The difference between the upper and the lower cut-off frequency**

**values of a band pass filter, or the range of frequencies over which an**

**instrument will measure.**

**Baud rate**

**The rate at which data is transferred between the computer and the vb**

**instrument. Baud rate is measured in “bits per second” or “kilobits per**

**second”.**

**Baseline spectrum**

**See Reference spectrum.**

**Bearing tones**

**The frequencies of rotation of the elements of a rolling element**

**bearing. The bearing tones of a rolling element bearing include the**

**frequency of rotation of the cage (FTF), the frequency of rolling**

**elements making contact with a certain point on the inner race (BPFI),**

**the frequency of rolling elements making contact with a certain point on**

**the outer race (BPFO), and the frequency of rolling elements spinning**

**around their own axes (BSF). See also Ball pass frequency, Ball**

**spin frequency, and Fundamental train frequency.Beating**

**A phenomenon where a signal pulsates periodically because the signal**

**comprises two signals of nearly the same frequency. The frequency of**

**pulsation or beating is equal to the difference between the frequencies**

**of the two signals. Beating can occur when there are identical**

**machines operating at about the same speed, or when the frequency of**

**the excitation force is close to the natural frequency.**

**Bending moment**

**The cause of bending and shear stress. A force applied**

**perpendicularly to the tip of a cantilever causes a bending moment at**

**every position of the cantilever. The higher the bending moment, the**

**higher the shear stress, and the more the bending.**

**Bin**

**See Spectral line.**

**Bit**

**Binary digit. The binary number system uses only two digits, “0” and**

**“1” (as opposed to the decimal number system which uses ten digits,**

**“0” to “9”). Each “0” or “1” appearing in a binary number is a “bit”.**

**Blade pass frequency**

**The speed at which fan blades rotate past a fixed reference point. This**

**is equal to the operating speed of the fan multiplied by the number of**

**fan blades. The vibration spectrum of a fan shows a peak at the blade**

**pass frequency. The term “blade pass frequency” is often abbreviated**

**as “BPF”.**

**Bode plot**

**A set of two graphs, one showing how amplitude varies with frequency**

**and the other showing how phase varies with frequency. A Bode plot**

**is used to show the frequency response of a system. See also**

**Nyquist plot.BPFI**

**See Ball pass frequency.**

**BPFO**

**See Ball pass frequency.**

**BSF**

**See Ball spin frequency.**

**Brinneling**

**Indentation of the races of a bearing by its rolling elements. The**

**indentation is usually caused by vibration of the shaft while the shaft is**

**not rotating. The indentation could also be due to large static forces**

**being applied to the shaft while it is not rotating. Brinneling causes**

**spectral peaks at the ball pass frequencies.**

**Broad band analysis**

**See Broad band measurement.**

**Broad band measurement**

**The measurement of the overall vibration level over a large frequency**

**range. A broad band measurement indicates any change to the overall**

**vibration energy of the system but cannot indicate specifically at what**

**frequencies energy change is taking place. See also Narrow band**

**measurement.**

**Bump test**

**A test for determining the natural frequencies of a system. The system**

**is struck with an impulsive force, e.g. by a hammer, and allowed to**

**vibrate freely. The frequencies corresponding to spectral peaks in the**

**free vibration spectrum of the system are the natural frequencies of the**

**system.C**

**Cage defect frequency**

**See Fundamental train frequency.**

**Calibration**

**The verification and/or correction of the accuracy of an instrument,**

**using a known standard as the reference.**

**Carrier frequency**

**The frequency of a signal that is being modulated by another signal**

**e.g. the rotor bar pass frequency of a motor is often a carrier frequency**

**that is modulated by the shaft rotation frequency. See also Amplitude**

**modulation, Frequency modulation, and Modulation.**

**Cascade plot**

**See Waterfall chart.**

**Cavitation**

**A condition where the inlet pressure of a pump or water turbine is too**

**low and therefore causes a mixed flow of fluid and vapor. Cavitation**

**causes random high frequency vibration.**

**Center of mass**

**The center point of mass concentration in a body. The weight of the**

**body acts through the center of mass of the body. The imaginary line**

**connecting the center of mass at every cross-section of a rotor is the**

**mass centerline of the rotor. See also Principal inertia axis and**

**Unbalance.Centrifugal force**

**The force that keeps a rotating object in a circular path. The centrifugal**

**force acts through the center of mass of the object and towards the**

**center of rotation. The magnitude of the centrifugal force is**

**proportional to the mass and the square of the speed of the rotating**

**object, and inversely proportional to the radius of rotation.**

**Cepstrum**

**A graph that shows the Fourier transform of a spectrum i.e. the**

**spectrum of a spectrum. A cepstrum extracts periodic patterns from a**

**spectrum in the same way a spectrum extracts periodic patterns from a**

**waveform. A cepstrum is useful for analyzing spectra containing many**

**harmonics and sidebands just as a spectrum is useful for analyzing**

**waveforms made up of many sinusoids. Cepstrum analysis is**

**particularly useful for gearboxes and rolling element bearings as the**

**vibration spectra often contain many harmonics and sidebands. A**

**series of equally spaced harmonics or sidebands on a spectrum**

**appears as a single peak on a cepstrum.**

**Coherence**

**A measure of the level of proportionality between two signals. For**

**example, there is coherence between the response and the excitation**

**force in a linear system. On the other hand, there is no coherence**

**between an excitation force and random noise. Coherence is rated on**

**a scale ranging from zero to one. A directly proportional relationship is**

**given a coherence of one, and where there is no relationship**

**whatsoever between the two signals, the coherence is zero. See also**

**Cross-correlation.**

**COM port**

**Communications port of a computer, which allows data transfer to or**

**from the computer.Continuous (w.r.t. signals)**

**Having data corresponding to all time values, all frequency values, or**

**all values on the x-axis. The analog signal output by an accelerometer**

**is a continuous signal. See also Discrete.**

**Correction weights**

**Weights that are attached to a rotating part in order to adjust the mass**

**distribution of the rotating part such that the axis of rotation and mass**

**centerline of the rotating part are coincident. See also Unbalance.**

**Cosine wave**

**The sine wave phase-shifted by 90° i.e.**

**cos θ = sin (θ + 90°)**

**where “cos” and “sin” denotes “cosine” and “sine” respectively, and θ**

**is the angle.**

**Coulomb damping**

**The dissipation of vibration energy due to friction between dry surfaces.**

**Friction in movable joints and hinges is a common source of Coulomb**

**damping. The quantity of energy dissipated is dependent on the texture**

**of the sliding surfaces, the force pressing the sliding surfaces together,**

**and the distance over which friction occurs. The French physicist,**

**Charles A. de Coulomb first expounded the proportionality of friction to**

**applied pressure. See also Hysteretic damping and Viscous**

**damping.**

**Couple**

**A pair of forces distanced apart and acting in opposite directions. A**

**couple acting on a body causes the body to rotate. See also Couple**

**unbalance.Couple unbalance**

**An unbalance condition where the mass centerline of a rotor is not**

**parallel to the axis of rotation but intersects it. This is caused by two**

**heavy spots one located at each end of the rotor and which are on**

**opposite sides of the rotor surface. When rotated, the centripetal**

**forces associated with the oppositely positioned heavy spots give rise**

**to a couple that rotates at the rotational speed of the rotor. The**

**rotating couple in turn causes out-of-phase repeating forces to act on**

**the support bearings i.e. the force acting on one bearing is always**

**pointing in a direction opposite to that acting on the other bearing. As a**

**result, the rotor rocks from side to side. Couple unbalance can be**

**corrected by adding two correction weights to the appropriate locations**

**on the rotor. See also Dynamic unbalance and Static unbalance.**

**cpm**

**A measurement unit for the frequency of periodic motion. cpm stands**

**for “cycles per minute”. One cpm is equal to a sixtieth of a Hertz (1/60**

**Hz). See also cps.**

**cps**

**A frequency unit equivalent to 60 times the frequency unit, cpm i.e. one**

**cps (cycles per second) is equal to 60 cpm (cycles per minute). See**

**also Hertz.**

**Crest factor**

**The ratio of the peak amplitude of a waveform to the rms amplitude of**

**the waveform. The crest factor of a vibration waveform provides**

**information regarding the nature of the vibration. For example, the**

**waveform from an unbalanced rotor is roughly the same as a**

**sinusoidal waveform and has a crest factor roughly equal to √2**

**(approximately 1.4). If the dominant cause of vibration is misalignment,**

**the crest factor will usually be less than √2 and if there is impacting in**

**gear teeth or bearing rolling elements, the crest factor will generally be**

**higher than √2.Critical damping**

**The quantity of damping just enough to stop a system from vibrating. A**

**critically damped system that is momentarily excited will complete only**

**part of an oscillation before returning to and remaining at its equilibrium**

**position. If the damping is more than the critical amount, the system**

**will return to its equilibrium position more slowly, though without**

**vibrating. Large guns are usually critically damped to ensure they**

**return to their original position after recoil in the minimum time without**

**vibrating. Over-damping a gun would cause delays between firings.**

**See also Over-damped system and Under-damped system.**

**Critical frequency**

**See Critical speed.**

**Critical speed**

**A machine operating speed that matches one of the natural**

**frequencies of the machine. A machine operated at any of its critical**

**speeds will vibrate excessively due to resonance. To avoid machine**

**damage, the operating speed of the machine should be increased or**

**decreased rapidly past its critical speeds.**

**Cross-correlation**

**A measure of how similar a waveform is to another waveform. The**

**cross-correlation of two identical waveforms is one, and of two**

**completely dissimilar waveforms is zero. See also Coherence.**

**Cycle**

**One complete sequence of the shortest signal pattern that**

**characterizes a periodic waveform or motion.**

**cyc/sec**

**See cps.D**

**Damped natural frequency**

**The natural frequency of a damped system. In practice, all machines**

**are damped to a certain extent. When a machine is undergoing free**

**vibration, it will vibrate at its damped natural frequencies. If all**

**damping were removed from the machine (something impossible in**

**practice), the free vibration of the machine would occur at its**

**undamped natural frequencies or resonant frequencies. Damped**

**natural frequencies are always slightly lower than their corresponding**

**resonant frequencies.**

**Damping**

**The dissipation of vibration energy as heat and/or sound. The gradual**

**decrease in amplitude of a freely vibrating object is evidence of the**

**presence of damping. See also Coulomb damping, Hysteretic**

**damping, and Viscous damping.**

**Data block**

**A collection of instantaneous amplitude values derived from sampling a**

**continuous time domain signal (using an A/D converter). FFT**

**calculations are performed on time domain data blocks to produce**

**frequency domain spectra.**

**Data folder**

**A MAS file that contains the data transferred to it from the vb**

**instrument.**

**Data structure**

**The hierarchical structure of data storage in an instrument. In the vb**

**instrument, there are five levels in the hierarchy: machine, point, axis,**

**parameter set, and recording.dB**

**See decibel.**

**decibel**

**A dimensionless logarithmic unit for amplitude often abbreviated as**

**“dB”, and defined as follows:**

**Amplitude dB = 20 log10 (Amplitude / Reference Amplitude)**

**dB units can be used for displacement, velocity, or acceleration**

**amplitude. Due to the use of the logarithm function, dB units are useful**

**for displaying signals with both very large and very small amplitudes. A**

**6 dB increase, for instance, represents a 100% increase in amplitude**

**on the linear scale. See also vdB.**

**Degree**

**A measurement unit for angle, often denoted by the symbol, °. One**

**complete rotation is equal to 360°, half a rotation is equal to 180°, a**

**quarter rotation is equal to 90°, etc. See also Radian.**

**Degrees of freedom**

**The minimum number of independent coordinates required to**

**determine completely the positions of all parts of a system at any**

**instant of time. The motion of a simple pendulum can be described by**

**one coordinate: its angle around the axis of rotation. It is thus a single**

**degree-of-freedom system. In comparison, a shaft has an infinite**

**number of mass points and an infinite number of coordinates is**

**required to specify its deflected configuration. Thus, it has an infinite**

**number of degrees of freedom. The larger the number of degrees of**

**freedom, the more complex the system. See also Natural frequency**

**and Natural mode shape.Demodulation**

**The process of extracting the modulating signal from a modulated**

**signal. Shaft rotation signals sometimes modulate higher frequency**

**signals such as rotor bar pass frequencies and gear mesh frequencies.**

**A demodulator can be used to recover the shaft rotation signals. See**

**also Amplitude modulation, Frequency modulation, and**

**Modulation.**

**Deterministic**

**Not random and the value of which can be determined at any given**

**time. Deterministic signals can be non-periodic. As most machine**

**vibration is deterministic as well as periodic, their spectra show welldefined harmonics.**

**DFT**

**See Discrete Fourier transform.**

**Differentiation**

**A mathematical operation which yields the rate at which a variable is**

**changing with respect to another variable. For example, acceleration is**

**the rate at which velocity is changing with respect to time, and may be**

**derived from velocity by way of differentiation (with respect to time). In**

**vibration analyzers, differentiation can be performed on analog signals**

**by means of hardware or it can be calculated from a discrete signal by**

**means of software. Differentiation however amplifies noise signals and**

**is seldom performed in vibration analyzers. See also Integration.**

**Digital (w.r.t. signals)**

**That which has quantized signal values. Digital signals are obtained**

**from analog signals and may or may not be continuous. Digital signals**

**are easier to manipulate than analog signals. Most vibration**

**measurement instruments display digital rather than analog signals.**

**See also A/D converter and Quantization.Discrete**

**Finite, discontinuous, that can be counted. A discrete waveform does**

**not have data corresponding to all time values, but has data**

**corresponding to certain time values only. Similarly, a discrete**

**spectrum does not have amplitude data corresponding to all frequency**

**values, but to certain frequency values only. See also Continuous.**

**Discrete Fourier transform**

**A mathematical operation which calculates a discrete spectrum from a**

**discrete waveform. The term “discrete Fourier transform” is often**

**abbreviated as “DFT”. The FFT algorithm is a method of performing**

**the DFT operation in an efficient manner typically on a computer.**

**Displacement**

**The position of an object relative to a fixed reference point, measured**

**in a particular direction. Two objects positioned at equal distance but**

**in opposite directions from the reference point have displacements of**

**equal magnitude but of opposite signs. Displacement units commonly**

**used in the field of vibration analysis are mm (metric) and mil**

**(imperial).**

**Displacement transducer**

**A transducer with an electrical output directly proportional to the**

**displacement of the vibrating point to which the transducer is attached.**

**An example of a displacement transducer is the proximity probe.**

**Domain**

**A set of values to which is mapped another set of values. The x-axis of**

**a graph is often the domain. See also Frequency domain and Time**

**domain.Drive current**

**The constant electric current supplied to an accelerometer. ICP**

**accelerometers require this constant current. When using an ICP**

**accelerometer with the vb instrument, the drive current should be**

**turned on.**

**Dynamic range**

**The difference between the highest and the lowest amplitude an**

**instrument can measure, with the amplitudes expressed in dB.**

**Dynamic unbalance**

**An unbalance condition involving both static and couple unbalance.**

**The mass centerline is both offset from and not parallel to the axis of**

**rotation. Most cases of unbalance in machines are dynamic**

**unbalance.E**

**Eccentricity**

**The distance between the center of mass and the center of rotation.**

**The larger the eccentricity, the larger the unbalance force.**

**Engineering units**

**See Unit.**

**EU**

**See Unit.**

**Elastic**

**That can be easily distorted, and that tends to revert to an original**

**shape after being distorted e.g. a guitar string is elastic. In an**

**engineering sense, an “elastic” material is one that exhibits linear**

**proportionality between mechanical stress and strain e.g. a steel rod is**

**elastic when deflected slightly i.e. the amount by which the steel rod**

**deflects is linearly proportional to the force applied to it.**

**Equilibrium**

**The state of a body where either no force is acting on the body or the**

**resultant force acting on the body is zero (i.e. the forces acting on the**

**body cancel out one another).**

**Equilibrium position**

**The position of lowest potential energy or the position a freely**

**oscillating object will come to rest.Excitation force**

**A force that initiates free vibration or sustains forced vibration.**

**Excitation forces may be periodic, non-periodic, or random in nature.**

**Machine vibration is usually caused by excitation forces originating**

**from unbalanced, misaligned, loose, or defective parts. See also**

**Repeating force.**

**Excitation function**

**See Excitation force.**

**Exponential averaging**

**A method of spectra or waveform averaging where more weighting is**

**given to the most recent spectrum or waveform than to preceding ones.**

**This allows the average to better reflect time-varying vibration patterns**

**while maintaining a measure of noise suppression. Exponential**

**averaging is a continuously running average and for a spectrum, is**

**given by:**

**Average i,k = Average i,k-1 + (Amplitude i,k – Average i,k-1) / n**

**where i = spectral line number;**

**k = average number (in the sequence of averages done for**

**spectral line i); and**

**n = number of spectra used for averaging.F**

**f max**

**The maximum frequency displayed on a vibration spectrum i.e. the**

**frequency range (starting from zero Hz) over which amplitudes are**

**displayed. Increasing the f max (while keeping other parameters the**

**same) reduces the measurement duration required, but also reduces**

**the resolution of the spectrum.**

**Fast Fourier transform**

**An algorithm for performing the DFT operation efficiently i.e. an**

**algorithm for calculating a discrete spectrum from a discrete waveform.**

**The term “fast Fourier transform” is often abbreviated as “FFT”. The**

**FFT algorithm determines the frequencies and the amplitudes**

**corresponding to the frequencies that are present in the waveform.**

**Jean B. J. Fourier was a French mathematician who developed a**

**means of expanding periodic functions in terms of harmonic functions,**

**thereby contributing much to the fields of heat flow and vibration**

**analysis. See also Fourier transform.**

**Fatigue**

**The progressive development of the size of cracks in a material due to**

**the action of cyclic forces. Vibration is a cause of fatigue. The rate of**

**growth of a fatigue crack is proportional to the size of the crack.**

**Fatigue can be minimized by grinding surfaces to remove surface**

**imperfections and by minimizing stress spots in the design.**

**Fault frequency**

**The frequency of repeating forces caused by faulty machine**

**components. Usually, the vibration spectrum shows spectral peaks at**

**the fault frequencies and their harmonics. Some examples of fault**

**frequencies are blade pass frequencies, rotor bar pass frequencies,**

**ball pass frequencies, gear mesh frequencies, and the operating speed**

**of the machine.FFT**

**See Fast Fourier transform.**

**FFT analyzer**

**A spectrum analyzer that uses the FFT algorithm to calculate spectra**

**from waveforms. Most spectrum analyzers are FFT analyzers.**

**File**

**A collection of data in a computer.**

**Filter**

**A device that allows certain frequency components of a signal to pass**

**through, but blocks other frequency components. See also Band pass**

**filter, High pass filter, and Low pass filter.**

**Firmware**

**The operating system of an electronic instrument e.g. that of the vb**

**instrument. The firmware of the vb instrument can be upgraded with a**

**later version by means of PROFLASHing.**

**First harmonic**

**See Fundamental frequency.**

**First natural frequency**

**See Fundamental natural frequency.**

**Flat top window**

**The window that gives the best amplitude accuracy at spectral peaks,**

**at the expense of more signal leakage. The flat top window does not**

**separate closely spaced spectral peaks as well as the Hanning**

**window. See also Windowing.Fluid-film bearing**

**See Journal bearing.**

**Force**

**The cause of acceleration or mechanical stress. The higher the force**

**applied to an object, the higher the acceleration of the object, or the**

**higher the stress in the object.**

**Forced response**

**Response of a system to an excitation force. See also Free response.**

**Forced vibration**

**The vibration of an object due to an excitation force acting on the**

**object. Most kinds of machine vibration are due to periodic excitation**

**forces. Forced vibration due to a periodic excitation force typically**

**occurs at the frequency of the excitation force, but can also occur at**

**other frequencies, especially at integral multiples of the frequency of**

**the excitation force. See also Free vibration.**

**Forcing frequency**

**The frequency of an excitation force. Several forcing frequencies may**

**be simultaneously present in a vibrating system.**

**Forcing function**

**See Excitation force.**

**Fourier transform**

**A mathematical operation that transforms a time domain function into**

**an equivalent frequency domain function. The fast Fourier transform, a**

**computational version of the Fourier transform, is used to calculate**

**discrete frequency domain spectra from discrete time domain**

**waveforms. See also Discrete Fourier transform.Free response**

**Response of a system that is left to vibrate by itself without the**

**influence of an excitation force. See also Forced response.**

**Free run**

**The measurement mode of an instrument where measurements are**

**taken continually until manually stopped by the user.**

**Free vibration**

**The natural vibration of an object i.e. vibration without the influence of**

**an excitation force. The free vibration of an object can be initiated by**

**exciting the object with a force and then leaving it to vibrate freely by**

**itself. In practice, a freely vibrating object will eventually stop due to**

**damping. See also Forced vibration, Natural frequency, and**

**Natural mode shape.**

**Frequency**

**The number of periodic cycles or oscillations completed per unit time.**

**Frequency is the reciprocal of period, and is usually expressed in Hz**

**(which is equivalent to cps or cycles per second), cpm (cycles per**

**minute), rad/s (radians per second), or derivatives of these units. See**

**also Angular frequency.**

**Frequency band**

**A portion of the frequency range of a spectrum.**

**Frequency domain**

**That which has a frequency axis as its x-axis, or a set of frequency**

**values to which are mapped a set of other values e.g. amplitude. A**

**spectrum is a frequency domain graph i.e. a spectrum has a frequency**

**axis as its x-axis (and an amplitude axis as its y-axis).Frequency modulation**

**The fluctuation in the frequency of a signal due to the influence of**

**another signal, often of lower frequency. In rotating machinery, gear**

**mesh signals are often frequency-modulated by the lower frequency**

**signals of rotating shafts. The spectrum corresponding to a sinusoid**

**frequency-modulated by another is characterized by a peak located at**

**the frequency of the sinusoid, and many sidebands located**

**symmetrically on either side of the peak, with the spacing between the**

**sidebands equal to the frequency of the modulating sinusoid. The term**

**“frequency modulation” is often abbreviated as “FM”.**

**Frequency range**

**See f max.**

**Frequency response**

**The vibration amplitude and phase of a system at various vibration**

**frequencies in response to a particular force. The frequency response**

**of a system can be plotted on a Bode plot or on a Nyquist plot. The**

**response amplitude is usually normalized through division by the**

**amplitude of the input force, and expressed as a dimensionless**

**quantity.**

**FTF**

**See Fundamental train frequency.**

**Fundamental frequency**

**The rotational speed of the shaft or rotor, known also as the “1X” or**

**“first harmonic”. A machine usually vibrates at more than one**

**frequency, but the dominant frequency is often the fundamental**

**frequency, or a multiple of it. See also Harmonic (n.).Fundamental natural frequency**

**The first or lowest natural frequency of a system. When a system**

**vibrates freely, it vibrates at all its natural frequencies, but the first**

**natural frequency will be the dominant vibration frequency.**

**Fundamental train frequency**

**The frequency of rotation of the cage of a rolling element bearing. The**

**term “fundamental train frequency” is often abbreviated as “FTF”. A**

**spectral peak at the FTF is rare as the inertia of the cage is relatively**

**small. The FTF usually modulates other bearing tones so that**

**sidebands appear at those bearing tones. If a spectral peak appears at**

**the FTF, damage to one of the rolling elements should be suspected.G**

**g**

**The acceleration due to gravity i.e. the acceleration of an object**

**towards the center of the earth when the object is allowed to fall freely**

**in vacuum at sea level. One g is taken to be 9.80665 m/s² or 32.1740**

**ft/s². The acceleration of a vibrating body is sometimes measured in**

**terms of g’s.**

**Gear mesh frequency**

**The rate at which gear teeth contact. This is equal to the number of**

**teeth on the gear multiplied by the rotation speed of the gear. A**

**machine with gears will potentially vibrate at the gear mesh frequency.**

**Ghost frequency**

**A gearbox vibration frequency which does not relate to the geometry of**

**the gearbox. “Ghost” frequencies are caused by irregularities in gears**

**and usually disappear as the gears wear.H**

**Hamming window**

**A mathematical function named after its inventor and defined as**

**follows:**

**Hamming window = 0.54 – 0.46 cos θ for 0 ≤ θ ≤ 2π**

**The Hamming window is used to reduce signal leakage but because it**

**is not as effective as some other windows, it is now not popularly used.**

**See also Windowing.**

**Hanning window**

**A mathematical function named after its inventor and defined as**

**follows:**

**Hanning window = ½ (1 – cos θ) for 0 ≤ θ ≤ 2π**

**When multiplied with a data block, the Hanning window suppresses**

**amplitude values at the beginning and end of the data block while**

**preserving those in the middle. Multiplying a data block by the Hanning**

**window makes the data block appear like a complete wave, thereby**

**reducing signal leakage associated with limitations of the FFT**

**algorithm. See also Windowing.**

**Harmonic (adj.)**

**Sinusoidal. See also Harmonic function and Harmonic motion.Harmonic (n.)**

**A spectral peak at a frequency that is a whole number multiple of the**

**fundamental frequency or of the frequency of any excitation force**

**present. A harmonic of a frequency n times that of the fundamental**

**frequency is called “nX”. The frequency at which a harmonic occurs**

**may or may not be a whole number multiple of the fundamental**

**frequency e.g. the frequencies of harmonics of the ball pass and ball**

**spin frequencies are not whole number multiples of the fundamental**

**frequency. Most kinds of machine vibration are periodic and can be**

**described as the sum of a series of sinusoids. The harmonics in a**

**spectrum correspond to these sinusoids. See also Synchronous**

**peak.**

**Harmonic excitation**

**Excitation by a harmonic force.**

**Harmonic force**

**An excitation force that is sinusoidal in nature i.e. of the form:**

**F(t) = Fo sin (ωt – ∅)**

**where F(t) = the instantaneous force magnitude;**

**Fo = amplitude of the excitation force;**

**ω = angular frequency;**

**t = time; and**

**∅ = phase angle.**

**Harmonic function**

**Sinusoidal function. See also Sinusoid.Harmonic motion**

**Sinusoidal motion i.e. motion that can be described by a sinusoid. The**

**free vibration of an undamped single degree-of-freedom system is**

**harmonic motion e.g. the swinging of a simple pendulum, in the**

**absence of friction, is harmonic motion. Harmonic motion is often**

**called simple harmonic motion or SHM.**

**Harmonic response**

**The response of a system to harmonic excitation. The response is**

**dependent on the number of degrees of freedom and the damping in**

**the system.**

**Hertz**

**A frequency unit equivalent to cps (cycles per second) and often**

**abbreviated as “Hz”. One Hz is equal to one cps or 60 cpm. Heinrich**

**R. Hertz was a German physicist famous for his works on radio waves.**

**High pass filter**

**A filter that allows only signal components of frequencies higher than a**

**particular cut-off frequency value to pass through. A high pass filter**

**may be used to remove low frequency noise and to reduce ski slope**

**distortions.**

**HTF**

**See Hunting tooth frequency.Hunting tooth frequency**

**The frequency at which a particular tooth on a gear makes contact with**

**a particular tooth on a mating gear. The hunting tooth frequency is**

**equal to the gear mesh frequency divided by the least common multiple**

**of the numbers of teeth on the gears. For example, if a 24-toothed**

**gear is driven by a 12-toothed pinion rotating at 1000 rpm, then the**

**hunting tooth frequency is equal to 500 cpm. The term “hunting tooth**

**frequency” is often abbreviated as “HTF”. Spectral peaks will appear at**

**the HTF and multiples of the HTF if both the gear and pinion have**

**defective teeth.**

**Hysteretic damping**

**The dissipation of vibration energy by materials that convert energy to**

**heat when deformed. Hysteretic behavior is exhibited by most**

**materials but is most prevalent in viscoelastic materials such as**

**rubbers and plastics. A car tire that feels hot following a long journey is**

**in part due to hysteretic damping. The quantity of energy dissipated is**

**dependent on the volume of the material undergoing deformation, the**

**amount of deformation, the hardness of the material, and the ability of**

**the material to dissipate energy. See also Coulomb damping and**

**Viscous damping.**

**Hz**

**See Hertz.I**

**ICP accelerometer**

**A piezoelectric accelerometer with a built-in charge amplifier (an**

**integrated circuit) which performs signal conditioning. When supplied**

**with a constant current of typically 2 to 6 mA, the voltage across the**

**accelerometer varies with acceleration with a sensitivity of typically 100**

**mV/g. ICP stands for “integrated circuit piezoelectric” and is a**

**registered trademark of PCB Piezotronics, Inc. See also Piezoelectric**

**transducer.**

**Imbalance**

**See Unbalance.**

**Impact test**

**See Bump test.**

**Imperial units**

**A system of measurement units based on measurement units used in**

**England in the past. Imperial units are sometimes called English units.**

**Common imperial units include “foot”, “inch”, “pound”, and “ounce”.**

**Unlike metric units, imperial units are not decimally related, and are no**

**longer commonly used in most parts of the world except in North**

**America. See also Metric units and S.I **

**Inertia**

**Resistance to motion change. Mass is a measure of inertia. The**

**larger the inertia of an object, the more force it takes to move or stop**

**the object.**

**In-phase signals**

**See Phase.Instantaneous**

**That which pertains to an infinitesimal moment e.g. the instantaneous**

**velocity of a vibrating object is the velocity of the object at a particular**

**instant in time.**

**Integration**

**A mathematical operation that yields the area under a graph. For**

**example, velocity is derived from acceleration by calculating the area**

**under the acceleration waveform. Integration is the inverse operation**

**of differentiation.**

**Integrator**

**A piece of electronic hardware that integrates an analog signal over**

**time. An integrator is often used to integrate accelerometer signals**

**over time to produce velocity signals.**

**Interpolation**

**The mathematical process of estimating or inserting values between**

**known or measured values. Various interpolation methods exist, the**

**simplest being linear interpolation. For example, if a discrete spectrum**

**contains amplitude information at 1000 Hz and 1002 Hz but not at 1001**

**Hz, then linear interpolation can be used to estimate the amplitude at**

**1001 Hz by taking the average of the amplitudes at 1000 Hz and 1002**

**Hz.**

**Isolation**

**A method of reducing machine vibration by means of placing a flexible**

**member between the machine and its supporting structure. The**

**flexible member, known as the “isolator”, is made of materials such as**

**rubber, cork, felt, or metallic springs. The isolator reduces the**

**magnitude of the force transmitted from the machine to its supporting**

**structure, and from the supporting structure to the machine.J**

**Jerk**

**The rate of change of acceleration. A rapid change in acceleration is**

**apparent as “jerking”. Jerk can be derived by differentiating the**

**acceleration signal with respect to time.**

**Journal**

**The part of a shaft that spins within a bearing. The load is imparted to**

**the bearing by the journal.**

**Journal bearing**

**A bearing without rolling elements but which depends on a fluid film to**

**enable the smooth spinning of the journal. See also Oil whirl and Oil**

**whip.K**

**k (w.r.t. springs)**

**See Spring constant.**

**k (pref.)**

**1000 times. The prefix “k” stands for “kilo”. One kHz (kiloHertz) is**

**equivalent to 1000 Hz, one kg (kilogram) to 1000 grams, one kcpm**

**(kilocycles per minute) to 1000 cpm.**

**kcpm**

**A frequency unit equivalent to 1000 times the frequency unit, cpm i.e.**

**one kcpm (kilocycles per minute) is equal to 1000 cpm (cycles per**

**minute).**

**kgf**

**A measurement unit for force. “kgf” is short for “kilogram force”. One**

**kgf is equivalent to the weight of a one-kg mass.**

**Kinetic energy**

**The energy associated with motion. The vibratory motion of an object**

**involves a continual interchange of kinetic energy and potential energy.**

**When the object is moving, it possesses kinetic energy, and when it**

**attains maximum displacement (during which time it is momentarily**

**stationary), it possesses potential energy but zero kinetic energy.L**

**lbf**

**A measurement unit for force. “lbf” is short for “pound force”. One lbf**

**is equivalent to the weight of a one-lb mass.**

**Leakage**

**See Signal leakage.**

**Linear averaging**

**A commonly used method of averaging spectra or time-synchronized**

**waveforms. The amplitude at each frequency or time value of the**

**“average” spectrum or waveform is the arithmetic mean of amplitudes**

**of the individual spectra or waveforms at that frequency or time value**

**i.e. for an average spectrum:**

**n **

**Average i = E (Amplitude i,j) / n**

**j=1**

**where i = spectral line number;**

**j = spectrum number; and**

**n = number of spectra used for averaging.**

**Linear motion**

**Motion along an axis i.e. motion along a straight line.**

**Linear relationship**

**A relationship governed by direct proportionality. See also**

**Proportional, directly.Linear scale**

**A scale with uniformly spaced marks, the distance between adjacent**

**marks representing a fixed quantity. See also Logarithmic scale.**

**Linear system**

**A system which, when excited by a composite excitation force, outputs**

**a response that is the sum of its responses to the individual**

**components of the excitation force i.e. if the response to excitation**

**force F1 is x1 and to F2 is x2, then the response to the composite**

**excitation force F1 + F2 is x1 + x2 if the system is linear. At small**

**vibration amplitudes, most mechanical systems are linear systems.**

**Lines**

**See Spectral lines.**

**Load zone (w.r.t. bearings)**

**The part of a bearing that is subject to the greatest load e.g. load**

**associated with the weight of the rotor it is supporting.**

**Logarithm function, base-10**

**A mathematical function that yields the base-10 exponent of a number**

**e.g. the base-10 logarithm of the number 100 is equal to 2 (since 100 =**

**10²). The logarithm function is a useful tool for working with numbers**

**that vary greatly in magnitude e.g. the base-10 logarithm of a thousand**

**is 3 and of a million is 6 (which is not much bigger than 3 and therefore**

**easily displayed together on a graph). The symbol for “base-10**

**logarithm” is “log10”.**

**Logarithmic scale**

**A scale with marks representing the logarithm of a value rather than**

**the actual value. Logarithmic scales are useful for displaying values of**

**greatly varying magnitudes. See also Linear scale.Looseness**

**The condition where there are undesired gaps between mating parts.**

**Looseness is usually caused by excessive bearing clearances, loose**

**mounting bolts, mismatched parts, and cracked structures. Depending**

**on the type of looseness, the vibration spectrum can appear different.**

**Bearing looseness is the most common form of looseness and**

**produces a vibration spectrum that contains many harmonics.**

**Low pass filter**

**A filter that allows only signal components of frequencies lower than a**

**particular cut-off frequency value to pass through. See also Aliasing.M**

**Machine (w.r.t. the vb instrument)**

**A data group of the vb data structure, for grouping recordings taken of**

**the same physical machine. See also Data structure.**

**Machine vibration**

**The reciprocating or back-and-forth movement of a machine or**

**machine component involving a continual interchange of kinetic energy**

**and potential energy. The most common cause of machine vibration is**

**the rotation of unbalanced or misaligned parts. See also Free**

**vibration and Forced vibration.**

**Magnetostriction**

**The distortion of magnetic materials in the presence of magnetic fields.**

**Magnetostriction worsens the vibration caused by the reciprocation of**

**motor magnetic poles (which occurs at twice the line frequency).**

**Main unit (w.r.t. the vb instrument)**

**The part of the vb instrument which houses the LCD, keypad, RS232**

**COM port, battery pack and charger circuitry.**

**MAS**

**See Measurement Analysis Software.**

**Mask**

**See Alarm envelope.Measurement Analysis Software**

**A Windows-based analysis software developed by COMMTEST**

**INSTRUMENTS, that facilitates the archiving and analysis of vb data on**

**a PC. The software is also known as MAS, the abbreviation of**

**“Measurement Analysis Software”. MAS allows vibration data to be**

**graphed, analyzed, and printed.**

**Measurement parameters**

**The details about a measurement or recording, that must be specified**

**before the measurement or recording is taken e.g. before a spectrum is**

**taken, the f max, number of spectral lines to be used, averaging type,**

**windowing type, etc. need to be specified. The way in which**

**parameters are set can and often does affect measurement results.**

**Measurement unit**

**See Unit.**

**Mechanical looseness**

**See Looseness.**

**Mechanical runout**

**See Runout.**

**Metric units**

**A decimal system of measurement units based on S.I. units. For**

**example, the metric units for length, “kilometer”, “centimeter”,**

**“millimeter”, “micrometer”, etc. are related by factors of 10, 100, 1000,**

**etc., and are based on the S.I. unit for length, “meter”. See also**

**Imperial units and S.I.**

**Micrometer**

**A measurement unit for small distances, known also as “micron”. One**

**micrometer (µm) equals one millionth of a meter i.e. 10-6 meter.Micron**

**See Micrometer.**

**mil**

**A measurement unit for small distances. One mil is equal to 0.001**

**inch.**

**Misalignment**

**The condition where the axes of machine components are not**

**positioned or orientated accurately with respect to one another.**

**Angular misalignment is the situation where the axes of mating parts**

**are tilted with respect to one another, and parallel misalignment is**

**where the axes are parallel but do not coincide. Usually, both kinds of**

**misalignment are involved. Misalignment is one of the most common**

**causes of vibration in machines.**

**Modal analysis**

**The process of developing a mathematical model for the vibration of a**

**system so that the mode shapes of the system can be determined for**

**different excitation forces.**

**Mode of vibration**

**See Mode shape.**

**Mode shape**

**The collection of vibration amplitudes at all points of a system, or the**

**“shape” of a system, when it is subjected to a particular excitation**

**force. The mode shape of a vibrating system is a mixture of all the**

**natural mode shapes of the system, the dominant mode being that**

**corresponding to the natural frequency closest to the frequency of**

**vibration.Modulation**

**The varying or fluctuation of a signal due to the influence of another**

**signal. The signal that is being modulated is called the “carrier” and**

**the signal causing the modulation of the carrier is called the**

**“modulating signal”. See also Amplitude modulation and Frequency**

**modulation.**

**Module**

**A hardware unit within the vb instrument, that performs most of the**

**calculations and stores most of the data associated with recordings.**

**The module has the accelerometer port attached to it.**

**Moment**

**The cause of rotation or bending. The moment about a point on a body**

**is caused by a force being applied on the body at a distance away from**

**the point. The greater the force, or the greater the distance, the**

**greater the moment about the point. If motion of the body is**

**unobstructed, the body will rotate because of the moment, but if the**

**body is restrained, the moment will cause the body to bend. See also**

**Bending moment.**

**Momentum**

**The product of mass and velocity. Momentum is a measure of the**

**tendency of a moving object to continue moving.N**

**Narrow band analysis**

**See Narrow band measurement.**

**Narrow band measurement**

**The measurement of the vibration spectrum of a system i.e. the**

**measurement of the vibration amplitude at individual frequency values**

**or for small frequency bands. See also Broad band measurement.**

**Natural frequency**

**The frequency at which a system will vibrate when it is vibrating freely**

**by itself without the influence of an excitation force. An n degrees-offreedom system has n natural frequencies. A shaft (which has an**

**infinite number of degrees of freedom) has an infinite number of natural**

**frequencies. See also Fundamental natural frequency and Natural**

**mode shape.**

**Natural mode shape**

**The collection of vibration amplitudes at all points of a system, or the**

**“shape” of a system, when the system is vibrating at a particular**

**natural frequency. Each natural frequency has a corresponding natural**

**mode shape e.g. a simply-supported shaft vibrating at its first natural**

**frequency will have the shape of a bow, but when vibrated at its second**

**natural frequency will have an “s” shape. The natural mode shape**

**corresponding to the nth natural frequency is called the nth natural mode**

**shape. See also Mode shape and Nodal points.**

**Natural vibration**

**See Free vibration.Navigator**

**A MAS tool that allows the locating and display of vibration data**

**archived on the PC. The navigator is displayed on the left side of the**

**MAS Main window and consists of two windows. The top window, the**

**Outline window, shows a “tree” of all machines, points, and axes in the**

**current data folder, and the bottom window, the List window, lists the**

**contents of the item highlighted in the Outline window. Any number of**

**items in the List window can be selected to be viewed, annotated,**

**printed, exported, plotted and/or deleted.**

**Nodal points**

**The points in a mode shape where there is no motion e.g. the second**

**natural mode shape of a simply-supported shaft is an “s” shape that**

**has a nodal point at the center of the shaft and one at each end of the**

**shaft. The nth natural mode shape of a shaft has n+1 nodal points.**

**Noise**

**Unwanted signal, often of a random nature, caused by electrical and/or**

**mechanical effects.**

**Noise floor**

**The amplitude level below which amplitude peaks cannot be**

**distinguished from noise.**

**Non-synchronous peak**

**A spectral peak occurring at a frequency that is not a whole number**

**multiple of the fundamental frequency. See also Harmonic (n.).**

**Normal mode shape**

**See Natural mode shape.Normalization**

**The dividing of all values by the largest value e.g. amplitude**

**normalization involves dividing all amplitude values by the largest**

**amplitude, so that all amplitude values are expressed as a fraction of**

**the largest amplitude. See also Order normalization.**

**Nyquist frequency**

**The maximum frequency that can be sampled correctly i.e. without**

**aliasing occurring. The Nyquist frequency is half the sampling rate.**

**The vb instrument uses a sampling rate 2.56 times the f max, thus**

**ensuring that the Nyquist frequency is greater than the f max.**

**Nyquist plot**

**A complex numbers graph used to show the frequency response of a**

**system. The amplitude and phase of a system vibrating at a particular**

**frequency can be represented by a complex number (i.e. a number**

**consisting of a real part and an imaginary part). By plotting the**

**imaginary part against the real part for a range of frequencies, the**

**Nyquist plot is obtained.O**

**Octave**

**A frequency interval over which the frequency value is doubled. For**

**example, the 2X frequency is one octave above the fundamental**

**frequency. Vibration frequency is seldom expressed in octaves. It is a**

**term used in the fields of music and sound measurement.**

**Oil whip**

**An oil whirl condition where the journal orbits around the bearing at one**

**of the resonant frequencies of the shaft. Oil whip causes the shaft to**

**vibrate at large amplitudes.**

**Oil whirl**

**A condition in a journal bearing where the oil film whirls and orbits the**

**journal around the bearing at about 40 to 49% of the shaft rotation**

**speed. Oil whirl is undesirable and is caused by excessive clearance**

**in the journal bearing or insufficient radial loading on the bearing. See**

**also Oil whip.**

**Operating speed**

**The shaft speed of the motor or engine in a rotating machine.**

**Orbit (w.r.t. journal bearings)**

**The circular path of the journal within the bearing. A large orbit**

**indicates the presence of oil whirl.**

**Order**

**The frequency of a spectral peak expressed as a proportion or multiple**

**of the fundamental frequency e.g. a spectral peak at twice the**

**fundamental frequency has an order of 2X.Order analysis**

**See Order normalization.**

**Order normalization**

**The division of all frequency values on the frequency axis of a**

**spectrum by the fundamental frequency. Spectral peak frequencies**

**are thus expressed as multiples or fractions of the fundamental**

**frequency. This helps the analyst to identify the root cause of vibration.**

**Order tracking**

**See Order normalization.**

**Oscillation**

**To-and-fro, back-and-forth, or reciprocating motion. Vibration is**

**mechanical oscillation. “One oscillation” means one cycle of**

**reciprocating motion.**

**Out-of-phase signals**

**See Phase.**

**Overall level**

**See Root-mean-square.**

**Overall rms level**

**See Root-mean-square.**

**Over-damped system**

**A system with a quantity of damping that is more than necessary to**

**prevent the system from vibrating. An over-damped system does not**

**vibrate but has a slow response. See also Critical damping and**

**Under-damped system.Overlap processing**

**The combining or overlapping of data from adjacent time domain data**

**blocks for FFT calculations. A percentage of data from the most**

**recently collected data block is combined with a portion of data of the**

**preceding data block, and the resultant data block is fed to the FFT**

**algorithm to obtain a spectrum more quickly than if no overlapping is**

**done. 50% overlap processing, as shown below, is ideal in most**

**situations.**

**FFT 1 FFT 3 FFT 5 FFT 7**

**FFT 2 FFT 4 FFT 6**

**Data block 1 Data block 2 Data block 3 Data block 4**

**Time**

**50% of**

**a data**

**blockP**

**Parallel misalignment**

**See Misalignment.**

**Parameters**

**See Measurement parameters.**

**Parameter set (w.r.t. the vb instrument)**

**A data group of the vb instrument data structure, for grouping**

**recordings taken at a particular location using the same measurement**

**parameter values. See also Data structure.**

**Peak (w.r.t. a spectrum)**

**The highest amplitude value in a spectrum.**

**Peak (w.r.t. a wave)**

**The highest point in a wave. See also Trough.**

**Peak amplitude**

**The maximum amplitude attained by a vibrating object in a given time**

**period e.g. the peak velocity amplitude of a vibrating object during a**

**given time period is the maximum velocity achieved by the object**

**during that time period. The terms “peak amplitude” and “zero-to-peak**

**amplitude” are synonymous.Peak hold**

**A mathematical operation resulting in the “largest-so-far” amplitude of**

**each line of a spectrum to be always displayed. This is done by**

**comparing each line of the most recent spectrum with the**

**corresponding line in the preceding spectrum and displaying the larger**

**of the two amplitudes. Although sometimes regarded as a form of**

**averaging, “peak hold” does not involve averaging.**

**Peak-to-peak amplitude**

**The difference between the highest positive value and the lowest**

**negative value in a waveform. Displacement amplitudes are usually**

**expressed in terms of the peak-to-peak amplitude.**

**Period**

**The time taken to complete one oscillation or one cycle. Period is**

**usually expressed in s (seconds) or ms (milliseconds). See also**

**Frequency.**

**Periodic**

**Having a pattern that is repeated over and over again, each cycle**

**taking a fixed amount of time. See also Period and Repeating force.**

**Periodic force**

**See Repeating force.**

**Periodic motion**

**Motion of a pattern repeated over and over again, each cycle or**

**oscillation taking a fixed amount of time. Examples of periodic motion**

**are circular motion, simple harmonic motion, and most kinds of steadystate vibration. Periodic motion can be mathematically described by**

**the arithmetic sum of a series of sinusoids. See also Period and**

**Repeating force.Phase**

**The time relation of a signal to another signal of the same frequency, or**

**the time relation of a vibrating object to another object vibrating at the**

**same frequency. The vibratory motion of an object is “in phase” with**

**that of another object if they oscillate at the same frequency in a**

**synchronized manner e.g. the two objects attain maximum positive**

**displacement simultaneously and zero displacement simultaneously. If**

**the motions of the objects are not synchronized e.g. if one object**

**attains maximum displacement when the other attains the minimum,**

**and vice versa, the vibratory motions are said to be “out of phase”.**

**Phase angle**

**A quantity that indicates the phase of a waveform or vibratory motion in**

**relation to another waveform or vibratory motion. Phase angle can be**

**expressed in degrees or radians. For example, a waveform that leads**

**a reference waveform by half a cycle, is ascribed a phase angle of**

**180°.**

**Phase difference**

**The difference between the phase of a vibratory motion and that of**

**another vibratory motion occurring at the same frequency. Phase**

**difference is measured in terms of cycles, degrees, or radians. The**

**phase difference between two objects vibrating in phase is zero cycles**

**or zero degrees. If an object attains maximum positive displacement**

**when another object (vibrating at the same frequency) attains minimum**

**negative displacement, the phase difference between the two vibratory**

**motions is 180°. A phase difference of 360° i.e. a phase difference of**

**one complete cycle, is equivalent to no phase difference or zero**

**degrees phase difference.**

**Phase shift**

**The number of cycles, degrees, or radians a waveform or vibratory**

**motion leads or lags another waveform or vibratory motion of the same**

**frequency. A sine waveform phase-shifted forward a quarter cycle**

**(90°) is equivalent to a cosine waveform.Pi**

**A constant value roughly equal to 3.14 and often denoted by the**

**symbol, π. The circumference-to-radius ratio of a circle is equal to 2π.**

**See also Radian.**

**Picket fence effect**

**A lack of accurate representation of peaks and troughs by a discrete**

**spectrum. Since amplitude data is not available for frequencies**

**between spectral lines, peaks generally appear too low and troughs,**

**too high. This effect may be reduced by increasing the sampling**

**duration (thereby increasing the number of spectral lines) and/or by**

**interpolating between spectral values.**

**Piezoelectric transducer**

**A transducer in which a crystal converts mechanical force to electricity.**

**Most accelerometers are piezoelectric transducers and often have an**

**in-built mass – called the seismic mass – which exerts a force on the**

**piezoelectric crystal when vibrated. Due to the force exerted on it, the**

**piezoelectric crystal, typically a quartz crystal, generates an electrical**

**signal that is proportional to the force. See also ICP accelerometer.**

**Pink noise**

**Noise of which the level decreases with increasing frequency at the**

**rate 3 dB per octave. It is a term used in the field of sound**

**measurement.**

**Point (w.r.t. the vb instrument)**

**A data group of the vb instrument data structure, for grouping**

**recordings taken of the same physical location on a particular machine.**

**See also Data structure.Potential energy**

**The energy associated with the state of an object e.g. a pendulum at its**

**highest point possesses gravitational potential energy (that will cause it**

**to continue swinging), and a compressed spring possesses strain**

**potential energy (that will cause it to return to its equilibrium state).**

**Preload**

**Static force applied to a bearing to ensure that the rolling elements roll**

**(and not slide) within the bearing and that the shaft makes proper**

**contact with the bearing. Too little or too much preload can cause**

**bearing damage.**

**Principal inertia axis (w.r.t. rotors)**

**The mass centerline of a rotor, constructed by joining the centers of**

**mass at every cross-section of the rotor. To avoid unbalance, the axis**

**of rotation must coincide with the principal inertia axis.**

**PROFLASH**

**A way by which the firmware in the vb instrument can be upgraded to**

**later versions without hardware changes.**

**Proportional**

**See Proportional, directly.**

**Proportional, directly**

**Increases or decreases along with another value, in a linear way e.g.**

**the acceleration of an object (with a constant mass) is directly**

**proportional to the force causing it to accelerate i.e. if the force**

**increases by 10%, then the acceleration will also increase by 10%.Proportional, inversely**

**Increases or decreases linearly in an opposite way in relation to**

**another value e.g. for a given applied force, the acceleration of an**

**object is inversely proportional to the mass of the object i.e. if the mass**

**increases by 10%, then the acceleration will decrease by 10%.**

**Proportional, linearly**

**See Proportional, directly.**

**Proximity probe**

**A transducer that measures displacement e.g. the displacement of a**

**shaft. Proximity probes are normally used to measure low frequency**

**signals only.Q**

**Quantization (w.r.t. signals)**

**The process of assigning values from a discrete and finite range to**

**represent the signal values of an analog signal. Quantization is**

**inherent in the sampling and digitization of analog signals using an A/D**

**converter. See also Digital.**

**Quasi-periodic waveform**

**A waveform with a period that varies over time but which has sufficient**

**periodicity to have a corresponding spectrum that shows clear peaks.**

**Spectral peaks corresponding to quasi-periodic motion occur at**

**frequencies that are not whole number multiples of the fundamental**

**frequency. Loose or worn rotating belts often cause quasi-periodic**

**vibration.R**

**Radial direction**

**A direction perpendicular to the centerline of a shaft or rotor.**

**Radial vibration**

**Vibration in a direction perpendicular to the centerline of a shaft or**

**rotor. Radial vibration is seen in unbalanced rotors. See also Axial**

**vibration.**

**Radian**

**A measurement unit for angle. 2π radians (2π being the**

**circumference-to-radius ratio of a circle) is equivalent to a full circle of**

**rotation, or 360°. Thus one radian is roughly equal to 57°.**

**Mathematical calculations are often more conveniently done in radians**

**than in degrees. See also Angular frequency.**

**Random**

**Non-deterministic or not having a specific pattern. Random signals can**

**only be described in terms of statistical quantities. Vibration caused by**

**turbulent fluid flow is usually random in nature. The spectrum of**

**random vibration shows no clear peaks but shows energy spread over**

**a range of frequencies.**

**Recording (w.r.t. the vb instrument)**

**The data collected for a particular location during a single recording**

**session. See also Data structure.Rectangular window**

**A mathematical function with a constant value of one throughout. All**

**values of a data block multiplied by a rectangular window, are**

**multiplied by one i.e. the values are preserved. This is equivalent to**

**not using a window. See also Signal leakage and Windowing.**

**Reference spectrum**

**A spectrum that is the basis for an alarm envelope. A reference**

**spectrum should be “ideal” or “normal” for the measurement point and**

**axis for which it is used as a reference. See also Alarm envelope.**

**Repeating force**

**A periodic force i.e. a force with a pattern repeated over and over**

**again, each cycle taking a fixed amount of time. Machine vibration is**

**most often due to repeating forces originating from the rotation of**

**unbalanced or misaligned parts. A repeating force may or may not be**

**harmonic, and can be mathematically described by the arithmetic sum**

**of a series of sinusoids. See also Excitation force.**

**Resolution (w.r.t. waveforms and spectra)**

**The finest frequency or time “step” possible on the horizontal axis of a**

**discrete spectrum or waveform. The resolution of a spectrum improves**

**with the number of spectral lines used i.e. the more spectral lines used,**

**the better the spectrum represents the true spectrum. However, the**

**more spectral lines used, the more instrument memory is used up to**

**store the spectrum, and the longer the data collection time. Likewise,**

**for waveforms, the larger the number of samples used (for a given**

**measurement duration), the better the resolution of the waveform is,**

**but the more instrument memory space is used to store the waveform.**

**Resolution bias error**

**See Picket fence effect.Resonance**

**The situation where the vibration amplitude increases rapidly due to the**

**natural frequency of the system being excited by a periodic force that**

**has a frequency similar to the natural frequency. A machine should**

**never be operated continuously at its natural frequency. If it is**

**necessary for a machine to operate at a frequency higher than its first**

**natural frequency, the speed of the machine should be increased past**

**the natural frequency as quickly as possible.**

**Resonant frequency**

**The natural frequency of a system when there is no damping in the**

**system. An n degree-of-freedom system has n resonant frequencies.**

**See also Damped natural frequency.**

**Response spectrum**

**See Frequency response.**

**Rest position**

**See Equilibrium position.**

**Rigid**

**Infinitely stiff and does not deform. There are no truly “rigid” objects in**

**the real world. The concept of “rigid” objects is invented by engineers**

**for the purpose of simplifying mathematical modeling. In practice, a**

**rotor is considered “rigid” if it does not bend significantly at its rotating**

**speed.**

**Rigid body motion**

**Movement of a body as a unit with no relative movement or**

**deformation within the body.rms**

**See Root-mean-square.**

**Rolling element bearing**

**A bearing with rolling elements to enable smooth shaft rotation. The**

**shape of a rolling element is usually cylindrical, conical, or spherical.**

**See also Angular contact bearing and Thrust bearing.**

**Root-mean-square**

**An amplitude expression defined as the square root of the arithmetic**

**mean of a set of squared instantaneous signal values. The term “rootmean-square” is often abbreviated as “rms”. For a discrete waveform**

**with n instantaneous values, the overall rms amplitude is given by:**

**n**

**Overall rms amplitude = E xi² / n**

**i = 1**

**where xi = the ith instantaneous signal value in the set of n**

**instantaneous signal values.**

**For a discrete spectrum with n spectral lines, the overall rms amplitude**

**(with no windowing) is given by:**

**n**

**Overall rms amplitude = E xi²**

**i = 1**

**where xi = the amplitude of the ith spectral line in the set of n**

**spectral lines.**

**For true sinusoidal waves (only), the rms amplitude is times (i.e.**

**approximately 0.7 times) the peak amplitude.**

**Rotary motion**

**Motion around an axis i.e. circular motion.**

**√**

**1**

**√2**

**√Rotor**

**A machine part that rotates. See also Rigid.**

**Rotor bar pass frequency**

**The speed at which the rotor bars of an AC induction motor rotate past**

**a fixed reference point. This is equal to the operating speed of the**

**motor multiplied by the number of rotor bars. The vibration spectrum of**

**an induction motor usually shows a peak at the rotor bar pass**

**frequency.**

**Running speed**

**See Operating speed.**

**Runout**

**The error that is indicated by a displacement probe when it is used to**

**measure the position of the centerline of a shaft. Runout can be**

**caused by the axis of rotation not coinciding with the shaft centerline,**

**or a lack of roundness. Runout is sometimes called “TIR” or “total**

**indicator reading”. The larger the runout, the larger the excitation force**

**generated when the shaft is rotated.S**

**Sampling**

**The extracting of discrete, instantaneous data, usually at regular**

**intervals, from a continuous signal e.g. from the output signal of an**

**accelerometer. In a sampled time domain signal, data is not available**

**for all time values, but only for time values corresponding to when data**

**was sampled. See also Aliasing.**

**Sampling duration**

**The total time period data is sampled from a continuous signal.**

**Increasing the number of spectral lines or the number of averages for a**

**spectrum increases the sampling duration. On the contrary, increasing**

**the f max or the overlap percentage reduces the sampling duration.**

**Sampling frequency**

**See Sampling rate.**

**Sampling rate**

**The rate at which data is sampled from a continuous signal e.g. from**

**the output signal of an accelerometer. See also Aliasing.**

**Scalar**

**A quantity that denotes magnitude but not direction e.g. speed is a**

**scalar quantity: it is the magnitude of velocity. See also Vector.**

**Seismic**

**Caused by the movement of a mass. The output of a seismic**

**transducer are signals originating from the movement of a mass within**

**the transducer.Sensitivity (w.r.t. accelerometers)**

**The change in the magnitude of the output signal per unit change in the**

**acceleration sensed. The sensitivity of an accelerometer is usually**

**expressed in mV/g (where “mV” stands for “milliVolts”, and “g” is**

**“acceleration due to gravity”).**

**Settling time (w.r.t. the vb instrument)**

**The period of time that must be allowed for the electrical hardware in**

**the vb instrument and accelerometer to stabilize before accurate**

**measurements can be taken. The settling time required for the**

**accelerometer is a value specified by the manufacturer of the**

**accelerometer and typically ranges from 1 to 3 seconds. The settling**

**time required for the vb instrument is dependent on the frequency**

**range (f max) or duration of the measurement, and ranges from 4 to 13**

**seconds. The lower the f max or the longer the duration of the**

**measurement, the longer the settling time required for the vb**

**instrument. The total settling time i.e. the sum of the settling time**

**required for the accelerometer and that for the vb instrument is**

**automatically calculated by the instrument.**

**SHM**

**See Harmonic motion.**

**Shock**

**A suddenly applied force that results in the transient response of a**

**system. The force experienced by a system struck with a hammer is**

**an example of shock. The severity of the shock can be measured in**

**terms of the maximum value of the response of the system.**

**S.I.**

**Abbreviation of “Systeme Internationale”, the international system of**

**measurement units. The primary S.I. units, from which all other units**

**can be derived, are “meter”, “kilogram”, “second”, “Kelvin”, “Ampere”,**

**“mol”, and “candela”. S.I. units are widely used throughout the world**

**except in North America. See also Imperial units and Metric units.**

**Sidebands**

**Minor peaks, caused by amplitude or frequency modulation, located**

**symmetrically on either side of spectral peaks. The distance between**

**adjacent sidebands is equal to the frequency of the modulating signal.**

**Sidebands are often seen in the spectra of faulty gearboxes and**

**electrical motors with faulty rotor bars.**

**Signal**

**An electrical voltage or current that is proportional to the magnitude of**

**a physical quantity. The output signal of an accelerometer is a**

**continuous voltage that is proportional the acceleration of the point**

**being measured. A signal may be analog or digital, and continuous or**

**discrete.**

**Signal conditioning**

**The modification of a signal by devices such as attenuators, filters, and**

**amplifiers, before the signal is processed or displayed. The main**

**purposes of signal conditioning are to alter signal amplitude to a**

**suitable level for sampling, and to remove noise and other errors from**

**the signal.**

**Signal leakage**

**A spectral distortion where the amplitude of a spectral line affects or**

**“leaks” to adjacent spectral lines. If FFT calculations are performed on**

**a data block not consisting of an integral number of waves, signal**

**leakage will be evident in the resulting spectrum. Signal leakage can**

**be minimized by multiplying data blocks with a suitable “window” prior**

**to performing FFT calculations on the data blocks. See also**

**Windowing.**

**Signature**

**The vibration spectrum of a system, from which much can be inferred**

**regarding the vibration behavior of the system.Simple harmonic motion**

**See Harmonic motion.**

**Sine**

**The ratio of the length of the side opposite an angle, to the length of**

**the longest side (hypotenuse) in a right-angled triangle i.e. the sine of**

**the angle θ shown below is equal to b/h. The symbol for “sine” is “sin”.**

**See also Cosine wave.**

**sin θ = b/h**

**cos θ = a/h**

**Sine function**

**See Sine.**

**Sine wave**

**The signal or graph generated by plotting the sine of angles. A sine**

**wave oscillates between maximum and minimum values of 1 and -1.**

**A sine wave may be considered to represent the vertical projection of**

**the position of a point on a shaft rotating at a constant speed, as shown**

**above. On an unbalanced rotor, the vertical projection of the rotational**

**motion of the heavy spot is a sine wave. This causes an excitation**

**force with a sine wave pattern that in turn causes a vibration response**

**that resembles a sine wave. See also Cosine wave.**

**Sin θ**

**θ**

**1**

**-1**

**θ1 0**

**θ2**

**θ1 θ2**

**θ**

**b h**

**aSine waveform**

**A time domain signal described by the function:**

**f(t) = sin (ωt – ∅)**

**where f(t) = the instantaneous value at time t;**

**ω = angular frequency;**

**t = time; and**

**∅ = phase angle.**

**See also Sine.**

**Sinusoid**

**A mathematical function of the form:**

**x(t) = A sin (ωt – ∅)**

**where x(t) = the instantaneous value of x at time t;**

**A = maximum x value (zero-to-peak amplitude of x);**

**ω = angular frequency;**

**t = time; and**

**∅ = phase angle.**

**See also Sine.**

**Sinusoidal**

**That can be described by a sinusoid. The free vibration of an**

**undamped single degree-of-freedom system is sinusoidal e.g. the**

**undamped free vibration of a mass suspended on a spring is**

**sinusoidal. In practice, true sinusoidal behavior is not observed – the**

**amplitude will decay exponentially due to damping present in the**

**system.Ski slope**

**An amplitude distortion that resembles the shape of a “ski slope” at the**

**low frequency end of a spectrum. The distortion is due to the**

**integration of a signal containing low frequency noise. Because**

**integrating sinusoids (of which periodic signals comprise) causes their**

**amplitudes to be multiplied by the inverse of their frequencies, low**

**frequency noise is accentuated. Hence the increased amplitude values**

**at the low frequency end of the spectrum. The distortion will become**

**worse if the settling time allowed for the accelerometer is not long**

**enough.**

**Slip**

**The difference between the rotation speed of an induction motor and**

**the synchronous speed e.g. if the rotation speed is 2900 rpm and the**

**synchronous speed is 3000 rpm, then the slip is 100 rpm and the slip**

**percentage is 3.3% (100 rpm / 3000 rpm). The greater the load on the**

**motor, the higher the slip will be.**

**Slow roll speed**

**Low operating speed that makes excitation forces negligible. The**

**amplitude of excitation forces associated with unbalance is proportional**

**to the square of the operating speed. At low operating speeds, the**

**amplitude of the excitation force becomes very small.**

**Soft foot**

**A condition where the feet of a machine do not lie on a level plane, and**

**structural distortion occurs when the hold-down bolts are tightened.**

**Soft foot can also be caused by some bolts being fastened more tightly**

**or more loosely than other bolts. The resulting structural distortion**

**causes misalignment in machine parts, thereby causing vibration.**

**Spectra**

**Plural of Spectrum.Spectral lines**

**Vertical lines that make up a discrete spectrum. The height of a**

**spectral line represents the amplitude of vibration at the frequency**

**indicated by the spectral line. The more spectral lines used for a**

**spectrum, the better the resolution of the spectrum (but the more**

**instrument memory used and the longer the sampling duration**

**required). See also Resolution and Spectrum.**

**Spectral map**

**See Waterfall chart.**

**Spectral peak**

**See Peak (w.r.t. spectrum).**

**Spectrum**

**An amplitude (e.g. of velocity) versus frequency graph e.g. of**

**measured vibration. A discrete vibration spectrum consists of a series**

**of “spectral lines”, the height of each spectral line representing the**

**amplitude at the frequency indicated by the spectral line. See also**

**Waveform.**

**Spectrum analyzer**

**An instrument capable of calculating a spectrum from a waveform. See**

**also Fast Fourier transform.**

**Spring constant**

**The ratio of applied force to the amount of distortion e.g. a spring that**

**is compressed by 0.2 inch by a 2 lb force has a spring constant of 10**

**lbf/in. “k” is the symbol for spring constant. See also Stiffness.Standard deviation**

**A statistical value that indicates the variation in signal level in a given time period. For a discrete waveform,**

**the standard deviation over a given time period is defined as follows:**

**n**

**Standard deviation = E (xi – x)² / n**

**i = 1**

**where xi = the ith instantaneous signal value during the time period;**

**x = the average signal value during the time period; and**

**n = total number of instantaneous signal values for the time**

**period.**

**Because the average vibration signal value is zero or close to zero, the**

**standard deviation may be written as:**

**n**

**Standard deviation = E xi² / n**

**i = 1**

**Thus the standard deviation is simply equal to the rms amplitude. The**

**larger the standard deviation, the larger the vibration amplitude.**

**Static unbalance**

**An unbalance condition where the mass centerline of a rotating part is**

**parallel to the axis of rotation but offset from it. This causes “in-phase”**

**repeating forces to act on the support bearings i.e. the force acting on**

**one bearing is always pointing in the same direction as that acting on**

**the other bearing. As a result, all points on the rotating part vibrate in a**

**synchronized manner. Static unbalance can be corrected by adding**

**one correction weight to the appropriate location on the rotating part.**

**See also Couple unbalance and Dynamic unbalance.**

**Steady-state response**

**See Steady-state vibration.**

**√ √Steady-state vibration**

**The vibration behavior of a system after it has stabilized. Most kinds of**

**machine vibration settle into a steady state. See also Transient**

**response.**

**Stiffness**

**Resistance against deformation. The stiffness of a spring is quantified**

**by the spring constant, k. The stiffness of a component is dependent**

**on the material it is made of and its physical dimensions.**

**Strain**

**The ratio of elongation to original length e.g. a shaft, of length L, that is**

**being elongated lengthwise by an amount x, is said to experience an**

**axial strain of x/L.**

**Strain gage**

**A transducer that measures strain. A strain gage is usually glued on**

**the surface being measured and outputs a voltage proportional to the**

**strain.**

**Stress**

**The force experienced per unit area e.g. a shaft, of cross-sectional**

**area A, that is being stretched lengthwise by a force, F, is said to**

**experience an axial stress of F/A.**

**Subharmonic**

**A spectral peak that occurs at a frequency that is a whole number**

**fraction of the fundamental frequency e.g. at 1/2, 1/3, 1/4, 1/5, or 1/6**

**times the fundamental frequency. The spectrum of shaft rubbing the**

**surface of a journal bearing exhibits a subharmonic at 1/2 the**

**fundamental frequency.Subsynchronous peak**

**A spectral peak that occurs at any frequency below the fundamental**

**frequency. A subsynchronous peak may or may not be a subharmonic.**

**The spectrum of a journal bearing subjected to an oil whirl condition**

**usually has a subsynchronous peak at roughly 0.45 times the**

**fundamental frequency.**

**Synchronous averaging**

**See Time-synchronous averaging.**

**Synchronous peak**

**A spectral peak at a frequency that is an integer multiple of the**

**fundamental frequency. The gear mesh frequency, blade pass**

**frequency, vane pass frequency, rotor bar pass frequency, and their**

**multiples, are synchronous with the fundamental frequency and have**

**synchronous peaks corresponding to them in the spectrum. In**

**contrast, spectral peaks corresponding to ball pass and ball spin**

**frequencies are not synchronous peaks. See also Harmonic (n.).**

**Synchronous speed**

**The speed at which the magnetic field in the stator of an AC motor is**

**rotated. The synchronous speed is usually the same as the AC line**

**frequency i.e. if the line frequency is 50 Hz, then the synchronous**

**speed is 50 cycles per second or 3000 rpm.**

**System (w.r.t. vibration)**

**A mechanism or machine which has a means of storing potential and**

**kinetic energy, and a means by which energy is dissipated. In most**

**vibratory systems, potential energy is stored in elastic members, kinetic**

**energy is stored in moving masses and energy is dissipated through**

**friction or other damping devices.T**

**Tagging (w.r.t. the vb instrument)**

**The identifying of data to be collected or transferred to a computer.**

**Tagging is a means of creating a “plan” for data collection, and a**

**means of mass-transferring data automatically to a computer.**

**Tangential direction**

**A direction perpendicular to the axial and radial directions. The**

**tangential direction of a shaft is a direction perpendicular to the**

**centerline of the shaft and at a tangent to the surface of the shaft.**

**Thrust**

**See Axial force.**

**Thrust bearing**

**A bearing that supports loads that act in the axial direction of the shaft.**

**Thrust bearings usually have rolling elements, and are used to support**

**vertical rotors. See also Angular contact bearing.**

**Time averaging**

**See Time-synchronous averaging.**

**Time domain**

**That which has a time axis as its x-axis, or a set of time values to which**

**are mapped a set of other values e.g. amplitude. A waveform is a time**

**domain graph i.e. a waveform has a time axis as its x-axis (and an**

**amplitude axis as its y-axis).Time-synchronous averaging**

**The averaging of waveforms to produce a relatively noise-free average**

**waveform. To obtain an accurate average spectrum, the phases of the**

**waveforms used in the averaging process must be the same. This is**

**achieved by taking the waveforms by means of a common reference**

**trigger e.g. by means of a tachometer sensing the key way on a shaft.**

**Since noise values are equally likely to be positive or negative, they**

**cancel one another when they are averaged. The average spectrum is**

**thus relatively free of noise. The higher the number of waveforms used**

**in the averaging process, the more accurately the average waveform**

**represents true vibration behavior.**

**TIR**

**See Runout.**

**Tolerance**

**The maximum allowable variation from a specified quantity e.g. if a**

**dimension is specified as “20.0 ± 0.2 inches”, then the tolerance for the**

**dimension is “± 0.2 inch”, and the maximum and minimum allowable**

**dimensions are 20.2 inches and 19.8 inches.**

**Tone**

**A sharp distinct peak at a specific frequency. Bearing tones are**

**spectral peaks that correspond to the motion of moving elements in the**

**bearing.**

**Torque**

**The rotational force that causes rotational acceleration or stress. The**

**higher the torque applied to an object, the higher the rotational**

**acceleration of the object, or the higher the stress in the object.**

**Torsion**

**Twisting of a body about an axis. The quantity of torsion is measured**

**by the angle of twist.Torsional vibration**

**Oscillation of a body about an axis. The displacement of the body is**

**measured by an angular coordinate. An example of torsional vibration**

**is the oscillation of a heavy rotor about its axis when the rotor is**

**suddenly stopped.**

**Total indicator reading**

**See Runout.**

**Transducer**

**A device that translates the magnitude of one quantity into another**

**quantity e.g. an accelerometer is a transducer that translates**

**acceleration into voltage.**

**Transient**

**See Transient response.**

**Transient response**

**The temporary behavior of a system immediately after a change in the**

**excitation to the system e.g. the transient response of a machine can**

**be observed while it is being powered up, or just after it has been**

**struck by a hammer. When analyzing a transient response, windowing**

**and averaging are not normally used. See also Steady-state**

**vibration.**

**Trending**

**The analyzing, usually by way of waterfall and trend charts, of vibration**

**data taken of a particular physical point and collected regularly over a**

**period of time so that changes in spectrum or time-synchronized**

**waveform characteristics can be detected, physical explanations**

**assigned, and corrective actions taken accordingly. See also Trend**

**chart and Waterfall chart.Trend chart**

**A cross-sectional view of a waterfall chart at a particular frequency or**

**time value. If the recordings plotted in the waterfall chart are arranged**

**chronologically and pertain to the same physical point, the crosssectional view depicts the “trend” of vibration pattern at that point for**

**the particular frequency or time value. See also Trending and**

**Waterfall chart.**

**Trial weight**

**A weight that is used during the process of balancing a rotor. By noting**

**the change in vibration amplitude and phase after a trial weight (of**

**known mass) is attached to the rotor, the size and location of the**

**correction weight required to balance the rotor can be determined.**

**Triaxial accelerometer**

**An accelerometer that is capable of measuring vibration in three**

**orthogonal directions simultaneously at a particular point.**

**Trigger**

**A signal that is used as a timing reference or to initiate a process e.g. a**

**tachometer signal can be used to derive phase angles and/or to start a**

**measurement.**

**Triggering Mode**

**The method by which measurements or recordings are started on the**

**vb instrument. Measurements can be triggered “manually” one-byone, or using the “free run” mode whereby measurements are**

**continuously taken and displayed (until manually stopped).**

**Trough (w.r.t. a wave)**

**The lowest point in a wave. See also Peak.U**

**Unbalance**

**The condition where the axis of rotation and mass centerline of a**

**rotating part do not coincide. This condition causes a centripetal force**

**to act on the bearings on every cycle of rotation. With the presence of**

**such a “repeating force”, vibration occurs. Unbalance is one of the**

**most common causes of vibration in machines. See also Couple**

**unbalance, Dynamic unbalance, and Static unbalance.**

**Undamped**

**Not having any means of dissipating energy. In practice, no vibrating**

**system is truly undamped. See also Damping.**

**Under-damped system**

**A system with a quantity of damping that is insufficient to prevent the**

**system from vibrating. A machine that vibrates is an under-damped**

**system. See also Critical damping and Over-damped system.**

**Uniform window**

**See Rectangular window.**

**Unit**

**A standard quantity used as a measure e.g. “inch” is a unit for**

**quantifying length. In the engineering field, there are two generally**

**accepted systems of units: S.I. units and imperial units. See also**

**Metric units.V**

**Vane pass frequency**

**The speed at which pump vanes rotate past a fixed reference point.**

**This is equal to the operating speed of the pump multiplied by the**

**number of pump vanes. The vibration spectrum of a pump usually**

**shows a peak at the vane pass frequency.**

**Vector**

**A quantity that denotes magnitude as well as direction e.g. velocity is a**

**vector quantity. Although two objects may be moving at the same**

**speed, their velocities, depending on the direction of movement of the**

**objects, may not be the same. See also Scalar.**

**vdB**

**A dimensionless logarithmic unit for velocity amplitude, defined as 20**

**times the logarithm (base-10) of the ratio of velocity amplitude to a**

**reference amplitude of 10-6 mm/s rms (or 10-5 mm/s rms as used by**

**some US government departments) i.e.**

**Amplitude vdB = 20 log10 (Amplitude / 10-6 mm/s rms)**

**or for some US government departments,**

**Amplitude vdB = 20 log10 (Amplitude / 10-5 mm/s rms)**

**Due to the use of the logarithmic function, the vdB unit is useful for**

**displaying signals with both very large and very small amplitudes. See**

**also decibel and Logarithm function, base-10.Velocity**

**The rate of change of displacement, or the speed of an object in a**

**particular direction e.g. if an object is moving Northward, the velocity of**

**the object in the North direction is its speed, but its velocity in the East**

**or West direction is zero, and its velocity in the South direction is the**

**negative of its speed. Velocity units commonly used in the field of**

**vibration analysis are mm/s (metric), in/s (imperial), and vdB**

**(logarithmic).**

**Velocity transducer**

**A transducer that measures velocity. Compared to accelerometers,**

**velocity transducers have many drawbacks e.g. they are subject to**

**wear and require frequent calibration.**

**Vibration**

**A reciprocating or back-and-forth movement involving a continual**

**interchange of kinetic energy and potential energy. The vibration of a**

**mass supported by a spring is an up-and-down motion that involves**

**continual interchange of kinetic energy associated with motion of the**

**mass and potential energy associated with distortion of the spring.**

**Vibration signature**

**See Signature.**

**Vibratory system**

**See System.**

**Viscous damping**

**The dissipation of vibration energy due to viscous fluid flowing through**

**constricted gaps e.g. oil flowing around a piston in a cylinder (as in car**

**shock absorbers) and lubricant circulating in a journal bearing. The**

**quantity of energy dissipated is dependent on the viscosity of the fluid**

**and the velocity of vibration. See also Coulomb damping and**

**Hysteretic damping.W**

**Waterfall chart**

**A three-dimensional graphical view of recordings laid out in succession**

**on the third axis. Waterfall charts are useful for “trending” vibration**

**patterns i.e. recordings taken of the same physical point and collected**

**over a period of time can all be displayed chronologically on a waterfall**

**chart so that changes in spectrum or waveform characteristics can be**

**detected. See also Trending and Trend chart.**

**Waterfall plot**

**See Waterfall chart.**

**Wave**

**A disturbance traveling through a medium. Throwing a stone into**

**water causes ripples or waves to travel through the water. Vibrating a**

**metal sheet causes waves to travel through it. As a result, each point**

**of the metal sheet oscillates. See also Peak, Trough, and**

**Wavelength.**

**Waveform**

**A signal level (e.g. of velocity) versus time graph e.g. of measured**

**vibration.**

**Wavelength**

**The distance between two adjacent peaks or troughs in a wave. The**

**wavelength is equal to the speed of the wave divided by its frequency.**

**The stiffer the material, the faster waves travel through it, and the**

**longer the wavelength (for a given vibration frequency).**

**Weighting**

**See Windowing.White noise**

**Noise that has the same magnitude for all frequency values.**

**Window**

**See Windowing.**

**Windowing**

**The multiplying of time domain data block values by a mathematical**

**function (the window) before FFT calculations are performed on the**

**data block. The purpose of windowing is to compensate for certain**

**FFT algorithm limitations that cause signal leakage. “Windowing” or**

**multiplying data block values by a suitable mathematical function to**

**ensure that the data block begins and ends with zero amplitude,**

**thereby making the data block appear like a complete wave, is a way of**

**reducing signal leakage. The Hanning window is commonly used. See**

**also Flat top window, Hamming window, and Rectangular window.X**

**X**

**Operating speed. 1X, or one time the operating speed, is the**

**Fundamental frequency. 2X is twice the fundamental frequency, 3X is**

**three times the fundamental frequency, etc.**

**x-axis (w.r.t. graphs)**

**The horizontal line on which the horizontal scale of a graph is marked.**

**The x-axis of a vibration waveform represents the time elapsed since**

**the beginning of the measurement, and that of a vibration spectrum**

**represents the frequency of vibration.Y**

**y-axis (w.r.t. graphs)**

**The vertical line on which the vertical scale of a graph is marked. The**

**y-axis of a vibration waveform represents the instantaneous vibration**

**level, and that of a vibration spectrum represents the amplitude of**

**vibration.Z**

**Zero-to-peak amplitude**

**See Peak amplitude**

**Zooming**

**Image enlargement, or scale enlargement. Zooming into a particular**

**part of a spectrum enlarges the view of that part of the spectrum.
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