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 موضوع: كتاب Beginner’s Guide to Machine Vibration الجمعة 28 مايو 2021, 1:40 am  

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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 base10 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 rootmeansquare 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 “antialiasing” 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”, “peaktopeak”, and “rootmeansquare” (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 amplitudemodulated 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. Analogtodigital 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. Antialiasing filter A low pass filter that removes all signal components of frequencies higher than the specified f max. See also Aliasing. Asynchronous peak See Nonsynchronous 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. Autocorrelation The level of similarity between two “snapshots” of the same waveform. Two snapshots that are identical have an autocorrelation of one, and if they are entirely different, the autocorrelation 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 xaxis and yaxis. 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 cutoff 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 cutoff 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 crosssection 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 Crosscorrelation. 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 xaxis. 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 phaseshifted 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 outofphase 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. Overdamping a gun would cause delays between firings. See also Overdamped system and Underdamped 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. Crosscorrelation A measure of how similar a waveform is to another waveform. The crosscorrelation 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 degreeoffreedom 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 nonperiodic. 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 xaxis 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, nonperiodic, 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 timevarying 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,k1 + (Amplitude i,k – Average i,k1) / 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.Fluidfilm 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 xaxis, 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 xaxis (and an amplitude axis as its yaxis).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 frequencymodulated by the lower frequency signals of rotating shafts. The spectrum corresponding to a sinusoid frequencymodulated 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 degreeoffreedom 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 cutoff 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 24toothed gear is driven by a 12toothed 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 builtin 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. Inphase 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 onekg 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 onelb mass. Leakage See Signal leakage. Linear averaging A commonly used method of averaging spectra or timesynchronized 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, base10 A mathematical function that yields the base10 exponent of a number e.g. the base10 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 base10 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 “base10 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 cutoff 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 backandforth 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 Windowsbased 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. 106 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 degreesoffreedom 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 simplysupported 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 simplysupported 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. Nonsynchronous 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 Toandfro, backandforth, or reciprocating motion. Vibration is mechanical oscillation. “One oscillation” means one cycle of reciprocating motion. Outofphase signals See Phase. Overall level See Rootmeansquare. Overall rms level See Rootmeansquare. Overdamped system A system with a quantity of damping that is more than necessary to prevent the system from vibrating. An overdamped system does not vibrate but has a slow response. See also Critical damping and Underdamped 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 “zerotopeak amplitude” are synonymous.Peak hold A mathematical operation resulting in the “largestsofar” 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. Peaktopeak 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 peaktopeak 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 phaseshifted 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 circumferencetoradius 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 inbuilt 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.
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