The specific effects also depend on the vibration frequencies to which the worker is exposed. Very low frequency vibration (less than one Hz or cycle per second) can result in motion sickness; frequencies between four and eight Hz are likely to affect the gastrointestinal and spinal systems; higher frequency vibration (15 to 40 Hz) can interfere with vision. Whole body vibration usually originates from a moving vehicle or from the operation of heavy machinery. Much can be gained by routine maintenance of the
Whole body vibration transmitted to vehicle operators may be reduced by proper maintenance of roadways, vehicle maintenance and control of vehicle speed. Tire pressure, track and suspension systems, as well as seating and engine mounts should be routinely checked and serviced when required. Vehicle cab isolation is available in some vehicles and can effectively reduce vibration exposure. If vibration control available through vehicle and roadway maintenance is insufficient, improved seating selection may provide further protection for the worker.
Generally, two types of seating systems are considered when addressing a vibration problem: conventional foam seats or suspension seats. Conventional foam seats tend to amplify vibration frequencies in the range of greatest susceptibility for the human body. Anti-vibration suspension seats include a damper and a spring in the seat system. The spring may be constructed of steel or it may be a column of air. There are large differences between seats and the performance of an individual seat may change during its lifetime. It is important to know the vibration levels and frequencies in the vehicle in order to select an appropriate suspension seat.
Control room vibration may result from machinery operation or heavy vehicles traveling in the vicinity.
This vibration may be addressed in a number of ways:
1. reduce vibration at the source (in the case of heavy machinery this may be accomplished by balancing moving parts)
2. modify a vibrating system to reduce the likelihood of excessive vibration due to resonance (in the case of a cover panel, this may be accomplished by •
2.1. stiffening the system by welding a steel section to it);
2.1.1. increase the damping in the system (damping materials may be coated on the system);
or •
2.1.2. isolate the system from the vibration source (mount the system on anti-vibration mounts).
Glossary
A
Accelerometer
Transducer for measuring vibration in the form of acceleration. It is one of the most rugged transducers for vibration measurements and also has the widest frequency range.
AC
Literally Alternating Current but often used to imply a time-fluctuating signal.
Acceleration
The rate of change of velocity in inches/second/second or G’s (acceleration due to gravity is 1 G). This is a good indicator of the forces inside a machine since F = m.a (Newton’s 2nd law).
ADC
Acronym for Analog to Digital conversion Alarm
Alarms are used to identity specific operating conditions or to define the boundaries between safe and unsafe conditions. When an amplitude reaches or exceeds the alarm amplitude then the software
American Standards Code for Information Interchange.
Attenuation
The weakening of a signal by distance from the source or a mechanical interface.
Averaging
In general, averaging many spectra together improves the accuracy and repeatability of measurements.
B
Band Pass Filter
A measurement filter that removes data below the low cutoff frequency and above the high cutoff frequency. The band pass filter only passes the data between the cutoff frequencies.
Bin
See “resolution”
Blackman-Harris Window
with) power in the input channel. Coherence is a unitless quantity which varies from 0 to l. If the coherence is 1, all the power of the output signal is due to the input signal. If the coherence is 0, the input and output are completely random with respect to one another. Coherence is related to signal to noise ratio (S/N) by the formula:
S/N = γ2/(l -γ2) where γ2 is the traditional notation for coherence.
Correlation
The two channel analyzer may also compute auto and cross correlation. Correlation is a time domain measurement which is defined as follows:
Auto Correlation(τ) = ∫x*(t)x(t-τ)dt
Cross Correlation(τ) = ∫x*(t)y(t-τ)dt
where x and y are the channel 1 and channel 2 input signals and the integrals are over all time. It is clear that the auto correlation at a time t is a measure of how much overlap a signal has with a delayed-by-t version of itself, and the cross-correlation is a measure of how much overlap a signal has with a delayed-by-t version of the other channel. Although correlation is a time domain measurement the some analyzers use frequency domain techniques to compute it in order to make the calculation faster.
Cross Spectrum
The cross spectrum is defined as:
cross spectrum = FFT2 conj(FFT1)
The cross spectrum is a complex quantity which contains magnitude and phase information. The phase is the relative phase between the two channels. The magnitude is simply the product of the magnitudes of the two spectra. Frequencies where signals are present in both spectra will have large components in the cross spectrum.
CPM
Abbreviation for Cycles per Minute - the most common format for displaying frequency in vibration analysis.
D
Database
A collection of information files that are ties together by a common topic. A database allows rapid access of the database files.
Data Collector
Hardware device for collecting vibration data off line.
Decibel (dB)
A convenient unit for displaying logarithmic data.
dB = 10 log (X/Xο) where X or Xο is
a power or squared quantity
or dB = 20 log (Y/Yο)
where Y or Yο is a linear quantity.
Decibels are usually referenced to a standard. e.g. 0.1 GdB re 0.001G.
DC
Literally Direct Current. In PdM terms this may be used to check the accelerometer or for a process measurement.
Differentiate
Differentiation changes displacement to velocity and velocity to acceleration relative to time using the formulae:
Acceleration = Velocity /(2.π.f) Velocity = Displacement /(2.π.f) or Acceleration = Displacement /(2.π.f)2 where f = frequency
To have an alarm condition. Data is outside the defined “safe” area.
Exponential Averaging
Exponential averaging weights new data more than old data. Averaging takes place according to the formula,
New Average = (New Spectrum - I/N) +(Old Average) - (N-l)/N where N is the number of averages.
FFT Spectrum Analyzers take a time varying input signal, like you would see on an oscilloscope trace, and compute its frequency spectrum.
Fourier or FFT
Fourier's theorem states that any waveform in the time domain can be represented by the weighted sum of sines and cosines. The FFT spectrum analyzer samples the input signal, computes the magnitude of its sine and cosine components, and displays the spectrum of these measured frequency components.
Frequency
The rate at which periodic events happen. Typical units are Hertz (Hz), Cycles per Minute (cpm) or orders (multiples of run speed).
Fundamental Frequency
Primary frequency, such as operating speed, to which other frequencies may be referred back.
H
Hanning Window
The Hanning window is the most commonly used window. It has an amplitude variation of about 1.5 dB (for signals between bins) and provides reasonable selectivity. Its filter rolloff is not particularly steep. As a result, the Hanning window can limit the performance of the analyzer when looking at signals close together in frequency and very different in amplitude.
Harmonic
Frequencies at direct multiples of a fundamental frequency. The fundamental is not necessarily the run speed.
Hertz (Hz)
Common frequency units in cycles per second. Named after, Heinrich Rudolf Hertz (1857-94).
German physicist born in Hamburg and educated at the University of Berlin. From 1885 to 1889 he was a professor of physics at the technical school in Karlsruhe and after 1889 a professor of physics at the university in Bonn. Hertz clarified and expanded the electromagnetic theory of light that had been put forth by the British physicist James Clerk Maxwell in 1884. Hertz proved that electricity can be transmitted in electromagnetic waves, which travel at the speed of light and which possess many other properties of light. His experiments with these electromagnetic waves led to the development of the wireless telegraph and the radio. The unit of frequency that is measured in cycles per second was renamed the hertz; it is commonly abbreviated Hz.
A measurement filter that removes data below its low cutoff frequency.
I
Input Couple
Measurements may be AC or DC coupled. Use DC coupling for process measurements and use AC for vibration measurements. DC coupling includes both DC and AC signals whereas AC coupling does not include any DC offsets.
Integrate
Integration is the opposite to differentiation and changes acceleration to velocity and velocity to displacement where A = V x (2.π.f)
K
Kaiser
The Kaiser window, which is available on IRD analyzers, combines excellent selectivity and reasonable accuracy (about 0.8 dB for signals between exact bins). The Kaiser window has the lowest side-lobes and the least broadening for non-bin frequencies. Because of these properties, it is the best window to use for measurements requiring a large dynamic range.
L
Leakage
Errors resulting from Fourier transforming nonperiodic time domain data. This effect is reduced by using windows such as Hanning or Flat Top.
Linear
Linear scaling displays all data on an equal basis. Small signals may be hard to detect with linear scaling but become visible with logarithmic scaling.
Linear Averaging
Linear averaging combines N (number of averages) spectra with equal weighting in either RMS, Vector or Peak Hold fashion. This type of averaging is useful for eliminating transients.
Line of Resolution see “resolution”
Logarithmic
Although the linear magnitude scale is used most often for displaying spectra, another way of displaying amplitude is the Log Magnitude. The Log Mag display graphs the magnitude of the spectrum on a logarithmic scale using dBEU (Engineering Units) as units.
The 16 bit analyzer has a dynamic range of about 90 dB. below full scale. Imagine what something 0.01% of full scale would look like on a linear scale. If we wanted it to be 1 inch high on the graph, the top of the graph would be 833 feet above the bottom - It turns out that the log display is both easy to understand and shows features which have very different amplitudes clearly.
The real and imaginary parts are always displayed on a linear scale. This avoids the problem of taking the log of negative voltages.
Low Pass Filter
A measurement filter that removes data above the cutoff frequency.
The 1/3 octave bands have center frequencies given by:
Center Freq: = 1 kHz x 2(n-30/3) Operating System
A form of software that controls and supervises how the computer operates. It loads programs, handles input and output operations and accepts and executes commands issued by the user.
Orbit
The orbit is simply a two dimensional display of the time record of channel 1 vs. the time record of channel 2. The orbit display is similar to an oscilloscope displaying a "Lissajous" figure.
Orders
A frequency axis scale which is useful for viewing data as a function of the operating speed. The first order corresponds to the operating speed, the second order is two times the operating speed and so on.
Overall
A single value representing the vibration or some other measurement parameter. For vibration measurements this value includes vibration at all frequencies.
Overlap Processing
What about narrow spans where the time record is long compared to the processing time which is what we normally see when taking vibration measurements? The analyzer computes one FFT per time record and can wait until the next time record is complete before computing the next FFT. The update rate would be no faster than one spectra per time record. With narrow spans, this could be quite slow.
And what is the processor doing while it waits? Nothing. With overlap processing, the analyzer does not wait for the next complete time record before computing the next FFT. Instead it uses data from the previous time record as well as data from the current time record to compute the next FFT. This speeds up the processing rate. Remember, most window functions are zero at the start and end of the time record. Thus, the points at the ends of the time record do not contribute much to the FFT. With overlap, these points are “re-used" and appear as middle points in other time records. This is why overlap effectively speeds up averaging and smoothes out window variations.
Typically, time records with 50% overlap provide almost as much noise reduction as non-overlapping time records when RMS averaging is used. When RMS averaging narrow spans, this can reduce the measurement time by a factor of two.
The amount of overlap is specified as a percentage of the time record. 0% is no overlap and 99.8% is the maximum (511 out of 512 samples re-used). The maximum overlap is determined by the amount of time it takes to calculate an FFT and the length of the time record and thus varies according to the span.
Peak
The maximum value as seen in the time domain data. For a sine wave peak = RMS x 1.414 measurements, the display shows the real or imaginary part or phase of the complex peak value.
Phase
In general, phase measurements are only used when the analyzer is triggered. The phase is relative to the pulse of the trigger. The phase is displayed in degrees or radians on a linear scale, usually from -180 to +180 degrees. The phase of a particular frequency bin is set to zero in most analyzers if neither the real nor imaginary part of the FFT is greater than about 0.012% of full scale (-78 dB below f.s.). This avoids the messy phase display associated with the noise floor. (Remember, even if a signal is small, its phase extends over the full 360 degrees.)
Power Spectral Density (PSD)
The PSD is simply the magnitude of the spectrum normalized to a 1 Hz bandwidth. This measurement approximates what the spectrum would look like if each frequency component were really a 1 Hz wide piece of the spectrum at each frequency bin.
What good is this? When measuring broad band signals such as noise, the amplitude of the spectrum changes with the frequency span. This is because the line width changes so the frequency bins have a different noise bandwidth. The PSD, on the other hand, normalizes all measurements to a 1 Hz bandwidth and the noise spectrum becomes independent of the span. This allows measurements with different spans to be compared. If the noise is Gaussian in nature, then the amount of noise amplitude in other bandwidths may be approximated by scaling the PSD measurement by the square root of the bandwidth. Thus the PSD is displayed in units of V/√Hz or dBV/√Hz.
Since the PSD uses the magnitude of the spectrum, the PSD is a real quantity. There is no real or imaginary part or phase.
R
Rayleigh’s Principle
This principle states that ∆f is the lowest measurable frequency for a time record length T:
∆f = 1/T
Real Time Bandwidth
What is real time bandwidth? Simply stated, it is the frequency span whose corresponding time record exceeds the time it takes to compute the spectrum. At this span and below, it is possible to compute the spectra for every time record with no loss of data. The spectra are computed in "real time". At larger spans, some data samples will be lost while the FFT computations are in progress.
Rectangular Window (Uniform or No Window)
RMS averaging computes the weighted mean of the sum of the squared magnitudes (FFT times its complex conjugate). The weighting is either linear or exponential.
RMS averaging reduces fluctuations in the data but does not reduce the actual noise floor. With a sufficient number of averages, a very good approximation of the actual random noise floor can be displayed.
Since RMS averaging involves magnitudes only, displaying the real or imaginary part or phase of an RMS average has no meaning. The RMS average has no phase information.
Route
For off-line data collectors this is a an ordered list of points containing the sequence for collecting data.
S
Sampling Rate
The original digital time record comes from discrete samples taken at the sampling rate. The corresponding FFT yields a spectrum with discrete frequency samples. In fact, the spectrum has less than half as many frequency points as there are time points. Suppose that you take 1024 samples at 2560 Hz. It takes 0.4 Seconds to take this time record. The FFT of this record yields 400 frequency points or lines, but over what frequency range? The highest frequency will be determined by the in-built ratio of F-max to data sampling rate - 2.56. The lowest frequency is just the F-max divided by the
= 2.5 Hz (the same as the lowest measurable frequency)
Everything below 2.5 Hz is considered to be DC. The output spectrum thus represents the frequency range from DC to 1000 Hz with points every 2.5 Hz.
Sideband
A frequency which occurs either side of a fundamental frequency. Sidebands occur because of a modulation of the fundamental by another frequency.
Spectrum
The spectrum is the basic measurement of an FFT analyzer. It is simply the complex FFT. Normally, the magnitude of the spectrum is displayed. The magnitude is the square root of the FFT times its complex conjugate. (Square root of the sum of the real (sine) part squared and the imaginary (cosine) part squared). The magnitude is a real quantity and represents the total signal amplitude in each frequency bin, independent of phase.
If there is phase information in the spectrum, i.e. the time record is triggered in phase with some component of the signal, then the real (cosine) or imaginary (sine) part or the phase may be displayed.
The phase is simply the arc tangent of the ratio of the imaginary and real parts of each frequency component. The phase is always relative to the start of the triggered time record.
T
Tachometer
A device for measuring the speed of rotation.
Time Record
The time record measurement displays the filtered data points before the FFT is taken For baseband spans (spans that start at DC), the time record is a real quantity. For non-baseband spans (zooms) the heterodyning discussed earlier transforms the time record into a complex quantity which can be transfer function to be valid, the input spectrum must have amplitude at all frequencies over which the transfer function is to be measured.
Two-Channel Measurements
Two-channel analyzers offer additional measurements such as transfer function, cross-spectrum, coherence and orbit.
U
Uniform Window
The uniform window is actually no window at all. The time record is used with no weighting. A signal will appear as narrow as a single bin if its frequency is exactly equal to a frequency bin. (It is exactly- periodic within the time record). If its frequency is between bins, it will affect every bin of the spectrum. These two cases also have a great deal of amplitude variation between them (up to 4 dB).
In general, this window is only useful when looking at transients which do not fill the entire time record.
Windowing
What is windowing? Let's go back to the time record. What happens if a signal is not exactly periodic within the time record? We said that its amplitude is divided into multiple adjacent frequency bins. This is true but it's actually a bit worse than that. If the time record does not start and stop with the same data value, the signal can actually smear across the entire spectrum. This smearing will also change wildly between records because the amount of mismatch between the starting value and ending value changes with each record.
Windows are functions defined across the time record which are periodic in the time record. They start and stop at zero and are smooth functions in between. When the time record is windowed, its
Windows are functions defined across the time record which are periodic in the time record. They start and stop at zero and are smooth functions in between. When the time record is windowed, its