Vibration signal processing (Overlap) :

Overlap
Consider the following example: If there is a need to collect and analyze a frequency range of 1 kHz, the data collection time (also known as the time window) for collecting 1024 samples could be exactly 40 ms. The FFT processor (Figure 4.7) can calculate and display a spectrum in 10 ms, after which it encounters an idle duration of 30 ms until the acquisition of the next block is completed.

Once the first block is collected, rather than waiting for the next block to be fully collected, it is possible to proceed and calculate a new spectrum by using part of the data from the new block and part of the data from the old block. If the process under consideration is stationary (not varying with time), the data from the two blocks can be averaged.

Considering the example mentioned above, we could initiate a new FFT calculation by using 75% of the previous block and 25% of the new one. We would then be performing a 75% overlap processing and our apparent processing time (after the first block) would be 10 ms per spectrum, rather than 40 ms. The method of overlapping becomes even more significant when we are operating at very low frequencies, or when we want to calculate many spectral averages.

For example, let us assume we are collecting data in a 100-Hz frequency range and wish to calculate 16 averages. The data collection time is 4 s, and without overlap processing we will need 64 s. With 75% overlap, we need 4 s for the first block and 1 s for each successive one, or 4 × 1 + 1 × 15 = 19 s to perform the same task. A considerable amount of time can be saved during data collection by the use of overlapping. Themethod enables more efficient use of the collected data. 

Vibration signal processing (Averaging):

Averaging
Averaging is another feature provided in analyzers/data collectors. The purpose is to obtain more repeatable results, and it also makes interpretation of complex and noisy signals significantly easier. There are various types of averaging:

• Linear averaging
• Peak hold
• Exponential
• Synchronous time averaging.

Linear averaging
Each FFT spectrum collected during a measurement is added to one another and then divided by the number of additions. This helps in obtaining repeatable data and tends to average out random noise. This is the most commonly used averaging technique. The spectra are typically averaged 2, 4, 8, 16 or 32 times, but any number could be used.

Peak hold
With this method, the peak value in each analysis cell is registered and then displayed. In other words, it develops an envelope of the highest spectral line amplitude measured for any average. This technique is used for viewing transients, such as coastdowns or random excitations that may be required during stress analysis studies.

Exponential
In this method, the most recent spectra taken are considered to be more important than older ones, and thus given more mathematical weight when adding and averaging them. This is used for observing conditions that change very slowly with respect to sampling time.

Synchronous time
This method uses a synchronising signal from the machine under investigation, and is used for averaging in the time domain. The synchronising signal is usually in the form of a pulse generated by a photocell or an electromagnetic pickup at a reference position on the shaft circumference. The vibration samples can in this way be taken at the same instant with respect to shaft rotation during averaging.

Non-synchronous vibrations in the system are effectively nullified by this method. The method is generally used if a machine has many rotational components rotating at different speeds. Thus, the vibrations synchronous with the synchronising signal are emphasized while others are averaged out.

Vibration signal processing (Lines of resolution,Fmax,bandwidth)

Lines of resolution, F-max, bandwidth

After calculation of the FFT on the digital signal, the frequency domain of the signal can be displayed on the collector/analyzer screen. The FFT is a spectrum of amplitude vs frequency. The resolution is the number of lines (or bins) that are used to display the frequency spectrum. The number of lines could be 200, 400, 800, 1600, 3200, 6400 and 12 800. F-max is the maximum frequency selected on the analyzer by the user when the data are collected. Bandwidth is calculated by dividing the F-max by resolution.

It can now be deduced that when resolution is high there is a better distinction between frequency peaks. Selection of F-max upon collecting data requires experience. If F-max is set too high, the bandwidth gets larger and resolution is affected. On the other hand, if the F-max is set too low, valuable high-frequency vibration data could be lost.

Furthermore, some may find it amusing to know that the time required for collecting the data varies inversely with F-max. The higher F-max, the quicker the FFT can be displayed. This is due to a fixed mathematical relationship between sampling rate and the number of bins in the FFT. As a general guideline, the following advice is provided to

select F-max values:
• For general rotating machinery likes pumps, fans, blowers and motors, set the F-max to 20× or 40×, where × is the running speed.
• When measuring vibrations on gearboxes, the F-max setting should be at least three times higher than the gear mesh frequency, where the gear mesh frequency is the number of teeth of pinion and gear times their respective running speeds.
• However, if an analysis on a machine is conducted for the first time, it is advisable to begin by taking two spectra, one at 10× the running speed and another at 100× running speed. This is to ensure that no important frequencies are lost in the high- or low-frequency zone. Once the range of the suspicious frequencies is noted, the F-max setting should be selected accordingly.

Vibration signal processing (Filters) :

Filters

Vibration signal from a transducer requires signal processing to produce the data that we need. The process usually involves filtering, setting sample rates and resolution, windowing, etc. It is important to understand what filters do and how they are used in the field of vibration. Filtering is a process that removes some frequencies from a signal in order to suppress interfering frequencies and reduce noise.

They are four types of commonly used filters:

1. Low pass filters
Low pass filters allow low frequencies to pass through. Low pass filters are the most common filter type because of the popularity in removing alias signals, and for other aspects of data acquisition and signal conversion.

2. High pass filters
High pass filters allow high frequencies to pass through. High pass filters are normally used in early bearing wear detection. A high pass filter is useful to block the high amplitude, lower frequencies to enable to “amplify” to the low amplitude levels of early bearing wear in the higher frequencies.

3. Band pass filters
Band pass filters allow frequencies within a band to pass through. Band pass filters transmit only those signal components within around a center frequency. Band pass filters are usually applied in situations that require extracting a specific tone, such as a test tone, from adjacent tones or broadband noise.

4. Band stop filters
Band stop filters block frequencies within a band from passing through. Band stop filters transmit all signals except those between specified ranges.

Ideally, filters would block unwanted frequencies and provide a clean cutoff and keep out of unwanted signals. However this is not the case. In reality, there is a transition region where some frequencies will be attenuated, but not blocked. The actual filter designs are shown in Figures. It can be concluded that it’s very important to understand filter types to enable us to look at the data that we are only interested in.

Vibration signal processing (Windowing) :

Windowing
After the signal was digitized using an A/D converter, the next step in the process (before it can be subjected to the FFT algorithm) is called windowing. A ‘window’ must be applied to the data to minimize signal ‘leakage’ effects. Windowing is the equivalent of multiplying the signal sample by a window function of the same length.

When an analog signal is captured, it is sampled with fixed time intervals. Sampling fixed time intervals can cause the actual waveform to get truncated at its start and end. The results obtained can vary with the location of the sample with respect to the waveform’s period.

This results in discontinuities in the continuous waveform. Windowing fills the discontinuities in the data by forcing the sampled data to zero at the beginning and at the end of the sampling period.

Windows can be thought of as a way to fill in the discontinuities in the data by forcing the sampled data to zero at the beginning and end of the sampling period (or time window), thereby making the sampled period appear to be continuous. When the signal is not windowed and is discontinuous, a ‘leakage error’ occurs when the FFT algorithm is applied.

The FFT algorithm sees the discontinuities as modulating (varying) frequencies and it shows as sidebands in the spectrum when none of these frequencies are actually present in the signal. The usage of windows also affects the ability to resolve closely spaced frequencies while attempting to maintain amplitude accuracy. However, it is possible to optimize one at the expense of the other.

There are many window functions. Some used in vibration signal processing are:
1. Rectangular & Uniform (basically no window)
2. Flat top
3. Hanning
4. Hamming
5. Kaiser Bessel
6. Blackman
7. Barlett.

Generally, only the first three window functions mentioned above are available in most
analyzers.

Rectangular (basically no window) When conducting a bump test for resonance or when trying to measure a single event or transient, use the “rectangular” window, which is the same as no window. This gives a good frequency reading but errs on the amplitude side of things. (Bump = Rectangular) .

Uniform
A Uniform window has a value of 1.0 across the entire measurement time . In reality, a Uniform window could be called “no window”.  Depending on the data acquisition system used, sometimes the term “Rectangular” window is also used.

Hanning or Hamming When collecting continuous vibration, say on a machine that is running at steady state; use the “Hanning” or “Hamming” window. These provide a good compromise between amplitude and frequency accuracy. (Continuous = Hanning, Hamming) .
When a Hanning window is applied to a non-periodic signal, the leakage is greatly reduced and the amplitude is higher.

Flattop The Flattop window has a better amplitude accuracy in frequency domain compared to the Hanning window . When calibrating a sensor, or when in need of very accurate amplitude readings, use the “flat top” window as this gives the most accurate amplitude reading but the worst frequency reading. (Accurate Amplitude = Flat Top) .

Vibration signal processing (Leakage) :

Leakage The FFT analyzer is a batch processing device; that is it samples the input signal for a specific time interval collecting the samples in a buffer, after which it performs the FFT calculation on that “batch” and displays the resulting spectrum .

When an analog signal is captured, it is sampled with fixed time intervals. Sampling fixed time intervals can cause the actual waveform to get truncated at its start and end. The results obtained can vary with the location of the sample with respect to the wave form’s period. This results in discontinuities in the continuous waveform.

The shape of the “leaky” spectrum depends on the amount of signal truncation, and is generally unpredictable for real signals. A ‘window’ must be applied to the data to minimize signal ‘leakage’ effects. Windowing is the equivalent of multiplying the signal sample by a window function of the same length .

Vibration signal processing (sampling & Aliasing) :

Sampling rate
Sampling is the process of recording the amplitude of a wave at given instants, and then generating a curve from the recorded points. Thus, the collected discrete sampled data points (digital) are used to reconstruct the wave, which was originally in an analog form. If the reconstructed digital wave has to look similar to the original wave, how fast should we record the amplitude, or in other words, take samples so that the digitized wave is an exact replica of the original analog wave?

The answer lies in the Nyquist sampling theorem, which states: ‘If we are not to lose any information contained in a sampled signal, we must sample at a frequency rate of at least twice the highest frequency component of interest.’

Aliasing
This phenomenon of formation of a lower-frequency wave due to undersampling is called aliasing. All data collectors/analyzers have automatically selected built-in sampling rates to ensure that no aliasing occurs. In theory, there should be no vibrations with frequencies of more than half of this sampling rate. However, this can never be ensured in practice.

Therefore all analyzers are fitted with anti-aliasing filters. These are low-pass electronic filters, which allow low frequencies to pass but block higher ones. The filters remove all vibrations in the analog signal that have frequencies greater than half the sampling rate. These filters are automatically tuned to the proper values as the sampling frequency is changed (this occurs when the frequency range of the analyzer is changed by the user). It is very important to note that filtering has to occur before digitization of the analog commences.

Vibration signal processing (Analog to Digital signal conversion ):

The vibration of a machine is a physical motion. Vibration transducers convert this motion into an electrical signal. The electrical signal is then passed on to data collectors or analyzers. The analyzers then process this signal to give the FFTs and other parameters. We will take a brief look at the processing of the signals, which finally provide us with the necessary information for condition monitoring. To achieve the final relevant output, the signal is processed with the following steps:

• Analog signal input
• Anti-alias filter
• A/D converter
• Overlap
• Windows
• FFT
• Averaging
• Display/storage.

Before we can discuss the above-mentioned digital signal processing steps, we need to take note of a few more terms and concepts.
A vibration or a system response can be represented by displacement, velocity and acceleration amplitudes in both time and frequency domains . Time domain consists of amplitude that varies with time. This is commonly referred to as filter-out or overall reading .

Analog to digital converters
The vibration waves collected by transducers are analog signals. Analog signals must be converted to digital values for further processing. This conversion from an analog signal to a digital signal is done by an Analog to Digital (A/D) converter. The A/D conversion is essentially done by microprocessors. Like any digital processor, A/D conversion works in the powers of two (called binary numbers). A 12-bit A/D converter provides 4096 intervals whereas a 16-bit A/D converter would provide 65 536 discrete intervals .

The greater the number of intervals, the better is the amplitude resolution of the signal. A 12-bit A/D converter would result in a resolution of 0.025% of the full scale, whereas a 16-bit A/D converter would yield a resolution of 0.0015%. It is thus possible to collect a signal with large and small amplitudes accurately.

It can be seen here that the sampling rate determines the highest frequency in the signal that can be encoded. The sampled waveform cannot know anything about what happens in the signal between the sampled times. Claude Shannon, the developer of the branch of mathematics called information theory, determined that to encode all the information in a signal being sampled, the sampling frequency must be at least double the highest frequency present in the signal. This fact is sometimes called the Nyquist criterion.

Reference Standards for Vibration Monitoring and Analysis

Standards are documented agreements containing technical specifications or other precise criteria to be used consistently as rules, guidelines, or definitions of characteristics, to ensure that materials, products, processes and services are fit for their purpose. A good standard represents consensus of opinion, is easy to use, and contains no ambiguities or loopholes.

In the field of machinery vibration monitoring and analysis, a variety of relevant standards are developed and published by ISO (International Organization for Standardization). ISO is a worldwide federation of national standards bodies from 145 countries, and considers itself a bridge between the public and private sectors.

In addition to ISO, various trade organizations such as National Electrical Manufacturers  Association (NEMA) and American Petroleum Institute (API) have developed and published vibration standards, which are widely accepted and applied (and therefore relevant). In most cases, these standards have been developed by consensus of consumers and manufacturers, and their use is considered voluntary.

Most of the ISO standards for machinery vibration monitoring and analysis are guided by technical committee TC108, Mechanical vibration and shock. TC108 is comprised of 22 Participating (P-member) countries and 25 Observer countries. As of May 2003, there are a total of 98 published ISO standards related to TC108 and its SCs (subcommittees). Noteworthy subcommittees include; SC1, Balancing, including balancing machines, SC2, Measurement and evaluation of mechanical vibration and shock as applied to machines, vehicles and structures, and SC5, Condition monitoring and diagnostics of machines .

Standards for evaluation of vibration severity are considered one of the most important activities of ISO/TC108. Unfortunately, due to the range of machinery categories and classifications, itmay also be the most confusing. A wide variety of published standards describe acceptablevibration limits, including the ISO/7919 series (5 parts) “Mechanical vibration of nonreciprocating machines – Measurements on rotating shafts and evaluation criteria” and the ISO/10816 series (6 parts) “Mechanical vibration – Evaluation of machine vibration by measurements on non-rotating parts”.

As detailed in Table 1, ISO 7919-1 is the basic document describing the general requirements for
measurement and evaluation of machinery vibration using shaft measurements. Similarly, ISO 10816-1 is the basic document describing the general requirements for evaluating machinery vibration using casing and/or foundation measurements. Subsequent parts of each series of documents apply to different classes and types of machinery, and include specific evaluation criteria used to assess vibration severity .

The evaluation procedures in the ISO/7919 and ISO/10816 series of standards are limited to broadband measurements, without reference to frequency components or phase. Measurement procedures are detailed in Part 1: General Guidelines of each series, including shaft relative, shaft absolute, and pedestal vibration measurements

At the May 13 – 16, 2003 meeting of ISO/TC108/SC2, Professor Hiroshi Kanki of Japan proposed “Guidelines for selecting vibration evaluation methods by measurement on the rotating shaft and/or on non-rotating parts”, referred to as the “umbrella document”. The scope of the umbrella document is to provide general guidelines for selecting the appropriate vibration standards for a specific machinery classification. The proposed method includes 2 key evaluation criteria; 1) shaft displacement from the journal centerline, and 2) stiffness ratio of pedestal to bearing (which determines the ratio of the shaft relative vibration to the pedestal vibration) .

In general, machines equipped with rolling element bearings will tend to have high bearing stiffness, a stiffness ratio less than 1, and are better suited to vibration measurements at the pedestal and/or casing. Conversely, machines using fluid film bearings and supported on relatively soft pedestals, will have a much higher stiffness ratio, and are better suited to shaft vibration measurements.

Vibration Magnitude is defined within this group of standards as the maximum value of the broadband rms velocity in the specified frequency range (typically from 10 to 1,000 Hz), as evaluated on the structure at prescribed points. Note that other quantities such as displacement or acceleration and peak values instead of rms values are permitted, but may not easily correlate to criteria based on rms values. Evaluation criteria to assess vibration severity include both vibration magnitude and changes in vibration magnitude.

ISO Standards For Vibration Measurements
ISO 13373-1:2001 Condition monitoring and diagnostics of machines — Vibration condition monitoring — Part1: General procedures provides general guidelines for the measurement of machinery vibration for condition monitoring. Recommendations are provided for the following;

• measurement methods and parameters .
• transducer selection, location, and attachment
• data collection
• machine operating conditions
• vibration monitoring systems
• signal conditioning systems
• interfaces with data processing systems
• continuous and periodic monitoring

Due to the wide variety of approaches to condition monitoring, specific topics will be addressed in more detail in additional parts of 13373. At the time of writing this article, Part 2: Processing, analysis and diagnostics is at the committee draft stage.

ISO 17359:2003 Condition monitoring and diagnostics of machines — General guidelines sets out guidelines for the general procedures to be considered when setting up a condition monitoring program.

ISO Standards For Training and Certification
ISO standards for personnel training and certification are a relatively new and significant initiative for ISO/TC108. In August, 2003, ISO 18436-2:2003 Condition monitoring and diagnostics of machines — Requirements for training and certification of personnel — Part 2: Vibration condition monitoring and diagnostics received an affirmative vote at the FDIS stage, and was affirmed as an international standard. 18436-2 describes a 4-category scheme for certification of vibration analysis personnel who perform condition monitoring and diagnostics.

Certification candidates are required to meet prerequisite education, training, and experience, and successfully pass a qualification examination.

Future parts of the 18436 series will include;
1. Part 1: Requirements for certifying bodies and the certification process
2. Part 3: Requirements for training bodies
3. Part 4: Lubrication management and analysis
4. Part 5: Thermography
5. Part 6: Diagnostics and prognostics
6. Part 7: Condition monitoring specialists
7. Part 8: Balancing

American Petroleum Institute (API) Standard
API produces a wide range of documents, including reference standards which are well suited for shop testing of new and rebuilt machinery. Note that these standards generally apply to equipment for use in the petrochemical industries, below, shows a selection of API standards.

Vibration Units & Relationship

THE RELATIONSHIP BETWEEN TIME AND FREQUENCY
Time
When we say that AC line frequency is 60 cycles per second, this means if a one second time period was observed, 60 cycles . However, it is not always practical to observe one second of time and count the number of cycles.

We can measure the time period for one cycle and calculate the frequency. We can also calculate the time period for one cycle if the frequency is known. Time and frequency are the reciprocal of each other.

If 60 cycles occur in one second and the time period for one cycle is 0.0167 seconds, the calculation can be verified by: F x T =1 or 60 x 0.0167 = 1.

Frequency
Frequency is the number of cycles that occur in one time period, usually one second. Until a few years ago, frequency was identified as cycles per second (CPS). CPS was changed to Hertz, honoring the man who developed the frequency theory. Today Hertz (cycles per second) is the standard measurement of frequency. Machine speed is measured in revolutions per minute (RPM), but the frequencies generated by those machines are measured in Hertz.

Example : What is the frequency of a time period of 50 milliseconds?
Answer: T = 50 ms x 0.001 =0.05 sec, F =1/t=1/0.05 = 20 Hz
In the above formula, when determining frequency in cycles per second, time must be in
seconds.
Example : What is the speed of a machine that generates a fundamental frequency of
29.6 Hz?
Answer: 29.6 Hz x 60 Sec/min = 1776 RPM
Example : What is the fundamental frequency a machine will generate if the machine
speed is 1180 RPM?
Answer: 1180 C.PM /60 Sec /min= 19.7 Hz

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AMPLITUDE MEASUREMENT
The four different ways to express the vibration amplitude level are: peak-to-peak, zeroto-peak, RMS, and average.

Peak-to-peak is the distance from the top of the positive peak to the bottom of the negative peak. This type of measurement is most often used when referring to displacement amplitude. Zero-to-peakor peak is the measurement from the zero line to the top of the positive peak or the bottom of the negative peak. The zero-to-peak value of the vibration level . This type of measurement is used to describe the vibration level from a velocity transducer /accelerometer.

The Root Mean Square (RMS)is the true measurement of the power under the curve. In the RMS value is the cosine of 45 degrees times peak (0.707 x peak only applies to pure sine waves). The true RMS value is calculated by the square root of the sum of the squares of a given number of points under the curve.

When calculating true RMS, the crest factor and duty cycle must be considered for signals that contain pulses. The crest factor (CF)is the ratio of the peak value to the RMS value with the DC component removed .

Analog meters measure average amplitude. Various constants are then used to calculate peak, peak-to-peak, or RMS. Most measurements that are not true RMS measurements are either overstated or understated.

When describing the vibration level of a machine, the RMS value should be used if possible. However, some cases require peak-to-peak measurements, for example, when measuring mils of displacement. Other cases require zero-to-peak displacement .

Average = 0.637 x Peak
Average = 0.90 x R M S
Peak to Peak = 2 x Peak
Peak = 1.414 x R M S
Peak = 1.57 x Average
RMS = 0.707 x Peak
R M S = 1.11 x Average

RELATIONSHIP BETWEEN VELOCITY, DISPLACEMENT, AND ACCELERATIO

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Velocity is the measurement of how fast an object is moving from zero-to-peak and is normally measured in tenths of one inch per second (IPS). The effective frequency range of most velocity transducers is from about 10 to 2,000 Hz. Velocity is the most accurate measurement because it is not frequency related. For example, 0.15 IPS is the same at 10 Hz as it is at 2,000 Hz.

Displacement is the measurement of how far an object is moving from peak-to-peak and is normally measured in thousandths of one inch (mils). Displacement is frequency related. Therefore, any measurement of displacement must be at a specified frequency. The effective frequency range of non contacting displacement transducers is from about 0 to 600 Hz. For contacting displacement transducers, the effective frequency range is about 0 to 200 Hz

Acceleration measures the rate of change of velocity from zero-to-peak and is normally measured in units of gravitational force (g’s). This means that high frequencies generate high g levels, and acceleration is frequency related. The effective frequency range for low frequency accelerometers is from about .2 to 500 Hz. The effective range of high frequency accelerometers is from about 5 to 20,000 Hz.

Please note the displacement curve is downward and outward sloping. This indicates low frequencies generate high levels of displacement and high frequencies generate low levels of displacement. Therefore, the displacement transducer most effectivelymeasures lower frequencies.

The frequency response of the velocity transducer is relatively flat from about 10Hz to about 2,000 Hz. It is the most accurate transducer to use in this frequency range.

The acceleration curve is an outward and upward sloping curve, which means that high frequencies generate high levels of acceleration. The accelerometer must be used for frequencies above 2,000 Hz and may not be as effective for frequencies below 100Hz.

The displacement of a body undergoing simple harmonic motion is a sine wave as we have seen. It also turns out (and is easily proved mathematically), that the velocity of the motion is sinusoidal. When the displacement is at a maximum, the velocity will be zero because that is the position at which its direction of motion reverses. When the displacement is zero (the equilibrium point), the velocity will be at a maximum. This means that the phase of velocity waveform will be displaced to the left by 90 degrees compared to the displacement waveform. In other words, the velocity is said to lead the displacement by a 90-degree phase angle.

Remembering that acceleration is the rate of change of velocity, it can be shown that the acceleration waveform of an object undergoing simple harmonic motion is also sinusoidal, and also that when the velocity is at a maximum, the acceleration is zero. In other words, the velocity is not changing at this instant. Then, when the velocity is zero, the acceleration is at a maximum — the velocity is changing the fastest at this instant. The sine curve of acceleration versus time is thus seen to be 90 degrees phase shifted to the left of the velocity curve, and therefore acceleration leads velocity by 90 degrees.

UNITS OF MEASUREMENT
The following symbols are used in the vibration field:
D = Displacement in inches peak-to-peak
V = Velocity in inches per second zero-to-peak
g = Acceleration in g’s zero-to-peak
F = Frequency in Hertz

RELATIONSHIPS
The relationships between these measurements and the conversion from one engineering
unit to another can be accomplished with the use of the following equations:

Example : The vibration level on a variable speed motor operating at 400 RPM is 0.12
IPS (measured with a velocity transducer).
The displacement in peak-to-peak can be calculated by using equation
First, frequency in Hertz must be determined.
F= 400 R.P.M/60 = 6.67 Hz
D= 0.3183(V/F) = 0.3183(0.12/6.67) = 5.7 mils

Example: If the vibration level for the motor in above Exampe is determined with an accelerometer to be 0.013 g’s, then the displacement can be calculated by using equation 6 .
D = 19.57 (g/f*f) = 19.57 (0.13/6.67*6.67 ) = 5.7 mils

Vibration Data Acquisition

It is important for predictive maintenance programs using vibration analysis to have accurate, repeatable data. In addition to the type and quality of the transducer, three key parameters affect data quality: the point of measurement, orientation, and transducer mounting techniques.

An analysis is only as good as the data used, therefore, the equipment used to collect the data are critical and determine the success or failure of a predictive maintenance or reliability improvement program. The accuracy and proper use and mounting of equipment determines whether or not valid data are collected. Specifically, three basic types of vibration transducers can be used for monitoring the mechanical condition of plant machinery: displacement probes, velocity transducers and Accelerometer probes .

Each type transducer and proves have its advantages and limitation over another one and theirs usages will vary in different conditions .

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Displacement Probes
Displacement, or eddy-current, probes are designed to measure the actual movement, or displacement, of a machine’s shaft relative to the probe. Data are normally recorded as peak-to-peak in mils, or thousandths of an inch. This value represents the maximum deflection or displacement from the true center line of a machine’s shaft. Such a device must be rigidly mounted to a stationary structure to obtain accurate, repeatable data.

Permanently mounted displacement probes provide the most accurate data on machines having a rotor weight that is low relative to the casing and support structure. Turbines, large compressors, and other types of plant equipment should have displacement transducers permanently mounted at key measurement locations. The useful frequency range for displacement probes is from 10 to 1000 Hz, or 600 to60,000 rpm. Frequency components above or below this range are distorted and, therefore, unreliable for determining machine condition.

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Velocity Transducers
Velocity transducers are electromechanical sensors designed to monitor casing, or relative, vibration. Unlike displacement probes, velocity transducers measure the rate of displacement rather than the distance of movement. Velocity is normally expressed in terms of inches per second (in./sec) peak, which is perhaps the best method ofexpressing the energy caused by machine vibration.

Like displacement probes, velocity transducers have an effective frequency range of about
10 to 1000 Hz. They should not be used to monitor frequencies above or below this range.
The major limitation of velocity transducers is their sensitivity to mechanical and thermal damage. Normal use can cause a loss of calibration and, therefore, a strict recalibration program is required to prevent data errors. At a minimum, velocity transducers should be recalibrated every 6 months. Even with periodic recalibration, however, velocity transducers are prone to provide distorted data due to loss of calibration.

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Accelerometers
Acceleration is perhaps the best method of determining the force resulting from machine vibration. Accelerometers use piezoelectric crystals or films to convert mechanical energy into electrical signals and . Data acquired with this type of transducer are relative acceleration expressed in terms of the gravitational constant, g, in inches/second/second.

The effective range of general-purpose accelerometers is from about 1 to 10,000 Hz. Ultrasonic accelerometers are available for frequencies up to 1 MHz. In general, vibration data above 1000 Hz (or 60,000 cpm) should be taken and analyzed in acceleration or g’s. A benefit of the use of accelerometers is that they do not require a calibration program to ensure accuracy. However, they are susceptible to thermal damage. If sufficient heat radiates into the piezoelectric crystal, it can be damaged or destroyed. However, thermal damage is rare because data acquisition time is relatively short (i.e., less than 30 sec) using temporary mounting techniques.

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Cables
Most portable vibration data collectors use a coiled cable to connect to the transducer. The cable, much like a telephone cord, provides a relatively compact length when relaxed, but will extend to reach distant measurement points. For general use, this type of cable is acceptable, but it cannot be used for all applications.

The coiled cable is not acceptable for low-speed (i.e., less than 300 rpm) applications or where there is a strong electromagnetic field. Because of its natural tendency to return to its relaxed length, the coiled cable generates a low-level frequency that corresponds to the oscillation rate of the cable. In low-speed applications, this oscillation frequency can mask real vibration that is generated by the machine.

A strong electromagnetic field, such as that generated by large mill motors, accelerates cable oscillation. In these instances, the vibration generated by the cable will
mask real machine vibration.

DATA MEASUREMENTS
Most vibration monitoring programs rely on data acquired from the machine housing or bearing caps. The only exceptions are applications that require direct measurement of actual shaft displacement to obtain an accurate picture of the machine’s dynamics.

This section discusses the number and orientation of measurement points required to profile a machine’s vibration characteristics. The fact that both normal and abnormal machine dynamics tend to generate unbalanced forces in one or more directions increases the analyst’s ability to determine the root-cause of deviations in the machine’s operating condition. Because of this, measurements should be taken in both radial and axial orientations.

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TRANSDUCER-MOUNTING TECHNIQUES

For accuracy of data, a direct mechanical link between the transducer and the machine’s casing or bearing cap is absolutely necessary. This makes the method used to mount the transducer crucial to obtaining accurate data. Slight deviations in this link will induce errors in the amplitude of vibration measurement and also may create false frequency components that have nothing to do with the machine.

Permanent Mounting
The best method of ensuring that the point of measurement, its orientation, and the compressive load are exactly the same each time is to permanently or hard mount the transducers. This guarantees accuracy and repeatability of acquired data. However, it also increases the initial cost of the program.

Quick-Disconnect Mounts
To eliminate the capital cost associated with permanently mounting transducers, a well-designed quick-disconnect mounting can be used instead. With this technique, a quick-disconnect stud having an average cost of less than $5 is permanently mounted at each measurement point. A mating sleeve built into the transducer is used to connect with the stud. A well-designed quick-disconnect mounting technique provides almost the same accuracy and repeatability as the permanent mounting technique, but at a much lower cost.

Magnets
For general-purpose use below 1000 Hz, a transducer can be attached to a machine by a magnetic base. Even though the resonant frequency of the transducer/magnet assembly may distort the data, this technique can be used with some success. However, since the magnet can be placed anywhere on the machine, it is difficult to guarantee that the exact location and orientation are maintained with each measurement.


Handheld Transducer
Another method used by some plants to acquire data is handheld transducers. This approach is not recommended if it is possible to use any other method. Handheld transducers do not provide the accuracy and repeatability required to gain maximum benefit from a predictive maintenance program. If this technique must be used, extreme care

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ACQUIRING DATA
Three factors must be considered when acquiring vibration data: settling time, data verification, and additional data that may be required.

Settling Time
All vibration transducers require a power source that is used to convert mechanical motion or force to an electronic signal. In microprocessor-based analyzers, this power source is usually internal to the analyzer. When displacement probes are used, an external power source must be provided.

When the power source is turned on, there is a momentary surge of power into the transducer. This surge distorts the vibration profile generated by the machine. Therefore, the data-acquisition sequence must include a time delay between powering up and acquiring data. The time delay will vary based on the specific transducer used and type of power source.

Data Verification
A number of equipment problems can result in bad or distorted data. In addition to the surge and spike discussed in the preceding section, damaged cables, transducers, power supplies, and other equipment failures can cause serious problems. Therefore, it is essential to verify all data throughout the acquisition process.

Most of the microprocessor-based vibration analyzers include features that facilitate verification of acquired data. For example, many include a low-level alert that automatically alerts the technician when acquired vibration levels are below a preselected limit. If these limits are properly set, the alert should be sufficient to detect this form of bad data.

Unfortunately, not all distortions of acquired data result in a low-level alert. Damaged or defective cables or transducers can result in a high level of low-frequency vibration. As a result, the low-level alert will not detect this form of bad data. However, the vibration signature will clearly display the abnormal profile that is associated with these problems.

In most cases, a defective cable or transducer generates a signature that contains a skislope profile, which begins at the lowest visible frequency and drops rapidly to the noise floor of the signature. If this profile is generated by defective components, it will not contain any of the normal rotational frequencies generated by the machinetrain.

With the exception of mechanical rub, defective cables and transducers are the only sources of this ski-slope profile. When mechanical rub is present, the ski slope will also contain the normal rotational frequencies generated by the machine-train. In some cases, it is necessary to turn off the auto-scale function in order to see the rotational frequencies, but they will be clearly evident. If no rotational components are present, the cable and transducer should be replaced.

Additional Data
Data obtained from a vibration analyzer are not the only things required to evaluate machine-train or system condition. Variables, such as load, have a direct effect on the vibration profile of machinery and must be considered. Therefore, additional data should be acquired to augment the vibration profiles.

Most microprocessor-based vibration analyzers are capable of directly acquiring process variables and other inputs. The software and firmware provided with these systems generally support preprogrammed routes that include almost any direct or manual data input. These routes should include all data required to analyze effectively the operating condition of each machine-train and its process system .

VIBRATION DATA TYPES

There are several options regarding the types of vibration data that can be gathered for machine-trains and systems and the formats in which it can be collected. However, selection of type and format depends on the specific application.

The two major data-type classifications are time domain and frequency domain. Each of these can be further divided into steady-state and dynamic data formats. In turn, each of these two formats can be further divided into single-channel and multiple channel formats.

Time-Domain Data
Most of the early vibration analyses were carried out using analog equipment, which necessitated the use of time-domain data. The reason for this is that it was difficult to convert time-domain data to frequency-domain data.

Time-domain data are presented with amplitude as the vertical axis and elapsed time as the horizontal axis. Time-domain profiles are the sum of all vibration components (i.e., frequencies, impacts, and other transients) that are present in the machine-train and its installed system. Time traces include all frequency components, but the individual components are more difficult to isolate than with frequency-domain data.
 

Frequency-Domain Data
Most rotating machine-train failures result at or near a frequency component associated with the running speed. Therefore, the ability to display and analyze the vibration spectrum as components of frequency is extremely important.

The frequency-domain format eliminates the manual effort required to isolate the components that make up a time trace. Frequency-domain techniques convert time domain data into discrete frequency components using a fast Fourier transform (FFT). Simply stated, FFT mathematically converts a time-based trace into a series of discrete frequency components. In a frequency-domain plot, the X-axis is frequency and the Y-axis is the amplitude of displacement, velocity, or acceleration.
With frequency-domain analysis, the average spectrum for a machine-train signature can be obtained. Recurring peaks can be normalized to present an accurate representation of the machine-train condition.