1. INTRODUCTION

Vibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road. Vibration is occasionally "desirable". For example the motion of a tuning fork, the reed in a woodwind instrument or harmonica, or the cone of a loudspeaker is desirable vibration, necessary for the correct functioning of the various devices. More often, vibration is undesirable, wasting energy and creating unwanted sound – noise. For example, the vibration motions of engines, electric motors, or any mechanical device in operation are typically unwanted. Such vibrations can be caused by imbalances in the rotating parts, uneven friction, the meshing of gear teeth, etc. Careful designs usually minimize unwanted vibrations. The study of sound and vibration are closely related. Sound, or "pressure waves” by brating structures (e.g. vocal cords); these pressure waves can also induce the vibration of structures (e.g. ear drum). Hence, when trying to reduce noise it is often a problem in trying to reduce vibration.

Types of vibration

Free vibration occurs when a mechanical system is set off with an initial input and then allowed to vibrate freely. Examples of this type of vibration are pulling a child back on a swing and then letting go or hitting a tuning fork and letting it ring. The mechanical system will then vibrate at one or more of its "natural frequency" and damp down to zero.

Forced vibration is when an alternating force or motion is applied to a mechanical system. Examples of this type of vibration include a shaking washing machine due to an imbalance, transportation vibration (caused by truck engine, springs, road, etc.), or the vibration of a building during an earthquake. In forced vibration the frequency of the vibration is the frequency of the force or motion applied, with order of magnitude being dependent on the actual mechanical system.

1.1 Single degrees of freedom

Fig.1.1

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A single degree of freedom system is the simplest mechanical system possible. It can move by translation along one direction only, or can rotate about one axis. The motion of a single degree of freedom system is a sinusoid, having only a single frequency. Mechanical structures are always more complex than the single degree of freedom system, but they can be though of a being built up of a collection of single degree of freedom systems. This is somewhat analogous to a complex waveform being considered as a collection of sinusoidal components. The disciplines of modal analysis and finite element modeling treat mechanical systems in this way, and the number of degrees of freedom they possess determines their complexity.

The simplest vibratory system can be described by a single mass connected to a spring (and possibly a dashpot). The mass is allowed to travel only along the spring elongation direction. Such systems are called Single Degree-of-Freedom (SDOF) systems. A single degree of freedom system is a spring-mass-damper system in which the spring has no damping or mass, the mass has no stiffness or damping and the damper has no stiffness or mass. Furthermore, the mass is allowed to move in only one direction. The horizontal vibrations of a single-story building can be conveniently modeled as a single degree of freedom system.

The general form of the differential equations describing a SDOF oscillator is

mx¨(t) + cx˙ (t) + kx(t) = f(t)

Where x(t) is the position of the mass, m is the mass, c is the dampingRate, k is the stiffness, and f(t) is the external dynamic load. The initialDisplacement is doing, and the initial velocity is VO.

The vibration frequency of unforced spring-mass-damper systems depends on their mass, stiffness, and damping values. The ensuing time-behavior of such systems also depends on their initial velocities and displacements. Free vibration (no external force) of a single degree-of-freedom system with viscous damping can be illustrated as, Damping that produces a damping force proportional to the mass's velocity is commonly referred to as "viscous damping", and is denoted graphically by a dashpot. For an unforced damped SDOF system, the general equation of motion becomes

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This equation of motion is a second order, homogeneous, ordinary differential equation (ODE). If all parameters (mass, spring stiffness and viscous damping) are constants, the ODE becomes,

1.2 Multi degrees of freedom

Fig 1.2

A multi degree of freedom system is a system that can move along two directions, whether translation or can rotate about its axis. The motion of a multi degree of freedom system is a combination of both the values having dual frequency. Mechanical structures are always more complex like multi degree of freedom system, but they can be thought of a being built up of a collection of single degree of freedom systems. This is somewhat analogous to a complex waveform being considered as a collection of sinusoidal components. The disciplines of modal analysis and finite element modeling treat mechanical systems in this way, and the number of degrees of freedom they possess determines their complexity.

The multi vibratory system can be described by a masses connected to a spring (and possibly a dashpot). The mass is allowed to travel only along the spring elongation direction. Such systems are called Multi Degree-of-Freedom (MDOF) systems. A multi degree of freedom system is two nos. of spring-mass-damper system in which the spring has no damping or mass, the mass has no stiffness or damping and the damper has no stiffness or mass. Furthermore, the mass is allowed to move in two directions. The horizontal vibrations of a dual-story building can be conveniently modeled as a multi degree of freedom system.

The general form of differential equations describing a MDOF oscillator is

M1x1¨(t) + c1x1˙(t) + k1x1(t) = f(t)

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M2 (x1¨(t)-x2¨(t)) + c2(x1˙(t)- x2˙(t)) + k2(x1(t)- x2(t)) = 0

Where x(t) is the position of the mass, m is the mass, c is the dampingRate, k is the stiffness, and f (t) is the external dynamic load. The initialDisplacement is doing, and the initial velocity is VO.

The vibration frequency of unforced spring-mass-damper systems depends on their mass, stiffness, and damping values. The ensuing time-behavior of such systems also depends on their initial velocities and displacements. Free vibration (no external force) of a multi degree-of-freedom system with viscous damping can be illustrated as, Damping that produces a damping force proportional to the mass's velocity is commonly referred to as "viscous damping", and is denoted graphically by a dashpot. For an unforced damped MDOF system, the general equation of motion becomes

This equation of motion is a second order, homogeneous, ordinary differential equation (ODE). If all parameters (mass, spring stiffness and viscous damping) are constants, the ODE becomes,

1.3 Harmonic analysis

Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms. The basic waves are called "harmonics" (in physics), hence the name "harmonic analysis," but the name "harmonic" in this context is generalized beyond its original meaning of integer frequency multiples. In the past two centuries, it has become a vast subject with applications in areas as diverse as signal processing, quantum mechanics, and neuroscience. The classical Fourier transform on Rn is still an area of ongoing research, particularly concerning Fourier transformation on more general objects such as tempered distributions.

If, we can attempt to translate these requirements in terms of the Fourier transform of f. The Paley-Wiener theorem is an example of this. The Paley-Wiener theorem immediately implies that if f is a nonzero distribution of compact support (these include functions of compact support), then its Fourier transform is never compactly supported. This is a very elementary form of an uncertainty principle in a harmonic analysis setting. See also series. Fourier series can be conveniently studied in the context of Hilbert spaces, which provides a connection between harmonic analysis and functional analysis.

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1.3.1 Abstract harmonic analysis

One of the more modern branches of harmonic analysis, having its roots in the mid-twentieth century, is analysis on topological groups. The core motivating idea is the various Fourier transforms, which can be generalized to a transform of functions are defined on Hausdorff locally compact topological groups. The theory for abelian locally compact groups is called Pontryagin duality; it is considered to be in a satisfactory state,[citation needed] as far as explaining the main features of harmonic analysis goes.Harmonic analysis studies the properties of that duality and Fourier transform; and attempts to extend those features to different settings, for instance to the case of non-abelian Lie groups.For general nonabelian locally compact groups, harmonic analysis is closely related to the theory of unitary group representations.

For compact groups, the Peter-Weyl theorem explains how one may get harmonics by choosing one irreducible representation out of each equivalence class of representations. This choice of harmonics enjoys some of the useful properties of the classical Fourier transform in terms of carrying convolutions to pointwise products, or otherwise showing a certain understanding of the underlying group structure. See also: Non-commutative harmonic analysis. If the group is neither abelian nor compact, no general satisfactory theory is currently known. By "satisfactory" one would mean at least the equivalent of Plancherel theorem. However, many specific cases have been analyzed, for example SLn. In this case, it turns out that representations in infinite dimension play a crucial role.

1.4Frequency Frequency is the reciprocal of time. If an event is periodic in time, i.e. if it repeats at a fixed time interval, then its frequency is one divided by the time interval. If a vibrating element takes one tenth of a second to complete one cycle and return to its starting point, then its frequency is defined to be 10 cycles per second, or 10 hertz (Hz). Although the SI standard unit of frequency is the Hz, when analyzing machinery vibration we often find it more convenient to express frequency in cycles per minute, which corresponds to rpm. Frequency in rpm is simply frequency in Hz times 60. Another common frequency representation used in machinery monitoring is multiples of turning speed, or "orders".

Frequency in orders is frequency in rpm divided by the turning speed of the machine. The second order is then the second harmonic of turning speed, etc. This is especially convenient if the machine is varying in speed,

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for the frequency representation on a spectrum will be the same regardless of speed. Two machine spectra can therefore more easily be compared if they are both expressed in orders. Conversion of the frequency axis of a spectrum to orders is called "order normalization", and is done by the monitoring software.

Frequency = 1/time period1.5 Bearing

Fig 1.3

A bearing is a device to allow constrained relative motion between two or more parts, typically rotation or linear movement. Bearings may be classified broadly according to the motions they allow and according to their principle of operation as well as by the directions of applied loads they can handle.

A ball bearing is a type of rolling-element bearing that uses balls to maintain the separation between the moving parts of the bearing. However, there are many applications where a more suitable bearing can improve efficiency, accuracy, service intervals, reliability and speed of operation, size, weight, and costs of purchasing and operating machinery. Thus, there are many types of bearings, with varying shape, material, lubrication, principal of operation, and so on.

For example, rolling-element bearings use spheres or drums rolling between the parts to reduce friction; reduced friction allows tighter tolerances and thus higher precision than a plain bearing and reduced wear extends the time over which the machine stays accurate. Plain bearings are commonly made of varying types of metal or plastic depending on the load, how corrosive or dirty the environment is, and so on.

In addition, bearing friction and life may be altered dramatically by the type and application of lubricants. For example, a lubricant may improve bearing friction and life, but for food processing a bearing may be lubricated

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by an inferior food-safe lubricant to avoid food contamination; in other situations a bearing may be run without lubricant because continuous lubrication is not feasible, and lubricants attract dirt that damages the bearings.

1.5.1 Types of BearingsRoller bearingBall bearing Roller thrust bearingTapered roller bearingJournal bearing

1.5.2 Bearing Signals

Bearing vibrates while in operation. Signals may be digital (also called logic signals sometimes) or analog depending on the transducer used.

1.5.3 Time Domain

Time domain is a term used to describe the analysis of mathematical functions, or physical signals, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the case of continuous time, or at various separate instants in the case of discrete time. An oscilloscope is a tool commonly used to visualize real-world signals in the time domain. Speaking non-technically, a time domain graph shows how a signal changes over time.

Fig 1.4

1.5.4 Frequency Domain

Frequency domain is a term used to describe the domain for analysis of mathematical functions or signals with respect to frequency, rather than time.[1]Speaking non-technically, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. A frequency-domain representation can also include information on the phase shift that must be applied to each sinusoid in order to be able to recombine the frequency components to recover the original time signal.

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A given function or signal can be converted between the time and frequency domains with a pair of mathematical operators called a transform. An example is the Fourier transform, which decomposes a function into the sum of a (potentially infinite) number of sine wave frequency components. The 'spectrum' of frequency components is the frequency domain representation of the signal. The inverse Fourier transform converts the frequency domain function back to a time function.

A spectrum analyzer is the tool commonly used to visualize real-world signals in the frequency domain. (Note that recent advances in the field of signal processing have also allowed defining representations or transform that result in a joint time-frequency domain, with the instantaneous frequency being a key link between the time domain and the frequency domain). Different frequency domains Although "the" frequency domain is spoken of in the singular, there are a number of different mathematical transforms which are used to analyze time functions and are referred to as "frequency domain" methods. These are the most common transforms, and the fields in which they are used:

• Fourier series – repetitive signals, oscillating systems• Fourier transform – nonrepetitive signals, transients• Laplace transform – electronic circuits and control systems• Wavelet transform – digital image processing, signal compression• Z transform – discrete signals, digital signal processing

More generally, one can speak of the transform domain with respect to any transform. The above transforms can be interpreted as capturing some form of frequency, and hence the transform domain is referred to as a frequency domain.

Fig.1.5

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1.5.6 Signal analysis

Average = 0.637xPeak value

RMS Value = 0.707xPeak value

Peak Value = 1.414xRMS Value

Peak to peak value = 2xPeak value

Peak to peak value = 2.828xPeak value

1.5.7 Fast Fourier Transform

A fast Fourier transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT) and it’s inverse. There are many distinct FFT algorithms involving a wide range of mathematics, from simple complex-number arithmetic to group theory and number theory; this article gives an overview of the available techniques and some of their general properties, while the specific algorithms are described in subsidiary articles linked below. A DFT (Discrete Fourier Transform) decomposes a sequence of values into components of different frequencies.

This operation is useful in many fields (see discrete Fourier transform for properties and applications of the transform) but computing it directly from the definition is often too slow to be practical. An FFT is a way to compute the same result more quickly: computing a DFT of N points in the naive way, using the definition, takes O(N2) arithmetical operations, while an FFT can compute the same result in only O(N log N) operations. The difference in speed can be substantial, especially for long data sets where N may be in the thousands or millions—in practice, the computation time can be reduced by several orders of magnitude in such cases, and the

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improvement is roughly proportional to N/log (N). This huge improvement made many DFT-based algorithms practical; FFTs are of great importance to a wide variety of applications, from digital signal processing and solving partial differential equations to algorithms for quick multiplication of large integers.

The most well known FFT algorithms depend upon the factorization of N, but (contrary to popular misconception) there are FFTs with O(N log N) complexity for all N, even for prime N. Many FFT algorithms only depend on the fact that is an Nth primitive root of unity, and thus can be applied to analogous transforms over any finite field, such as number-theoretic transforms. Since the inverse DFT is the same as the DFT, but with the opposite sign in the exponent and a 1/N factor, any FFT algorithm can easily be adapted.

Fig 1.6

1.6 Data acquisition

Data acquisition is the process of real world physical conditions and conversion of the resulting samples into digital numeric values that can be manipulated by a computer. Data acquisition and data acquisition systems (abbreviated with the acronym DAS) typically involves the conversion of analog waveforms into digital values for processing. The components of data acquisition systems include:

• Sensors that convert physical parameters to electrical signals. • Signal conditioning circuitry to convert sensor signals into a form that

can be converted to digital values. • Analog-to-digital converters, which convert conditioned sensor signals

to digital values.

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1.6.1 Data Acquisition Systems

Data acquisition systems are used to acquire, store and analyze vibration data received from sensors. Sensing Systems utilizes state of the art computer based data acquisition systems. The equipment is optimized to sample at rates commensurate with the highest frequency expected during testing. Data may be acquired and submitted in different formats for further review and analysis by our customers. Filtering may be performed during acquisition or digitally following data acquisition. Data analysis such as Fourier Transforms may be performed following data acquisition.

1.6.2 Methodology of DAQ System

Data acquisition begins with the physical phenomenon or physical property to be measured. Examples of this include temperature, light intensity, gas pressure, fluid flow, and force. Regardless of the type of physical property to be measured, the physical state that is to be measured must first be transformed into a unified form that can be sampled by a data acquisition system. The task of performing such transformations falls on devices called sensors. A sensor, which is a type of transducer, is a device that converts a physical property into a corresponding electrical signal (e.g., a voltage or current) or, in many cases, into a corresponding electrical characteristic (e.g., resistance or capacitance) that can easily be converted to electrical signal.

The ability of a data acquisition system to measure differing properties depends on having sensors that are suited to detect the various properties to be measured. There are specific sensors for many different applications. DAQ systems also employ various signal conditioning techniques to adequately modify various different electrical signals into voltage that can then be digitized using an Analog-to-digital converter (ADC).

1.6.3 DAQ hardware

DAQ hardware is what usually interfaces between the signal and a PC. It could be in the form of modules that can be connected to the computer's ports (parallel, serial, USB, etc.) or cards connected to slots (S-100 bus, Apple Bus, ISA, MCA, PCI, PCI-E, etc.) in the mother board. Usually the space on the back of a PCI card is too small for all the connections needed, so an external breakout box is required. The cable between this box and the PC can be expensive due to the many wires, and the required shielding.DAQ cards often contain multiple component. These are accessible via a bus by a microcontroller, which can run small programs.

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A controller is more flexible than a hard wired logic, yet cheaper than a CPU so that it is alright to block it with simple polling loops. For example: Waiting for a trigger, starting the ADC, looking up the time, waiting for the ADC to finish, move value to RAM, switch multiplexer, get TTL input, let DAC proceed with voltage ramp. Many times reconfigurable logic is used to achieve high speed for specific tasks and Digital signal processors are used after the data has been acquired to obtain some results. The fixed connection with the PC allows for comfortable compilation and debugging. Using an external housing a modular design with slots in a bus can grow with the needs of the user.

1.6.4 DAQ software

DAQ software is needed in order for the DAQ hardware to work with a PC. The device driver performs low-level register writes and reads on the hardware, while exposing a standard API for developing user applications. A standard API such as COMEDI allows the same user applications to run on different operating systems, e.g. a user application that runs on Windows will also run on Linux and BSD. Not all DAQ hardware has to run permanently connected to a PC, for example intelligent stand-alone loggers and oscilloscopes, which can be operated from a PC, yet they can operate completely independent of the PC.

1.7 Signal processing

Signal processing deals with operations on or analysis of signals, in either discrete or continuous time, to perform useful operations on those signals. Signals of interest can include sound, images, time-varying measurement values and sensor data, for example biological data such as electrocardiograms, control system signals, telecommunication transmission signals such as radio signals, and many others. Signals are analog or digital electrical representations of time-varying or spatial-varying physical quantities. In the context of signal processing, arbitrary binary data streams and on-off signals are not considered as signals, but only analog and digital signals that are representations of analog physical quantities.

Processing of signals includes the following operations and algorithms with application examples:[1]

• Filtering. (for example in tone controls and equalizers)• Smoothing, deblurring. (for example in image enhancement)• Adaptive filtering. (For example for echo-cancellation in a conference

telephone, or denoising for aircraft identification by radar).

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• Spectrum analysis. (for example in magnetic resonance imaging, tomography reconstruction and OFDM modulation)

• Digitization, reconstruction and compression. (for example, image compression, sound coding and other source coding)

• Storage. (in digital delay lines and reverb)• Feature extraction. (for example speech-to-text conversion)• Modulation. (in modems)• Wavetable synthesis. (in modems and music synthesizers)• Prediction.• System identification and classification.• A variety of other operations.

1.7.1 Categories of signal processing

1.7.1.1 Analog signal processing

Analog signal processing is for signals that have not been digitized, as in classical radio, telephone, radar, and television systems. This involves linear electronic circuits such as passive filters, active filters, additive mixers, integrators and delay lines. It also involves non-linear circuits such as companders, multiplicators (frequency mixers and voltage-controlled amplifiers), voltage-controlled filters, voltage-controlled oscillators and phase-locked loops.

1.7.1.2 Discrete signal processing

Discrete time signal processing is for sampled signals that are considered as defined only at discrete points in time, and as such are quantized in time, but not in magnitude.

Analog discrete-time signal processing is a technology based on electronic devices such as sample and hold circuits, analog time-division multiplexers, analog delay lines and analog feedback shift registers. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals. The concept of discrete-time signal processing also refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking quantization error into consideration.

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1.7.1.3 Digital signal processing

Digital signal processing is for signals that have been digitized. Processing is done by general-purpose computers or by digital circuits such as Asics, field-programmable gate arrays or specialized digital signal processors (DSP chips). Typical arithmetical operations include fixed-point and floating-point, real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are circular buffers. Examples of algorithms are the Fast Fourier transforms (FFT), finite impulse response (FIR) filter, Infinite impulse response (IIR) filter, Wiener filter.

1.8 Condition monitoring

Signal conditioning may be necessary if the signal from the transducer is not suitable for the DAQ hardware being used. The signal may need to be amplified, filtered or demodulated. Various other examples of signal conditioning might be bridge completion, providing current or voltage excitation to the sensor, isolation, and linearization. For transmission purposes, single ended analog signals, which are more susceptible to noise can be converted to differential signals.

1.8.1 Permanent Monitoring Systems

Sensing Systems also installs permanent monitoring systems in the field. Monitoring vibration levels overtime and trending are especially useful in predicting equipment failure and scheduling maintenance activities. Installation, planning and implementation of permanent systems are similar to field testing projects. The data acquisition equipment selected for permanent systems typically has communications capabilities using telephone connections or wireless systems for downloading data to computers at the custom Condition monitoring is the process of monitoring a parameter of condition in machinery, such that a significant change is indicative of a developing failure.

It is a major component of predictive maintenance. The use of conditional monitoring allows maintenance to be scheduled, or other actions to be taken to avoid the consequences of failure, before the failure occurs. Nevertheless, a deviation from a reference value (e.g. temperature or vibration behavior) must occur to identify impeding damages. Predictive Maintenance does not predict failure. Machines with defects are more at risk of failure than defect free machines. Once a defect has been identified, the failure process has already commenced and CM systems can only measure the deterioration of the condition.

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Intervention in the early stages of deterioration is usually much more cost effective than allowing the machinery to fail. Condition monitoring has a unique benefit in that the actual load, and subsequent heat dissipation that represents normal service can be seen and conditions that would shorten normal lifespan can be addressed before repeated failures occur. Serviceable machinery includes rotating equipment and stationary plant such as boilers and heat exchangers.

1.8.2 Rotating equipment

The most commonly used method for rotating machines is called vibration analysis. Measurements can be taken on machine bearing casings with seismic or piezo-electric transducers to measure the casing vibrations, and on the vast majority of critical machines, with eddy-current transducers that directly observe the rotating shafts to measure the radial (and axial) vibration of the shaft. The level of vibration can be compared with historical baseline values such as former startups and shutdowns, and in some cases established standards such as load changes, to assess the severity. Interpreting the vibration signal so obtained is a complex process that requires specialized training and experience. Exceptions are state-of-the-art technologies that provide the vast majority of data analysis automatically and provide information instead of data.

Fig 1.7

One commonly employed technique is to examine the individual frequencies present in the signal. These frequencies correspond to certain mechanical components (for example, the various pieces that make up a rolling-element bearing) or certain malfunctions (such as shaft unbalance or

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misalignment). By examining these frequencies and their harmonics, the analyst can often identify the location and type of problem, and sometimes the root cause as well. For example, high vibration at the frequency corresponding to the speed of rotation is most often due to residual imbalance and is corrected by balancing the machine.

As another example, a degrading rolling-element bearing will usually exhibit increasing vibration signals at specific frequencies as it wears. Special analysis instruments can detect this wear weeks or even months before failure, giving ample warning to schedule replacement before a failure which could cause a much longer down-time. Beside all sensors and data analysis it is important to keep in mind that more than 80% of all complex mechanical equipment fails accidentally and without any relation to their life-cycle period.

Most vibration analysis instruments today utilize a Fast Fourier Transform (FFT) which is a special case of the generalized Discrete Fourier Transform and converts the vibration signal from its time domain representation to its equivalent frequency domain representation. However, frequency analysis (sometimes called Spectral Analysis or Vibration Signature Analysis) is only one aspect of interpreting the information contained in a vibration signal. Frequency analysis tends to be most useful on machines that employ rolling element bearings and whose main failure modes tend to be the degradation of those bearings, which typically exhibit an increase in characteristic frequencies associated with the bearing geometries and constructions.

In contrast, depending on the type of machine, its typical malfunctions, the bearing types employed, rotational speeds, and other factors, the skilled analyst will often need to utilize additional diagnostic tools, such as examining the time domain signal, the phase relationship between vibration components and a timing mark on the machine shaft (often known as a keyphasor), historical trends of vibration levels, the shape of vibration, and numerous other aspects of the signal along with other information from the process such as load, bearing temperatures, flow rates, valve positions and pressures to provide an accurate diagnosis. This is particularly true of machines that use fluid bearings rather than rolling-element bearings. To enable them to look at this data in a more simplified form vibration analysts or machinery diagnostic engineers have adopted a number of mathematical plots to show machine problems and running characteristics, these plots include the bode plot, the waterfall plot, the polar plot and the orbit time base plot amongst others.

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Handheld data collectors and analyzers are now commonplace on non-critical or balance of plant machines on which permanent on-line vibration instrumentation cannot be economically justified. The technician can collect data samples from a number of machines, and then download the data into a computer where the analyst (and sometimes artificial intelligence) can examine the data for changes indicative of malfunctions and impending failures. For larger, more critical machines where safety implications, production interruptions (so-called "downtime"), replacement parts, and other costs of failure can be appreciable (determined by the criticality index), a permanent monitoring system is typically employed rather than relying on periodic handheld data collection.

1.8.3 Other techniques

The most rudimentary form of condition monitoring is visual inspection by experienced operators and maintainers. Failure modes such as cracking, leaking, corrosion, etc. can often be detected by visual inspection before failure is likely. This form of condition monitoring is generally the cheapest and is a vital part of workplace culture to give ownership of the equipment to the people that work with it. Consequently, other forms of condition monitoring should generally augment, rather than replace, visual inspection.

• Slight temperature variations across a surface can be discovered with

visual inspection and non-destructive testing with thermography. Heat is indicative of failing components, especially degrading electrical contacts and terminations. Thermography can also be successfully applied to high-speed bearings, fluid couplings, conveyor rollers, and storage tank internal build-up.

• Using a Scanning Electron Microscope of a carefully taken sample of debris suspended in lubricating oil (taken from filters or magnetic chip detectors). Instruments then reveal the elements contained their proportions, size and morphology. Using this method, the site, the mechanical failure mechanism and the time to eventual failure may be determined. This is called WDA - Wear Debris Analysis.

• Spectrographic oil analysis that tests the chemical composition of the oil can be used to predict failure modes. For example high silicon content indicates contamination of grit etc, and high iron levels indicate wearing components. Individually, elements give fair indications, but when used together they can very accurately determine failure modes e.g. for internal combustion engines, the presence of iron/alloy, and carbon would indicate worn piston rings.

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• Ultrasound can be used for high-speed and slow-speed mechanical applications and for high-pressure fluid situations. Digital ultrasonic meters measure high frequency signals from bearings and display the result as a dBuV (decibels per microvolt) value. This value is trended over time and used to predict increases in friction, rubbing, impacting, and other bearing defects. The dBuV value is also used to predict proper intervals for re-lubrication. Ultrasound monitoring, if done properly, proves out to be a great companion technology for vibration analysis.

Headphones allow humans to listen to ultrasound as well. A high pitched 'buzzing sound' in bearings indicates flaws in the contact surfaces, and when partial blockages occur in high pressure fluids the orifice will cause a large amount of ultrasonic noise.

• Performance analysis, where the physical efficiency, performance, or condition is found by comparing actual parameters against an ideal model. Deterioration is typically the cause of difference in the readings. After motors, centrifugal pumps are arguably the most common machines. Condition monitoring by a simple head-flow test near duty point using repeatable measurements has long been used but could be more widely adopted. An extension of this method can be used to calculate the best time to overhaul a pump based on balancing the cost of overhaul against the increasing energy consumption that occurs as a pump wears. Aviation gas turbines are also commonly monitored using performance analysis techniques with the original equipment manufacturers such as Rolls-Royce plc routinely monitoring whole fleets of aircraft engines under Long Term Service Agreements (LTSAs) or Total Care packages.

• Wear Debris Detection Sensors are capable of detecting ferrous and non-ferrous wear particles within the lubrication oil giving considerable information about the condition of the measured machinery. By creating and monitoring a trend of what debris is being generated it is possible to detect faults prior to catastrophic failure of rotating equipment such as gearboxes, turbines, etc.

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1.9 LabviewThis section discusses obtaining data and some key issues when

acquiring or simulating dynamic signals to ensure valid measurement results. The three techniques that allow you to obtain data are as follows:

• Acquire data with a data acquisition (DAQ) device system• Read data from a file• Simulate data with a generation VI or other source

Table 1.1 Relationship of Data Source to the Sound and Vibration Measurement Process1.9.1 Aliasing

When a dynamic signal is discretely sampled, aliasing is the phenomenon in which frequency components greater than the Nyquist frequency are erroneously shifted to lower frequencies. The Nyquist frequency is calculated with the following formula:

fNyquist = sample rate/2When acquiring data with an NI Dynamic Signal Acquisition (DSA) device, aliasing protection is automatic in any acquisition. The sharp

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anti-aliasing filters on DSA devices track the sample rate and filter out (Attenuate) all frequencies above the Nyquist frequency.When performing frequency measurements with an NI E Series DAQ device, you must take steps to eliminate aliasing. These anti-aliasing steps can include the following actions:

• Increasing the sample rate• Applying an external lowpass filter• Using an inherently bandlimited DUT

Simulated data also can exhibit aliasing. The signals often are generated according to a time-domain expression and, therefore, have high-frequency components that are aliased in the discretely sampled data.

1.9.2 Performing Measurements with the Sound and Vibration ExpressEach S&V Express Measurements Express VI displays simulated data

in the configuration view when you configure the measurement from the block diagram for the first time. You also can use the S&V Express Measurements Express VIs to display and analyze the actual data acquired. To display and analyze acquired data, wire the Express VI to the data source, such as the DAQ Assistant, the DAQmx Read VI, or a simulated signal, and run the VI. To inspect the data wired to the Express VI, double-click the Express VI to view the configuration dialog box for that Express VI.

Express VI Simulated dataVibration Level 100 Hz tone with harmonics and

noise in units of gSound Level-Octave analysis 1 kHz tone with harmonics and noise

in units of PaPower spectrumZoom power spectrumPower in band Peak searchTone measurementsNoise measurements

2 kHz tone with harmonics, noise, and DC in units of EU

Frequency Response Stimulus—chirp from 0 Hz to Nyquist in units of V

Table 1.2 Express VI Simulated Data

1.9.3 Weighting filtersIn many applications involving acoustic measurements, the final sensor

is the human ear. In other words, acoustic measurements typically attempt to describe the subjective perception of a sound by the human ear. Because instrumentation devices are usually built to provide a linear response and the ear is a nonlinear sensor, special filters, known as psophometric Weighting filters, are used to account for these nonlinearities.

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1.9.4 Continuous Signal Acquisition

Fig 1.7The block shows the description of continuous signal acquisition programme for vibration signal data acquisition. With this further data analysis can be easily performed.

1.9.5 Frequency AnalysisUse the Express VIs on the Frequency Analysis palette to develop and

Interactively configure the following measurements:• Power spectrum• Zoom power spectrum• Frequency response• Peak search•Power in band

1.9.5.1 FFT FundamentalsThe FFT resolves the time waveform into its sinusoidal components.

The FFT takes a block of time-domain data and returns the frequency spectrum of that data. The FFT is a digital implementation of the Fourier transform. Thus, the FFT does not yield a continuous spectrum. Instead, the FFT returns a discrete spectrum where the frequency content of the waveform is resolved into a finite number of frequency lines, or bins.1.9.6.2 Frequency Resolution

Because of the properties of the FFT, the spectrum computed from the sampled signal has a frequency resolution df. Calculate the frequency resolution with the following equation:

1.9.6.3 Increasing Frequency ResolutionIncreasing the frequency resolution helps you distinguish two

individual tones that are close together. For example, if you analyze a signal that contains two tones at 1,000 Hz and 1,100 Hz, use a sampling frequency of 10,000 Hz. Acquire data for 10 ms and the frequency resolution is 100 Hz.

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In this particular case, you cannot distinguish one tone from the other.

Fig 1.8 Power Spectrum Obtained with an Acquisition Time of 10 ms

Fig 1.9 Power Spectrum Obtained with an Acquisition Time of 1 s

1.9.6.2 Zoom FFT AnalysisIn some applications, you need to obtain the spectral information with

very fine frequency resolution over a limited portion of the baseband span. In other words, you must zoom in on a spectral region to observe the details of that spectral region. Use the zoom FFT to obtain spectral information over a limited portion of the baseband span and with greater resolution. Just as in baseband analysis, the acquisition time determines the frequency resolution of the computed spectrum. The number of samples used in the transform determines the number of lines computed in the spectrum. Zoom FFT analysis achieves a finer frequency resolution than the baseband FFT.

The Zoom FFT VI acquires multiple blocks of data, modulates, and down samples to obtain a lower sampling frequency. The block size is decoupled from the achievable frequency resolution because the Zoom FFT VI accumulates the decimated data until you acquire the required number of points. Because the transform operates on a decimated set of data, you only need to compute a relatively small spectrum. The data is accumulated, so do not think of the acquisition time as the time required acquiring one block of

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samples. Instead, the acquisition time is the time required to accumulate the required set of decimated samples.1.9.6.3 Windowing

Periodicity is one of the basic assumptions made in FFT-based frequency analysis. The FFT algorithm implicitly assumes that every block of acquired data indefinitely repeats in both positive and negative time. Windowing is one method of ensuring periodicity. Windowing multiplies the time-domain data by a window function before the FFT is performed. Window functions typically have a value of zero at the start and end of the measurement period. Figure below shows how a signal that is not the same at the start and end of the measurement period.

Fig 1.10 Effect of Windowing on PeriodicityWindow ENBW

None 1Hanning 1.5

Hamming 1.36Blackman-Harri 1.71Exact Blackman 1.69

Blackman 1.73

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METHODOLOGY

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EXPERMENTAL SET-UP

DATA AQCUTATION

TIME DOMAIN

FAST FOURIER TRANSFORM

FREQUENCY DOMAIN

FEATURE EXTRACTION

ARTIFICIAL NEURAL NETWORK

PATTERN RECOGNITION

DATA BASE