ABSTRACT
A laser-based contact less displacement
measurement system is used for data acquisition to analyze the mechanical
vibrations exhibited by vibrating structures and machines. The analysis of
these vibrations requires a number of signal processing operations which include
the determination of the system conditions through a classification of various
observed vibration signatures and the detection of changes in the vibration
signature in order to identify possible trends. This information is also
combined with the physical characteristics and contextual data (operating mode,
etc.) of the system under surveillance to allow the evaluation of certain
characteristics like fatigue, abnormal stress, life span, etc., resulting in a
high level classification of mechanical behaviors and structural faults
according to the type of application.
Smart sensors or latest
generation sensors are now use for vibration measurements. Where the first
generation sensors are piezoelectric
accelerometers, second generation sensors are modification of piezoelectric accelerometers and
latest are the smart sensors. Third-generation smart sensors use mixed mode
analogue and digital operations to perform simple unidirectional communication
with the condition monitoring equipment.
INTRODUCTION
The study of vibrations
generated by mechanical structures and electrical machines are very important. The
advent of machines and processes that are more and more complex and the ever
increasing exploitation and production costs have favored the emergence of
several application fields requiring vibration analysis. Among these application
fields, we find machine monitoring, modal analysis, quality control, and
environment tests. These functions are used in fields such as aeronautics,
space industry, automotive industry, energy production, civil engineering, and
audio equipment.
The signal processing
application described here uses a laser-based vibrometer in order to analyze
the vibrations exhibited by mechanical systems. This technique can be used in
the numerous applications mentioned above. The problem is to develop an
intelligent system that has the ability to determine the system conditions
based on a classification of the possible vibration signatures, detect changes
in the vibration signature, and analyze their trends.
The classification of the
various possible vibration signatures requires a priori knowledge of the
mechanical system under healthy conditions as well as for the various fault
conditions; when possible a mathematical model of the system should be
provided. The latter is often crucial for the good interpretation of the
observations, since it predicts the dynamic behavior of the structure and thus
the healthy vibration signature.
Vibration spectra are in
general “peaky” due to either the periodic nature of the system’s excitation or
to the natural resonance properties of the mechanical system. Changes in a vibration
signal can result from a variation of the amplitude, frequency, and/or phase of
one or many of the components. Moreover, new peaks may add to the existing
spectrum, or some peaks may fade out. Changes can also appear in the form of
short transients or spikes in the time domain. At the extreme, if the
vibrations become so strong that the structure actually starts to move, then
the overall average level of vibration would change, that is, a DC component
would appear.
All of the above changes may
occur gradually, like fatigue stress slowly deteriorating the material’s
properties, or they may occur suddenly, like the rupture of a mechanical part within
a machine. They may also occur periodically or in a random fashion depending on
the process generating the vibrations. For multiple state systems, changes must
be interpreted carefully. For example, if the operating speed of a rotating machine
is raised from A to B, the vibration analysis system should not declare the
observed changes as being the result of a mechanical failure, but should adapt
itself to this new mode of operation.
LASER VIBROMETER
The laser vibrometer is a
transducer which converts relative displacement into an electrical signal
readily available for digital signal processing (DSP). Laser-based systems
provide several advantages over conventional accelerometers since the
measurements are performed in a contact less manner, i.e., the transducer does
not affect the dynamic behavior of the system under measurement. This is
especially important in the case of light-weight and low-density structures.
Vibrations can be measured remotely and in environments presenting hostile
Conditions such as high
temperature, pressure, and electromagnetic fields the frequency range of the
laser vibrometer extends down to DC which is not possible with most
accelerometers. There is no calibration required since the basic unit of
measurement is the laser wavelength λ.
A schematic of the laser
vibrometer is shown in Fig. 1. The optical portion of the vibrometer is a
Mach-Zender interferometer. The laser beam is split into a reference beam and a
measurement beam which is directed toward the moving target; this beam is then
reflected back into the interferometer. Polarizations, as shown by arrows and
dots, are used in order to combine the beams properly. The recombination of the
beams results in interference since the moving target changes the length of the
measurement path while the length of the reference path remains constant. The
resulting light intensity recorded at the detector is maximum when the phase difference
between the beams equals an integral multiple 2Ï€ of, i.e., an integer number of
wavelengths λ.furthermore, to
provide the direction of motion of the target; the reference beam is single
sideband phase-modulated with an acousto-optic modulator.
The
actual displacement measurement is performed by counting the number of maximum
intensities (or fringes) encountered as the moving target constantly shifts the
phase of the measurement beam. In other words, a count of one means that a
displacement of (i.e., a phase shift of 2Ï€) has been recorded. Note that a change
of λ in the total measurement
path length (incident plus reflected) corresponds to an actual target
displacement of λ/2
The digital displacement signal
is provided by an electronic module (not shown in Fig. 1). The electronic
module filters and demodulates the detector signal into an in-phase (I) component
and a quadrature (Q) component. Both I and Q signal components are then
converted to logic levels and are fed into a quadrature decoder. By decoding
all of the possible I-Q transitions, the displacement resolution is effectively
increased by a factor of four. The decoder outputs, which consist of a counter
trigger and a direction flag, drive a counter, the output of which represents
the target displacement. Because of the quadrature decoder, a count of ± 1
indicates a displacement of ± λ/8;
this means that for a HeNe laser with λ=632, 8 nm,the maximum resolution is
equal to 79,1nm.
VIBRATION ANALYSIS PROCESS
The first step in the vibration
analysis process is to identify a set of parameters which can be used for
vibration analysis. These parameters reflect the physical characteristics of
the system, and each parameter represents a particular feature of the vibration
signature. The parameters may be determined theoretically from a mathematical
model, intuitively by inspection or simple deduction, or experimentally. Fig. 2
shows the vibration analysis system used
.
The second step is to create a
classification space based on the parameter set. The classification space
contains a healthy area or sub-space corresponding to the normal dynamic behavior,
and one or more fault areas corresponding to the various possible fault cases
[1]. Areas are obtained through training either from a set of actual
experimental data or from simulations. Each area then forms a cluster in the classification
space.
The signal processing
requirements for vibration analysis must fulfill three goals. First, the raw
signal must be conditioned and transformed in order to map the vibration signature
to the system parameters. Second, decision tools must be able to evaluate the
system conditions by classifying the observed parameters according to the
discrimination rules. The discrimination rules for choosing which
classification area a given observation belongs to is based on an existing pattern
recognition technique. Popular techniques include nearest-neighbor, neural
networks, template matching, statistical methods, etc. Third, adequate tools
must be able to detect changes in the parameters. The observed trends must be analyzed
in order to eventually predict the future behavior of the system.
Changes in a vibration signal
due to failures are intrinsically non-stationary phenomena. The use of
stationary analysis techniques can sometimes be justified in situations where
the observed changes are slowly varying, thus providing a piecewise stationary
signal. However, this is not always the case for mechanical failures. Changes
are therefore best analyzed using non-stationary transformation techniques. Unlike
stationary techniques, they allow the detection of incipient failures which, at
their early stage, often occur in a non-repetitive manner in the form of
transients . In this case, non-stationary techniques should be used for the
signalto- parameter transformation task.
Data acquisition can be
performed in two different modes: continuous mode and sample mode. The
continuous mode performs a non-stop surveillance of the mechanical system. In this
mode, data is acquired and processed continuously in real time. In the sample
mode, finite length data are collected and the processing can be performed
either in real time or off-line. The choice of one particular mode over another
is a function of the application. Note that trend analysis can be performed in
either mode and can cover multiple time scales.
APPLICATION: GEAR SYSTEM
The vibration analysis system
was used for the detection of broken teeth in gears. The type of defect that we
want to study is the presence of a broken tooth on one of the gears. The passage
of the broken tooth on the engagement point creates a discontinuity in the load
applied on the gears, resulting in the generation of a pulse once every
rotation . The signal can therefore be mathematically described as follows:
Where Ï„e is the period
of engagement, he is the signal generated by the contact of the teeth at
the engagement point and is defined on the interval [0, te]. The
modulation term, m(t), is defined as:
Where Ï„r is the period
of rotation of the defective gear and hr is the pulse signal due to the
broken tooth and is defined on the interval [0, tr].
More precisely, the mechanical system
consisted in two gears, one with 15 teeth (gear 1) and the other with 36 teeth (gear
2). Three cases were analyzed. Case A was when both gears presented no
imperfections. In case B, gear 1 had a broken tooth and gear 2 was normal,
while in case C, gear 2 that had a broken tooth and gear 1 was normal.
In order to characterize the
imperfections, we have used the auto covariance of the spectrum of the
vibration signature, given by:
where X is the vibration
signature vector of length N, n is the frequency index, and d is
the frequency displacement index. The spectral auto covariance measures the
degree of correlation of the spectrum with itself. If the spectrum has e q u i
d i s t a n t f r e q u e n c y c o m p o n e n t s , t h e s p e c t r a l auto
covariance will contain peaks at the frequency displacements corresponding to
multiples of these frequency components.
Fig. 3 shows the operations
performed. We have focused our attention on the maxima at 19.5 and 46.9 Hz, the
frequencies corresponding to the rotating speed of the broken gears. We performed several measurements. The
results were put on a two dimensional classification space. The classification
regions for the three cases are clearly identifiable. These regions are
obtained using the technique of principal components. In this method, each
region is delimited
by an ellipse, oriented according to the
eigenvectors of the covariance matrix of the observations .
We should mention that is not at all excluded
that another defect (a different broken tooth) could be classified in one of the
three classes. Since we are only using the presence of multiples of 19.5 Hz and
46.9 Hz frequency components in the spectrum, other phenomenon causing these
frequencies could be detected and fall within one of the three classes. Misalignment
and eccentricity of the gears are two examples of situations that can generate
spectral components at harmonics of the rotating frequency. Also, since we are limited
to three classes, a defect not considered in our model (e.g. two broken teeth)
could not be detected. We thus have to be prudent in the use of this apparatus
and in the physical interpretation of its results.
Another important factor is the
rotation speed. In our experiments, the gear system was rotating at a constant
speed, resulting in spectral components at constant positions. The parameters
of the system were thus oscillating around an average value. An increase or a
decrease in speed, as would be the case in the gear box of a truck, would
produce erroneous results, because our system was calibrated for a certain
speed.
NEXT GENERATION SENSORS
Piezoelectric
accelerometers are the most common vibration sensor technology used in
condition monitoring systems. These sensors have evolved from the first
generation; un amplified ‘charge mode’ sensors used during the 1960s to the
second-generation, internally-amplified designs that are widely used today.
Second generation transducers convert the low-level or high-impedance charge
output of a piezoelectric crystal into a low impedance, voltage output signal
by using internal amplifier circuitry. Through advanced amplifier design,
second generation transducers can provide protection against over-current,
reverse powering, radio frequency (RF) interference, shock, electrostatic
discharge (ESD), and inter-modulation distortion. Smart sensors The
introduction of ‘smart sensors’ began with third-generation vibration
transducers. Third-generation smart sensors use mixed mode analogue and digital
operations to perform simple unidirectional communication with the condition
monitoring equipment. After the proper triggering protocol has been received,
the smart sensor outputs all of the digital information stored in its digital
electronic ‘data-sheet’. Once the data transmission from memory is complete,
the sensor immediately returns to a second generation mode of operation where
it continues to output an analogue signal that is proportional to the vibration
input. The two-wire interface makes the sensors compatible with the existing
legacy systems.
Third-generation, smart mixed-mode
accelerometers are already used in embedded military applications. Using a
current detecting operational amplifier, the digital electronics are triggered
by a 2 mA drop in the current source that lasts for 11 ms. Programmable read
only memory (PROM) chips store an auto-test sequence and a sensor
identification code that consists of manufacturer, model and serial number
codes. Figure 2 shows the digital output sequence for the sensor used in this
application.
The auto-test, which consists
of a 65 ms string of zeros and ones, is used by the military to verify
operation of the piezoelectric sensing element. This application required only
the digital output of the sensor identification code, but more data could have
been programmed if it had been needed.
FOURTH GENERATION SENSORS
The development of
fourth-generation smart vibration sensors has not happened as quickly as many
had envisaged. The development of smart sensors for condition monitoring
applications has lagged behind the development of smart pressure, temperature,
flow and other sensory modalities primarily because of the shear magnitude of
data to be processed and transmitted. Fourth-generation smart vibration
transducers will be characterized by a number of attributes. These are:
1.
bi-directional command and data communication;
2.
all digital transmission;
3.
local digital processing;
4.
pre-programmed decision algorithms;
5.
user-defined algorithms;
6.
internal self-verification or self-diagnosis;
7.
compensation algorithms; and
8.
On board data/command storage.
Figure 5 shows a block diagram
of a fourth-generation smart vibration transducer.
Bi-directional Communications
In contrast to third-generation
smart sensors, which have unidirectional control and data communication, the
functions built in to fourth-generation smart sensor allow them to send control
commands to the decision support processor and accept commands. Data flow will
be bi-directional, which means that the user can download information to the
sensor, and upload it from the sensor. For this reason a particular mounting
point can maintain location- specific data — even when the sensor is replaced —
by downloading the old sensor’s site-specific data before it is replaced.
All-digital communications
Another feature of a
fourth-generation smart sensor is that all communications are performed
digitally. One particular benefit is error immune transmission that results
from the use of techniques such as parity, cyclical redundancy checks (CRCs),
or check sums followed by a re-transmission of missing or corrupted data.
Electromagnetic interference (EMI) concerns are therefore greatly reduced.
Cable runs using regeneration techniques such as repeaters will enable data to
be transmitted over extremely long distances without it being corrupted.
Fourth-generation smart vibration transducer networks are expected to use
two-wire interfaces and a daisy-chain topology. This structure minimizes
cabling cost per unit length, and it simultaneously minimizes total cable usage
(length) in a given application. Two-wire networks have been identified by a
number of user-groups as the desired solution for sensor networks.
Local digital processing
Recently significant processing
power has become available at a low cost. This combined with low-cost
sigma-delta analogue-to-digital (A/D) converters will be responsible for
revolutionary changes in monitoring technology. Does this mean that centralised
conditionbased monitoring (CBM) processors will disappear, and all processing
will be performed by the smart sensor? The answer is unequivocally, no. The
processing power of distributed sensors will actually enhance CBM capabilities.
With hundreds of individual smart sensor DSPs each calculating their own Fast
Fourier Transform (FFT) functions, higher order FFTs could be calculated in the
same time that current systems take to calculate one FFT. This would lead to
more powerful and sophisticated algorithms involving phase and complete vibration
state analysis of machinery vibration. Subtle changes in machine state that
currently go unnoticed will be recognised as significant indicators of
machinery health. This higher order analysis can only be performed by a central
processor that integrates all of the sensor states into a single cohesive unit.
Combine this with temperature data from each sensor and the number of
possibilities is enormous. ‘Sensor fusion’ can only occur at the higher
processor level which takes into account the overall picture of machinery
condition and health. Think of this as a ‘whole-body gestalt’ of condition
monitoring. This is akin to a mechanic that analyses a problem by integrating
knowledge, feel, observation, temperature and sounds.
Pre-programming
The algorithms that can be
embedded in a smart transducer range from ones which are simplistic in nature
to those which are highly sophisticated. Alarm-level triggering, based on
absolute levels is an example of simple decision making. More sophisticated
types of alarm-level triggering are priority levels, delta change, windowing
and band alarming. Even more sophisticated concepts such as neural nets and
fuzzy logic could be used within the sensor to aid in localized decision
making. Historical data comparisons such as trending of data also could be
easily performed by an intelligent sensor. Interestingly, the storage
requirements for trending are minimal, since spectral data is a very compact
representation of considerable real-time data.
Defined by users
This level of functionality
would allow each sensor’s computational power to be tailored to the specific
needs of the customer. For example, after an accelerometer has been in place
for a few months, the user may decide that its amplitude range is too low
during machine start-up and shut-down, resulting in distortion, but perfect for
normal operation. The sensor could be commanded to lower the gain during
start-up and shut-down, and then increase the gain as a function of machine
stability and speed, for maximum resolution during normal operation. The
concept of extensible sensor object models would allow local smart sensors to
be reconfigured for new tasks when required.
Self-verification
Sensor data will also become
more reliable in fourth-generation sensors, because such devices will be able
to constantly monitor their own health. These capabilities can be built into
both software and hardware to ensure sensor integrity. Instances can occur
where CBM systems are unaware that a sensor has failed because a faulty sensor
is mimicking a healthy machine. In addition to self-verification, another
useful smart sensor function would be a self-diagnostic capability. Once an
error has been detected, the ability to diagnose the problem and localized the
fault will ensure that the problem is fixed quickly. Also, when a problem is
suspected by the user, the capacity to command all sensors to verify and
diagnose can help to locate hidden problems.
Compensation algorithms
A smart sensor can monitor
parameters such as temperature, age and signal amplitude, and compensate
directly for local conditions. For example, piezoelectric crystal sensitivity
changes with age. Smart sensors could automatically compensate for this drift,
saving any costs that are associated with re-calibration. Another compensation
algorithm — direct compensation of sensor non- linearity, that is, calibration
— could be implemented by using look-up tables to linearize the output to a
high degree of accuracy. In Figure 6 a sensor which is attached to a machine
with a ‘glitch’ can be easily compensated in the frequency domain by applying a
simple algorithm.
All instrumentation systems are
affected by temperature, but these effects can be readily removed by a smart
sensor before the data is even processed. Yet another compensation technique
involves rescaling of the input amplitude to the amplifier to prevent ‘wash
over’ distortion from ‘aliasing’ the data.
On board storage
A main advantage of a sensor
having on board storage is that it allows look-up tables to be used to adjust
and/or compensate for sensor environmental deviations. For example, if once
every fifteen seconds a large transient occurs, brought about by another
machine’s operation, the sensor can create a look-up table that compensates for
the transient deviation, thereby avoiding false triggers. There are other
important advantages of having on board storage. In general, most CBM systems
are typically set by the users to ‘round-robin’ poll the sensors once a day,
with once-an-hour polling being the exception rather than the rule. This means
that if random or unexpected events occur, the likelihood of catching an event
is small. Dedicated sensor processors would allow the CBM manager to record all
significant events for subsequent analysis. This form of event storage would be
similar to an aircraft’s ‘black box’. This could be easily interrogated after
an unexpected accident. Another feature of on board data and command storage is
that it enables extensible object models to be downloaded and uploaded. The
means that the sensor can be represented as an ‘object’ to the CBM system — an
‘object’ that has all of the associated benefits of object-oriented programming
such as reuse and portability, type casting, information hiding, specification
and re-specification of allowed operations and domain values, and machine or
application independencies.
Sensor reality
The realization and
implementation of fourth-generation CBM sensors ultimately will be decided by
the market-place. Customers will base their decisions on cost, size, interface
utility, functionality, and most importantly the benefits that they can
potentially gain As processing and decision support are incorporated into the
sensor package — at low-cost through the use of ASICs — and if the data can be
accessed in real-time without simplification, fourth-generation CBM smart
sensors will become a reality.
CONCLUSION
We have used the vibration
analysis system for the detection and the characterized of broken teeth in
gears. Our results show that the laser-based measurement system can detect gear
imperfections and successfully classify them. The system is both highly
sensitive and very accurate. Also by using the new generation sensors the
vibration analysis becomes easier.
BIBLIOGRAPHY
1.
Vibration Studies at National Optical Institute,
Canada
2. www.mtiinstruments.com
3. www.fdb.no
4. www.intellisense.com
5. Institute of Engineers
1 comments:
Write commentsThe great information provided by you with the help of your blog.
ReplyThanks for the sharing a valuable blog that will teach how to know about Vibration Analysis and another like tools.
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