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.
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 systemâ„¢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 materialâ„¢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.
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 ?.
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 2p of, i.e., an integer number of wavelengths ?.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 2p) has been recorded. Note that a change of ? in the total measurement path length (incident plus reflected) corresponds to an actual target displacement of ?/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 Ã‚Â± 1 indicates a displacement of Ã‚Â± ?/8; this means that for a HeNe laser with ?=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 . 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 te 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 tr 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 Ëœcharge modeâ„¢ 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 Ëœsmart sensorsâ„¢ 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 Ëœdata-sheetâ„¢. 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.
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 â€ even when the sensor is replaced â€ by downloading the old sensorâ„¢s site-specific data before it is replaced.
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. ËœSensor fusionâ„¢ 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 Ëœwhole-body gestaltâ„¢ of condition monitoring. This is akin to a mechanic that analyses a problem by integrating knowledge, feel, observation, temperature and sounds.
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 sensorâ„¢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.
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.
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 â€ direct compensation of sensor non- linearity, that is, calibration â€ 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 Ëœglitchâ„¢ 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 Ëœwash overâ„¢ distortion from Ëœaliasingâ„¢ 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 machineâ„¢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 Ëœround-robinâ„¢ 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 aircraftâ„¢s Ëœblack boxâ„¢. 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 Ëœobjectâ„¢ to the CBM system â€ an Ëœobjectâ„¢ 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.
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 â€ at low-cost through the use of ASICs â€ and if the data can be accessed in real-time without simplification, fourth-generation CBM smart sensors will become a reality.
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.
1. Vibration Studies at National Optical Institute, Canada
5. Institute of Engineers Journals