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Comparison of integrated micro-electrical-mechanical system and piezoelectric accelerometers for machine condition monitoring S Thanagasundram and F S Schlindwein Department of Engineering, University of Leicester, Leicester, UK The manuscript was received on 16 May 2005 and was accepted after revision for publication on 21 April 2006. DOI: 10.1243/09544062C07405

Abstract: The design and implementation of instrumentation to collect real-time vibrational data from a quasi-steady state machine (a dry vacuum pump) for fault prediction diagnostics is presented. When simultaneous multiple data collection points are required on the same machinery, the use of conventional transducers such as piezoelectric accelerometers becomes impractical due to their price, as each needs an expensive associated charge amplifier. The use of inexpensive micromachined integrated micro-electrical-mechanical system accelerometers such as ADXL105 has been explored here as an alternative to piezoelectric accelerometers for obtaining reliable and predictable data for diagnostics. Surface micromachined accelerometers are a new technology and their usage for vibrational analysis has been conservative due to concerns over increased noise levels and tolerance to high temperatures. In this article, it is shown that such concerns can be allayed. The time and frequency domain vibration signatures obtained using both types of accelerometers are compared. The study shows that ADXL105 accelerometers can be an effective alternative low-cost high-quality solution for machine condition monitoring. Keywords: integrated micro-electrical-mechanical system accelerometers, condition monitoring, dry vacuum pumps, vibrational analysis, autoregressive modelling

1

INTRODUCTION

Much work has been done in the spectrum analysis of vibration signals for monitoring rotating machinery such as rotary pumps, turbomolecular pumps, piston pumps, screw compressors, turbines, and motors, but very little has been done in the area of oil-free dry vacuum pumps [1]. One such pump is used as the test-bed in this experiment. The dry pump used has a five-stage roots and claws design. The study of this kind of pump is important to industry because nowadays the dry vacuum pump is the common choice for clean room applications for IC semiconductor manufacturing. In metal etching and LPCVD processes, chemical corrosive 

Corresponding author: Department of Engineering, University

of Leicester, University Road, Leicester LE1 7RH, UK. email: [email protected]

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vapours are abundant, there are huge amounts of residual particulates, and pump failures are frequent, causing substantial financial losses due to the wafer costs involved. For these reasons, continuous realtime monitoring of dry vacuum pumps is valuable to pump operators, in an attempt to reduce machine downtime and maintenance costs. Accelerometers are a popular choice of transducers used to monitor the vibration produced by rotating machinery. The voltage output of the accelerometer is digitized using an analogue to digital converter (ADC) and the resulting time-domain discrete signal is often converted to frequency domain using Fourier techniques. In this study, a parametric spectral approach autoregressive (AR) modelling is adopted because of its higher spectral resolution compared with Fourier approaches for the same sample size. AR modelling allows the use of smaller sample sizes or lower sampling rates to achieve the same resolution when Proc. IMechE Vol. 220 Part C: J. Mechanical Engineering Science

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compared with the Fourier technique [2]. When the signals are weak or when the noise level is high, AR modelling performs better than the Fourier techniques, as Fourier techniques have considerably more difficulty dealing with the noise in the vibration signal as noted by Mechefske [3].

2

INSTRUMENTATION

In this study, it was desired to monitor simultaneously and continuously the health of a dry vacuum pump at several measurement points. The use of piezoelectric accelerometers for instrumentation appeared infeasible on the basis of cost. Alternative solutions had to be investigated. Doscher [4] suggested that the surface micromachined capacitive ADXL105 accelerometer can rival the performance of more expensive sensors such as the conventional piezoelectric accelerometers. In that article, the author also showed that integrated micro-electrical-mechanical system (iMEMs) accelerometers have a more stable sensitivity as a function of frequency and temperature when compared with piezoelectric accelerometers. In another article [5], it has been cited how surface micromachined accelerometers have reduced the cost of real-time monitoring diagnostics from $1000 to $100 US dollars per point. The author has also illustrated how effectively micromachined accelerometers can be used to monitor machine vibrations [6]. Hence, it was decided that the performance of an iMEMs accelerometer ADXL105 from analogue devices would be evaluated as an alternative vibration sensor. The ADXL105 accelerometer is a second generation surface micromachined device that carries a differential capacitive sensor and electronic signalconditioning circuitry on a single integrated chip. The device measures accelerations with a full-scale range up to +5 g, has a sensitivity of 250 mV/g, has an on-board ‘uncommitted amplifier’ (UCA) which can be used to change its output scale factor with external resistors or to add an one- or two-pole p active filter, has a 225 mg/ Hz noise floor, a 0 – 10 kHz bandwidth of frequency response, and an on-board temperature sensor which can be used for calibrating against temperature effects for high accuracy applications. The zero-g voltage is 2.5 V, but it is ratiometric to power supply. In our application, it was decided to keep the sensitivity at 250 mV/g so that the full acceleration range may be used. With a 2.5 V zero-g voltage, the accelerometer can measure 2.5 V + 0.25  5 V ¼ 2.5 + 1.25 V without saturating the output waveform with a supply voltage of 5 V and having a safety margin of +1.25 V. Also a summing Proc. IMechE Vol. 220 Part C: J. Mechanical Engineering Science

amplifier stage with a potentiometer was added using the UCA, so that the zero-g voltage can be set at precisely 2.5 V. To keep a stable supply voltage of 5 V, a regulator stage was also added. Piezoelectric accelerometers, such as the Bru¨el and Kjær 4370V accelerometer, used as a comparison in this study have been around for many years. The desirable features of this type of accelerometer are its accuracy, low noise, and operability at high temperatures. However, they are quite expensive and need extra signal-conditioning circuitry such as preamplifiers. The specifications of the Bru¨el and Kjær 4370V accelerometer are compared with those of the micromachined integrated micro-electrical-mechanical ADXL105 accelerometer in Table 1. The noise floor of the ADXL105 is proportional to square root of the measurement bandwidth required. As the measurement bandwidth increases, the noise floor increases and the signal to noise ratio (SNR) of the measurement decreases. In our application, it was decided that the full frequency response up to 10 kHz would be monitored to include resonating frequencies for demodulated envelope spectra allowing detection of bearing defect frequencies. The minimum noise resolution for the ADXL105 was calculated from the following formula given in the datasheet [7] Noise (rms) ¼ 225 mg(Hz)1=2  (K  B)1=2

(1)

where K depends on the number of poles of the filter used with the uncommitted on-chip operational amplifier. As there was no filter stage used in our circuit design, K is 1. Hence, the minimum noise floor is calculated to be 22.5 mg. The random error, 1, of noise with 95 per cent confidence level corresponds to 2 standard deviations of the measurement. The random error for a given bandwidth and averaging time is equal to 1 1 ¼ pffiffiffiffiffiffiffiffi 2 BT0

(2)

Table 1 Piezoelectric accelerometer performance compared with ADXL105 as given in datasheet specifications Accelerometer property

Piezoelectric

ADXL105

Range Sensitivity Noise density Temperature range Frequency range

Up to 2000 g 100 pC/g 0.02 mg 274– 2508C 0.1–4800 Hz

Resonance

16 kHz

+5 g 250 mV/g 0.225 mg 240–85 8C 0 –10 000 Hz (includes DC response) Around 7 kHz

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Comparison of iMEMs and piezoelectric accelerometers

where B is the bandwidth of the measurement in hertz and T0 is the time, of the frame to be used for analysis in seconds. The signals from both accelerometers were low-pass filtered with a cut-off frequency of 10 kHz, sampled at fs ¼ 50 kHz, and sample sizes of N ¼ 8192 were used for the noise analysis. Hence, with B ¼ 10 kHz and T0 ¼ 0.16384 s, 1 was derived to be 0.012 or 1.2 per cent. To measure the noise accurately, both accelerometers were powered and mounted on the same measurement point on the pump. The pump was not switched on. Spectral analysis of the acceleration signals gave estimations of the DC level (bin 0) and the AC level (the root mean square (RMS) sum of the rest of the bins). These AC measurements are indicative of the noise present in both accelerometers. The experimental RMS value of noise measured in the laboratory (23 mg, as shown in Fig. 1(a)) agreed very closely with the theoretical value calculated from equation (1). In comparison, the RMS noise value of the Bru¨el and Kjær piezoelectric

accelerometer was measured to be 1.4 mg (Fig. 1(b)) (this was slightly less than the value stated in specification for this accelerometer). Hence, the measured noise level of the ADXL105 accelerometer was approximately 16 times greater than the noise level for the piezoelectric accelerometer. In the frequency spectrum, the ADXL105 noise floor was around 260 dB and the Bru¨el and Kjær accelerometer noise floor was around 2100 dB as shown in Fig. 2. This greater noise level of the ADXL105 limits the resolution of this accelerometer and thus its ability to detect small signal changes [6]. This becomes important when measuring very low g amplitudes. This was not a major limitation in our studies, as the pump is known to produce levels of vibration of up to +2 g (peak-to-peak) when running at 6000 r/min or 100 Hz. The accelerometer to be used for condition monitoring must be capable of accommodating peak-topeak values of higher magnitude or at least two orders of the magnitude of vibration measured in the normal working conditions in order to be used effectively in non-standard operations such as fault conditions. The higher noise level of the ADXL105 only becomes a major limitation when used in very low g level applications or when used to measure vibrations from very low-speed rotating machinery (machines that have a rotating speed of much less than 100 Hz). Fault detection and diagnosis of low speed machinery [8] is a subject of study itself where other types of transducers such as displacement transducers or proximity probes or special techniques, such as pulse shock methods or highfrequency resonance techniques [9], have to be employed.

3

Fig. 1

Noise level in both ADXL105 (a) and Bru¨el and Kjær (B&K) 4370V accelerometer (b) measured with 1.2 per cent uncertainty in the testing environment (pump off, circuitry on). Notice the change of scale from (a) to (b)

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DESIGN

A small prototype with the circuit shown in Fig. 3 was built and tested. Much care was taken when soldering the ADXL105 chip, as the chip was of the Cerpak package type, and after soldering, epoxy glue was applied to prevent resonance that can saturate the output of the accelerometer (the resonance is due to the mechanical system made up of the mass of the package and the ‘springs’ made up of the leads of the IC). Figure 4 shows the timedomain responses of the ADXL105 (a) when the chip was not glued and (b) when it was glued to the PCB. It can be clearly seen that higher g levels are measured due to resonance when the ADXL105 chip is not glued to the PCB even though the pump was rotating at 110 Hz in both cases. The resonance can also be seen in the frequency-domain spectrum Proc. IMechE Vol. 220 Part C: J. Mechanical Engineering Science

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Fig. 2

¨ el and Kjær (B&K) 4370 V (b) Noise floor measurements of ADXL105 (a) and Bru accelerometers in the frequency domain in the same testing environment (pump off, circuitry on)

in Fig. 5(a). The vibration level of the ADXL105 accelerometer spectrum rises above the piezoelectric accelerometer spectrum around 6.7 kHz as measured in the experimental set-up. In Fig. 5(b), the spectra of both accelerometers are very similar when the ADXL105 chip was glued. Figure 5(b) also shows how effectively the ADXL105 can be used in vibration analysis, as both accelerometers have produced almost identical spectra in the range of 0 – 10 kHz. Notice the close

Fig. 3

correlation in the zoomed frequency-domain spectrum from 0 to 1 kHz for both accelerometers illustrated in Fig. 6. Surface mount capacitors and resistors were used to keep the PCB size small (Fig. 7) and for easier mounting purposes. The application note [10] can be referred to for other mechanical design considerations for the ADXL105. The PCB with the soldered components was then fixed into a small nylon plastic box and the space filled up with epoxy.

Accelerometer circuit

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Fig. 4

Resonance occurring (a) when the chip is not glued to PCB and (b) when it is glued. Pump was rotating at 110 Hz in both cases. Notice the change of scale from (a) to (b)

A very important aspect of accelerometer accuracy and repeatability is the mounting technique. Optimum performance can only be guaranteed if the accelerometer is properly mounted. Accelerometers can be probed, glued, screwed, or magnetically mounted. In a production environment, permanent stud mounting for continuous monitoring systems is generally preferred, as this is the best form of mounting and mounting errors by inexperienced operators can be avoided. This is also economical in terms of reduction of manpower. In our experiment, the Bru¨el and Kjær 4370V accelerometer was magnetically mounted. To measure the quality of the measurements on a fair basis, the ADXL105 in the casing was also magnetically mounted.

4

THERMAL PROPERTIES

The issue of the survivability of the ADXL105 chip at a high temperature was another major concern in our design, as it was known that the pump can heat C07405 # IMechE 2006

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up to and in excess of 80 8C at the high vacuum end when run for more than 3 h. The temperature measured by the ADXL105 depends on the mounting point on the pump. The temperature at any given point will also vary with inlet pressure applied. At ultimate pressure, the high vacuum end is the coolest part of the pump, but at higher inlet pressures, it can get hotter. The low vacuum end can achieve temperatures greater than 100 8C even at ultimate pressure. The datasheet states that the typical operating range of the ADXL105 (AQC industrial type package) chip is 240 to 85 8C but the chip can be tested up to its absolute maximum ratings of 255 to 125 8C before experiencing any permanent structural damage. The ADXL105 accelerometer was mounted on the high vacuum end of the pump’s bearing casing, which is the hottest point of the dry vacuum pump at an inlet pressure of 50 mbar and the temperature of the device was monitored using the TOUT reading (Fig. 3) from the built-in temperature sensor for a period of 157.5 min. The pump’s motor speed was set to 110 Hz and a high gas load of 50 mbar was applied at the inlet pressure gauge. The results are shown in Fig. 8. The ADXL105 reaches steady-state temperature of 55 8C after approximately 5000 s, as the pump itself reaches its steady-state temperature for the given operating conditions. It was noted that the temperature of the ADXL105 accelerometer was always about 20 8C less than the temperature readings given by temperature transducers mounted directly inside the pump casing. The reason for this is the way the accelerometer was mounted: it was exposed to the air and it was in a position adjacent to the coolant water supply around the pump. Precautions were also taken in the mechanical design of the ADXL105 accelerometer to avert high temperature failures. The plastic nylon casing and the epoxy filling were acting as thermal insulators, thus reducing the conduction of heat from the pump to the chip inside the casing. Special thermal wires were used in the wiring. One figure of merit of the ADXL105 accelerometer is that its sensitivity is nearly invariant with temperature changes. The device’s sensitivity changes by only +1 per cent over the 240 to þ85 8C temperature range, whereas the sensitivity of typical piezoelectric accelerometers can vary as much as +10 per cent over the same temperature range [4]. However, the zero-g drift of the ADXL105 can be as much as 50 mV from its initial value over the operating temperature range from 25 to 85 8C, as stated in the datasheet. The zero-g drift of the ADXL105 was monitored with increasing temperature (Fig. 8). As the temperature of the ADXL105 increased by 28 8C, the zero-g Proc. IMechE Vol. 220 Part C: J. Mechanical Engineering Science

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Fig. 5 Resonance occurring (a) when the chip is not glued to PCB (rising of the ADXL105 vibration level near the resonating frequency 6.7 kHz) and (b) when it is glued (the spectrum of the ADXL105 and that of the B&K piezoelectric accelerometer are very similar). The pump was rotating at 110 Hz in both cases

level decreased as much as by 0.04 g, as shown by the results. This equates to 0.04 g  250 mV/ g ¼ 10 mV change and 10 mV/28 8C ¼ 0.36 mV/8C drift. This value of drift is much less than the worst-case value stated in the datasheet. A drift compensation algorithm can be implemented to correct the zero-g

drift with variations in the temperature. If the temperature is constantly monitored by the temperature sensor and the accelerometer’s zero-g drift for the corresponding temperature is subtracted out from the accelerometer’s output voltage, deviations of the readings caused by the zero-g drift with temperature can be rectified.

Fig. 6 Close correlation in the zoomed spectrum for both accelerometers

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5

Fig. 7

ADXL105 PCB with surface mount components

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HARDWARE

The following equipment was used in obtaining and analysing the vibration signals (Fig. 9). The pump has a single row of deep groove ceramic bearings at both the low and high vacuum ends. The acceleration was captured on the bearing casing on the high vacuum end in the radial direction where the inlet port of the pump is located. The pump has one stage of twolobed rotors near the high vacuum end and four stages of claws near the low vacuum end. The outlet port of the pump is located at the low vacuum end. The temperature of the pump is regulated by an external coolant water supply that prevents the pump from overheating. The motor, together with the inverter, can be used to vary the speed of the

Fig. 8 Monitoring the temperature and the zero-g drift of the ADXL105. As the temperature of the ADXL increases, the (negative) zero-g drift also increases. The pump was rotating at 110 Hz and a 50 mbar gas load was applied

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Fig. 9

Schematic configuration of the complete system. The ADXL105 and Bru¨el and Kjær 4370V accelerometers were mounted radially on the point marked X on the dry vacuum pump near the high vacuum end. The ADXL105 signal was pre-filtered with our in-house built anti-aliasing filter. The piezoelectric signal was low-pass filtered with a Bru¨el and Kjær 2692 conditioning preamplifier. The analogue to digital conversion was performed with a NI 6034E ADC card

pump, but for this experiment the speed of the motor was fixed at 110 Hz with the ultimate pressure being set to 0 mbar. The signals from the ADXL105 were filtered with a low-pass anti-aliasing filter that was custom-built in our laboratory. The filter is an eighth-order elliptic low-pass with a cut-off frequency of 10 kHz. A high order of eight was implemented as it was desired to have a steep cut-off rate at 10 kHz and an attenuation of 70 dB in the stop band. Though the elliptic filter has a highly non-linear phase and hence a not-flat group delay, the phase characteristics of the signal were not important in our study; only the amplitude level of the vibration signal is of concern. The signals from the Bru¨el and Kjær 4370V accelerometer were conditioned using a Bru¨el and Kjær 2692 preamplifier, which transduced the signal from charge to voltage form, changed its gain, and band-pass filtered it from 0.1 Hz to 10 kHz. The vibration signals were digitized using a 16-bit National Instruments NI6034E card at a sampling rate of fs ¼ 50 kHz. They were suitably amplified by the on-board gain amplifier on the ADC card before the A/D conversion took place to make full use of the available dynamic range. The generation of the Fourier and AR spectra was carried out using Labview and MATLAB signal processing packages on a 2.4 GHz Pentium-based microcomputer. The number of samples taken for each vibration record was kept at a constant size of N ¼ 8192. Proc. IMechE Vol. 220 Part C: J. Mechanical Engineering Science

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AR ANALYSIS

There are a number of practical considerations to take into account when choosing a spectral estimator. Some of these include its performance in terms of resolution, variance, and potential for real-time application. The power spectral density estimation of the acquired vibration signals was done using both FFT and AR techniques in this study. The parametric method of AR modelling was the preferred method because of its superior frequency resolution capability. In an AR model [2], the current value of the series, x(n) can be expressed as a linear function of previous values plus an error term e[n] (equation (3))

x½n ¼ 

p X

ak x½n  k þ e½n

(3)

k¼1

where e½n is the white noise with zero mean and variance s 2 , p the order of the model, and ak the AR coefficients. Once the ak coefficients of the AR model are known, PAR ðf Þ, the AR power spectrum is given by equation (4), where T is the sample period PAR ðf Þ ¼

j1 þ

s2 T j2pfkT j2 k¼1 ak e

Pp

(4)

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Comparison of iMEMs and piezoelectric accelerometers

The AR method generates an equirripple estimate of a flat power spectral density (PSD) because of the underlying all-pole model. The spectrum produced by the AR method is smooth and continuous because only the behaviour of the trends in the data series is captured [2, 11]. The traditional FFT-based method models the signal as a sum of sines and makes the assumption that the process is periodic and stationary. The performance of FFT tools degrades when applied to non-stationary signals. The AR method is known to perform better for non-stationary signals. Also because AR PSD estimators do not assume periodicity, they do not exhibit spectral leakage behaviour that is inherent in the FFT-based methods that cause the side-lobe phenomenon that can mask weaker signals. The main advantage of the FFT PSD is that it is computationally efficient. The use of FFT algorithm of Cooley and Tukey [11] for the Fourier transformation leads to a reduced computer effort, and this advantage in the computational influence is the main reason for the popularity of the FFT PSD method. The approximate frequency resolution of the FFT technique is linearly dependent on the sample size used and, in our case, can be obtained using equation (5)

Df (Hz) ¼

fs 50 000 Hz ¼ 6:1 Hz ¼ 8192 N

(5)

Such a high resolution was required because it was known beforehand that the bearing defect frequencies were closely spaced from 0 to 1000 Hz. No antileakage windowing and frame averaging were used for the FFT method. The frequency resolution of the AR method depends mainly on the order of the AR model and SNR of the signal. The selection of the optimal order of the AR model is important and affects the resolution of the AR technique [12]. Too low an order can mask spectral peaks and too high an order might introduce spurious peaks. The behaviour of the estimated spectrum with the order of the AR model is illustrated in Fig. 10. The improvement in resolution as model order is increased is evident. As p increases from 0 to 30, the AR spectra are too smooth and the important peaks of interest are not very well resolved. As p increases from 30 to 60 samples, the spectral peaks get sharper. If an order higher than the optimal model order is used, there will also be wastage of computational power. As illustrated by Schlindwein and Evans [12 –14], the AR technique is slower than the FFT technique by a factor of more than 2 for the same sample size and processor. C07405 # IMechE 2006

Fig. 10

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Modelling the vibration spectrum using the AR technique. The sampling rate was kept at fs ¼ 50 kHz

The main advantage of using the AR technique is its improved frequency resolution compared with that of the FFT approach for the same sample size, and this is particularly interesting for short frames. Also the AR technique does not require oversampling, i.e. a sampling rate just above the Nyquist frequency is sufficient. By using shorter frames and slower sampling frequency for the AR technique, savings can be achieved in the processing power requirements without sacrificing frequency resolution. The main advantages and disadvantages of both PSD methods are summarized in Table 2. To keep the model order low for our analysis, the data were down-sampled from 50 to 2 kHz to produce the results obtained in Fig. 11. The AR model order of p ¼ 60 was arbitrarily chosen. Figure 11 shows the frequency spectra of the vibration signals obtained using both the Fourier and AR techniques when the pump was rotating at 110 Hz. It can be seen that AR technique has produced a smoother spectrum than the Fourier technique. The main peaks required for analysis are clearly visible in both spectra, even though the sample size of the AR model has been decreased by 25 times because of the down-sampling. The motor was running at 110 Hz but the rotor frequency or the shaft rotational speed was seen at 107 Hz because of rotor slip. The shaft rotational frequency of 107 Hz and the first and second harmonics can be clearly seen in both FFT and AR spectra in Fig. 11. The vibrations from the dry vacuum pump can arise from two major sources: either from the defects inherent in the pump or from the geometry of the pump [1]. In the dry vacuum pump, the gas trapped in the different stages undergoes a series of Proc. IMechE Vol. 220 Part C: J. Mechanical Engineering Science

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Table 2 Comparing AR and FFT spectral estimation methods

Resolution Sampling rate Spectral variance Applicability to non-stationary signals Spectral leakage Performance in noise Computational effort

Fig. 11

AR

FFT

Better than the FFT method. Dependent on model order p used Just above twice the Nyquist rate is sufficient Less than the FFT method

Depends on frame size used

Performs better than the FFT method because shorter segments can be used Non-existent as the technique does not assume periodicity of signal Spectral resolution decreases with noise, but AR method performs better than FFT Can be computationally intensive. Processing effort required is proportional to p 2

Typically six or seven times the Nyquist rate is required for good spectral estimates Averaging required to reduce variance and to get smoother spectrum Performs poorly because longer segments are required Spectral leakage is a problem that can be reduced with the use of suitable windows, but at the cost of frequency resolution Performs poorly if SNR of signal is low Requires less processing power than AR method. Processing power required is proportional to N log N of frame size N

Comparing the AR and FFT methods for the ADXL vibration spectra (a) dB scale (b) linear scale. For the FFT technique, sampling rate was kept at 50 kHz. For AR-based spectral estimation the model order was p ¼ 60 and sampling rate was fs ¼ 2 kHz

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Comparison of iMEMs and piezoelectric accelerometers

compressions and expansions due to the synchronized rotation of the rotors. Sudden expansions of the compressed gas pockets manifest themselves as pulsation frequencies of the pump, and these pulsation frequencies, more commonly known as lobe-pass frequencies, are related to the number of lobes in each stage of the pump. The dry vacuum pump has two lobed rotors in the form of figure eight, also known as roots. The roots mechanism produces four pulses of gas per revolution of the shaft and the lobe-pass frequency of the roots will be four times the shaft rotational frequency. In Fig. 11, this peak can be seen at 428 Hz (107 Hz  4) and is clearly visible in the spectra produced by both techniques. The claw mechanism in the pump produces two gas pulses per revolution of the shaft but because this is a multi-stage pump and the rotation of the rotors are synchronized and the pulsation frequencies are additive, a lobe-pass frequency exists at six times the shaft rotational frequency. In Fig. 11, this peak can be seen at approximately 642 Hz (107 Hz  6) both in the AR and in the FFT spectra. It is to be noted that at higher gas loads this effect of pulsation frequencies will be more prominent. The frequency spectrum can also be used to identify vibration-related faults such as imbalance, misalignment, bearing failures, cavitation problems, shaft imbalance, and lubricant deficiency. By monitoring the amplitude levels of characteristic frequencies, such as ball spin frequency, ball pass frequency of outer race, ball pass frequency of inner race, and fundamental train frequency (also known as cage frequency) in the frequency spectrum [15], bearing wear failure can be diagnosed and malfunctions can be identified if severe overall vibration levels exist.

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CONCLUSIONS

This article has validated the usage of a surface micromachined accelerometer ADXL105 for spectral analysis of vibration data from a dry vacuum pump. The performance of the ADXL105 accelerometer has been verified and was found to give the same quality of data as that of a piezoelectric accelerometer. The main advantages for the use of the ADXL105 accelerometer are its low cost, its ability to measure DC response, its better temperature stability, and the presence of an on-chip signal conditioning circuitry. The main drawbacks would be that it cannot be used at high temperatures, it can resonate if proper mounting techniques are not adopted, and it has a higher noise level than piezoelectric accelerometers. However, if proper measures are taken, all these limitations can be C07405 # IMechE 2006

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overcome and micromachined accelerometers can be used successfully for machine diagnostics, as validated by this article. As this is not a low g application, the higher noise level is not a great concern. The low cost of the ADXL105 sensors allows permanent sensor placement on multiple measurement points on the dry vacuum pump and makes it economically possible to extend on-line monitoring. This is an excellent solution for acquiring consistent, reliable, and accurate data, as many of the errors and inconsistencies of temporary mounting can be prevented. The ability to use more data might improve the success of automatic fault diagnostics techniques. In this study, a parametric approach of spectral analysis, AR modelling, was also briefly introduced for fault diagnosis.

ACKNOWLEDGEMENTS This work was supported by EPSRC grant GR/S42866/ 01. The authors would like to thank BOC Edwards for the supply of the pump and for helpful comments on the draft manuscript of the article.

REFERENCES 1 Sabin, E. Vibration analysis of dry pumps. Semicond. Int., 1995, 18(8), 249 – 250. 2 Kay, S. M. and Marple, S. L., Jr. Spectrum analysis – a modern perspective. Proc. IEEE, 1981, 69(11), 1380 – 1419. 3 Mechefske, C. K. Machine condition monitoring: part 2 – the effects of noise in the vibration signal. Brit. J. NonDestr. Test., 1993, 35(10), 574 – 579. 4 Doscher, J. ADXL105: a lower-noise, wider-bandwidth accelerometer rivals performance of more expensive sensors. Analogue Dialogue, 1999, 33(6), 27– 29. 5 Doscher, J. Using iMEMS accelerometers in instrumentation applications. Proceedings of the 45th International Instrumentation Symposium, Instrument Society of America, 1999, pp. 395 – 404. 6 Doscher, J. Monitoring machine vibration with micromachined accelerometers. Sensors, 1997, 14(5), 33– 38. 7 ADXL105, Datasheet, 1999 (Analog Devices Inc.). 8 Barret, R. Low frequency machinery monitoring: measurement considerations. Wilcoxon Research, Application Note, 1993. 9 Prashad, H., Ghosh, M., and Biswas, S. Diagnostic monitoring of rolling-element bearings by high-frequency resonance technique. ASLE Trans., 1985, 28(4), 439 –448. 10 Shuster, M., Briano, B., and Kitchin, C. Mounting considerations for ADXL series accelerometers. AN-379, Analog Devices Application Note. 11 Lawrence Marple, S., Jr. Digital spectral analysis with applications, 1987 (Prentice-Hall, Inc., Englewood Cliffs, NJ).

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12 Schlindwein, F. S. and Evans, D. H. Selection of the order of autoregressive models for spectral analysis of Doppler ultrasound signals. Ultrasound Med. Biol., 1990, 16(1), 81 – 91. 13 Schlindwein, F. S. and Evans, D. H. Real time spectral analysis of doppler signals using a digital signal processor. Report no. 57, Physics in Medical Ultrasound II, 1988. 14 Schlindwein, F. S. and Evans, D. H. A real-time autoregressive spectrum analyzer for Doppler ultrasound signals. Ultrasound Med. Biol., 1989, 15(3), 263– 272. 15 Tandon, N. and Choudhury, A. A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings. Tribol. Int., 1999, 32, 469 – 480.

B e½n

T T0 x½n

bandwidth of measurement (Hz) white noise of AR process frequency (Hz) sampling rate (Hz/s) number of poles of analogue filter sample size order of AR model power spectral density estimation using AR method sampling period of AR process (Hz) time in seconds of frame(s) current sample of AR series

Df 1 s2

frequency resolution (Hz) random error variance of white noise

f fs K N p PAR (f )

APPENDIX Notation ak

AR coefficients

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