The remainder of the paper is organized as follows. The theoretical background of the proposed method for measuring the rotor speed of a motor by means of the spectral analysis of the audible noise is introduced in Section 2 . The main results of the tests performed to experimentally validate the method are presented in Section 3 , where the advantages of the proposed method will also be shown. A brief discussion of the method is presented in Section 4 . Finally, Section 5 summarizes the main findings of the work.
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Nowadays, mobile computing technology is suffering a rapid development thanks to multi-core chips and larger memories. Thus, in a wide variety of applications, smartphones are used instead of other types of sensors since they provide several advantages [ 18 ], including the low cost of equipment, that they are widely connected to the Internet, and that their number is continuously increasing. Smartphones have different sensors such as camera, microphone, accelerometer, or GPS. This opens an opportunity to use these devices to develop sensor systems capable of monitoring application areas as different as agriculture [ 19 ], human health [ 20 ], or road traffic [ 21 ], among others. In this work, a new, low-cost, non-intrusive method for in-field motor speed measurement, based on the spectral analysis of the audible motor noise is proposed. The motor noise is initially acquired using a smartphone or a web microphone, for example, and sent to a PC by means of a wired or wireless link. A MATLAB-based algorithm, especially developed for this application, loads the data file and determines the harmonic spectrum of the noise signal, from which the motor&#;s rotation speed is finally estimated. The new method can be used for measuring (and eventually recording) the motor&#;s rotor speed over time. It is very simple and easy to use since the motor noise is broadly available and does not rely on motor parameters. The proposed method is contactless, completely non-intrusive and can be used for in-field applications without any interruption or alteration to the motor&#;s service.
As mentioned previously, the interaction between alternating currents and electromagnetic fields leads to the production of the desired motor torque and additional mechanical forces in the air gap which drives mechanical vibrations. However, in addition, mechanical vibrations finally excite the surrounding air, resulting in the emission of audible motor noise. These acoustic signals have been recently used by Glowacz et al. for fault diagnosis applied to angle grinders and electric impact drills [ 17 ]. However, the motor noise, like the mechanical vibrations, must also contain a frequency component due to the rotational speed which, to the authors&#; knowledge, has thus far been overlooked for the purpose of speed measurement.
The interaction between alternating currents and electromagnetic fields that takes place in an induction motor leads to the production of the desired electromagnetic torque. Nevertheless, and as a side effect, that same interaction between alternating currents and electromagnetic fields also gives rise to the production of unwanted mechanical forces in the air gap between the stator and the rotor. These unwanted radial and axial forces lead to mechanical vibrations which are spread and transmitted through the whole motor frame and the adjoining mechanical structure. The amplitude of motor vibration at any point of the motor depends on the combination of the magnitude of the mechanical forces and the mechanical response of the motor frame and the adjoining mechanical structure [ 14 ]. Techniques for motor condition monitoring have widely taken advantage of the analysis of motor vibrations [ 15 ]. However, the vibration of motors has also been used to measure rotor speed [ 6 16 ], since the mechanical vibration also contains a component related to the rotation speed.
Although vision-based measurement systems were originally developed for special applications, their use is growing rapidly because of the increasing affordability and capability of cameras. An overview of vision-based measurement from the perspective of instrumentation and measurement (metrological) was developed in [ 11 ]. A rotational speed measurement system based on a low-cost imaging system was proposed in [ 12 ]. The method requires sticking a simple marker on the rotor shaft and using a commercial webcam to capture the rotation of the shaft at a maximum rate of 30 frames per second. Another nonintrusive webcam-based tachometer was also proposed in [ 13 ] as a vision-based rotor speed measurement system. The authors stated that the proposed tachometer can be used, for example, in industrial electrical energy audits to continuously estimate the load variation in three-phase squirrel-cage induction motors using the slip-based method. Vision-based measurement methods are contactless; however, the motor shaft must be in the field of observation of the camera in order to capture its movement.
There is a broad collection of published papers on rotational (and linear) speed measurement techniques, including contact and contactless sensors, relying on sensors based on optical reflection, and electromagnetic field fluctuations and conductive strips. A contact-type synchro was used in [ 8 ] as a primary transducer where a rotating magnetic field was used to measure rotational speed with high accuracy. The principal applications of contactless electrostatic sensors and correlation signal processing techniques to real-time measurement of rotational speed are presented in [ 9 ]. The results of the work suggested &#;that the distance between the electrodes and the surface of the rotating object is a key factor affecting the performance of the measurement system&#;. Another electrostatic sensor to measure the speed of rotational equipment under a condition of high temperature and heavy dust was also proposed in [ 10 ]. Nevertheless, although the electrostatic sensor is contactless, the measurement method remains rather invasive.
A proper measurement of motor rotation speed is a key component of most industrial drives in order, for example, to control the process, monitor the performance or identify the main parameters of the motor (or drive). As an example, the measurement of rotor speed is a simple and broadly used method in industry to estimate the motor&#;s efficiency or its mechanical load [ 3 4 ]. For continuous speed monitoring, the coupling of a tachometer to the motor shaft is often used. On other occasions, an alternative (more sophisticated and expensive) method of rotor speed estimation, by means of on-line analysis of the input current, is also used [ 5 7 ]. For occasional speed measurements a portable optical tachometer can be used, although this solution often requires sticking a reflective adhesive strip on the motor shaft. This kind of situation takes place typically during audit (monitoring) periods of the plant, when the performance of induction motors must be evaluated a few times a day (hourly) or over a few days. In such cases, the estimation of the mechanical load and/or the efficiency of the motor, based on rotor speed measurement, is a common solution since the method combines acceptable precision with low cost. For those cases, the use of a portable optical tachometer is often the preferred choice. Unfortunately, sticking the reflective strip on the motor shaft is not always possible since the shaft is not always accessible (for safety reasons, or because the shaft coupling is protected by a cover) or visible (motor inside a housing).
Electric motors are extensively used as drivers of a large variety of equipment in industry, services and even household appliances. As a result, nearly half of the electric energy produced worldwide is converted into mechanical energy by means of electric motors and integrated as added value into the process or final application. Almost 90% of industrial drives are based on three-phase squirrel-cage induction motors [ 1 2 ]. Therefore, the ways in which induction motors are selected, used, controlled, and managed have a great influence both on the electric energy bill for consumers (industrial or domestic) as well as on energy consumption, the volume of CO, and other polluting emissions for society.
&#;m
, along all the tests, the motor speed was measured twice by two different tachometers and the average value of the two speed measurements was considered as the actual rotor speed,&#;m
.The proposed method is based on the use of a smartphone to acquire and record the audible noise emitted by an induction motor, by means of two free apps downloaded from a web store. An educational electric machines test was used. Figure 1 outlines the test bench and the configuration of the different tests carried out on the induction motor. As can be seen, the core focus of the test bench is the induction motor, whose noise is acquired and recorded by means of a smartphone. That induction motor can be fed either from the network through a variable ratio transformer, which allows for the adjusting of the supply voltage, or by means of an inverter, which allows for the adjusting of both the voltage and frequency supplied to the motor. On the mechanical port, the motor shaft can be coupled either to a separately excited direct current generator, which feeds a variable resistive load allowing the adjustment of the motor load torque, or it can be left free, without mechanical load. A portable optical tachometer was used to measure the rotation speed of the motor shaft by a conventional and well-established contactless method, while a low-performance smartphone was used to acquire and record the motor noise. In order to improve the determination of the actual speed of the motor,, along all the tests, the motor speed was measured twice by two different tachometers and the average value of the two speed measurements was considered as the actual rotor speed, Appendix A includes details on the audio recording apps, smartphones, tachometers, and test bench used in this work.
f
(t
), was performed using the Fourier transform [F ( j · ω ) = &#; 0 ( N &#; 1 ) · T f ( t ) · e &#; j · ω · d t
(1)
F
(j
·ω
) represents the function in the frequency domain related to the function in the time domain,f
(t
),N
represents the number of samples through which the time signal has been acquired andT
is the uniform sampling period. In this work, the fast Fourier transform (FFT) algorithm was used, as this method takes advantage of the periodicity and symmetry in the calculation of the discrete Fourier transform and has a low computational cost [Once the appropriate test configuration was decided upon, that is, the voltage source of the motor (variable ratio transformer or inverter) and the mechanical load (DC generator with a load resistance, or no mechanical load at all), the tests on the laboratory bench were performed. After setting the proper voltage source and mechanical load, the voltage (and frequency in the case of inverter) and the load resistance (in the case of DC generator) were adjusted to reach the desired conditions of load and shaft speed. Once the value of the rotor speed was verified, a smartphone placed just in front of the nameplate of the motor was used to acquire and record the motor noise by means of the apps. The recorded *.wav file was processed with a MATLAB-based routine specifically designed to obtain the frequency decomposition of the noise signal. The frequency spectrum of the motor noise signal,), was performed using the Fourier transform [ 22 ],where) represents the function in the frequency domain related to the function in the time domain,),represents the number of samples through which the time signal has been acquired andis the uniform sampling period. In this work, the fast Fourier transform (FFT) algorithm was used, as this method takes advantage of the periodicity and symmetry in the calculation of the discrete Fourier transform and has a low computational cost [ 23 ].
ωF
(Hz or revolutions per second), from some selected frequencies of the spectrum. Finally, the corresponding rotor speed,&#;
(rad/s), is determined as:Ω = 2 · π · ω F
(2)
After performing the spectral analysis of the motor noise, the tailor-made speed estimation routine determines the fundamental rotor shaft mechanical frequency,(Hz or revolutions per second), from some selected frequencies of the spectrum. Finally, the corresponding rotor speed,(rad/s), is determined as:
&#;
, with the actual value obtained with tachometers,&#;m
, the relative value of the error speed is determined as:ε = | Ω &#; Ω m Ω m |
(3)
Comparing the noise-estimated speed,, with the actual value obtained with tachometers,, the relative value of the error speed is determined as:
σ
, was used as a measure of the dispersion of the results. It is determined as:σ = 1 N · &#; i = 1 N ( x i &#; μ ) 2
(4)
N
represents the number of recordings,xi
represents the value of thei
th recording in the data set andμ
is the mean value of the data set.The standard deviation,, was used as a measure of the dispersion of the results. It is determined as:whererepresents the number of recordings,represents the value of theth recording in the data set andis the mean value of the data set.
The flowchart sketched in Figure 2 summarizes the general procedure followed to estimate the rotor speed in experimental tests.
&#;m
= r/min = 295. rad/s (tachometers). It was obtained after applying the FFT transform to the corresponding audio file, the first step of the noise-estimation speed routine. The smartphone T1 with app &#;App1&#; (As an example, Figure 3 shows the frequency spectrum of the noise signal for a no-load motor feed at rated voltage at a measured speed of= r/min = 295. rad/s (tachometers). It was obtained after applying the FFT transform to the corresponding audio file, the first step of the noise-estimation speed routine. The smartphone T1 with app &#;App1&#; ( Appendix A ) was used to acquire and record a 30 s length noise signal with a sampling frequency of 44 kHz, well above the expected Shannon limit.
ω
1 =ωF
,ω
2 = 2·ωF
,ω
3 = 3·ωF
,ω
5 = 5·ωF
, andω
11 = 11·ωF
, corresponding to the harmonics 1, 2, 3, 5, and 11, approximately, clearly stand out. The lowest peak frequency, that is, the fundamental frequency of the noise signal,ωF
= 47. Hz, should correspond to the rotor shaft mechanical rotation frequency. Then, the remaining frequencies should be related to the second, third, fifth, and 11th harmonics of the rotor shaft frequency.ωF
1 =ω
1/1 = 47. Hz, the estimation of the rotor speed from that fundamental frequency, using (2), leads to&#;
= 2·π·ω
1 = 2·π·ωF
1 = 2·π·47. = 295. rad/s = . r/min. Using (3), the relative error for the example shown isε
= 0.%, which is quite small. The preliminary results of this case demonstrate, pending further validation experiments, that the proposed method allows a proper rotor speed estimation.As can be seen in Figure 3 , the amplitudes corresponding to five frequencies (in ascending order),= 2·= 3·= 5·, and= 11·, corresponding to the harmonics 1, 2, 3, 5, and 11, approximately, clearly stand out. The lowest peak frequency, that is, the fundamental frequency of the noise signal,= 47. Hz, should correspond to the rotor shaft mechanical rotation frequency. Then, the remaining frequencies should be related to the second, third, fifth, and 11th harmonics of the rotor shaft frequency. Table 1 shows the values of the frequencies corresponding to the five peaks of the magnitude of the spectrum of the noise signal. In this table, when the frequency of the first peak of amplitude is considered as the fundamental frequency,/1 = 47. Hz, the estimation of the rotor speed from that fundamental frequency, using (2), leads to= 2·π·= 2·π·= 2·π·47. = 295. rad/s = . r/min. Using (3), the relative error for the example shown is= 0.%, which is quite small. The preliminary results of this case demonstrate, pending further validation experiments, that the proposed method allows a proper rotor speed estimation.
ωk
=k
·ωFk
,k
&#;{2,3,5,11}, could also have been considered to determine the fundamental (the mechanical shaft frequency) asωFk
=ωk
/k
and therefore the speed:&#; k = &#; ( ω k ) = 2 · π · ω F k = ( 2 · π · ω k ) / k
(5)
Nevertheless, the remaining four peak frequencies,&#;{2,3,5,11}, could also have been considered to determine the fundamental (the mechanical shaft frequency) asand therefore the speed:
&#;mean
= &#;&#;k
/5 = 295. rad/s = .416 r/min. In this case, the relative error is reduced toεmean
= 0.%, which is smaller than that corresponding to the estimation based solely on the frequency of the first peak (7.9% error reduction). Nevertheless, in this case, the best estimation of the fundamental frequency and speed should have been based on the 11th harmonic. In this case the estimated speed result&#;
11 = 295. rad/s = .989 r/min and the corresponding relative error would have been reduced to its minimum value,ε11
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= 0.%, as shown in the last row ofωF
, can lead to a further improvement of the speed estimation.The third row of Table 1 shows the estimation of the fundamental frequency based on the five most significant harmonics of the spectrum of the motor noise, while the fourth and fifth rows show the corresponding values of the speed calculated by means of (5). Since there are five credible values of speed available, the estimation could be improved by using the mean value of the five estimated speed results,= &#;/5 = 295. rad/s = .416 r/min. In this case, the relative error is reduced to= 0.%, which is smaller than that corresponding to the estimation based solely on the frequency of the first peak (7.9% error reduction). Nevertheless, in this case, the best estimation of the fundamental frequency and speed should have been based on the 11th harmonic. In this case the estimated speed result= 295. rad/s = .989 r/min and the corresponding relative error would have been reduced to its minimum value,= 0.%, as shown in the last row of Table 1 . Although the speed can be estimated from any harmonic with a rather small error, this simple case was only intended to illustrate how a proper selection of the harmonic or harmonics used for calculating the rotor shaft frequency,, can lead to a further improvement of the speed estimation. Section 2.1 shows the proposed method to improve the fundamental frequency and the corresponding speed estimations.
The analysis of about 700 motor-noise audio files, recorded with sampling frequencies from 8 kHz to 44 kHz, shows that when truncating the spectrum after the 11th harmonic, a sufficient number of frequency peaks are obtained to be able to properly identify the rotation frequency of the motor shaft (
ωF
) and, consequently, its speed (&#;
). To optimize computing resources, the identification of the motor shaft rotation frequency (ωF
) is performed by looking for the 11 largest frequency peaks below 665 Hz. That frequency limit is just 5 Hz above 660 Hz, the frequency corresponding to the 11th harmonic for 60 Hz motors, which also includes the case of 50 Hz motors.ωm
= r/min, that is, with a shaft mechanical rotation frequency ofωF
= 47 Hz.The flowchart in Figure 4 (corresponding to the third block, &#;Algorithm&#;, in Figure 2 ) summarized the steps for computing the motor speed from the analysis of the recording of a motor-noise signal. For a better understanding, the procedure of analysis of a motor-noise recording will be described step-by-step by means of an example. The case shown corresponds to a two-pole induction motor at no-load, rotating at a measured speed (tachometer) of= r/min, that is, with a shaft mechanical rotation frequency of= 47 Hz.
W
, with the 11 most significant harmonics in magnitude is set:W = ( ω 1 , ω 2 , ω 3 , ω 4 , ω 5 , ω 6 , ω 7 , ω 8 , ω 9 , ω 10 , ω 11 )
(6)
First, the frequency spectrum is restricted from 0 Hz to 665 Hz (although it could have been limited to 555 Hz in this case). Then, the row vector of peak frequencies,, with the 11 most significant harmonics in magnitude is set:
ωn
, components ofW
, are shown in the upper part ofThe peak frequencies of the spectrum in decreasing order of magnitude,, components of, are shown in the upper part of Figure 5
W
have been identified, the algorithm proceeds to test the possibility that its first element,ω
1 (517. Hz), the frequency with the larger amplitude, could correspond to the first, second, &#;, or to the 11th harmonic of the shaft rotation frequency,ωF
. That is, it tests the possibility thatk
·ωF
=ω
1 = 517. Hz, withk
&#; {1,2,&#;11}. With that purpose, first, a draft version of the normalized frequency row vectorH
1 =H
(1·ωF
=ω
1) is computed. The elements ofH
1 = (hn
1) = (1·ωn
/ω
1) are the normalized frequency (possible harmonic orders) of the considered case (1·ωn
/ω
1). They are computed with three decimal digits.H 1 = H ( ω F = ω 1 ) = ( 1 · ω n 517. ) = ( 1.000 0.182 1.000 0.091 0.182 0.091 0.273 0.182 1.000 0.455 1.000 )
(7)
Once the vector of peak frequencieshave been identified, the algorithm proceeds to test the possibility that its first element,(517. Hz), the frequency with the larger amplitude, could correspond to the first, second, &#;, or to the 11th harmonic of the shaft rotation frequency,. That is, it tests the possibility that= 517. Hz, with&#; {1,2,&#;11}. With that purpose, first, a draft version of the normalized frequency row vector(1·) is computed. The elements of= () = (1·) are the normalized frequency (possible harmonic orders) of the considered case (1·). They are computed with three decimal digits.
H
1 has been computed, the elementshn
1 are rounded to the nearest integer when the difference between the frequency ratio,hn
1 and the nearest integer is lower than 10&#;3. In any other case, the element is discarded and replaced by 0.H 1 = H ( ω F = ω 1 ) = ( 1 0 1 0 0 0 0 0 1 0 1 )
(8)
After the draft version of the row vectorhas been computed, the elementsare rounded to the nearest integer when the difference between the frequency ratio,and the nearest integer is lower than 10. In any other case, the element is discarded and replaced by 0.
H
1 has four non-null elements and seven null elements, as can be seen inωF
=ω
1 leads to the identification of only four harmonics (non-null elements), all of them identified as the first (fundamental) harmonic of the shaft rotation frequency.In this case, the vectorhas four non-null elements and seven null elements, as can be seen in Figure 5 . This means that the hypothesisleads to the identification of only four harmonics (non-null elements), all of them identified as the first (fundamental) harmonic of the shaft rotation frequency.
H 2 = H ( 2 · ω F = ω 1 ) = ( 2 · ( ω n / 517. ) ) H 3 = H ( 3 · ω F = ω 1 ) = ( 3 · ( ω n / 517. ) ) &#; H k = H ( k · ω F = ω 1 ) = ( k · ( ω n / 517. ) ) &#; H 11 = H ( 11 · ω F = ω 1 ) = ( 11 · ( ω n / 517. ) )
(9)
Similarly, the remainder of the row vectors are obtained, as shown in Figure 5
HM
=
(hnM
), which has the highest non-null number of integers (or the highest number of possible harmonics of the considered case), is chosen as the best candidate for describing the proper harmonic order,M
, of each element of the frequency vector,W
= (ωn
). This finally leads to the best identification of the rotor shaft frequency,ωF
, as the average ratio of each non-null component divided by its respective order:ω F = ( &#; ( ω n / h n M ) ) / n
(10)
Then, the number of integer ratios, or possible harmonics, for each considered case are quantified ( Figure 5 ). Finally, the row vector,), which has the highest non-null number of integers (or the highest number of possible harmonics of the considered case), is chosen as the best candidate for describing the proper harmonic order,, of each element of the frequency vector,= (). This finally leads to the best identification of the rotor shaft frequency,, as the average ratio of each non-null component divided by its respective order:
H
11 is the vector with the highest number of integer ratios or possible harmonic coincidence. In other words, the highest number of harmonic identifications occurs under the hypothesis that the highest amplitude frequency,ω
1 = 517. Hz, represents the 11th harmonic.H 11 = ( 11 , 2 , 11 , 1 , 2 , 1 , 3 , 2 , 11 , 5 , 11 ) = ( h 1 11 , h 2 11 , h 3 11 , h 4 11 , h 5 11 , h 6 11 , h 7 11 , h 8 11 , h 9 11 , h 10 11 , h 11 11 , )
(11)
For the example in Figure 5 is the vector with the highest number of integer ratios or possible harmonic coincidence. In other words, the highest number of harmonic identifications occurs under the hypothesis that the highest amplitude frequency,= 517. Hz, represents the 11th harmonic.
H
11 leads to a likely identification of the rotor shaft frequencyω F n 11 = ( ω n / h n 11 ) , n &#; { 1 , 2 , &#; , 11 }
(12)
Ω n 11 = 2 · π · ω F n 11 = 2 · π · ( ω n / h n 11 ) , n &#; { 1 , 2 , &#; , 11 }
(13)
It is interesting to observe that, in this case, under that hypothesis, five different harmonics (1, 2, 3, 4, 5, and 11) of the rotor shaft frequency are identified. Each element ofleads to a likely identification of the rotor shaft frequencyand rotor speed,
ωF
, is obtained as the average ratio of each component divided by its respective order (10). In this case, the result is:ω F = 1 11 &#; n = 1 11 Ω n 11 = 1 11 &#; n = 1 11 ω n h n 11 = 47. Hz
(14)
Finally, the estimation of the rotor shaft (fundamental) frequency,, is obtained as the average ratio of each component divided by its respective order (10). In this case, the result is:
Thus, the estimation of the motor speed is calculated using (2), resulting in
&#;
= .3 r/min.Want more information on coaxial drone? Feel free to contact us.