Method and device for monitoring a bearing equipping a rotary device

Abstract

A method includes obtaining a vibration signal acquired by an accelerometer sensor; eliminating a deterministic component of the vibration signal; obtaining, for a determined defect, a characteristic theoretical frequency of this defect and a determined maximum deviation around this theoretical frequency; computing, as a function of a cyclic frequency, an integrated cyclic coherence of the processed vibration signal; estimating an actual frequency of the defect on the basis of the integrated cyclic coherence, of the theoretical frequency of the defect and of the maximum deviation; computing a diagnostic indicator of the defect by summing M integrated cyclic coherences of the vibration signal evaluated as M cyclic frequencies respectively equal to M harmonics of the estimated actual frequency of the defect; comparing the diagnostic indicator of the defect with a predetermined threshold, and in the event of it being exceeded, detecting the defect on the bearing.

Claims

1. A method for monitoring a bearing equipping a rotary device, comprising: obtaining a vibration signal acquired by an accelerometer sensor, said vibration signal containing a vibrational signature of the bearing; processing the vibration signal comprising elimination of a deterministic component of the vibration signal; obtaining, for a determined defect liable to affect the bearing, a characteristic theoretical frequency of the defect and a determined maximum deviation around the theoretical frequency; computing, as a function of a cyclic frequency, an integrated cyclic coherence of the processed vibration signal averaged over a predetermined band of spectral frequencies; estimating an actual frequency of the defect on a basis of the integrated cyclic coherence, of the characteristic theoretical frequency of the defect and of the determined maximum deviation around this theoretical frequency; computing a diagnostic indicator of the defect by summing an integer number M of integrated cyclic coherences of the vibration signal evaluated as M cyclic frequencies respectively equal to M harmonics of the estimated actual frequency of the defect; comparing the diagnostic indicator of the defect with a predetermined threshold for the defect; and in an event of the threshold being exceeded by the diagnostic indicator, detecting the defect on the bearing.

2. The monitoring method as claimed in claim 1, wherein the processing comprises spectral whitening of the vibration signal.

3. The monitoring method as claimed in claim 1, wherein the computing the integrated cyclic coherence comprises: estimating, for a given cyclic frequency, the cyclic correlation of the processed vibration signal as a function of a spectral frequency; computing, on a basis of the estimated cyclic correlation, the cyclic coherence of the processed vibration signal for said given cyclic frequency as a function of the spectral frequency; and averaging, over said predetermined band of spectral frequencies, a square of an amplitude of the cyclic coherence of the processed vibration signal computed for said given cyclic frequency, a result of said average supplying the integrated cyclic coherence for said given cyclic frequency.

4. The monitoring method as claimed in claim 3, wherein the cyclic correlation of the processed vibration signal is estimated with a Welch estimator.

5. The monitoring method as claimed in claim 1, wherein the estimating the actual frequency of the defect comprises computing of the integrated cyclic coherence for a plurality of cyclic frequencies contained in an interval defined between the characteristic theoretical frequency of the defect minus the maximum deviation defined for the theoretical frequency and the characteristic theoretical frequency of the defect plus the maximum deviation defined for the theoretical frequency, the actual frequency of the defect corresponding to the cyclic frequency among said plurality of cyclic frequencies for which the integrated cyclic coherence is at a maximum.

6. The monitoring method as claimed in claim 5, wherein two consecutive cyclic frequencies of said plurality of cyclic frequencies, respectively denoted α and α+Δα, are chosen such that a ratio α/dα is an integer number.

7. The monitoring method as claimed in claim 1, wherein the integer number M is contained between 6 and 10.

8. The monitoring method as claimed in claim 1, further comprising giving notification of said defect comprising at least one item of information from among at least one of: an identification of the defective bearing; an indication of a defective element on said bearing; and an indication of a severity of the defect detected on the bearing.

9. The monitoring method as claimed in claim 1, wherein the vibration signal has been acquired by the accelerometer sensor in a stationary rating of the rotary device.

10. The monitoring method as claimed in claim 1, wherein the cyclic frequency is normalized with respect to a rotation frequency of the bearing.

11. A non-transitory information medium readable by a computer on which is stored a computer program including instructions for executing the method as claimed in claim 1, when the program is executed by a processor.

12. A device for monitoring a bearing equipping a rotary device, said monitoring device comprising: at least one memory; an interface for communicating with an accelerometer sensor; and a processor configured to: obtain a vibration signal acquired by the accelerometer sensor, said vibration signal comprising a vibrational signature of the bearing; process the vibration signal including eliminating a deterministic component of the vibration signal; obtain for a determined defect liable to affect the bearing, a characteristic theoretical frequency of the defect and a determined maximum deviation around the theoretical frequency; compute, as a function of a cyclic frequency, an integrated cyclic coherence of the processed vibration signal averaged over a predetermined band of spectral frequencies; estimate an actual frequency of the defect on a basis of the integrated cyclic coherence, of the characteristic theoretical frequency of the detect and of the determined maximum deviation around the theoretical frequency; compute a diagnostic indicator of the defect by summing an integer number M of integrated cyclic coherences of the vibration signal evaluated as M cyclic frequencies respectively equal to M harmonics of the estimated actual frequency of the detect; and compare the diagnostic indicator of the defect with a predetermined threshold for this defect and detect the defect on the bearing in an event of the threshold being exceeded by the diagnostic indicator.

13. The monitoring device as claimed in claim 12, wherein the bearing is a ball bearing or a roller bearing and the rotary device is installed in an aircraft.

14. An aircraft engine comprising at least one bearing equipping a rotary device of the aircraft engine, at least one accelerometer sensor able to acquire a vibration signal comprising a vibrational signature of said bearing, and a device for monitoring the bearing as claimed in claim 12.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other features and advantages of the present invention will become apparent from the description given below, with reference to the appended drawings which illustrate an exemplary embodiment thereof, devoid of any limiting nature. In the figures:

(2) FIG. 1 schematically represents a device for monitoring a bearing in accordance with the invention in a particular embodiment;

(3) FIG. 2 represents the hardware architecture of the bearing monitoring device of FIG. 1; and

(4) FIG. 3 illustrates, in the form of a block diagram, the main steps of the monitoring method according to the invention in a particular embodiment in which it is implemented by the monitoring device of FIG. 1.

DETAILED DESCRIPTION OF AN EMBODIMENT

(5) FIG. 1 shows, in its environment, a device 1 for monitoring a bearing 2 equipping a rotary mechanical device 3 in accordance with the invention in a particular embodiment.

(6) In the example envisioned in FIG. 1, the bearing 2 is a ball bearing and the rotary device 3 equipped with this ball bearing is for example a compressor of a turbojet engine 4 in accordance with the invention. The bearing 2 is here assumed to permit the driving in rotation of a shaft of the compressor 3 of the turbojet engine 4 about a predefined axis of rotation.

(7) This example is however given only by way of illustration, and the invention can also be applied to other contexts. Thus for example, the bearing 2 can be a roller bearing, the rotary device 3 can be any rotary mechanical device, an element of which is driven in rotation by means of the bearing 2, and other aircraft engines than a turbojet engine can be envisioned. The invention can also be applied to another context than the aeronautical context.

(8) In accordance with the invention, the monitoring device 1 is able to effect the monitoring of the bearing 2, on the basis of a vibration signal acquired by a sensor 5 equipping the turbojet engine 4 over at least one predefined time period of duration T. The sensor 5 is an accelerometer placed here on the casing of the compressor 3 so as to sense the vibrations emitted by the bearing 2 and more specifically by its elements (the vibrational signature of the bearing within the meaning of the invention).

(9) In a manner known per se, a ball bearing is composed of various elements, and more specifically two coaxial bushes (a so-called inner or internal bush and a so-called outer or external bush) between which are placed balls held spaced apart by a cage. In this way, the balls can roll between the inner bush and the outer bush. The invention is intended to allow the detection of a defect affecting at least one of these elements.

(10) The placement of the accelerometer 5 to allow it to acquire a vibration signal containing the vibrational signature of the bearing 2 does not pose any difficulty to those skilled in the art, and depends on the rotary mechanical device under consideration and on the context in which the latter is used. It is not described in detail here. In the case of a shaft of a compressor of a turbojet engine as envisioned in FIG. 1, the accelerometer 5 is for example placed on the casing of the compressor 3.

(11) In a variant, the accelerometer 5 can be placed in a place further from the bearing 2 strictly speaking as long as it makes it possible to acquire a signal containing a vibrational signature of the bearing 2 with a signal-to-noise ratio preferably greater than 5%.

(12) The time-based vibration signal denoted X(t) acquired by the accelerometer 5 over the period T when the rotary mechanical device 3 is in rotation, is processed by an acquisition system integrated here into the accelerometer 5 comprising a conditioner, a sample and hold and an analog-to-digital converter. Such an acquisition system is known per se, and is not described in detail here. It delivers a sampled digital signal at a predefined sampling frequency Fs derived from the vibration signal X(t) acquired by the accelerometer. The sampling frequency Fs is chosen to be high enough to preserve the kinetic and dynamic information about the bearing 2. In an aeronautical context such as that envisioned in FIG. 1, Fs is taken as equal, for example, to 50 kHz. It is assumed here that the period T over which the vibration signal X is acquired is a multiple L of the sampling period, i.e. T=L/Fs. L denotes in an equivalent manner the digital length of the vibration signal (i.e. the number of samples Xb(n) derived by the acquisition system on the basis of the vibration signal X(t) acquired by the accelerometer 5).

(13) The sampled vibration signal (vibration signal within the meaning of the invention), the samples of which are referred to in the rest of the description as X.sub.b(n), where n denotes an integer greater than 1, is then transmitted to the monitoring device 1 for analysis with a view to detecting the presence of any defect on the bearing 2. In the embodiment described here, this analysis is intended to be carried out in real time, and the monitoring device 1 is installed on board the aircraft propelled by the turbojet engine 4 (for example in an electronic control unit of this turbojet engine 4).

(14) In a variant, the monitoring device 1 can be located in a remove device, for example in the example envisioned here, in a device on the ground able to communicate via a telecommunications network with the accelerometer 5 or with an electronic control unit of the turbojet engine 4 able to retrieve the vibration signal X(t) acquired by the accelerometer 5.

(15) In the embodiment described here, the monitoring device 1 has the hardware architecture of a computer, as illustrated in FIG. 2.

(16) It comprises in particular a processor 6, a random access memory 7, a read-only memory 8, a non-volatile flash memory 9 along with communicating means 10 particularly allowing the monitoring device 1 to communicate with the accelerometer 5 to obtain the vibration signal s(t) generated by the bearing 2 and acquired by the accelerometer. These communicating means for example comprise a digital data bus or any other communication interface, in particular a communication interface on a telecommunications network, when the monitoring device 1 is not found on board the aircraft propelled by the turbojet engine 4.

(17) The read-only memory 8 of the monitoring device 1 forms a storage medium in accordance with the invention, readable by the processor 6 and on which is stored a computer program PROG according to the invention.

(18) The computer program PROG here defines functional and software modules, configured to implement a method for monitoring the bearing 2 in accordance with the invention. These functional modules are based on and/or control the hardware elements 6-10 of the monitoring device 1 mentioned previously. Here they include in particular, as illustrated in FIG. 1: a first obtaining module 1A, configured to obtain the vibration signal s(t) acquired by the accelerometer 5; a module 1B for processing the vibration signal s(t), configured to eliminate a deterministic component of the vibration signal; a second obtaining module 1C, configured to obtain for a determined defect denoted d liable to affect the bearing 2, a characteristic theoretical frequency of this defect written β.sub.d.sup.th and a maximum deviation denoted δβ.sub.d determined around this theoretical frequency. This maximum deviation characterizes the maximum possible deviation that is allocated between the characteristic theoretical frequency of the defect and the actual or exact frequency of this defect; a first computing module 1D, configured to compute, as a function of the cyclic frequency here denoted α, a so-called integrated cyclic coherence of the processed vibration signal, averaged over a predetermined band of spectral frequencies chosen here so as to maximize the signal-to-noise ratio; an estimating module 1E, configured to estimate the actual frequency of the defect denoted β.sub.d.sup.act on the basis of the integrated cyclic coherence computed by the first computing module 1D, the characteristic theoretical frequency β.sub.d.sup.th of the defect and the determined maximum deviation δβ.sub.d around this theoretical frequency; a second module 1F for computing a diagnostic indicator of the defect, configured to compute this indicator by summing an integer number M of integrated cyclic coherences of the processed vibration signal evaluated as M cyclic frequencies respectively equal to M harmonics of the estimated actual frequency of the defect; a comparing module 1G, configured to compare the diagnostic indicator of the defect computed by the second computing module 1F with a predetermined threshold for this defect and to detect the defect on the bearing in the event of the threshold being exceeded by the diagnostic indicator.

(19) In the embodiment described here, the monitoring device 1 further possesses a notifying module 1H, able to notify a user or a remote equipment item of the existence of a defect on the bearing 2 where applicable. This notifying module 1H can in particular rely on the communicating means 10 of the monitoring device 1 or on input/output means thereof, such as for example a screen or a microphone able to signal the detection of a defect on the bearing 2 to a user installed near the monitoring device 1.

(20) The functions of these different modules will now be described in more detail with reference to the steps of the monitoring method according to the invention.

(21) FIG. 3 illustrates, in the form of a block diagram, the main steps of a monitoring method according to the invention in a particular embodiment in which it is implemented by the monitoring device 1 to monitor the bearing 2 equipping the compressor 3 of the turbojet engine 4.

(22) It is assumed here that the accelerometer 5 is configured so as to acquire over a period of time of duration T=L/Fs, an acceleration vibration signal X(t) generated by the bearing 2 while the compressor 3 is in rotation driven by the bearing 2. The accelerometer 5 is configured here to acquire the vibration signal X(t) when the compressor 3 operates in a stationary or quasi-stationary rating: in the example envisioned here, this means that the rotation speed of the compressor and/or its load (i.e. its torque) are constant or quasi-constant (variation of less than 5% in the rotation speed of the compressor and its load). It should be noted that the duration T must not be chosen too short so as to ensure the accuracy of the diagnostic indicators derived by the invention. For a sampling frequency Fs=50 kHz, a duration T=2 s is a good trade-off.

(23) The vibration signal X(t) acquired by the accelerometer 5 is sampled by the acquisition system of the accelerometer 5, at the sampling frequency Fs. The sampled vibration signal Xb(n), n=1, . . . , L, is transmitted by the acquisition system of the accelerometer 5 to the monitoring device 1, and more particularly to its first obtaining module 1A (step E10). The sampled vibration signal Xb(n) is more simply referred to in the rest of the description as the “vibration signal”.

(24) The vibration signal Xb(n), n=1, . . . , L is supplied by the obtaining module 1A to the processing module 1B of the monitoring device 1. In a manner known per se, the vibration signal Xb(n), n=1, . . . , L comprises a deterministic component and a random component; it is in this random component that manifest, where applicable, the vibrations related to the defect(s) affecting the bearing 2.

(25) To better highlight the vibrations related to the defect(s), where applicable, affecting the bearing 2, the processing module 1B processes the vibration signal Xb(n), n=1, . . . , L in order to eliminate its deterministic component (step E20).

(26) In the embodiment described here, the elimination of the deterministic component of the vibration signal is carried out by the processing module 1B via a spectral whitening operation. To carry out this operation, the processing module 1B first computes the discrete Fourier transform of the vibration signal Xb(n). This discrete Fourier transform is denoted DFT.sub.n.fwdarw.m{Xb(n)}. It is defined in a known manner by:

(27) ${\mathrm{DFT}}_{n.fwdarw.k}^W\left\{X\left(n\right)\right\}={.Math.}_{n=0}^{W-1}X\left(n\right)e^{-j2\pi \left(n\Delta t\right)\left(k\Delta f\right)}$$\mathrm{where}:\Delta f=\frac{1}{\Delta t.Math.W}=\frac{F_s}{W}$

(28) denotes the frequency resolution, W representing the size of the window over which the discrete Fourier transform is computed, and

(29) $\Delta t=\frac{1}{F_s}$

(30) denotes the time-based resolution.

(31) Then the processing module 1B divides the discrete Fourier transform obtained by the modulo of the discrete Fourier transform, and computes the inverse discrete Fourier transform of the result obtained. In other words, the processing module 1B computes the following signal X(n), for n=1, . . . , L (processed vibration signal within the meaning of the invention):

(32) $X\left(n\right)={\mathrm{IDFT}}_{m.fwdarw.n}^L\left\{\frac{{\mathrm{DFT}}_{n.fwdarw.m}\left\{\mathrm{Xb}\left(n\right)\right\}}{.Math.{\mathrm{DFT}}_{n.fwdarw.m}\{\mathrm{Xb}\left(n\right).Math.}\right\}$

(33) where IDFT.sub.m.fwdarw.n.sup.L denotes the inverse discrete Fourier transform defined as follows

(34) ${\mathrm{IDFT}}_{n.fwdarw.k}^W\left\{X\left(n\right)\right\}=\frac{1}{W}{.Math.}_{n=0}^{W-1}X\left(n\right)e^{+j2\pi \left(n\Delta t\right)\left(k\Delta f\right)}$

(35) considering the same notations used during the definition of the discrete Fourier transform.

(36) In this way, the phase of the vibration signal Xb(n) is preserved.

(37) This whitening operation has the advantage of being simple to implement.

(38) In a variant, other techniques can be applied by the processing module 1B to eliminate the deterministic component of the signal Xb(n). Such a technique is for example described in the document by N. Sawalhi et al. Titled “Signal pre-whitening using cepstrum editing (liftering) to enhance fault detection in rolling element bearings”, Proceedings of the 24th International Congress on Condition Monitoring and Diagnostics Engineering Management (COMADEM), 2011. It consists in cancelling the entire complex cepstrum of the vibration signal by keeping only the component of the signal relating to the zero frequency.

(39) The processed (and whitened) vibration signal X(n), n=1, . . . , L is transmitted to the first computing module 1D of the monitoring device 1 so that it can analyze the cyclostationarity of the signal. Specifically, the presence of a defect on the bearing 2 manifests as a component in the cyclostationary signal which manifests as a periodic autocovariance function. This property of cyclostationarity is due mainly, on the one hand, to the recurrence of the defect on a periodic basis (related to the rotation of the rotary device driven by the bearing), and on the other hand, to the presence of a fluctuation between the time of arrival of the impacts caused by the slippage of the balls of the bearing 2.

(40) Each defect d liable to affect a bearing is characterized by a specific frequency. No limitation is attached to the nature of the defect d, the latter being able to concern one or more elements of the bearing. Thus for example, the defect d can be a defect of the outer bush of the bearing 2, a defect of the inner bush of the bearing 2, a defect of the cage of the bearing 2 or of a ball of the bearing 2. Each of these defects is characterized by a characteristic frequency that is specific to it.

(41) This characteristic frequency of the defect d under consideration can be easily estimated (obtained) theoretically by the second obtaining module 1C of the monitoring device 1 on the basis of the knowledge of the geometrical features of the bearing 2 and its kinetics (step E30). The characteristic theoretical frequency of the defect d is denoted β.sub.d.sup.th. The geometrical features of the bearing 2 can be easily obtained from the technical data sheet of the bearing 2. The kinetics of the bearing (i.e. its rotation speed) can be obtained via a sensor placed appropriately within the compressor 3, in a manner known per se. Thus, by way of illustration: the characteristic theoretical frequency f.sub.d=bext of a defect d of the outer bush of the bearing is given by:

(42) $f_{d=\mathrm{bext}}=\frac{f_r}{2}{N}_B\left(1-\frac{D_B\cos \psi }{D_p}\right)$ the characteristic theoretical frequency f.sub.d=bint of a defect d of the inner bush of the bearing is given by:

(43) $f_{d=\mathrm{bint}}=\frac{f_r}{2}{N}_B\left(1+\frac{D_B\cos \psi }{D_p}\right)$ the characteristic theoretical frequency f.sub.d=c of a defect d of the cage of the bearing is given by:

(44) $f_{d=c}=\frac{f_r}{2}\left(1-\frac{D_B\cos \psi }{D_p}\right)$ the characteristic theoretical frequency f.sub.d=bille of a defect d of a ball of the bearing is given by:

(45) $f_{d=\mathrm{bille}}=\frac{f_r}{2}{N}_B\left(1-{\left(\frac{D_B\cos \psi }{D_p}\right)}^2\right)$

(46) where: f.sub.r denotes the mechanical rotation frequency of the bearing 2; N.sub.B denotes the number of balls of the bearing 2; D.sub.B denotes the diameter of the balls of the bearing 2; D.sub.P denotes the average diameter of the bearing 2; and ψ denotes the angle of contact of the bearing 2.

(47) The second obtaining module 1C also obtains for each defect d under consideration a determined maximum deviation δβ.sub.d around the characteristic theoretical frequency β.sub.d.sup.th of the defect d. In the example envisioned here, it is assumed for the sake of simplification that this maximum deviation is the same in percentage whatever the defect d envisioned, i.e. δβ.sub.d=Aβ.sub.d.sup.th with A denoting a real constant independent of the defect d. In practice, the inventors have found that it suffices to choose a maximum deviation equal to a few percent of the characteristic theoretical frequency of the defect; for example A=3%.

(48) Then, in the embodiment described here, the first computing module 1D of the monitoring device 1 computes the cyclic coherence of the processed vibration signal X(n), n=1, . . . , L (step E40).

(49) In a known manner, the cyclic coherence of a signal is a statistical measurement that makes it possible to measure for each so-called cyclic frequency the degree of correlation between the signal and this same signal frequency-shifted. A coherence close to one for a cyclic frequency α indicates a strong correlation between the components of the signal under consideration at the frequencies f and f−α.

(50) To compute the cyclic coherence of the signal X(n) at the cyclic frequency α, n=1, . . . , L, the first computing module 1D here uses a Welch estimator of the cyclic correlation of the signal, which is written as follows, to the nearest factor:
(kΔf)=Σ.sub.s.sup.S-1DFT.sub.n.fwdarw.k.sup.Nw{w.sub.s(n)×(n)e.sup.jπαnΔt}*DFT.sub.n.fwdarw.k.sup.Nw{w.sub.s(n)×(n)e.sup.−jπαnΔt}

(51) where: * denotes the conjugation operator; w(n) denotes a sliding window (e.g. Hanning window, half-sine window, etc.) and w.sub.s(n)=w.sub.s(n−sR) is the shifted version of the sliding window with 1<R<Nw, Nw denoting an integer number (e.g. a power of 2) representing the size of the Welch window, Nw-R denoting the overlap between the windows; S is the largest integer less than or equal to (L−Nw)/R+1; Δf denotes the frequency-based or spectral resolution, which is equal to 1/(Δt.Math.Nw). The size of the Welch window Nw will preferably be chosen to have a spectral resolution in the order of a few hundred Hertz in the application situation envisioned here; k is an integer number, denoting the spectral channel under consideration.

(52) Here the resolution of the cyclic frequency is considered to be Δα=1/T for computing the cyclic correlation.

(53) It should be noted that in the Welch estimator defined above, the cyclic frequency α is a frequency expressed in Hertz.

(54) Of course, other estimators can be used in a variant to estimate the cyclic correlation of the processed vibration signal, such as for example an estimator by cyclic periodogram, an estimator by smoothed cyclic periodogram, an estimator by cyclic modulation spectrum, etc.

(55) Then the computing module 1D derives on the basis of the Welch estimator thus computed the cyclic coherence of the signal X(n), n=1, . . . , L as follows:

(56) $\stackrel{}{¯}\left(k\Delta f\right)=\frac{\left(k\Delta f\right)}{{\left(\left(k\Delta f-\alpha /2\right)\left(k\Delta f+\alpha /2\right)\right)}^{1/2}}$

(57) It should be noted that the cyclic correlation and the cyclic coherence thus computed are functions of the spectral frequency kΔf and are indexed by the cyclic frequency α (they are therefore also a function of this cyclic frequency), the latter being expressed in Hertz. The spectral frequency highlights the dynamic characteristics of the system under consideration, whereas the cyclic frequency pertains to the modulations (mainly related to the defect, where applicable, affecting the bearing 2). The inventors therefore wished to keep the cyclic information carried by the cyclic frequency, but averaged the information carried by the spectral frequency over a chosen frequency band so as to maximize the signal-to-noise ratio.

(58) For this purpose, the first computing module 1D computes a so-called integrated cyclic coherence by evaluating the average of the square of the amplitude of the cyclic coherence with respect to the cyclic frequency over a band of frequencies chosen so as to maximize the signal-to-noise ratio (step E50). This band of frequencies is defined here by the interval [k1Δf;k2Δf], where k1 and k2 denote two integers. The integrated cyclic coherence computed by the first computing module 1D is thus given by the following expression:

(59) 0$=\frac{1}{k1-k1+1}\underset{k1}{\overset{k2}{.Math.}}{.Math.\stackrel{}{¯}\left(k\Delta f\right).Math.}^2$
In the example envisioned here, for a sampling frequency Fs=50 kHz, k1Δf˜1 kHz and k2Δf˜20 kHz are chosen. These values make it possible to minimize the contribution of the stationary noise at low frequencies (below k1Δf) and eliminate cyclic aliasing at high frequencies (above k2Δf).

(60) Of course, these values are only given by way of illustration and other values can be considered. In general, it will preferably be ensured that k2Δf<Fs−α.sub.max where α.sub.max denotes the maximum cyclic value sought and therefore depends on the characteristic theoretical frequency of the defect and on its order of harmonics (here taking into account the principle that the useful information for diagnosing a defect of the bearing is generally not found at the ends).

(61) It should moreover be noted that in the embodiment described here, the square of the amplitude of the cyclic coherence has been considered when taking the average computed to obtain the integrated cyclic coherence. In a variant, it can be envisioned to raise the cyclic coherence to another order than the second order, for example the first order or the fourth order.

(62) The integrated cyclic coherence computed by the first computing module 1D is then used by the monitoring device 1 to derive a diagnostic indicator of the defect d.

(63) More specifically, for this purpose, the monitoring device 1, via its estimating module 1E, first estimates the “actual” (or else exact) frequency of the defect d (step E60). As mentioned previously and by definition, this characteristic actual frequency of the defect is contained within the interval [β.sub.d.sup.th−δβ.sub.d; β.sub.d.sup.th+δβ.sub.d]. To estimate this actual frequency, the estimating module 1E computes the integrated cyclic coherence for a plurality of cyclic frequencies α contained in this interval. In the embodiment described here, one assumes a resolution, respectively denoted Δα between two consecutive cyclic frequencies considered by the estimating module 1E chosen such that the ratio α/Δα is an integer number. This criterion makes it possible to optimize the computing cost of the integrated cyclic coherence at the different cyclic frequencies under consideration.

(64) Then the estimating module 1E estimates the actual frequency of the defect, denoted β.sub.d.sup.act, as being the value of the cyclic frequency corresponding to the maximum value of the computed integrated cyclic coherences, or:
β.sub.d.sup.act=argmax.sub.β.sub.d.sub.th.sub.−δβ.sub.d.sub.≤α≤β.sub.d.sub.th.sub.+δβ.sub.d

(65) It is noted that in the case where the bearing 2 does not have the defect d, the value β.sub.d.sup.act has no significance strictly speaking and does not have the frequency of a defect of the bearing. This does not constitute a problem in itself; this is because it is highly improbable that the bearing 2 is affected with a separate defect from the defect d having an actual frequency contained in the interval [β.sub.d.sup.th−δβ.sub.d; β.sub.d.sup.th+δβ.sub.d].

(66) Then the monitoring device 1, by way of its second computing module 1F, computes a diagnostic indicator of the defect d (step E70). This indicator, denoted μ.sub.X.sup.d, is the sum of the integrated cyclic coherences evaluated as M cyclic frequencies respectively equal to the M harmonics of the estimated actual frequency β.sub.d.sup.act of the defect, M denoting an integer number, or:

(67) ${\mu }_X^d\left(M\right)=\underset{m=1}{\overset{M}{.Math.}}$

(68) This indicator advantageously measures the cyclostationarity in the signal X, and consequently the contribution of the defect d associated with the frequency β.sub.d.sup.act.

(69) In the embodiment described here, M has a predetermined value chosen between 6 and 10.

(70) It should be noted that M denotes the number of harmonics of the defect d under consideration. The number of harmonics present in the signal generated by the defect depends on the impulsiveness of the signal, which in turn is linked to the severity of the defect. Thus, taking a large value of M supplies more information about the condition of the defect. However, taking a smaller value of M makes it possible to improve the earliness of the detection of the defect. Specifically, the inventors have found that in the case of a distributed defect, few harmonics are present in the integrated cyclic coherence, so the sum of a large number of harmonics leads to an increase in the estimating error, and therefore reduces the effectiveness of the computed indicator in terms of detection earliness.

(71) In a variant embodiment, the estimating module 1F can estimate different diagnostic indicators by considering different values of the integer M.

(72) The diagnostic indicator μ.sub.X.sup.d(M) thus computed is supplied to the comparing module 1G of the monitoring device 1. This then compares the indicator μ.sub.X.sup.d(M) with a predetermined alert threshold for the defect d, denoted THR(d) (step E80). This threshold is chosen so as to allow the detection of the defect d. It can be previously determined empirically by observing sound bearings and bearings having the defect d, or by a statistical computation based on the assumption of stationarity in the sound case. The threshold value THR(d) must not be chosen too high so as to ensure early detection, or too low to avoid numerous false alerts.

(73) If the comparing module 1G determines that the diagnostic indicator exceeds the threshold THR(d) (i.e. is greater than it) (yes answer to the test step E90), then it detects that the bearing 2 is affected with the defect d (step E100).

(74) In the embodiment described here, notification is then given of this detection by the notifying module 1H via an alert message, comprising all or part of the following information: identification of the defective bearing (namely here the bearing 2); indication of the defective element on the bearing (depends on the defect d detected); and indication of the severity of the defect detected on the bearing 2 (given by the value of the indicator μ.sub.X.sup.d(M)).

(75) Then the monitoring of the bearing 2 is resumed (repetition of the steps E10 to E100).

(76) It is noted that what has just been described for the defect d can be done for different defects liable to affect the bearing 2. In this way, the monitoring device 1 is in a position to provide a differential diagnostic and to identify which defect affects the bearing 2, i.e. to locate the origin or origins of the degradations undergone by the bearing 2 (inner bush, outer bush, balls, cage).

(77) In the embodiment described here, the vibration signal X(t) acquired by the accelerometer 5 has been acquired during a stationary rating of the compressor 3.

(78) In another embodiment of the invention, it is possible to consider a vibration signal acquired when the rotation rating of the compressor 3 is encountering a certain amount of variability, typically up to 15-20%.

(79) In such a context, one preferably considers a normalized cyclic frequency denoted {tilde over (α)} with respect to the average rotation frequency f.sub.r in Hertz of the bearing 2 over the acquisition period T under consideration, or:

(80) $\overline{\alpha }=\frac{\alpha }{f_r}$

(81) Such a normalized frequency is also more commonly called “order”.

(82) In this embodiment, in step E40, the first computing module 1D then uses the Welch estimator of the cyclic correlation of the corrected-phase signal, which is written as follows, to the nearest factor:

(83) $\mathrm{DF}{T}_{n.fwdarw.k}^{Nw}{\left\{w_s\left(n\right)X\left(n\right)e^{j\pi \tilde{\alpha }\theta \left(n\right)/2}\right\}}^{*}{\mathrm{DFT}}_{\mathrm{n\Delta t}.fwdarw.\mathrm{k\Delta }f}^{Nw}\left\{w_s\left(n\right)X\left(n\right)e^{-j\pi \overline{\alpha }\theta \left(n\right)/2}\right\}$

(84) where θ(n) denotes the angular measurement of a reference shaft (rotation shaft of the compressor 3 here) which makes it possible to evaluate the rotation frequency f.sub.r of the bearing.

(85) The first computing module 1D then derives from this Welch estimator the corrected-phase cyclic frequency of the signal X(n), n=1, . . . , L in the following way:

(86) $\stackrel{}{¯}\left(k\Delta f\right)=\frac{\stackrel{}{¯}\left(k\Delta f\right)}{{\left(\left(k\Delta f-\tilde{\alpha }.Math.f_r/2\right)\left(k\Delta f+\tilde{\alpha }.Math.f_r/2\right)\right)}^{1/2}}$

(87) The other steps of the method remain unchanged as long as one considers normalized frequencies instead of frequencies expressed in Hertz. Thus, the theoretical frequencies of the defects are the same as those previously introduced to the nearest factor f.sub.r (i.e. these theoretical frequencies are divided by f.sub.r).

(88) Moreover, in the embodiments described here, for the sake of simplification, the signal is considered to come from a single accelerometer. The invention can however be applied to several accelerometers. In the same way, it makes it possible to simultaneously monitor several bearings.

(89) The invention thus proposes a robust technique for monitoring bearings integrated into a rotary device. The inventors were able to observe, in various experiments, that this technique allows early detection of the defects affecting the bearings, notably earlier than the technique of the prior art proposed in the document EP 2 693 176, and this in various context (accelerometer placed on the defect bearing or away from it, in the presence of electromagnetic interference or not).

(90) It should be noted that the invention has been described with reference to a vibration signal acquired by means of an accelerometer. The monitoring method proposed by the invention can however also be applied to an acoustic signal, acquired for example by means of a microphone or any other acoustic sensor, and containing an acoustic signature of the bearing that one wishes to monitor.