GB2582597A - Method of decomposing a load of interest associated with bearing-supported equipment - Google Patents

Abstract

Bearing 9 has rolling elements 8 at even spacing λ, and n sensing elements Sn at even spacing θ connected with stationary race 6. In operation, the rolling elements induce strains in the stationary race. Sensor signals sn exhibit phase difference Φ, dependent on λ and θ. A payload on the bearing causes a payload signature in sn at a ball-pass frequency. A disturbance (e.g. distorted element or race) causes a disturbance load signature at another frequency. The sn are digitised. A signature matrix M is constructed, describing how unknown strain basis functions associated with the payload and disturbance load influence sn; n is selected and θ optimised such that the rows of M exhibit orthogonality. M is used to linearly transform the sn, from which the strain basis function of the load of interest (payload or disturbance load) is estimated and used to decompose and determine the load of interest.

Description

Method of decomposing a load of interest associated with bearing-supported equipment The present invention relates to the field of determining load parameters of interest associated with a system comprising one or more components supported by a rolling element bearing and is more particularly directed to a method and measurement system that enables several parameters of interests to be independently determined with improved accuracy.

Technical Background

An example of a bearing comprising a system for determining the amplitude A of the pseudo sinusoidal deformations induced during rotation is disclosed in US 7661320. The system comprises at least three strain gauges, a device for measuring three signals depending relatively on the temporal variations of the signal emitted by each gauge, whereby the device is configured to form two signals SIN and COS respectively of like angle and like amplitude and to determine the amplitude A of the deformation area as a function of time based on the expression SIN2 + COS2. The method of determining relies on a specific angular spacing 0 of the three strain gauges relative to the angular spacing A of the rolling elements of the bearing, whereby 0 = A/4. The system may also include additional sensors which are used to suppress various interference signals, but does not enable identification of one or more specific sources of the interference, or enable the magnitude of a specific interference signal to be determined. Furthermore, if the measured interference signal and measured signal of interest are non-orthogonal, suppression of the interference signal may also partly suppress the signal of interest, leading to decreased accuracy.

It is also known to use an optical sensing fibre to determine, for example, the radial load acting on a bearing. An example of bearing comprising a such sensing fibre attached to a circumferential surface of the non-rotating bearing ring is disclosed in US 2013188897, whereby the fibre is arranged in a circumferential groove in the bearing ring, so as to locate the sensing elements (Bragg gratings) of the fibre closer to the region of rolling contact between the bearing raceway and the rolling elements, thereby increasing the sensitivity of the fibre by weakening the bearing ring and creating relatively larger deformations for specific loads. A disadvantage of this solution is that the bearing must be modified, significantly increasing production costs.

A further disadvantage of sensing close to the region of rolling contact is that bearing defects resulting in high frequencies introduce aliasing components in the sensing signals, due to the limited sampling speed of the optical interrogator to which the sensing fibre is connected, which contributes to the noise content. The source of the noise is the rolling contact, so the closer to this contact, the more high-frequency noise is measured.

To counteract these disadvantages, the sensing fibre may also be arranged on a separate component, such as a sleeve, that is mounted in connection with the bearing ring. However, this reduces the deformations at the surface where the sensing fibre is arranged, which weakens the measured signal, leading to a relatively lower signal-to-noise ratio.

Consequently, there is a need for a method and measurement system that improves signal-to-noise ratio and enables several load parameters of interest, such as a process load acting on the bearing, to be determined with accuracy, even when the measurable deformations are relatively weak, and which further enables load contributors associated with specific types of disturbances to be isolated and determined.

Summary

Bearings comprising rolling elements are used to support moving parts of machinery relative to stationary parts. Loads on the moving part are transmitted to the stationary part via the rolling elements, which induce strains in the bearing raceways. These strains can be measured in order to derive the load acting on the bearing. The principal load acting on the bearing is a process load associated with the supported machine part, due to its weight and application forces. This will be referred to as the bearing payload.

The measured strains reflect all loads acting on the bearing and may thus also be affected by load contributors attributable to harmonic disturbance parameters associated with e.g. bearing defects, geometric variations, and misalignments or to disturbance parameters associated with e.g. system imbalances. Depending on the system, it may be desirable to suppress the contribution from one or more disturbance load parameters, to enable more accurate determination of the bearing payload, or it may be desirable to determine the load contribution from one or more of the disturbance parameters.

The present invention defines a method of decomposing at least one load of interest associated with a system comprising one or more components supported by a bearing io with a number of rolling elements of even spacing (A). The system further comprises a measuring arrangement mounted in connection with a stationary race of the bearing, whereby the measuring arrangement has at least one set of n sensing elements (Si, 82 Sn) disposed with a uniform spacing (8) and arranged so as to detect a strain induced in the stationary race by the passage of rolling elements during bearing operation. The sensor signals (Si, 52 sn) produced by the corresponding sensing elements thus exhibit a predetermined phase difference between observed signals, which is dependent on the spacing between the rolling elements and the uniform spacing between the sensing elements.

The measured strains are influenced by the bearing payload, which exhibits a payload signature observable at a ball-pass frequency (BPF) and by at least one load contributor associated with a source of disturbance, which exhibits a disturbance load signature observable at a different characteristic frequency. The at least one load of interest can be one or both of the bearing payload and the at least one disturbance load.

The method comprises sampling and digitizing the n sensor signals (si, 52 sn) and the measuring arrangement further comprising a processor configured to process the n digitized sensor signals and decompose the at least one load of interest. The method comprises further steps of: constructing a signature matrix M which describes how the digitized sensor signals are influenced by an unknown strain basis function associated with the bearing payload and by an unknown strain basis function associated with the at least one disturbance load, whereby the coefficients in the matrix M are dependent on the predetermined phase difference and the rows of the matrix exhibit orthogonality; ensuring the observability of all load signatures in the matrix M by selecting n twice the number of signatures Nsig in the matrix M and by optimising the sensor spacing (8) such that the rows of the matrix M exhibit orthogonality, whereby 8 = k*(A/n) and k is distribution factor being a positive integer or a positive real number; using the signature matrix M to linearly transform the n digitized sensor signals; io estimating the unknown strain basis function associated with the at least one load of interest from the linearly transformed signals.

decomposing and determining the at least one load of interest from the estimated strain basis function.

The bearing to which the measuring arrangement is mounted may be a radial rolling element bearing, such as a ball bearing, angular contact ball bearing, cylindrical, tapered or spherical roller bearing, comprising one or more rows of rolling elements, which in use is subject to a radial payload or a payload that has radial and axial components. The sensing elements are then arranged circumferentially at an outer ring of the bearing or at an inner ring of the bearing, depending on which ring is rotational during use. Preferably, the sensing elements are arranged on a sleeve that is mounted to the non-rotating bearing ring.

The bearing may also be a thrust bearing, which in use is subject to an axial payload. The sensing elements are then arranged at an axial distance from the rolling elements of the thrust bearing. Again, the sensing elements are preferably arranged on a separate component such as washer that is mounted to the non-rotating bearing ring.

The bearing may also be a linear bearing comprising e.g. rollers, which supports a component that moves back and forth reciprocally. The sensing elements are then arranged in linear fashion, preferably on a separate static component supporting the races over which the rollers roll.

Depending on the application, the sensing elements of the measuring arrangement may be arranged on other machine components in order to detect strains at the ball-pass frequency. These other machine components may be selected from a list which includes: bearing housings, shafts, calendar rolls, bearing seals, wheels, axles, fasteners, (retainer) rings. (lock) nuts.

When, for example, the bearing supports rotating components and is part of a rotational system, the disturbances which may be present in the rotational system and which could influence measured strain can be identified from analysis of io measurement data collected from sensors for measuring e.g. strain and vibration, mounted to e.g. a bearing outer ring. The analysis of such measurements reveals patterns in the data, i.e. a signature that can be attributed to a particular disturbance The following signature has been identified for parametric excitation, due to variation in bearing stiffness: [sin(Nharm. i. b. 4)1 at-Nharm cos (Arharm. 1. b. 03)1 where Nlharin=1,2,3,4...etc. represents the harmonics of the Ball Pass Frequency of the Outer ring (BPFO), b is the number of rolling elements and I) is the phase difference between observed sensor signals, given by (1) = 9.b.

In a further example, where the disturbance is shaft imbalance: Fat-N harm = sin(Nharm. I. b. O. (ratio/b + 1))1 cos (Nharm. i. b. O. (ratio/b + 1))1 where ratio=BPFO/SF and SF is the Shaft Frequency.

Signatures are also known for other disturbances, including inner ring-, outer ring-, ball-waviness/defects, ball diameter variations and cage run-out.

Periodic strain variations of interest can also be generated by the machine components other than the bearing, such as, for example: imbalance or out-of-roundness of a shaft or spindle axle; gear mesh frequencies, coupling (misalignment); imbalance, eccentricity, or out-of-roundness of a calendar roll or a wheel; gear mesh frequencies; coupling (misalignment); pulley teeth belt frequencies; leadscrew oscillating movement frequencies; eigen frequencies of belts or chains or cam and follower mechanisms. Each of these periodic variations can be associated with a signature that is observable at a characteristic frequency following from the assembly. Gear mesh frequency, for example, is the rate at which gear teeth mate together in a gearbox, which is calculated based on the number of teeth and the rotational speed of the gear.

Measurement data may thus be gathered in a test environment and analysed in order to identify the presence of disturbances from the characteristic signals. Suitably, the signal components attributable to the known bearing payload are suppressed, to isolate the disturbance as signals of interest.

A signature matrix is then constructed for the signature of each type of disturbance that has been identified within the system, based on experience, physical modelling and measurements which together capture most of the occurring disturbances in the system with their related patterns/signatures. A modelling technique may be applied to compute the coefficients which define how the unknown strain basis function associated with each of the identified disturbance loads are linearly combined to describe the sensor signals. The signature matrix also contains the coefficients which define how the unknown strain basis function associated with the bearing payload are linearly combined to describe the sensor signals. This may also be based on physical modelling and on measurements performed on the rotational system, using sensing elements arranged with the predetermined phase difference, under known conditions with varying, known loads.

Depending on the system and the identified disturbance loads, it may be desirable to decompose and determine the magnitude of the payload and/or one or more of the disturbance loads and to supress the contribution from other loads defined in the signature matrix. The signature matrix is then split in a first matrix A, being a load of interest matrix, and a second matrix B, being a disturbance matrix associated with the remaining signatures in the matrix M. A suppression matrix BO is computed, which is a null space of the matrix B, whereby B*B0 = 0. The step of linearly transforming the sensor signals then comprises using the BO matrix to remove the unwanted disturbance components that have a structured effect on the sensor signals, thereby improving the signal-to-noise ratio and enabling more accurate determination of the one or more loads of interest.

The orthogonality of the signature matrix enables decomposition of the load contributors from the sensor signals. The distance between the sensing elements of the measurement arrangement is preferably selected so as to produce an optimal io uniform spatial sensor spacing that maximizes orthogonality and observability of the signatures capturing the characteristic conditions within system.

In a particularly preferred embodiment, the n sensing elements are arranged with uniform sensor spacing 6= k*Mn, where k is a positive integer. In other embodiments, the value of k may be a positive real number.

The value of the distribution factor k is selected to give a distribution of sensing elements that covers the area of interest associated with the application needs. For example, to enable local analysis of local phenomena, such as radial load in the loaded zone of a radial bearing, k may be selected to be close to one, i.e. between one and three. To analyse phenomena that act on the bearing more globally, e.g. axial loads on the radial bearing, k is selected close to the number of rolling elements b, to globally cover the full 360 degrees of the bearing ring.

The value of k is also influenced by the number of sensing elements n, which is at least twice the number of signatures which need to be observed and decomposed or suppressed. Preferably, a larger number of sensors is used to improve accuracy. Furthermore, the number of sensing elements n is preferably a prime number, or is coprime with the number of harmonics N harm (= 1,2,3,4..) of the ball pass frequency, such that the greatest common divisor (n, Nharm) = 1. Again, this ensures that the harmonics of the ball pass frequency are observed optimally orthogonal.

Alternatively, if n is not coprime with Nharm, n is selected to be coprime with k and k is coprime with Nharm.

Suitably, the method comprises verifying the orthogonality of the signature matrix rows. The magnitude of orthogonality of the signature matrix rows is calculated and compared against a minimum value. Preferably, the calculated magnitude a. 2.0, more preferably 10. Initially, the calculation may be performed based on a value for the predetermined phase shift between observed sensor signals that arises from a preselected combination of a number of sensors n, a sensor spacing 8 and a value of k that is selected according to one or more of the criteria defined above. If the preselected combination delivers acceptable orthogonality, then that combination is used in the measuring arrangement and the corresponding signature matrix M is used to determine the one or more loads of interest.

If the calculated orthogonality, based on the preselected combination of n and 8 values, is lower than the acceptable minimum value, then a new signature matrix M is constructed using different values of 8 and/or higher values of n, until acceptable orthogonality is reached.

In one embodiment, the method comprises determining an optimal uniform sensor spacing Oopt for a specific number of sensors n, which leads to the highest calculated orthogonality. This is done by varying 0 within a certain range and calculating orthogonality for each value of 8 in the range. A list of the highest calculated orthogonalities may thus be obtained. Preferably, eopt is selected if the calculated orthogonality is acceptable.

If the calculated orthogonality is not acceptable for any value of 8, then the number of sensing elements n may be increased and a new signature matrix constructed for a new preselected combination of n and 0. Orthogonality is then verified as described above until acceptable orthogonality is achieved.

Alternatively, in embodiments where the signature matrix comprises two or more disturbance load signatures related to e.g. bearing defects that may not initially be present, but only develop over time, the step of verifying orthogonality may comprise deleting a signature and constructing a new signature matrix with a smaller number of signatures.

The method may comprise an additional step of analysing the measured signals offline, by means of e.g. FFT, to identify the presence of signatures not yet present in the signature matrix. If a new signature is revealed, testing/modelling is performed to derive relationships that describe how the new signature affects measured strain and the signature matrix is updated. This may mean that one or more additional sensing elements are added to the measurement arrangement.

In a preferred embodiment, the measurement arrangement comprises an optical sensing fibre comprising fibre-Bragg gratings (FBGs). The advantage of using an optical sensing fibre is that a relatively large number of sensing elements can be arranged to sense the passage of rolling elements without the need for complex physical wiring, as would be the case with strain gauges for example. Preferably, the measurement arrangement comprises at least 7 sensing elements (FBGs).

In an embodiment, the Bragg gratings are integrated in a single sensing fibre. In an alternative embodiment, the measurement arrangement comprises first and second optical sensing fibres. The first and second optical sensing fibres may comprise FBGs with the same spacing e or with a different spacings. In an example where the signature matrix comprises a bearing payload signature observable at the ball pass frequency and a shaft imbalance signature observable at the shaft frequency, the FBGs of the first fibre have a first spacing 01 based on BPF i.e. based on the ball spacing, while the FBGs of the second fibre have a second spacing 02 based on SF, where SF is the shaft frequency, which is related to BPF by a factor governed by the bearing geometry. In a further example, the measuring arrangement comprises first and second sensing fibres with the same uniform sensor spacing 6, but arranged with an offset relative to each other. As will be understood, the measuring arrangement may comprise more than two sensing fibres.

The one or more loads of interest are recovered from the estimated strain basis function, at the characteristic frequency associated with each load of interest. In the case of a rotational system, shaft speed, position (angle) and direction of rotation may also be determined.

The measuring arrangement comprises at least one set of n sensors. The signal from each sensor may be used to derive a global load acting on the bearing. It is also possible to use the signals from a changing subset of neighbouring sensors to derive the load more locally at the location of those sensors. For example, if the measuring arrangement comprises 7 sensing element Si -S7, the local load may be derived for sensors Si -S4 and then for S2 -S5, followed by S3 -S6, followed by S4 -S7, followed by S5 -Si, followed by S6 -S2 and finally for S7 -Ss. In this case, the local load at seven positions is calculated. If the bearing is a radial bearing subjected to a radial payload, the radial load may thus be calculated at different circumferential locations, enabling a loaded zone of the bearing to be identified. Such a calculation can be performed in real time after each sample.

The method and measuring arrangement of the invention enables the payload acting on a bearing to be determined in real time with improved accuracy, for variable operating speeds/acceleration, and enables decomposition of load contributors.

These and other advantages of the invention will be apparent from the following detailed description and accompanying drawings.

zo Brief Description of the Drawings

Fig. 1 shows an axial cross-sectional view of a rotational system including a rolling element bearing and a first example of a measurement arrangement according to the invention; 2.5 Fig. 2 shows an axial cross-sectional view of the rotational system of Fig. 1 comprising a second example of a measurement arrangement according to the invention.

Fig. 3 is a flowchart of a method of designing a measuring arrangement according to the invention Fig. 4 is a flowchart of a method of calculating loads of interest using a measuring arrangement of the invention

Detailed Description

An example of a rotational system 15 is shown in Fig. 1, comprising a bearing 9 having an outer ring 6, an inner ring 7 and plurality of rolling elements 8 which are retained in evenly spaced relation by a cage (not shown). The angular spacing between the rolling elements 8 -balls in the depicted example -is defined by the angle A, which is equal to 360 degrees divided by the number of balls b. The bearing is mounted in a machine housing 5 and rotationally supports a shaft 10 to which a rotational machine component (not shown) is connected. Let us assume that in the depicted example, the rotational machine component is a compressor impeller.

To monitor loads on the bearing and detect possible defects associated with the machine component, the system 15 is provided with a measurement arrangement according to the invention, which has a number n of neighbouring, uniformly spaced sensing elements Si, S2, S3.... Sn, whereby n = 7 in the depicted example. The sensing elements are arranged circumferentially at a radial distance from a contact region between the balls 8 and an outer raceway of the bearing outer ring 6 and are configured to detect strains induced in the bearing outer ring by the passage of the balls during bearing operation. In this example, the sensing elements Si -Sn are Bragg gratings in an optical sensing fibre 1 that is integrated on a sleeve 4 mounted between the bearing outer ring 6 and the housing 5. The sensing fibre 1 leaves the sleeve through an opening 11 and is connected to an interrogator (not shown) which is connected to processor (not shown) configured to receive and process the sensor signals to determine at least one load of interest associated with the rotational system 15.

The sensors Si.. Sn are arranged around the full circumference of the bearing with an even angular spacing 8, equal to 360°/7 i.e. 51.5° It is assumed that the signals Si 30 from the sensing elements are dominated by strain induced by the ball passes of the individual balls passing the sensing elements.

When strain is measured at multiple locations on the circumference of a bearing during operation, a periodic signal is obtained from each sensor, caused by the ball passes (and associated parametric excitation). The ball passes can be described by one or more sinusoidal (harmonic) components. If it is assumed that each of the b balls are identical and transfers an equal amount of load, in the case where uniform axial and/or radial load (loaded zone 360 degrees) is applied to the bearing, then the periodic sensor signals will be phase-shifted versions of a common "basis function", i.e. a sinusoidal basis (sin cos).

The phase shift or phase difference 4) between the signal from a sensor Si and a sensor Si depends on the angular spacing 8 of the sensing elements relative to the 10 number b of evenly spaced balls, which are known parameters, meaning that the phase shift can be calculated as follows: 0= (6 b) The sensor signals si, s2 sn associated with each sensing element Si, S2... Sn are assumed to provide unknown periodic (strain) signals, so can be mathematically described by a linear combination of (unknown) basis functions [sina cosa] with known phase shift 4), where a = 2.7.f.t where f is the basic frequency associated with the signature and t is time, as an example f=BPF, the Ball Pass Frequency measured at the outer ring in this example. BPF will be used to refer to this

frequency throughout the description.

Using goniometric angle sum and difference identity, the signals for the n sensors can be expressed as: s1 = sin(a + 143) = sin a. cos 14) + cos a. sin 14) s2 = sin(a + 243) = sin a. cos 24) + cos a. sin 24) sn = sin(a + n4)) = sin a. cos n(I) + cos a. sin ricl.) And described by matrix notation: [sin a cos a]. [cos 14) cos 24) ... cos n4)1 [s1s2.. sit] = [si sin 14) sin 2113... sin ncILI The analogue sensing elements Si, S2... Sn provide continuous signals si(t), 52(t) ....

sn(t) or, more generally, si(t).

The values si[m.Ts] are obtained from s(t) by 'sampling' at a sampling rate fs= 1 /Ts, whereby Ts is the sampling interval.

A discrete signal si[m] can be defined such that si[m]= si(m.Ts). This means that the values of the successive samples of si[m] correspond with the values si(m.Ts) exactly. It does not matter how the samples of si[m] are represented. They can be represented equally well by an analog quantity or by a binary word assuming the binary word represents the values of si(m.Ts) accurately. In the remainder of this description, the short notation si is used for si[m].

The sampled sensor signals si are stacked in a measurement matrix S [Si s2 sn], each column of the matrix S is composed of the sensor readings sampled at time t, t-Ts, t-2Ts, t-3Ts etc. si [m] s2 [m] ... sit [m] si [m -Ts] s2[m -Ts] ... sn[m -Ts] S= si[m -2Ts] s2[m -27;] ... sr, [m -27;] si [m -37;] s2 [m -3 Ts] ... sn[m -37;] Basis function [since cosa] is unknown, but may be derived from sured sensor signals si and the known values sir: (1) and cos 0.

If it is assumed that each sensor signal si (in the columns of matrix S) can be represented as a linear combination of the unknown basis functions, a matrix P can be defined which has columns corresponding to the unknown basis function. i.e. P = [sina cosa] whereby P represents an ideal case where the sensor signals are influenced only by the strain-induced ball passes.

The strain induced ball passes fully reflect the load of interest in this case, and a "load of interest matrix" A can be derived, which defines how the basis functions [sina cosa] are linearly combined to describe the measurements si"sn in the measurement matrix S, whereby: S = P*A A = [al a2... an] and ai = rsin(i.b. 0)1 [cos(i. b. 0)1 The relationships defined in the matrix A may be derived from a physical model based on first principles or from measurements under known load and operating conditions, whereby the coefficients of the matrix al capture the known phase shift 0.

Thus, [51 S2... Sn] = [shin cos a] [al az.... an].

The matrix P of unknown basis functions [sina cosa] can then be obtained by computing the so-called pseudo-inverse piny of the matrix A: P = S*pInvA However, the sensor signals si sn also contain disturbances and noise due to e.g. the excitation frequencies of different vibration sources in a ball bearing, that can be described by ball pass frequencies, parametric excitation, inner ring waviness, outer ring waviness, ball waviness, ball diameter variations, cage run-out but also rigid body movement of housings and shafts, unbalance, misalignment, gear meshing, belt vibrations etc, depending on the application. The phenomena are observed at specific frequencies related to cage frequency, shaft frequency, ball spin frequency and create specific phase shifts (modulation) between the sensor signals.

In other words, the disturbances contribute to the sensor signals, which in one example could be expressed as: [5152. . Sri] -[sin a cos a] .E cos 01 sin 01 cos 02 + [sin 2a cos + [sin 3a cos + [sin ka cos 2a]. sin 02 3a]. os 201 ka].[sin.

kcin 201 cos 301 [sin 301 [cos k01 koi cos 0,21 sin 0,1 cos 202 cos 20,1 sin 202 sin 20] cos 302 cos 30,1 sin 302 sin 30j cos k02 cos k0Thi sin k02 sin k0"_1 With itii=i*iti and 0=b*e if sensors Si (i=1, n) are uniformly distributed.

The relationship between the measurement matrix S and the applied load, including disturbances can be expressed as: S = P*A + Qi*Bi [Equation 1], where Qi is a matrix associated with one or more unknown basis functions of a source of disturbance i and Bi is a "disturbance load" matrix, which defines how the basis function(s) of the disturbance source i influences the sensor signals.

Assuming that a particular matrix B for a particular disturbance has r rows and n columns, B has a right null space of size n-r. A matrix BO therefore exists (of size (n-r, n)) such that B*BO = 0.

By multiplying the expression S = P*A + Q*B from the right with BO, we get: S*BO = P*A*B0 + Q*B*B0 [Equation 2] The n sensor signals S can thus be linearly transformed such that the disturbance components Q*B are eliminated from the linearly transformed sensor signals Strans (Strans = S*B0), whereby Strans is formed from a smaller number m of linearly recombined sensor signals, where m = n-r.

The matrix of unknown periodic strain basis functions can then be estimated in the linearly transformed sensor space as follows: Pest = Strans*pinv(A*B0) [Equation 3] The load on the bearing (payload) can then be calculated from the estimated (recovered) basis functions.

In principle, the matrices A and B form part of a signature matrix M, which defines how unknown basis functions associated with load components of the bearing payload and how unknown basis functions associated with load contributors due to various disturbances can be linearly recombined to describe the sensor signals.

Depending on the system, it may be desirable to determine the magnitude of a particular load contributor and to suppress others. The "A" matrix may therefore relate to more than one load parameter of interest and the "B" matrix may relate to more than one disturbance parameter to be suppressed. To enable this decomposition of the measured load, it is important that the rows in the signature matrix M are orthogonal. According to the invention, orthogonality is achieved by appropriate selection of the number of sensing elements and appropriate positioning of the sensing elements, which will be explained with reference to the following

example.

Example

Let us assume that for a system such as depicted in Fig. 1, the processor is configured to calculate a first load of interest corresponding to a radial payload acting on the bearing and a second load of interest, being a load contribution from a shaft unbalance load, and to suppress at least one disturbance parameter associated with a bearing defect in the outer raceway, which, if present, can be expected to interfere with the measured strain signals.

Each of these parameters is associated with a signature that can be identified within the measured signals at different characteristic frequencies. The signature associated with the payload is observed at the ball-pass frequency (BPF). An unbalance load, due to e.g. improper mounting of the compressor impeller or breakage of an impeller blade, will result in a rotating load vector that is observable at the rotation frequency of the shaft (SF). A developing defect in the outer raceway of the outer ring 9 will eventually cause vibrations that are observable at a frequency of 2*BPF.

Each load signature makes a contribution to the measured strain signals. In order for the signatures to be isolated and suppressed, the signatures need to be optimally orthogonal. Furthermore, the number of sensors n must be sufficient to enable the number of signatures Nsig to be observed, whereby n 2*Nsig. It is also advantageous if the number of sensors n is a prime number. In the present example, where three signatures need to be observable, n = 7, which satisfies these criteria.

The spacing 0 between the successive sensors Si S7 is also important.

Suitably, the spacing 8 is given by: = k*A/n, where k is a positive integer or a positive real number.

In the measurement arrangement depicted in Fig. 1, k = 12 and the sensing elements are evenly distributed around the full circumference of the bearing. Such a spacing is appropriate where the bearing payload acts around the full circumference.

In the case of a radial payload on a radial bearing, the rolling elements are loaded in a loaded zone of the bearing, which extends over a smaller angular range. It is therefore advantageous to arrange the sensing elements in the loaded zone, such as depicted in the arrangement of Fig. 2, which shows a bearing identical to that of Fig. 1, whereby the n = 7 sensing elements of the optical sensing fibre 1 disposed on the sleeve 4 are arranged within five ball spacings A. In the example of Fig. 2, k = 5 and = 5A/n.

As mentioned above, the phase shift 0 between observed sensor signals is calculated based on the number of balls b and the sensor spacing O. A signature matrix M is constructed, based on knowledge obtained from modelling and/or testing of a compressor impeller application. The signature matrix M in this example has six rows and seven columns. The first 2 rows of the signature matrix M relate to the payload signature (BPF signature), whereby the first row captures sin 0 and the second row captures cos 0. The third and fourth rows relate to the defect signature (2*BPF signature) whereby the third row captures sin 20 and the fourth row captures cos 20. The fifth and sixth rows relate to the unbalance signature (SF signature) whereby the fifth row captures sin ((factor +1)0) and the sixth row captures cos ((factor + 1)0), where factor = SF/BPF.

Like the matrix coefficients associated with the payload signature, the coefficients associated with the defect signature and the unbalance signature may be derived based on a model that is developed via finite element analysis and/or testing. In the case of the unbalance load for example, the model could be developed by running the bearing with a known payload and adding different unbalanced masses to the shaft.

With n = 7 and k = 5, the obtained signature matrix may be as follows: 1.0000 1.0000 1.0000 -0.9749 -0.2226 0.4341 -0.9009 -0.7680 0.6405 0.4341 -0.9009 -0.7821 0.6231 -0.9837 -0.1796 0.7816 0.6238 0.9751 -0.2218 -0.4922 -0.8705 -0.7821 0.6231 -0.9747 -0.2235 0.3533 -0.9355 -0.4333 -0.9012 0.7811 0.6244 0.9447 -0.3278 0.9751 -0.2218 -0.4326 -0.9016 0.8568 0.5156 M= In a next step, the orthogonality of the signature matrix rows is verified. The ratio of s the sum of absolute values of diagonal components divided by the sum of absolute values of off-diagonal components should be maximal. This can be verified via MGM', where M' is the transposed matrix of M. In the present example, M*M' = 3.5001 0.0004 0.0015 0.0004 0.0868 -0.00630.0004 3.4999 0.0008 -0.0011 -0.0711 0.0743 0.0015 0.0008 3.4983 0.0008 -0.0210 0.0024 0.0004 -0.0011 0.0008 3.5017 -0.0735 0.0437 0.0868 -0.0711 -0.0210 -0.0735 3.5513 -0.0853 -0.0063 0.0743 0.0024 0.0437 -0.0853 3.4487 This shows that the diagonal components are dominant and that the off-diagonal components are much smaller than the diagonal terms.

The magnitude of the orthogonality can be calculated as follows:

NORM-

absolute values of diagonal components E absolute off diagonal components The higher the ratio (NORM), the better the orthogonality. A ratio of »1 indicates good orthogonality. Preferably, the magnitude of the ratio (NORM) is greater than 20 two. More preferably, NORM a. 10.

The signatures captured in the matrix M are dependent on (1). A sufficient condition for recovering the basis function associated with each of the signatures described in the matrix is that the rows are orthogonal. Since the coefficients in these matrices 25 only depend on the number of sensors n and the spacing between the sensors 8 M*M'= [Equation 4] (assuming the number b of evenly spaced balls is fixed), the matrix M can be optimized as a function of 8.

In other words, different values of the distribution factor k can be computed which give the highest magnitude of orthogonality. This is done by varying the value of 8 in small steps over a range and calculating orthogonality for each value of 8 in the range. The values of 8 (and k) which give best orthogonality may thus be ranked, such as shown in table 1: k 9 (°) measurement coverage (°) NORM 5.00 21.4 150 22.36 10.00 42.9 300 9.48 5.25 22.5 158 3.13 5.81 24.9 174 2.75 5.83 25.0 175 2.72 4.00 17.1 120 2.68

Table 1

In the present example, k = 5 gives the highest value of the ratio (NORM) and is thus selected. If a different value of k gave better orthogonality, the coefficients in the signature matrix would be recalculated accordingly. If an acceptable orthogonality could not be obtained for any value of k using n = 7 sensing elements, the number of sensing elements n would be increased and the sensor spacing 8 optimized until an acceptable value of the ratio (NORM) is reached. Again, the coefficients in the signature matrix M would be recalculated accordingly.

The beneficial effect of using a higher number of sensing elements, which satisfy the condition of being a prime number or coprime with Nhami, can be seen from table 2, which shows the calculated orthogonality for a signature matrix based on n = 13 sensing elements: k 9 (°) measurement coverage (°) NORM 5.00 11.5 81 27.88 10.00 23.1 162 20.72 18.57 42.9 300 9.48 9.00 20.8 145 7.71 10.30 23.8 166 5.36 5.39 12.4 87 5.30

Table 2

Again, a distribution factor k = 5 provides the best orthogonality, and it can be seen that the magnitude of the orthogonality is higher when n = 13.

Once the orthogonality of the rows in the signature matrix M has been verified, the processor is programmed to calculate the loads of interest, using the signature matrix M. The loads of interest are the payload and the shaft unbalance load. These signatures are placed in the load of interest matrix A: 0 -0.9749 0.4341 0.7816 -0.7821 -0.4333 0.9751 A_ 1.0000 -0.2226 -0.9009 0.6238 0.6231 -0.9012 -0.2218 0 -0.7680 -0.9837 -0.4922 0.3533 0.9447 0.8568 1.0000 0.6405 -0.1796 -0.8705 -0.9355 -0.3278 0.5156 The disturbance signature for 2xBPFO is placed in the disturbance load matrix B: 0.4341 -0.7821 0.9751 -0.9747 0.7811 -0.4326-1 B=I- [1.0000 -0.9009 0.6231 -0.2218 -0.2235 0.6244 -0.90161 The right-null space of B is calculated, to obtain the suppression matrix BO: -0.1525 0.5919 0.7433 B0= 0.2172 -0.1346 0.0254 0.0889 -0.3317 -0.4742 0.2764 0.7288 0.2122 -0.1112 -0.0119 0.4451 0.2625 0.2413 0.2715 0.7522 0.1750 -0.0674 0.4703 0.0012 0.1584 -0.2179 0.2342 0.7960 0.1334 0.4023 -0.2648 -0.0441 0.1211 -0.1741 0.1926 0.8271 Recalling Equation 3, the matrix of unknown periodic strain basis functions Pest is derived based on: Pest =S*BO*pinv(A*BO) A calculation matrix C = BOVInv(A*B0) is thus obtained.

-0.0000 -0.2730 0.1311 C= 0.2264 -0.2263 -0.1307 0.2732 0.2802 -0.0719 -0.2619 0.1806 0.1859 -0.2502 -0.0622 0.0182 -0.2113 -0.2846 -0.1464 0.0994 0.2673 0.2312 0.2808 0.1848 -0.0552 -0.2589 -0.2723 -0.0858 0.1604 The first and second columns of the matrix C respectively contain the coefficients of how 51,52_57 should be linearly combined to recover the sine and cosine terms of the basis function related to the BPF. The third and fourth columns respectively contain the coefficients of how 51,52_57 should be linearly combined to recover the sine and cosine terms of the basis function related to the SF.

Pest is thus derived from the measured sensor readings and the BO*pinv(A*BO) matrix computed from the signature matrix M. From Pest we recover the load associated with 1xBPF and 1xSF.

This is done by calculating -\l(sin2+cos2) of the recovered signal in Pest at each sample: Pest in this example is a matrix with 1 row and 4 columns: Pest = [sin BPF cos BPF sin SF cos SF] whereby the sine components are Pest (1,1) for BPF and Pest (1,3) for SF and the cos components are Pest (1,2) for BPF and Pest (1,4) for SF Note that Pest (1,1) refers to a coordinate in the matrix, i.e. row=1, column=1.

Load@1xBPF = I (sin(BPF))2 + (cos(BPF))2 = Aksin(Pest(1,1)))2 + (cos(P0Si(1,2)))2 Load@1xSF = (sin(SF))2 + (cos(SF))2 = J(s!n(Pest(1,3)))2 + (cos(Pest(1,4)))2 The loads of interest can thus be determined in real time, and can be determined for variable shaft speeds and accelerations.

The ball pass frequency and direction of rotation can also be recovered from Load@1xBPF by calculating angular phase for each sample and determining the phase difference between two successive samples. The sign of the phase difference so indicates the direction of rotation. The shaft frequency can be derived from the determined BPF, using a conversion factor based on the geometry of the bearing. Thus, bearing speed of rotation can also be obtained. In combination with the calculated loads, this information could be used offline to estimate remaining bearing life.

The shaft frequency can also be derived directly from Load@1xSF, based on the angular phase difference between two successive samples, whereby the position of the shaft can be derived at every sample. The method may further comprise comparing the directly derived shaft frequency with shaft frequency derived from the BPF, to identify operating conditions of the bearing such as contact angle of the balls and ball slip.

The method as a whole for designing a measurement system for a particular bearing application is shown in Fig. 3 In a 1st step 100, the load signatures present in the application are identified. These signatures include the bearing payload signature, signatures associated with bearing defects or geometrical variations and signatures associated with the supported machine parts. If the supported parts are gears, for example, the gear mesh and backlash may affect measured strain. If the support parts are pulleys, belt tension, vibrations and slip may affect measured strain.

In a next step, 110 the number of sensing elements n that is required is selected, whereby n twice the number of identified load signatures, and a uniform sensor spacing 8 and distribution factor k relative to the number of evenly spaced rolling elements b is determined.

Preferably, n is a prime number. If n is not prime and the identified load signatures are observed at harmonics of the ball pass frequency (Warm = 1,2,3,4, ..), then n is preferably co-prime with Nnarrn. Otherwise, n and k are selected such that k and Warn, are coprime and k and n are coprime.

In a next step 120, a signature matrix M is constructed as described above for the identified load signatures, via modelling and testing.

In a next step 130, the orthogonality of the signature matrix M is verified. If the orthogonality M is unacceptable, a further step 140 comprises computing an optimal value of k and/or increasing the number of sensing elements or deleting a load signature from the signature matrix.

Steps 110 -130 are repeated until acceptable orthogonality is achieved.

In a final step 150, a calculation matrix C is derived from the signature matrix M matrix and programmed into the processor, such that the loads of interest are calculated and load contributors which are not of interest are suppressed, such as described in the example given above.

An embodiment of the method for calculating the loads of interest is summarized in the flowchart of Fig. 4.

In a first step 200, the signals from the n sensing elements si sn are received, sampled and digitized. Suitably, the digitized signals are stacked in a measurement matrix S. In a second step 210, the matrix of unknown sin cos basis functions Pes, is derived from the calculation matrix C and the digitized signals, whereby Pest = St and C =B0VInv(A*B0).

In a third step 220, the sin cos basis functions are recovered from Pest.

In a fourth step 230, an amplitude of each load of interest is calculated from the recovered sin cos basis functions, based on Isin2+cost.

In an optional fifth step 240, speed and direction of rotation and shaft position is calculated from the recovered sin cos basis functions.

The steps are continuously repeated such that the loads of interest and speed information are computed in real time.

A number of aspects and embodiments of the invention have been described. The invention is not restricted to these embodiments, but may be varied within the scope of the accompanying claims.

Claims (17)

1. Claims 1. A method of decomposing at least one load of interest associated with a system (15) comprising a component supported by a rolling element bearing having a number b of evenly spaced rolling elements (8), the system further comprising a measuring arrangement mounted in connection with a stationary race of the bearing, whereby the measuring arrangement has at least one set of n sensing elements (S1, S2... Sn) disposed with a uniform spacing (8) and arranged so as to measure strains induced in the stationary race by the passage of rolling 1.0 elements during bearing operation, such that sensor signals (si, 52 sn) produced by the corresponding sensing elements exhibit a predetermined phase difference cl) between observed signals, which is dependent on the rolling element spacing (A) and the uniform spacing (8) between the sensing elements, wherein during operation, the measured strains are influenced by a payload acting on the bearing, which exhibits a payload signature observable at a ball-pass frequency (BPF) and by at least one load contributor associated with a source of disturbance, which exhibits a disturbance load signature observable at a different characteristic frequency, whereby the at least one load of interest is one or both of the bearing payload and the at least one disturbance load, wherein the method comprises sampling and digitizing the n sensor signals (si, S2... Sri) and wherein the measuring arrangement further comprises a processor configured to process the n digitized sensor signals and decompose the at least one load of interest, the method comprising further steps of: constructing a signature matrix M which describes how the digitized sensor signals are influenced by an unknown strain basis function associated with the bearing payload and by an unknown strain basis function associated with the at least one disturbance load, whereby the coefficients in the matrix M are dependent on the predetermined phase difference (1) and the rows of the matrix exhibit orthogonality; ensuring the observability of all load signatures in the matrix M by selecting n twice the number of signatures Nsig in the matrix M and by optimising the sensor spacing (8) such that the rows of the matrix M exhibit orthogonality, whereby 0 = k*(iVn) and k is distribution factor being a positive integer or a positive real number; - using the signature matrix M to linearly transform the n digitized sensor signals; - estimating the unknown strain basis function associated with the at least one load of interest from the linearly transformed signals.- decomposing and determining the at least one load of interest from the estimated strain basis function.
2. Method according to claim 1, wherein the bearing is a linear slide bearing comprising balls or rollers.
3. 3. Method according to claim 1, wherein the bearing supports a rotating component, and is one of: * a radial bearing that experiences a purely radial payload or a payload comprising radial and axial components; * a thrust bearing that experiences a purely axial payload.
4. 4. Method according to any preceding claim, wherein the signature matrix M comprises one or more signatures associated with a disturbance load attributable to a geometric deviation in the bearing or the rolling elements or to a defect in one or both of the bearing races, or to an operating condition of the supported component.
5. 5. Method according to claim 3, wherein the signature matrix M comprises a signature associated with a disturbance load attributable to shaft imbalance.
6. 6. Method according to any preceding claim, wherein the n sensing elements are arranged on a separate part (4) mounted to the stationary bearing race.
7. 7. Method according to any preceding claim, wherein the number of sensors n is a at least seven.
8. 8.
9. 9.
10. 10.
11. 11.
12. 12. is
13. 13.Method according to any preceding claim, wherein the number of sensors n is a prime number.Method according to any preceding claim, wherein the distribution factor k is a positive integer, wherein n and k are coprime and wherein the at least one disturbance load in the signature matrix M is observable at a harmonic (Nharm) of the BPF.The method of claim 9, wherein n and Nhaim are coprime. The method of claim 9, wherein k and Warm are coprime.The method of any of claims 1 -7, wherein the distribution factor k is equal to, or substantially equal to 5, 10 or the number of rolling elements b.Method according to any preceding claim, wherein the step of optimising the sensor spacing (0) comprises: * calculating a magnitude of the orthogonality of the signature matrix M, based on a preselected number of sensing elements and a preselected sensor spacing; * verifying that orthogonality is acceptable by comparing the calculated magnitude with a predefined minimum value; and, if orthogonality is unacceptable, * increasing the number of sensing elements and/or selecting a different sensor spacing and recalculating the magnitude, based on the increased number of sensing elements and/or different sensor spacing, until acceptable orthogonality is achieved.
14. 14. Method according to any preceding claim, wherein each signature from the matrix M associated with the at least one load of interest is placed in a first matrix A and each of the remaining signatures from the matrix M are placed in a second matrix B, and wherein the step of linear transformation comprises suppressing the load contributors not associated with the at least one load of interest, using a suppression matrix BO, being a null space of the matrix B, whereby B*B0 = 0.
15. 15. Method according to claim 13, wherein a calculation matrix C is derived from the signature matrix M, whereby C= BOtInv(A*B0), and wherein the calculation matrix C is used to linearly transform the digitized sensor signals.
16. 16. Method according to any preceding claim, wherein the at least one set of sensing elements (Si, Sz, Sn) are Bragg gratings of one or more optical sensing fibres.
17. 17. Method according to any preceding claim, wherein the measuring arrangement comprises a second set of uniformly spaced sensing elements arranged with an offset to the first set, whereby the first set has a first spacing el and the second set has second spacing% that is equal to e1 or different to 91.