A METHOD AND SYSTEM FOR LUBRICATING ONE OR MORE ROTARY BEARINGS

Abstract

According to the method of the invention, a lubricant is supplied incrementally to a rotary bearing while the bearing is in operation rotating at a rotational speed. The lubricant is supplied in consecutive steps so that at each step a portion of a prescribed amount of lubricant is supplied, followed each time by an ultrasound measurement. A first ultrasound measurement is performed before the first supply step, and starting from the second supply step, each measurement result is compared at least to the previous result, in order to evaluate the bearing condition and decide on that basis whether to continue the sequence or not. Stopping the sequence is decided when the lubrication of the bearing is assessed as successful, a lubrication failure or over-lubrication. The invention is equally related to a system for lubricating one or more bearings, applying the method of the invention to each of said bearings.

Claims

1. A method for monitoring and lubricating at least one rotary bearing of a machine, by incrementally supplying a lubricant to the bearing in one or several consecutive supply steps, comprising: determining a prescribed lubricant amount, measuring an ultrasound signal before the first lubricant supply step using a transducer mounted in connection with the bearing, and obtaining an initial value of a scalar indicator extracted from the signal that is representative of the lubrication condition of the bearing, and said measurement and value extraction is repeated after each subsequent lubricant supply step, wherein each measurement is performed after a stabilization period following the lubricant supply, the duration of the stabilization period being such that it allows the supplied lubricant to be fully operational, the amounts of lubricant supplied in the consecutive steps are smaller than the prescribed lubricant amount, starting with the second extracted value, each value of the scalar indicator is evaluated, with respect to the initial value, and, starting from the third measurement, with respect to one or more of the previously extracted values, based on each of the evaluations, a decision is made about stopping or continuing the lubrication sequence.

2. The method according to claim 1, wherein the scalar indicator is the root mean square (RMS) of the signal.

3. The method according to claim 2, wherein the sequence is continued when an extracted value is significantly lower than the previously extracted value.

4. The method according to claim 2, wherein the sequence is continued when an extracted value is essentially the same as the previously extracted value, unless the extracted value has remained the same for a given number of consecutive measurements and value extractions, in which case the sequence is stopped and the lubrication condition is considered successful.

5. The method according to claim 2, wherein the sequence is stopped due to over-lubrication when an extracted value is higher than or at least a given amount higher than the initial value.

6. The method according to claim 2, wherein the sequence is stopped due to a successful lubrication condition when an extracted value is significantly higher than the previous value, after said previous value was significantly lower than the value preceding said previous value.

7. The method according to claim 2, wherein the sequence is stopped due to a failed lubrication condition when an extracted value is significantly higher than the previous value, after said previous value was essentially the same as the value preceding said previous value.

8. The method according to claim 2, further comprising an intermediate measurement of an ultrasound signal during the stabilization time after the first lubricant supply step, and before the first extraction of the scalar indicator value , and comprising the extraction of a value of the scalar indicator from the intermediate signal, and wherein the sequence is stopped due to a suspected bearing failure if the value M′ is significantly lower than the initial value, whereas the first extracted value is significantly higher than the intermediately extracted value.

9. The method according to claim 8, wherein the scalar indicator or an additional scalar indicator is the Kurtosis.

10. The method according to claim 2, further comprising determining of a replenishment interval.

11. The method according to claim 10, wherein the replenishment interval is updated between subsequent applications of the lubrication method, and wherein the update is based on the results of the steps of the lubrication method.

12. The method according to claim 11, wherein a shorter replenishment interval is applied when it is determined that a higher total amount of lubricant than the prescribed amount is required before the lubrication sequence is stopped.

13. The method according to claim 1, wherein the method is fully automated.

14. (canceled)

15. (canceled)

16. The method according to claim 1, is performed multiple times at intervals equal to or shorter than the replenishment interval.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0051] FIGS. 1a and 1b illustrate a system for supplying a lubricant to a bearing and for performing ultrasound measurements of the bearing’s lubrication condition.

[0052] FIG. 2 is a generic image of the shape of the Stribeck curve for non-conformal contacts, expressing different lubrication regimes of a bearing.

[0053] FIG. 3 is a flowchart of the initial sequences of the method of the invention, according to an embodiment of said method.

[0054] FIGS. 4a to 4d are examples of the measured RMS values converted in dB.Math.V in a number of possible sequences according to the flowchart of FIG. 3.

[0055] FIGS. 5a and 5b are flowcharts of the subsequent step following the chart of FIG. 3.

[0056] FIGS. 6a to 6e are examples of the measured RMS values in a number of possible sequences according to the flowcharts of FIG. 5a.

[0057] FIGS. 7a to 7d are examples of the measured RMS values in a number of possible sequences according to the flowcharts of FIG. 5b.

[0058] FIGS. 8a and 8b are generic flowcharts of the n-th step in a sequence of method steps applicable according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

[0059] According to preferred embodiments, the method of the invention is performed repeatedly during a period of active service of a machine comprising one or more rotary bearings, the method being applied on each of said bearings. For a bearing of given dimensions, and rotating at a given speed, the interval T between required lubricant replenishments may be calculated in accordance with existing methods, preferably by the formula (1) given above. Also, a prescribed amount G of lubricant that is to be supplied at each replenishment is calculated in a manner known as such, and referred to above. However, instead of supplying the full amount G, the method of the invention provides an incremental supply of sub-portions of G, monitored by consecutive ultrasound measurements configured to determine the influence of each sub-portion on the bearing condition. Hence, the method of the invention allows self-adjustment of the actual required amount of lubricant from the prescribed amount of lubricant (G).

[0060] The method of the invention is preferably performed in an automated way, by a “smart” automatic lubrication system according to the invention, as illustrated in FIGS. 1a and 1b. FIG. 1a schematically illustrates a rotary bearing 1 supporting a rotatable axle 2 of a piece of machinery 3. The system 4 is configured to supply the lubricant, for example a grease of a given viscosity, to the bearing, and for performing and evaluating the ultrasound measurements. FIG. 1b shows the components of the system 4: a piezo-electric transducer 5 suitable for performing ultrasound measurements, a signal processing unit 6, and a lubricant supply reservoir 7 provided with a flow control mechanism 8 for regulating the flow out of the reservoir 7 and into the bearing, through a supply tube 9. The signal processing unit 6 is configured to extract one or more scalar indicators, such as the RMS value, representative of the lubrication condition of the bearing, from an ultrasound signal produced by the transducer 5. The electronic signal processing components present in the processing unit 6 may be in accordance to known designs, as implemented for example in hand-held ultrasound lubrication monitors which are part of the state of the art. The signal processing unit 6 is furthermore configured to evaluate the measurements and to control the sequence of supply steps in accordance with the method of the invention. The unit 6 is also configured to communicate data on the bearing and/or lubrication condition to the user of the system, for example by showing messages on a screen (not shown). A system according to the invention may be configured to lubricate several bearings placed at different locations on the machine or on several machines. A single processing unit may be configured to monitor the lubrication state of a plurality of bearings and control the lubricant flow from a single reservoir to the multiple bearing locations. The flow control mechanism may comprise a pump for directing the flow of lubricant to the bearing locations. The system may comprise multiple transducers, some or all of which may be mounted permanently on the bearing locations.

[0061] Contrary to prior art methods requiring a target value of lubricant at an imposed periodicity, the method of the invention uses an algorithmic convergence. The algorithmic convergence results in a replenishment process performed step-by-step by means of a self-regulating loop. Consequently, the amount of lubricant fed to the rotary bearing is an optimal amount of lubricant, established by direct measurements, whereas prior art methods often rely on indirect measurements, such as the thickness of the lubrication film, or human decisions.

[0062] The sequence of lubricant supply steps according to the invention is equivalent to a decision tree algorithm that is rooted in the Stribeck curve that is well-known in the domain of tribology. A schematic view of the general appearance of the Stribeck curve for non-conformal contacts is illustrated in FIG. 2. The Stribeck curve for conformal contacts has a similar general shape, and the invention is applicable to bearings in which either conformal or non-conformal contacts occur. The curve illustrates a friction coefficient as a function of a dimensionless lubrication-related scalar indicator, i.e. a scalar indicator that increases when more lubricant is present in the interface between contacting surfaces, preferably contacting surfaces in the bearing. This may for example be the specific dimensionless film thickness (lambda) which expresses the ratio between a lubricant film thickness between contacting surfaces within the bearing, and the roughness of the contacting surfaces. The friction coefficient is a function of the friction forces affecting the bearing, for example between the rolling surfaces of the spheres of a ball bearing relative to the inner and outer race of the bearing. The Stribeck curve is characterised by the appearance of four operational regions, indicated by numerals I, II, III, and IV in FIG. 2: [0063] I : Boundary lubrication : Solid surfaces come into direct contact, the load is supported mainly by surface asperities (metal-metal contact) resulting in high friction. This region is typical for a severely underlubricated bearing. [0064] II : Mixed lubrication : Some asperity contacts occur; the load is supported by both asperities and the viscous lubricant, resulting in important variability of friction. This region characterizes the change in behaviour when an underlubricated bearing is supplied with lubricant: the roughness is gradually covered by the lubricant, as this lubricant is added (going from left to right along the curve), and the friction coefficient decreases quickly as the lubricant film thickness increases. [0065] III : fluid lubrication by an elasto-hydrodynamic (EHD) thin film which characterizes an optimal regime. [0066] IV : fluid lubrication by a hydrodynamic regime (full film-HD).Regions III and IV are characterised by a negligible asperity contact; the load is mainly supported by the lubricant due to the lift, pressure, the physical properties of the lubricant, etc. The friction coefficient is low in the EHD region but increases gradually as a function of the ratio film thickness/ roughness in the HD region. The EHD region is considered the ideal operational regime of the bearing. The graph shown in FIG. 2 is merely an example of a Stribeck curve. Details may vary for each bearing. For example the rate of change of the friction coefficient in the EHD and HD regions may differ from the curve shown in FIG. 2.

[0067] The relubrication interval T is calculated as described in the preceding paragraph, and is dependent on empirically determined factors, which depend on temperature, moisture, contamination of the bearing etc. The replenishment amount G is equally determined based on empirical formulae. Nevertheless, the actual lubricant requirement of a bearing can never be estimated correctly in all circumstances by these two empirical values T and G, but may be influenced by factors which are variable in time, or which are typical for the particular constructional details of the machinery in which a bearing is installed. For this reason, the supply of G at intervals T may in some circumstances lead to an underlubrication or an overlubrication of the bearing, or it may prohibit the detection of a malfunctioning bearing.

[0068] The present invention answers to this problem by not supplying the full amount of G at once, but by supplying the lubricant in a stepwise fashion, preferably by self-adjusting the amount of lubricant in a stepwise fashion, accompanied by ultrasound measurements to verify the effect of the consecutive additions of lubricant. A number of ultrasound-based scalars, in particular the RMS, are representative of the frictional behaviour of the bearing, as expressed by the Stribeck curve. The inventors have found therefore, that for a bearing that is assumed to operate correctly and that requires a replenishment of the lubricant, the method of the invention allows to supply the lubricant in such a way that the Stribeck curve is followed from left to right, until a point is reached where the bearing operates in the EHD regime, or in the lower area of the HD regime. In addition, specific embodiments of the method allow to detect a suspected malfunctioning of the bearing, a lubrication failure or an overlubrication of the bearing, by detecting a behaviour that deviates in an inadmissible manner from the Stribeck curve. The method of the invention does not require the exact knowledge of the Stribeck curve for the bearing on which the method is applied, but applies a decision logic that is based on the general trend observable in any Stribeck curve, for example a downward trend in region II followed by an upward trend in regions III and IV. When overlubrication is detected, the prescribed lubricant amount (G) can be automatically adjusted, here reduced, to avoid overlubrication in a next sequence. Alternatively or additionally, when overlubrication is detected, the initial time interval (T) can be automatically increased.

[0069] A preferred embodiment of a decision tree algorithm according to the invention is described in detail hereafter. The following description is however not limiting the scope of the present patent application. FIG. 3 shows a flow chart that represents the first steps of the method according to the preferred embodiment, performed on a rotating bearing using the installation shown in FIGS. 1a and 1b. For the bearing in question, the parameters T and G are determined. The sequence starts not longer than T seconds after a previous replenishment of the bearing with the lubricant. The sequence may be started earlier than T seconds after the last replenishment, for example at a ratio such as 0.5 T or 0.7 T. This may be decided when defining initial settings for applying the method. The ratio of T may also be changed during the lifetime of the bearing, in accordance with the results of the sequences applied in accordance with the invention. Additionally, the data storage of the system may be used as well to adjust the initial settings for applying the method.

[0070] The sequence starts with an initial ultrasound measurement, yielding an RMS value M0, measured in voltage units and expressed in dB(.Math.V where the reference voltage V0 is 1 .Math.V). M0 is stored in a memory incorporated in or coupled to the processing unit 6. Then, an amount g1 of lubricant equal to 0.25 G is supplied to the bearing, through the supply tube 9, by opening the flow control mechanism 8 in a controlled manner. A stabilization time is determined, preferably based on empirical and scientific data, so that after this stabilization time has elapsed, the added lubricant is assumed to be fully operational within the bearing. The stabilization time may be calculated as a function of the bearing speed parameter, defined as

[00003]$n_{\omega }=\frac{\left(d+D\right)}{2}\omega$

in [mm/min], wherein d and D are inner and outer diameters (in mm) of the bearing, and ω is the rotational speed of the bearing (in rpm), according to the following table :

TABLE-US-00001 n.sub.ω (mm/min) Stabilization time (s) =< 46000 18 ∈ ]4600,52000] 16 ∈ ]52000,58000] 14 ∈ ]58000,64000] 12 ∈ ]64000,70000] 10 ∈ ]70000,76000] 8 >76000 7

[0071] During the stabilization time, an intermediate RMS value M′ is measured, i.e. before reaching the stabilized operational regime. The value M′ is preferably determined by calculating RMS values which are refreshed at short intervals, for example 250 ms, throughout the stabilization time. At the end of the stabilization time, the minimum value of the acquired RMS values is kept in memory to be used in the decision tree algorithm as the value M′.

[0072] Then at or shortly after the moment when the stabilization time has elapsed, a further RMS value M1 is measured, representing the lubrication condition in the stabilized bearing following the addition of g1. The following differential scalars are then calculated and stored:

[00004]$\Delta 1=\text{M0-M1}$

[00005]$\Delta \text{'}=\text{M0}-\text{M'}$

[0073] And the following evaluations are made in accordance with the flowchart of FIG. 3 :

[0074] If Δ′ > 3 & Δ′- Δ.sub.1 >3, the bearing condition is assessed as malfunctioning. This corresponds to a case where M′ is more than 3 dB lower than M0 and M1, i.e. the RMS value drops more than 3 dB and rises again more than 3 dB during the stabilization interval. The sequence is stopped at this point and the bearing is inspected.

[0075] If Δ.sub.1 < -1, the bearing condition is assessed as ‘overlubricated’: M1 is more than 1 dB higher than M0. As the normal Stribeck trend is downward as a function of a thicker lubrication film, the upward trend indicates that no additional grease is required and the process is stopped, after which the bearing is preferably inspected.

[0076] The next verification step, if the condition is not assessed as ‘overlubricated’, is whether or not the condition ‘-1 ≤ Δ.sub.1 < 1’ is fulfilled. If not, this means that Δ.sub.1 ≥ 1, i.e. M1 is at least 1 dB lower than M0. In this case, it is considered that the lubrication condition has improved, and that a further amount of lubricant may be added. If the condition ‘-1 ≤ Δ.sub.1 < 1’ is fulfilled, this means that M1 is within a range of minus 1 dB or plus 1 dB with respect to M0, i.e. the lubrication condition has not significantly changed. The status ‘no change’ is registered, and the sequence also proceeds to a further addition of lubricant.

[0077] With reference again to the flowchart in FIG. 3, an amount g2 equal to 0.15 G is supplied to the bearing following the outcome ‘lubrication improved’ or ‘no change’ after the g1-supply. Following the supply g2, a stabilization interval is allowed to elapse, and then a further ultrasound measurement M2 is acquired and stored, which is subsequently evaluated as follows:

[0078] If Δ.sub.2 (= M0 - M2) < 0, the bearing condition is assessed as ‘overlubricated’. In other words, when the RMS value M2 is higher than the initial RMS value M0, following a first value M1 more than 1 dB lower than or more or less equal to M0, the bearing is assessed as overlubricated, and the sequence is stopped, and preferably followed by a bearing inspection. This sequence is illustrated in FIG. 4a.

[0079] If the bearing is not overlubricated, the following condition is verified: ‘Δ.sub.2-Δ.sub.1 < -1’. If this condition is fulfilled, the lubrication condition is assessed as ‘lubrication success’, and the sequence is stopped. In other words, when M2 (being lower than M0) is more than 1 dB higher than M1 after M1 is more or less equal to or at least 1 dB lower then M0, the lubrication condition is considered satisfactory. The condition ‘lubrication success’ is registered and the sequence is stopped. This sequence is illustrated in FIG. 4b.

[0080] If ‘Δ.sub.2- Δ.sub.1, < -1’ is not fulfilled, the condition ‘-1 ≤ Δ.sub.2 - Δ.sub.1 <1’ is verified. If the latter condition is fulfilled, i.e. M2 is equal to or within 1 dB above or below M1, the condition is again stated as ‘no change’, and a further supply step is performed. This sequence is illustrated in FIG. 4c. If -1 ≤ Δ.sub.2- Δ.sub.1 < 1 is not fulfilled, i.e. M2 is more than one dB lower than M1, the lubrication condition is assessed as ‘improved’, and the sequence is continued with a further supply g3(=0.1 G) and acquisition M3. This sequence is illustrated in FIG. 4d. After subsequent supplies of lubricant starting from g3, the evaluation is different according to the results of the previous steps, as explained hereafter. For example, three consecutive cases of status ‘no-change’ will lead to stopping the procedure.

[0081] FIGS. 5a and 5b illustrate the next steps of the sequence. An amount g3 = 0.1 G is supplied and a stabilization time is allowed to elapse. Then a further RMS value M3 is acquired, and the assessment now depends on the results of the previous steps. FIG. 5a illustrates the flowchart that is applicable if g3 is added after a condition of ‘no change’ following g2.

[0082] First, the condition ‘Δ3 (= M0 - M3) < 0’ is evaluated, i.e.: is M3 higher than MO? If the answer is yes, the lubrication condition is assessed as ‘overlubricated’ and the sequence is stopped, preferably followed by the inspection of the bearing. An example of this sequence is illustrated in FIG. 6a. If the answer is no, a further verification is made regarding the condition ‘Δ3-Δ2 < -1’, i.e. is M3 more than 1 dB higher than M2 ? If this is the case, i.e. a ‘no change’ after g2 is directly followed by a rise of more than 1 dB after g3, the lubrication condition of the bearing is assessed as ‘lubrication failure’. An example of this sequence is illustrated in FIG. 6b. The sequence is stopped and the bearing is inspected. Qualitatively, this means that a ‘no change’ after the second supply g2 followed by a rise of more than 1 dB after the third supply, while M3 is still lower than M0 illustrates an abnormal bearing behaviour. The rise of the RMS indicates that the bearing is potentially operating too far into the HD region IV of the Stribeck curve at this point.

[0083] If ‘Δ3 - Δ2 < -1’ is not true, an additional verification is made concerning the condition ‘Δ3 - Δ.sub.1 < -1,5’, i.e. is M3, being lower than M0 and less than 1 dB higher than M2, more than 1.5 db higher than M1? If yes, the lubrication condition is assessed as ‘failed’ and the sequence is stopped. In other words, if the ‘no change’ after g2 is followed by a rise of more than 1.5 dB compared to M1, the lubrication condition is ‘failed’. An example of this sequence is shown in FIG. 6c.

[0084] If ‘Δ3 - Δ.sub.1 < -1,5’ is not true, i.e. M3 not more than 1.5 dB higher than M1 and M3 is also not more than 1 dB higher than M2, the condition ‘-1 ≤ Δ3 - Δ2 < 1’ is assessed. If this condition is true, i.e. M3 is equal to or within 1 dB above or below M2, the lubrication condition is assessed as ‘no change’. At this third stage however, an additional verification is made, namely whether or not this ‘no change’ is the third consecutive ‘no change’ condition that has been evaluated. If this is the case, it is found that the bearing condition is stable and acceptable, i.e. ‘lubrication success’ is recorded and the sequence is stopped. An example of this sequence is shown in FIG. 6d. It may be assumed at this point that the bearing has entered the EHD region and that this EHD region exhibits a very low rate of change of the friction coefficient. If not, i.e. when M3 is more than 1 dB lower than M2 following a ‘no change’ after g2, the lubrication condition is assessed as ‘improved’, and a further amount g4 is supplied. This sequence is illustrated in FIG. 6e.

[0085] FIG. 5b illustrates the flowchart that is applicable if g3 is added after a condition of ‘lubrication improved’.

[0086] First, and as in the chart of FIG. 5a, the condition ‘ Δ3 (= M0 - M3) < 0′ is evaluated, i.e.: is M3 higher than M0? If the answer is yes, the bearing is considered as overlubricated and the sequence is stopped, preferably followed by the inspection of the bearing. This sequence is illustrated in FIG. 7a. If the answer is no, the further verification is made regarding the condition ‘Δ3-Δ2 < -1’, i.e. is M3 more than 1 dB higher than M2 ? If this is the case, i.e. if the condition ‘lubrication improved’ after g2 (M2 more than 1 dB lower than M1) is followed by an increase of more than 1 dB (M3 is more than 1 dB higher than M2), the lubrication condition is assessed as ‘lubrication success’ and the sequence is stopped. An example of this sequence is illustrated in FIG. 7b. Qualitatively, this means that the bearing has entered the EHD regime, as determined by the rising trend following a downward trend in the previous step.

[0087] If ‘Δ3- Δ2 < -1’ is not true, i.e. M3 is not more than 1 dB higher than M2, the condition ‘-1 ≤ Δ3 - Δ2 < 1’ is assessed. If this condition is true, i.e. M3 is equal to or within 1 dB above or below M2, the lubrication condition is assessed as ‘no change’. Given the fact that the previous condition was ‘lubrication improved’, the ‘no change’ is not the third consecutive ‘no change’ condition. In this case, a further supply step g4 is performed. An example of this sequence is shown in FIG. 7c. If not, i.e. when M3 is more than 1 dB lower than M2 following a ‘lubrication improved’ after g2, the lubrication condition is assessed as ‘improved’, and a further amount g4 is supplied. An example is this sequence is shown in FIG. 7d.

[0088] The sequences shown in FIGS. 5a and 5b may be generalized, resulting in the flowcharts shown in FIGS. 8a and 8b that describe the assessment of the measurement Mn in view of the result of the result of measurement Mn-1, for n ≥3.

[0089] The decision tree algorithm always converges to a given end status, either ‘lubrication success’, ‘lubrication failure’ or ‘overlubrication’. Looking at the graphs in FIGS. 4a to 4d, 6a to 6e and 7a to 7d, it is clear that for n≥3 a lubrication success is linked to a stabilization of the RMS through three consecutive supplies, or to a significant rise of the RMS following a preceding significant fall of the RMS. These conditions reflect the Stribeck curve, respectively when the bearing is in the EHD regime or when the bearing enters the EHD regime after a downward trend of the RMS in the mixed lubrication regime. The graphs which indicate a lubrication failure are related to a rise of the RMS after a preceding stabilization of the RMS, indicating that the bearing is entering the HD area which is not desirable for optimal operation of the bearing.

[0090] The stepwise supply of the lubricant thereby allows to assess the bearing condition in a much more detailed way compared to the supply of the full amount of G, so that a lubrication failure can be detected more effectively.

[0091] As stated, the above-described algorithm is but one example of a possible decision tree algorithm, and many details may vary with respect to the above-described sequences. For example, the sub-portions g1, g2 etc may represent higher or lower percentages of the amount G, or the supply amounts may differ in a predefined way as a function of n.

[0092] Not all verification steps need to be included. For example, the additional verification of Δn - Δn-2 < -1,5 could be omitted. Also, the intermediary measurement M′ could be omitted.

[0093] An additional verification of the absolute level of M0 and preferably also M1 may be performed, before launching the sequence or the rest of the sequence. An alarm could be raised if M0 or M1 are outside a particular safety range around a predefined absolute level.

[0094] The lubricant amounts of g1=0.25 G, g2=0.15 G, gn=0.1 G for n≥3 represent a preferred sequence applicable to most lubricants such as for grease supplied to rolling element bearing. Other ratios of G may however be applied within the scope of the invention. In most cases, the method converges to a ‘lubrication success’ or ‘failure/overlubrication’ status before the sum of the supplied amounts reaches G. However, it is also possible that the sum of the supplied amounts surpasses G, indicating that the estimation of G has been too conservative. According to an embodiment, the replenishment interval T is shortened when it is determined that the method has not converged at n≥9.

[0095] Instead of or in addition to the RMS, other lubrication-related scalar indicators could be used in the method of the invention to strengthen the decision, such as x.sub.K (Kurtosis), defined as :

[00006]$x_K=x_{\left\{Kurtosis\right\}}=\frac{\frac{1}{N}{\displaystyle {.Math.}_{k=1}^N{x}_k^4}}{{\left(\frac{1}{N}{\displaystyle {.Math.}_{k=1}^N{x}_k^2}\right)}^2}-3$

[0096] The precise criteria for assessing this scalar indicator at each step may be different compared to the assessment of the RMS.

[0097] As stated above, the method of the invention is especially suitable for being applied in a fully automated manner, by a smart automated lubrication system according to the invention. This may be a system as illustrated in FIG. 2, wherein the processing unit 6 is configured to perform the steps of the method automatically, i.e. to run through the decision tree algorithm and to perform the replenishment in an incremental manner until a state of ‘overlubrication’, ‘lubrication success’ or ‘lubrication failure’ is reached. In the first and the third case, the system may generate a signal or message for the bearing to be inspected or repaired. The system is configured to perform multiple replenishments at predefined intervals, for example separated by T seconds or lower. The system may also automatically recalculate the T-interval based on the results of the decision tree algorithm. The system may be comprise multiple transducers mounted permanently in contact with multiple bearings.

[0098] While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure and the appended claims. In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope.