METHOD FOR DETERMINING THE REMAINING LIFESPAN OF A BEARING

Description

TECHNICAL FIELD

[0001] The present invention relates to bearings and in particular rolling bearings.BACKGROUND

[0002] Rolling bearings are commonly and widely used subassemblies in rotary machinery systems (RMS). They are used in the bearing arrangements of small and precise devices as well as in large industrial machines. The elements of bearings, such as balls, rollers, or raceways are exposed to multiaxial and non-proportional low and high-cycle fatigue loadings, which are usually the source of the rolling contact fatigue (RCF).

[0003] The fatigue life of bearings depends on many factors and variables, such as the size and direction of the contact forces, the geometry and roughness of the contact surfaces, the kind of material, the operating temperature, applied lubricant, lubrication conditions, rolling speed, and sliding in the contact area. As the possible damage of the rolling bearing determines the operation of the RMS, the proper estimation of the fatigue life or loading capacity of a rolling bearing becomes a crucial task in the machine design process. Additionally, difficulties with the detection of bearing element damages at the initial stages (damage detection is possible when damage achieves a certain size) justify the fatigue life prediction of rolling bearings.

[0004] EP 1 510 805 A1 discloses a method to determine a bearing indentation size and the bearing remaining life based on bearing vibration analysis.SUMMARY

[0005] A bearing in a machine will eventually fail, and the most common reason for failure is the formation of surface defects from the propagation of fatigue cracks or the removal of surface grains during operation. These defects occur due to insufficient lubrication and high contact stresses between the rolling element and the raceway of the bearing, causing spalls, dents, and pits to form on the contact surfaces.

[0006] If the remaining useful life of a bearing can be accurately predicted the potential damage can be avoided by maintenance implementations, e.g., to a achieve a maximum lifetime and minimum maintenance costs for the rotatory machinery system.

[0007] Hence, according to a first aspect, an improved method for determining a remaining useful life of a bearing having a surface defect is proposed as defined in independent claim 1.

[0008] According to a further aspect a computer program according to claim 6 is proposed.

[0009] According to a further aspect an apparatus according to claim 7 is proposed.BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figures 1a and 1bshow a schematic illustration of a ball bearing having different surface defects. Figure 2shows a schematic illustration of a ball bearing. Figure 3a schematic illustration of a vibration frequency spectrum of a bearing. Figure 4shows a schematic illustration of exemplary steps for determining a remaining useful life of a bearing. Figure 5shows a schematic illustration of exemplary steps for determining a surface defect size. Figure 6shows a schematic illustration of exemplary steps for determining a bearing stress. Figure 7shows a first schematic illustration of exemplary steps for determining the remaining useful life of a bearing. Figure 8shows a second schematic illustration of exemplary steps for determining the remaining useful life of a bearing. Figure 9shows a third schematic illustration of exemplary steps for determining the remaining useful life of a bearing. Figure 10shows a schematic illustration of exemplary steps for training an artificial neural network. Figure 11shows a schematic illustration of frequency amplitudes and surface defect sizes. DETAILED DESCRIPTION

[0011] The present invention will be further described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the particular embodiments described herein are only used to illustrate the present invention but not to limit the present invention. Accordingly, while example embodiments of the invention are capable of various modifications and alternative forms, embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that there is no intent to limit example embodiments of the present invention to the particular forms disclosed.

[0012] Specific structural and functional details disclosed herein are merely representative for purposes of describing example embodiments of the present invention.

[0013] Figure 1a and 1b show a schematic illustration of a rolling element 3 of a bearing. Therein balls are used as rollingelements 3 to maintain the separation between the bearing races.

[0014] Bearings in a machine will eventually fail, and the most common reason for failure is the formation of surface defects 12, as shown in Figure 1a and 1b, from the propagation of fatigue cracks or the removal of surface grains during operation. These surface defects 12 occur due to insufficient lubrication and high contact stresses between the rolling element 3 and the raceway of the bearing, causing spalls, dents, and pits to form on the contact surfaces. Of course the surface defects may be on the outer ring and / or inner ring or corresponding race(s) of the bearing. These defects 12 cause the applied load on the rolling element 3 to differ, resulting in higher than normal vibration amplitudes, cf. Figure 3. The condition of a defective bearing can be determined by analyzing this vibration response, which then can be used for scheduling maintenance actions as will be described in greater detail in the following.

[0015] A defect size d1, d2 may be measured and / or classified according to surface defect's length and / or width. In addition, different edge discontinuities on the inner race and / or outer race of the roller bearing may be considered. For the purpose of simplicity only the surface defects length will be discussed in the following. The length may be measured along the direction of the rolling element's motion, i.e. the raceway. Furthermore, a surface defect 12 may correspond to one or more of the following: one or more spall, one or more dents, and one or more pits. These surface defects form the contact surface of the rolling element 3 and the raceway of the bearing and give rise to corresponding vibrations.

[0016] The paper "Modelling and defect size estimation of a defective bearing", Francesco Larizza, Carl Q. Howard, Steven Grainger and Wenyi Wang, Proceedings of ACOUSTICS 2018, 7-9 November 2018, Adelaide, Australia proposes a model that can predict the vibration response of a defective bearing with a defect profile as an input into the model. Several defect size estimation methods have been suggested previously for bearings with line spall-defects based on detecting the time separation between the entry and exit events from the vibration signal.

[0017] Figure 2 shows a bearing 1 comprising a bearing inner ring 2, rolling elements 3 (for example bearing balls), and a bearing outer ring 4. A sensor module 5 which may comprise a vibration sensor 6. Additionally or alternatively, a sound emission sensor 7, and / or a so-called acoustic emission sensor 8 may also be provided. The sensor module 5 is connected to an apparatus 11 for performing diagnosis, such as determining a remaining useful life of the bearing. The sensor generated signals, which are picked up by the sensor module 5 and / or the sensors 6, 7, and / or 8 are forwarded to the apparatus 11. The signals which are generated by the vibration sensor 6 are evaluated within the apparatus 11, e.g., with the aid of vibration analysis. The vibration analysis may comprise a Fourier transformation of the time series sampled by the vibration sensor 6.

[0018] Turning to Figure 3 the frequency spectrum and corresponding amplitudes of a bearing having different types of defects is shown. In case of outer ring defects, i.e. surface defects on the outer race, the spectrum is characterized by the presence of harmonic peaks of the outer race failing frequency, e.g., between 8 and 10 harmonics of the ball pass frequency of the outer ring, whereas in case of inner race defects the spectrum shows several harmonic peaks of the inner race failing frequency, e.g., between 8 and 10 ball pass frequency of the inner ring harmonics. Rolling element defects, not shown, are characterized by the presence in the spectrum of harmonics of the rolling element deterioration frequency, e.g., according to the ball spin frequency.

[0019] Determining the remaining useful life, RUL, of rolling bearings is of great importance for machine operators. The exact calculation of the remaining service life of the rolling bearings, which are used in, e.g., a motor, is always difficult to perform since the necessary simulation models are very complex and are only applicable for the respective motor. In addition, the effort to validate such models is very large. Existing methods calculate the remaining useful life without taking into account bearing defects that have arisen during operation of the bearing or calculate the remaining useful life up to the formation of the first defects. In practice, it is important to calculate the remaining useful life of a bearing after the formation of one or more defects and thereby consider the evolution and change of the defect size during the further operation of the bearing.

[0020] Remaining Useful Life (RUL) of an equipment or one of its components is defined as the time left until the equipment or component reaches its end of useful life. Accurate RUL estimation is exceptionally beneficial to Predictive Maintenance, and Prognostics and Health Management (PHM). Data driven approaches which leverage the power of algorithms for RUL estimation using sensor and operational time series data are gaining popularity. Existing algorithms, such as linear regression, Convolutional Neural Network (CNN), Hidden Markov Models (HMMs), and Long Short-Term Memory (LSTM), have their own limitations for the RUL estimation task.

[0021] Typically, the entire service life for a new rolling bearing is calculated and a maintenance interval is recommended based thereon. To this end, the harmonious amplitudes of the bearing are evaluated and a damage class is determined. Then, the remaining useful life is estimated based on experience.

[0022] Turning to Figure 4, exemplary steps for determining the remaining useful life of a bearing are shown. Using the harmonic frequencies' amplitudes of the vibrations of the bearing, e.g. of the inner ring and / or the outer ring, which result from damage caused by a surface defect, a size of the surface defect of the bearing is determined. For example, one or more of the following frequencies may be used: The Ball Pass Frequency Inner raceway (BPFI), the Ball Pass Frequency Outer raceway (BPFO) and / or the Fundamental Train Frequency (FTF). In particular, (only) the 1 st< , 2 nd< and 3 rd< harmonics of the BPFI, BPFO and / or FTF may be used. In that case (only) the maximum amplitude of those harmonics may be used. Higher order harmonics may be neglected or filtered out.

[0023] Subsequently, the principal stresses caused by the surface defect in the bearing are determined, preferably taking into account the specific operating conditions of the bearing. Preferably the maximum, i.e. the largest, of the principal stresses is determined and used for calculating the remaining useful life. The principal stresses are the eigenvalues of the stress tensor and the eigen value of maximum magnitude is the maximum principal stress. Then, the remaining useful life of the bearing is calculated based on at least one of the principal stresses. To that end, a simulation model, which is, e.g., based on a finite element method, FEM, or a substitute model for the FEM method may be used in order to determine the principal stresses of the bearing. The principal stress may then be used to determine the remaining useful life based on a "hight cycle fatigue", HCF, algorithm.

[0024] Turning to Figure 5, exemplary method steps for determining the surface defect size are shown. The size of the one or more surface defects is determined with the help of a machine learning algorithm, such as a trained artificial neural network. For that purpose an artificial neural network ML is trained, e.g. with data from the numerical simulations. For example, the hyperparameters of the artificial neural network ML, such as the number of epochs may be set, e.g., to 500, and the learning rate may be set, e.g., to 0,2. However, other hyperparameters may be used. The training data may be obtained as a result of a simulation of a bearing having one or more surface defects - as will be described later in connection with Figure 10.

[0025] In a first step, during operation of the bearing and / or rotary machinery systems (RMS), time series data of the bearing's vibrations are generated, e.g. by sampling the vibration sensor data, e.g. according to the embodiment of Figure 2. The sampled data may be stored in a memory of a gateway such as an edge device or in a cloud-computing environment. Subsequently the time-series data may be Fourier transformed into frequency space yielding a frequency spectrum of the bearing's vibrations. Therein, the frequencies and amplitudes may be characteristic for specific bearing damages, e.g., whether a damage is present on the inner ring, outer ring and / or the rolling element itself, cf. as described in connection with Figure 3. The frequency spectrum or only part thereof is then be input into a machine learning algorithm, such as a trained neural network ML. The trained artificial neural network ML is operative to infer a surface defect size (on the inner ring, the outer ring or the rolling element) based on the input frequencies and / or their amplitude values.

[0026] In Figure 6 a schematic illustration of exemplary steps for determining a bearing stress is shown. Based on the surface defect size as, e.g., determined according to the embodiment of Figure 5, a bearing stress may be determined. This can be achieved by a finite element method or as shown in Figure 6 by a substitute model of said finite element method. The substitute model may be a polynomial of degree 5 and may be obtained from the simulation model of the bearing: = Σ n x k a k σ wherein x k denotes input parameters, e.g., defect size, (rotor) speed, and / or stress and a k denotes corresponding coefficients. The coefficients a k of the polynomial, may be determined by polynomial interpolation of the stress calculated by the bearing simulation as a function of the input parameters.

[0027] The calculation with the finite element method (FEM) hence may be replaced by a simplified substitute model that describes the stress with sufficient precision. As a result the principal stresses caused by the surface defect are obtained.

[0028] Instead of the principal stresses the substitute model may serve to obtain the contact force caused by the surface defect. The contact force or load may be determined based on the geometry and contact stress of bearing. In that case the contact force F or load P may also be modelled by a polynomial of degree 5: P = Σ n x k a k wherein x k denotes input parameters, e.g., defect size, (rotor) speed, and / or stressstress and a k denotes corresponding coefficients, as in the above. The coefficients a k of the polynomial may be determined by polynomial interpolation of the contact force calculated by the bearing simulation as a function of the input parameters.

[0029] Turning to Figure 7, exemplary method steps for determining the remaining useful life of the bearing are shown. The principal stress or the contact force as determined in accordance with the previous embodiments may be used as input for a calculation which yields a RUL as a result. The RUL calculation may be performed according to a high cycle fatigue, HCF, model.

[0030] In Figure 8 further details for determining the remaining useful life of a bearing are shown. Based on calculations according to the substitute model SM, the principal stresses caused by the surface defect are determined. Then, in order to determine the HCF effects of the surface defect Basquin's equation may be used. Basquin's equation is a power law relationship which describes the linear relationship between the applied stress cycles (S) and the number of cycles (N) to failure: N f , i σ i = σ i S f 1 b

[0031] Hence, the RUL as a number of cycles to failure may be obtained.

[0032] Figure 9 shows exemplary steps for determining the remaining useful life of a bearing based on the contact force. Similarly to Figure 8, the contact force caused by the surface defect may be obtained in accordance with a substitute model for determining the contact force as explained earlier. For determining the remaining useful life the ISO 281 specification may be used. According to ISO 281 the nominal lifespan is determined in millions of revolutions L10 or in operating hours L10h: L 10 = C P p or L 10h = 10 6 60 ⋅ n ⋅ L 10 wherein C is the dynamic load rating, P is the equivalent dynamic load and p is the p life time exponential and wherein p = 3 for ball bearings; and p = 10 / 3 for roller bearings.

[0033] Hence a machine learning model for the calculation of a defect size and a substitute model for calculating the principal stresses based on the defect size, and / or based on the catalog data and the operating conditions of the rotary machinery systems, e.g., a motor, is disclosed

[0034] Figure 10 shows a schematic illustration of exemplary steps for training an artificial neural network. First, in order to arrive at a suitable training data set a finite element method FEM is used. Based on the FEM, a data set comprising vibration frequencies and corresponding amplitudes on the one hand and surface defect sizes on the other hand is obtained. Thereby, a data set is obtained that connects the vibration frequencies of surface defects, such as ball pass frequency of the outer ring or inner ring, with different surface defect sizes. This data set may be used to train an artificial neural network ML. This trained artificial neural network ML may then be used for determining the surface defect size. Accordingly the trained artificial neural network ML may be used to determined principal stresses and / or the remaining useful life of the bearing as described in the above.

[0035] Now, in order to generate the data set the FEM calculation may be based on input parameters such as static input parameters and dynamic input parameters. The static input parameters may comprise the geometry, material properties and weight of the bearing, whereas the dynamic properties -which are varied while the static properties remain the same- may comprise different surface defect sizes and / or different rotor speeds. Thus, the FEM calculation yields vibration frequencies and corresponding amplitudes dependent on different surface defect sizes.

[0036] Figure 11 shows a schematic illustration of frequency amplitudes and surface defect sizes. In order to validate the inference capabilities of the trained artificial neural network ML the surface defect size inferred by the artificial neural network as a function of the amplitude of a certain vibration frequency has been cross checked with the results of a simulation model of the bearing for the same frequency.

Claims

1. Method for determining a remaining useful life (RUL) of a bearing (1) having a surface defect (12), comprising the steps of: determining a defect size (d1, d2) of the surface defect (12), based on, preferably sampled, oscillations of the bearing (1), e.g., harmonic oscillations of an inner ring (2) and / or outer ring (4) of the bearing (1), characterized in that the size (d1, d2) of the surface defect (12) is determined based on associating, using a trained machine learning model (ML), the sampled oscillations of the bearing (1) with the defect size (d1, d2) of the surface defect (12), determining, based on the defect size (d1, d2), at least one of a principal stresses (σ) or a contact force (F) of the bearing (1) caused by the surface defect (12), wherein determining at least one of the principal stresses (σ) or contact force is based on a substitute model (SM) of the bearing, wherein the size (d1, d2) of the surface defect (12) serves as an input for the substitute model (SM), and wherein the substitute model associates defect sizes with the principal stress or the contact force of the bearing, and determining the remaining useful life (RUL) of the bearing (1) based on at least one of the principal stresses (σ) and / or the contact force (F).

2. The method according to the preceding claim, wherein the step of determining the remaining useful life (RUL) of the bearing (1) is based on the maximum principal stress (σ).

3. The method according to the preceding claims, wherein the step of determining the remaining useful life (RUL) of the bearing (1) is based on a high-cycle-fatigue model.

4. The method according to the preceding claim, further comprising: loading the substitute model (SM) of the bearing (1), wherein one or more parameters of the substitute model (SM) are based on the operational conditions of the bearing (1), and / or model specific bearing data.

5. The method according to the preceding claim, further comprising: wherein the remaining useful life (RUL) is determined based on the high-cycle-fatigue model (HCF) and wherein the at least one of the principal stresses (σ) serves as an input for the high-cycle-fatigue model (HCF), wherein preferably the cycle count and the material degradation serve as parameters of the high-cycle-fatigue model (HCF) .

6. A computer program for carrying out the method steps of any one of the preceding claims.

7. A data processing apparatus (11) comprising means to carry out the method steps of any of the preceding claims 1-5.