Apparatus for calibrating spall propagation model of bearing, and related methods and systems
By identifying and calibrating two calibration values in the bearing, the problem of unreliable bearing residual service life estimation in the prior art is solved, accurate calibration and reliable prediction of the bearing peeling propagation model are achieved, and maintenance plans are optimized.
Patent Information
- Application Number
- CN202410600471.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2023-06-14
- Filing Date
- 2024-05-15
- Publication Date
- 2024-12-17
AI Technical Summary
Existing bearing residual service life estimates are not scalable and unreliable, and the peeling propagation model cannot be accurately calibrated for reliable predictions, resulting in the inability to effectively plan maintenance operations.
By measuring the bearings within a predetermined duration, determining the number of revolutions of multiple recorded, and identifying the status index values through spectrum analysis and trend analysis, determining two calibration values to calibrate the peeling propagation model, only two calibration values are required Accurately predict peeling size.
Reliable estimates of the remaining service life of the bearing and accurate prediction of peeling size are achieved, accidental downtime caused by unreliable estimates are avoided, maintenance intervals are optimized and maintenance costs are reduced.
Smart Images
Figure CN119147261A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a model for determining spalling propagation in bearings.
[0002] More specifically, the present invention relates to a method and apparatus for calibrating an exfoliation propagation model, and a system comprising such an apparatus and an exfoliation propagation model. Background Art
[0003] Typically, when a critical spalling size is detected using spectral analysis of vibration measurements, the bearing is replaced so that preventive maintenance operations cannot be planned to prevent unplanned downtime of the machine comprising said bearing.
[0004] Currently, experts estimate the remaining service life RUL of bearings for specific applications in order to prevent catastrophic failures.
[0005] Thus, when the remaining service life is less than a predetermined value, a maintenance operation can be planned to replace the bearings, thereby optimizing the duration of use of the machine.
[0006] However, the estimation of the bearing RUL made by the experts is not scalable and is based on the experts' experience, so the estimation varies from expert to expert.
[0007] This estimate is unreliable.
[0008] Furthermore, spalling propagation models can be used to make predictions.
[0009] In order to issue reliable predictions, the spalling propagation models need to be calibrated.
[0010] However, without exact knowledge of the values of the model's input parameters, including, for example, relationships to bearing speed, load applied to the bearing, bearing material and heat treatment, lubricant, temperature and / or pressure, it is possible to accurately calibrate the spall propagation model to output a predicted spall size accurately enough to publish reliable predictions. Summary of the invention
[0011] Therefore, the present invention aims to calibrate the spall propagation model to accurately predict the spall size, for example to estimate the remaining useful life of the bearing in a reliable manner.
[0012] According to one aspect, a method for calibrating a spall propagation model of a bearing is presented.
[0013] The bearing comprises a stationary ring and a rotating ring which can rotate concentrically relative to the stationary ring, and a rolling element between the stationary ring and the rotating ring, and the method comprises:
[0014] - determining a measurement of the bearing during a predetermined duration to obtain a plurality of records and measuring the number of revolutions of the bearing,
[0015] - process measurements to determine condition indicators,
[0016] - determining, from the condition indicator, a first calibration value representative of the occurrence of spalling in the stationary or rotating ring after N1 number of revolutions of the bearing and a second calibration value representative of the evolution of spalling in the stationary or rotating ring after N2 number of revolutions of the bearing, N2 being greater than N1,
[0017] - identifying at least one propagation phase of the spalling from the two calibration values, and
[0018] - Calibrate the spalling propagation model from two calibration values.
[0019] In contrast to methods known in the prior art, which require knowing the values of the input parameters of the spall propagation model in order to predict the spall size accurately enough to determine the bearing RUL, for example for planning maintenance operations, only two calibration values need to be determined to calibrate the spall propagation model.
[0020] Preferably, processing the measurements and determining the first calibration value comprises, for each record:
[0021] - perform spectral analysis on the measurement to determine the frequency spectrum of the measurement result,
[0022] - determining a condition index value which is the sum of the amplitudes of the identified frequency bins having a frequency equal to an integer multiple of a predetermined frequency which depends on the number of bearing revolutions and which is representative of a bearing defect,
[0023] When determining the status indicator value for each record:
[0024] - performing a trend analysis of the condition indicator value to identify a first positive gradient of the condition indicator value associated with a minimum number of revolutions,
[0025] - identifying a first reference value associated with the condition indicator value of the first positive gradient and a number of revolutions associated with the first reference value,
[0026] The first calibration value is equal to the number of revolutions associated with the first reference value.
[0027] Advantageously, determining a second calibration value comprises identifying, for each recording, a local extremum of at least one frequency bin and an associated number of revolutions, the second calibration value being equal to a predetermined peeling size according to the parity of the frequency bin.
[0028] Preferably, when at least the first frequency bin has a local maximum amplitude associated with a minimum number of revolutions, the second calibration value is equal to the number of revolutions associated with said local maximum amplitude and represents a spalling size equal to half the circumferential distance between two contact points of two adjacent rolling elements on the bearing raceway.
[0029] Advantageously, processing the measurements and determining the first calibration value comprises, for each recording:
[0030] - performing a repeated Fourier transformation of the measurement to obtain an excitation spectrum associated with a predetermined frequency,
[0031] - determining a condition indicator value which is the sum of the amplitudes of the excitation frequency bins having an excitation frequency equal to an integer multiple of a predetermined frequency which depends on the number of bearing revolutions and which is representative of a bearing defect,
[0032] When determining the status indicator value for each record:
[0033] - performing a trend analysis of the condition indicator value to identify a first positive gradient of the condition indicator value associated with a minimum number of revolutions,
[0034] - identifying a first reference value associated with the condition indicator value of the first positive gradient and a number of revolutions associated with the first reference value,
[0035] The first calibration value is equal to the number of revolutions associated with the first reference value.
[0036] Preferably, determining the second calibration value comprises, for each record:
[0037] - performing a trend analysis of the condition indicator value to identify a gradient equal to zero associated with a minimum number of revolutions, the minimum number of revolutions associated with the gradient equal to zero being greater than the minimum number of revolutions associated with a first positive gradient of the condition indicator value,
[0038] - identifying a second reference value associated with a gradient equal to zero and a number of revolutions associated with the second reference value,
[0039] The second calibration value is equal to the number of revolutions associated with the second reference condition indicator value and represents a size of spalling equal to the size of the Hertzian contact between the rolling elements and the stationary ring or the rotating ring.
[0040] Advantageously, the predetermined frequency is equal to outside the ball pass frequency of the bearing, inside the ball pass frequency of the bearing or to the ball rotation frequency of the bearing.
[0041] Preferably, calibrating the spall propagation model comprises inputting first and second calibration values and varying at least one input parameter of the spall propagation model such that a predicted spall size output by the model is equal to a spall size associated with the calibration values.
[0042] According to another aspect, an apparatus for calibrating a spall propagation model of a bearing is presented.
[0043] The bearing includes a stationary ring, a rotating ring that can rotate concentrically relative to the stationary ring, and rolling elements interposed between the stationary ring and the rotating ring.
[0044] The equipment includes:
[0045] - processing means configured to determine a condition indicator based on the measurement of the bearing,
[0046] - determination means configured to determine, as a function of the condition indicator, a first calibrated value representative of the presence of spalling in a stationary or rotating ring of the bearing after N1 number of revolutions of the bearing and a second calibrated value representative of the evolution of spalling in the stationary or rotating ring after N2 number of revolutions of the bearing, N2 being greater than N1,
[0047] - identification means configured to identify at least one propagation phase of the spalling from two calibration values, and
[0048] - A calibration device configured to calibrate the spalling propagation model from two calibration values.
[0049] According to another aspect, a system comprises an apparatus for calibrating a spalling propagation model as defined above and a spalling propagation model of a bearing. BRIEF DESCRIPTION OF THE DRAWINGS
[0050] Other advantages and features of the invention will appear on examination of the detailed description of embodiments, which are in no way limiting, and of the accompanying drawings, in which:
[0051] Figure 1 An example of an apparatus for calibrating a spall propagation model of a bearing according to the invention is schematically shown;
[0052] Figure 2 A first example of a method for calibrating a spalling propagation model according to the present invention is schematically shown;
[0053] Figure 3 schematically shows an example of frequency bins determined during spectrum analysis according to the invention,
[0054] Figure 4 schematically shows a second example of a method for calibrating a spalling propagation model according to the present invention, and
[0055] Figure 5 An example of a condition index value of the bearing rotation number according to the present invention is schematically shown. DETAILED DESCRIPTION
[0056] refer to Figure 1 , which schematically shows an example of an apparatus 1 for calibrating a spall propagation model of a bearing.
[0057] The device 1 is connected to a first sensor 2 intended to determine a measurement of a bearing 3 .
[0058] The first sensor 2 may measure acceleration, rotational speed, absolute or relative displacement, strain or vibration.
[0059] In the following, it is assumed that the first sensor 2 determines the vibration of the sensor 3 .
[0060] The bearing 3 includes a stationary ring 4 and a rotating ring 5 which are rotatable concentrically relative to each other.
[0061] It is assumed that the stationary ring 4 is the outer ring of the bearing 3 and the rotating ring 5 is the inner ring of the bearing 3 , the inner ring being fastened to a shaft (not shown).
[0062] The stationary ring 4 includes a raceway 4a, and the rotating ring 5 includes a raceway 5a.
[0063] The bearing 3 further includes rolling elements 6 interposed between the stationary ring 4 and the rotating ring 5 and rolling on the raceways 4 a , 5 a of the stationary ring 4 and the rotating ring 5 .
[0064] At least one cage 7 maintains the circumferential spacing of the rolling elements 6 .
[0065] like Figure 1 As shown, the rolling elements 6 are rollers.
[0066] In a variant, the rolling elements 6 may be balls.
[0067] The bearing 3 comprises a row of rolling elements 6 . In a variant, the bearing 3 may comprise more than one row of rolling elements 6 .
[0068] The device 1 comprises processing means 8 , determination means 9 , identification means 10 and calibration means 11 .
[0069] The device 1 is also connected to a circuit 12 implementing a spalling propagation model 12 a and to a second sensor 13 intended to measure the rotation speed of the rotating ring 5 .
[0070] The spalling propagation model 12a receives the first calibration value CV1, the second calibration value CV2 and an input vector I including at least one input parameter N as input.
[0071] The spall propagation model 12a outputs a predicted spall size Sps.
[0072] Vector I N More than one input parameter may be included.
[0073] The input parameters are, for example, the load applied to the bearing 3 , the temperature of the bearing 3 , the pressure applied to the rolling elements 6 , the material properties of the bearing 3 , the type of lubricant used to lubricate the bearing 3 , and the lubrication conditions of the bearing 3 .
[0074] The device 1 connected to the circuit 12 forms a system intended, for example, to issue a prediction regarding the remaining useful life URL of the bearing 3 .
[0075] Figure 2 A first example of a method for calibrating a spall propagation model 12 implementing a device 1 is schematically shown.
[0076] In step 20 , the first sensor 2 transmits vibration measurements of the bearing 3 .
[0077] In step 21 , the processing means 8 process the measurements of the sensor 2 in order to determine a plurality of records and to correlate the number of revolutions of the rotating ring 5 determined by the rotation speed measurements delivered by the second sensor 13 .
[0078] In step 22 , the processing means 8 processes the vibration measurements to determine a condition indicator and the determination means 9 determine, from the condition indicator, a first calibration value CV1 representative of the occurrence of spalling in the stationary ring 5 or rotating ring 4 and a second calibration value CV2 representative of the evolution of spalling in the stationary ring 5 or rotating ring 4 .
[0079] The processing means 8 performs a spectral analysis of the measurement for each recording to determine the measured spectrum. The processing means 8 implements, for example, a Fast Fourier Transformation FFT algorithm to perform the spectral analysis.
[0080] The determination means 9 determines a status indicator value for each record.
[0081] The condition indicator value is equal to the identified frequency bin, and the frequency is equal to the sum of the amplitudes of the identified frequency bins that are integer multiples of a predetermined frequency that depends on the number of revolutions of the bearing 3 .
[0082] The predetermined frequency represents a defect of the bearing 3 .
[0083] The predetermined frequency is equal to the ball pass frequency outside BPFO of the bearing 3 , the ball pass frequency inside BPFI of the bearing 3 , or the ball rotation frequency BSF of the bearing 3 .
[0084] BPFI in the ball frequency is equal to:
[0085]
[0086] BPFI in the ball frequency is equal to:
[0087]
[0088] The ball rotation frequency BSF is equal to:
[0089]
[0090] Wherein, N is the rotation speed of the rotating ring 4, N B is the number of rolling elements, β is the contact angle of the rolling elements, B D is the diameter of the rolling element, P D It is the average value of the raceways 4a and 5a.
[0091] Figure 3An example of frequency bins determined during the spectrum analysis in step 22 of the recording is shown according to the normalized spalling size.
[0092] A spalling size equal to 1 means that the spalling size is equal to the circumferential distance between two contact points of two adjacent rolling elements 6 on one of the raceways 4a of the stationary ring 4 and the raceways 5a of the rotating ring 5a of the bearing 3.
[0093] B1, B2, B3, and B4 represent the first harmonic, second harmonic, third harmonic, and fourth harmonic, respectively.
[0094] Of course, more frequency bins may be considered.
[0095] During a step 23 , when determining the condition indicator value for each record, the processing means 8 perform a trend analysis of the condition indicator value in order to identify a first positive gradient of the condition indicator value associated with a minimum number of revolutions.
[0096] Point P0( Figure 3 ) is associated with a first positive gradient of the condition indicator value having a minimum number of revolutions.
[0097] The processing device 8 identifies the first reference value associated with the condition indicator value (point P0 ) of the first positive gradient and the number of revolutions associated with the first reference value (point P0 ).
[0098] The first calibration value CV1 is equal to the number of revolutions N1 associated with the first reference value.
[0099] During a step 24 , the processing means 8 determine a second calibration value CV2 .
[0100] For each record, the processing means identifies at least one local extremum of a frequency bin and the associated number of revolutions ( Figure 3 ).
[0101] The second calibration value CV2 is equal to a predetermined peeling size according to the parity of the frequency bin.
[0102] When the first frequency bin B1 has a local maximum amplitude E1 associated with the minimum number of revolutions, the second calibration value CV2 is equal to the number of revolutions N2 associated with the local maximum amplitude E1 and represents a size of spalling equal to half the circumferential distance between two contact points of two adjacent rolling elements 6 on one of the raceways 4a of the stationary ring 4 and the raceways 5a of the rotating ring 5a of the bearing 3.
[0103] In a variant, when the first frequency element B1 and the third frequency element B3 have local maximum amplitudes E1, E3 associated with the minimum number of revolutions N2, the second calibration value CV2 is equal to the number of revolutions associated with the local maximum amplitudes E1, E3, and represents a size of peeling equal to half of the circumferential distance between two contact points of two adjacent rolling elements 6 on one of the raceways 4a of the stationary ring 4 and the raceways 5a of the rotating ring 5a of the bearing 3.
[0104] In another variant, when the odd-frequency bins B1, B3 have local maximum amplitudes E1, E3, and the even-frequency bins B2, B4 have local minimum amplitudes E1, E3 associated with the minimum number of revolutions N2, the second calibration value CV2 is equal to the number of revolutions associated with the local maximum and minimum amplitudes E1, E3, E2, E4, and represents a size of spalling equal to half the circumferential distance between two contact points of two adjacent rolling elements 6 on one of the raceways 4a of the stationary ring 4 and the raceways 5a of the rotating ring 5a of the bearing 3.
[0105] Other extreme values of the frequency bin can be identified to determine the value of the spalling size, for example when the spalling size is equal to one quarter of the circumferential distance between two contact points of two adjacent rolling elements 6 on one of the raceways 4a of the stationary ring 4 and the raceways 5a of the rotating ring 5a of the bearing 3.
[0106] The number of revolutions N2 is greater than the number of revolutions N1.
[0107] In step 25 ( Figure 2 ), the recognition device 10 recognizes the propagation stage of the peeling based on the two calibration values CV1 and CV2.
[0108] In this case, the recognition device 10 recognizes the propagation of spalling between spalling occurring on one of the raceways 4a, 5a associated with the first calibration value CV1 until the spalling reaches a length of half the circumferential distance between two contact points of two adjacent rolling elements 6 associated with the second calibration value CV2.
[0109] During a step 26 , the calibration means 11 calibrate the spalling propagation model 12 according to the two calibration values CV1 , CV2 .
[0110] The calibration device 11 inputs the two calibration values CV1 and CV2 into the spalling propagation model 12a and changes the input vector I N The input parameters are such that the predicted spalling size Sps output by the model 12a is equal to the spalling size associated with the calibration values CV1, CV2.
[0111] Model 12a may be a linear model with one input parameter.
[0112] Figure 4A second example of a method for calibrating a spall propagation model 1 implementing a device 1 is schematically shown.
[0113] Execute steps 20 and 21.
[0114] During a step 30 , the processing means 8 process the vibration measurements to determine a condition indicator and the determination means 9 determine, from the condition indicator, a first calibration value CV1 representative of the occurrence of spalling in the stationary ring 5 or rotating ring 4 and a second calibration value CV2 representative of the evolution of spalling in the stationary ring 5 or rotating ring 4 .
[0115] The processing means 8 perform a repeated Fourier transformation RFT of the measurements for each recording in order to obtain the excitation spectrum.
[0116] Document US 5,698,788 describes an example of processing RFT.
[0117] The determination means 9 determines a status indicator value for each record.
[0118] The condition indicator value is equal to the sum of the amplitudes of the identified excitation frequency bins having a frequency equal to an integer multiple of a predetermined frequency that depends on the number of revolutions of the bearing 3 and represents a defect of the bearing 3 .
[0119] Figure 5 An example of a recorded condition index value (curve C1 ) according to the number of revolutions of the rotating ring 4 is shown, the predetermined frequency being the ball pass frequency outside BPFO of the bearing 3 .
[0120] When the status indicator value is determined for each record, step 23 is performed.
[0121] Point P1( Figure 5 ) is associated with a first positive gradient of the condition indicator value having a first minimum number of revolutions N1.
[0122] During a step 31, the processing device 8 performs a trend analysis of the status indicator value for each record to identify a gradient equal to zero associated with a minimum number of revolutions, the minimum number of revolutions associated with the gradient equal to zero being greater than a first minimum number of revolutions associated with a first positive gradient of the status indicator value, and to identify a second reference value associated with the gradient equal to zero and the number of revolutions associated with the second reference value.
[0123] Point P2( Figure 5 ) is associated with a gradient equal to zero of the condition indicator value having the second small number of revolutions N2.
[0124] The number of revolutions N2 is greater than the number of revolutions N1.
[0125] The second calibration value CV2 is equal to the number of revolutions associated with the second reference condition indicator value and represents a spalling size equal to the size of the Hertzian contact between the rolling element 6 and one of the stationary ring 4 and the rotating ring 5 in the axial direction of the bearing 3 .
[0126] Perform steps 25 and 26.
[0127] The method for calibrating the spall propagation model 12a is based on determining the input parameters of the model 12a such that the predicted spall size output by the model 12a at at least two calibration values is equal to the spall size associated with the calibration values.
[0128] Contrary to calibration methods known from the prior art, no values of input parameters need to be determined.
[0129] The calibrated spall propagation model 12a can be used to determine the remaining useful life RUL of a bearing 3 with growing damage on the raceway surface of the stationary ring 4 or the rotating ring 5, which is crucial for optimizing and extending the maintenance intervals of the bearing 3 to prevent costs and dangers.
Claims
1. A method for calibrating a spalling propagation model (12a) of a bearing (3), the bearing (3) comprising a stationary ring (4) and a rotating ring (5) that can rotate concentrically relative to the stationary ring (4), and a rolling element (6) between the stationary ring (4) and the rotating ring (5), the method comprising: - determining the measurement of the bearing (3) during a predetermined duration to obtain a plurality of records and measuring the number of revolutions of the bearing (3), - process measurements to determine condition indicators, - determining, based on the condition indicator, a first calibration value (CV1) representing the occurrence of spalling in the stationary ring (4) or the rotating ring (5) after N1 number of revolutions of the bearing and a second calibration value (CV2) representing the evolution of spalling in the stationary ring (4) or the rotating ring (5) after N2 number of revolutions of the bearing, N2 being greater than N1, - identifying at least one propagation phase of the spalling from the two calibration values (CV1, CV2), and - Calibration of the spalling propagation model (12a) from two calibration values (CV1, CV2).
2. The method according to claim 1, wherein: Processing the measurements and determining the first calibration value (CV1) includes for each record: - perform spectral analysis on the measurement to determine the frequency spectrum of the measurement result, - determining a condition index value which is the sum of the amplitudes of the identified frequency bins having a frequency equal to an integer multiple of a predetermined frequency which depends on the number of bearing revolutions and which is representative of a bearing defect, When determining the status indicator value for each record: - performing a trend analysis of the condition indicator value (C1) to identify a first positive gradient (P0) of the condition indicator value associated with a minimum number of revolutions, - identifying a first reference value associated with the condition indicator value of the first positive gradient (P1) and a number of revolutions (N0) associated with the first reference value, - a first calibration value (CV1) equal to the number of revolutions (N1) associated with a first reference value.
3. The method according to claim 2, wherein: Determining the second calibration value (CV2) comprises identifying for each recording a local extremum (E1, E3) of at least one frequency bin (B1, B3) and the associated number of revolutions, the second calibration value being equal to a predetermined peeling size according to the parity of the frequency bin.
4. The method according to claim 3, wherein: When at least the first frequency bin (B1) has a local maximum amplitude (E1) associated with a minimum number of revolutions, the second calibration value (CV2) is equal to the number of revolutions associated with the local maximum amplitude and represents a spalling size equal to half the circumferential distance between two contact points of two adjacent rolling elements (6) on the raceway of the bearing (3).
5. The method according to claim 1, wherein: Processing the measurements and determining the first calibration value (CV1) comprises for each recording: - perform repeated Fourier transformation of the measurement to obtain the excitation spectrum, - determining a condition indicator value which is the sum of the amplitudes of the excitation frequency bins having an excitation frequency equal to an integer multiple of a predetermined frequency which depends on the number of bearing revolutions and which is representative of a bearing defect, When determining the status indicator value for each record: - performing a trend analysis of the condition indicator value to identify a first positive gradient of the condition indicator value associated with a minimum number of revolutions, - identifying a first reference value (P1) associated with the condition indicator value of the first positive gradient and a number of revolutions (N1) associated with the first reference value, - A first calibration value (CV1) is equal to a number of revolutions associated with a first reference value.
6. The method according to claim 5, wherein: Determining the second calibration value (CV2) comprises, for each record: - performing a trend analysis of the condition indicator value to identify a gradient equal to zero associated with a minimum number of revolutions, the minimum number of revolutions associated with the gradient equal to zero being greater than the minimum number of revolutions associated with a first positive gradient of the condition indicator value, - identifying a second reference value (P2) associated with a gradient equal to zero and a number of revolutions (N2) associated with the second reference value, The second calibration value (CV2) is equal to the number of revolutions associated with the second reference condition indicator value and represents a size of spalling equal to the size of the Hertzian contact between the rolling element (6) and the stationary ring (4) or the rotating ring (5).
7. A method according to any one of the preceding claims, wherein: The predetermined frequency is equal to the ball pass frequency outside the bearing, the ball pass frequency inside the bearing, or the ball rotation frequency of the bearing.
8. A method according to any one of the preceding claims, wherein: Calibrating the spall propagation model (12a) includes inputting first and second calibration values (CV1, CV2) and varying at least one input parameter of the spall propagation model so that a predicted spall size output by the model is equal to a spall size associated with the calibration values.
9. A device (1) for calibrating a spall propagation model (12a) of a bearing (3), the bearing comprising a stationary ring (4) and a rotating ring (5) which can rotate concentrically relative to the stationary ring (4), and a rolling element (6) interposed between the stationary ring (4) and the rotating ring (5), the device comprising: - processing means (8) configured to determine a condition indicator based on measurements of the bearing (3), - determination means (9) configured to determine, based on the condition indicator, a first calibration value (CV1) representative of the occurrence of spalling in a stationary ring (4) or a rotating ring (5) of a bearing (3) after N1 number of revolutions of the bearing and a second calibration value (CV2) representative of the evolution of spalling in the stationary ring (4) or the rotating ring (5) after N2 number of revolutions of the bearing, N2 being greater than N1, - identification means (10) configured to identify at least one propagation phase of the spalling from two calibration values (CV1, CV2), and - a calibration device (11) configured to calibrate the spalling propagation model (12a) from two calibration values (CV1, CV2).
10. A system comprising the device (1) according to claim 9 and a spalling propagation model (12a) of a bearing (3).
Citation Information
Patent Citations
Method for analysing regularly recurring mechanical vibrations
US5698788A