Device for determining an updated statistical lifetime of a bearing, and associated wind turbine and method
By employing sensor-equipped rolling elements to measure real-time conditions and apply an evaluation life model, the method addresses the challenge of accounting for actual operating conditions in bearing life determination, enhancing reliability and reducing downtime.
Patent Information
- Application Number
- DE102024200162
- Authority / Receiving Office
- DE · DE
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2024-01-09
- Publication Date
- 2025-07-10
AI Technical Summary
Existing methods for determining the life of bearings, such as those used in wind turbines, fail to account for actual operating conditions, particularly variations in wind speed and turbulence, leading to uncertainties in load calculations and potential damage accumulation.
A method and apparatus using sensor-equipped rolling elements in bearings to continuously measure load, temperature, and rotational speed, coupled with an evaluation life model, to determine an updated statistical life value (USL) that considers real-time operating conditions, allowing for proactive maintenance and extended bearing life.
The USL provides a continuous assessment of bearing life, enabling early identification of critical conditions and reducing unscheduled downtime by allowing for timely countermeasures to extend bearing life and improve operational reliability.
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Abstract
Description
The present invention relates to determining the life rating of bearings, and more particularly to determining the updated statistical life of a bearing in a machine.The invention also relates to an apparatus for determining the updated statistical lifetime and a wind turbine comprising such an apparatus.During the design phase of a bearing, the calculation of the bearing's evaluation life is generally based on assumed or estimated application conditions and load cycles representative of the relevant application conditions of the bearing applied to a suitable simulation model of the bearings and the surrounding components.It is known to perform a simulation of the bearing, an accelerated life test of the bearing and a field test to validate the assumptions made during the design phase.However, the actual conditions of use of the bearing are not taken into account in this case.The bearing may be installed in a wind turbine so that the uncertainty of the loads due to variations in wind speed and turbulence acting on the bearing is not taken into account.Since the calculation of bearing life based on measurement data is not available, known condition monitoring systems and bearing inspection are used to analyze the bearing condition.Condition monitoring systems and bearing inspection are performed when the bearing is damaged to examine defects on the bearing, e.g., particles in the bearing, worn raceway surfaces.The present invention therefore contemplates considering the conditions of use of the bearing in the machine to determine the life rating of the bearing.According to one aspect, a method for determining an updated statistical service life value of a rolling bearing in a machine is proposed.The rolling bearing includes a stationary ring and a movable ring capable of rotating concentrically relative to each other, and at least one row of rolling elements interposed between a first raceway and a second raceway provided on the first and second rings, respectively.At least one of the rolling bodies is a sensor rolling body which comprises at least one load sensor which measures the load distribution via the sensor rolling body.The method comprises:determining a set of measurements, each measurement comprising at least load values of the load distribution measured by the load sensor of the sensor rolling element,determining a lifetime evaluation value for each measurement at least from the load values of the measurement and from an evaluation lifetime model of the bearing; anddetermining the updated statistical lifetime value at least from the lifetime evaluation values.The updated statistical lifetime USL is an indicator that allows the operating application conditions to be compared with the originally assumed or estimated application conditions, thus identifying critical application conditions that may lead to damage or accelerated damage accumulation, in order to increase the operating time of the bearing and to reduce unscheduled downtime of the machine.The USL with the method for determining the USL can be determined continuously, since the measurements are carried out continuously. The USL makes it possible to determine the trend of bearing life of the bearing. If the USL deviates, countermeasures may be initiated on the application to extend the bearing life of the bearing.Preferably, the sensor rolling element further comprises a temperature sensor measuring the temperature of the sensor rolling element and a speed sensor measuring the rotational speed of the sensor rolling element, each measurement further comprising a temperature value and a rotational speed value, wherein the life evaluation value of each measurement is further determined from the temperature value of the measurement, the rotational speed value of the measurement, geometric features of the bearing and features of a lubricant of the bearing and the evaluation life model.Advantageously, the method further comprises determining the misalignment value between the stationary ring raceway and the movable ring raceway from the load distribution, wherein the life evaluation value of each measurement is further determined from the misalignment value.Preferably, the method further comprises:determining a machine value of at least one parameter representative of the operating conditions of the machine associated with each measurement; andfor each measurement, storing the lifetime score value and the associated machine value.Advantageously, the method further comprises:determining an actual machine value of the parameter representative of the operating conditions of the machine; andcomparing the actual machine value and the stored machine values to find a stored machine value equal to the actual machine value, wherein the updated statistical life value is determined from the life evaluation values and the stored life evaluation value associated with the stored machine value equal to the actual machine value.Preferably, the machine is a wind turbine.According to a further aspect, a device for determining the updated statistical service life value of a rolling bearing in a machine is proposed.The rolling bearing includes a stationary ring and a movable ring capable of rotating concentrically relative to each other, and at least one row of rolling elements interposed between a first raceway and a second raceway provided on the first and second rings, respectively.The apparatus further comprises:a sensor rolling element which replaces a rolling element of the series of rolling elements, wherein the sensor rolling element comprises at least one load sensor which is designed to measure the load distribution over the sensor rolling element, wherein the load distribution comprises load values,an evaluation life model of the bearingfirst determining means configured to determine, for each measurement, a lifetime evaluation value from at least the load values of the load distribution of the measurement and from the lifetime evaluation value model of the bearing, andsecond determining means configured to determine said updated statistical lifetime value at least from said lifetime evaluation values.Preferably, the apparatus further comprises:third determining means adapted to determine a machine value of at least one parameter representative of the operating conditions of the machine associated with each measurement, andstoring means configured to store the lifetime evaluation value and the associated machine value for each measurement.Advantageously, the third determining means is further adapted to determine an actual machine value of the parameter representative of the operating conditions of the machine, wherein the apparatus further comprises comparing means adapted to compare the actual machine value and the stored machine values to find a stored machine value equal to the actual machine value, and wherein the second determining means is further adapted to determine the updated statistical lifetime value from the lifetime evaluation values and the stored lifetime evaluation value associated with the stored machine value equal to the actual machine value.According to a further aspect, a wind turbine is proposed which comprises a rolling bearing.The rolling bearing comprises a stationary ring and a movable ring capable of rotating concentrically relative to each other, and at least one row of rolling elements interposed between a first raceway and a second raceway provided respectively on the first and second rings, and a device as defined above.Further advantages and features of the invention will become apparent from the detailed, in no way restrictive, description of embodiments and the accompanying drawings, in which: FIG. 1 schematically shows an example of a machine according to the invention; FIG. 2 schematically shows an example of a roller bearing according to the invention; FIG. 3 schematically shows an example of a sensor rolling element according to the invention; FIG. 4 schematically shows an example of a processing module according to the invention; and FIG. 5 schematically shows an example of a method for determining the updated statistical life of the bearing in the machine according to the invention.Reference is made to FIG. 1, which schematically illustrates an example of a machine 1.The machine 1 may be a wind turbine comprising a generator 2, a screw 3, a shaft 4 connecting a shaft of the generator 2 to the screw 3, and a roller bearing 5 supporting the shaft 4.In other embodiments, the machine 1 may be a tunnel drilling machine, mining machine, or a large offshore crane.The machine 1 may further comprise a sensor 6 for measuring values of a parameter representative of the operating condition of the machine 1.The parameter representative of the operating condition of the machine may be e.g. the wind speed or the power generated by the wind turbine 1.The roller bearing 5 comprises at least one sensor rolling element 7.In a variant not shown, the wind turbine further comprises a gearbox connecting the shaft of the generator 2 to the shaft 4 of the wind turbine. A rolling bearing of the transmission can comprise the sensor rolling element 7. An example of the roller bearing 5 will be explained in more detail below.The sensor 6 and the sensor rolling element 7 communicate with a processing module 8.The sensor 6 can communicate with the processing module 8 via a wired or wireless connection.The sensor rolling element 7 communicates wirelessly with the processing module 8.An example of the processing module 8 will be explained in more detail below.FIG. 2 schematically shows an example of the roller bearing 5.The bearing 5 comprises an outer ring or stationary ring 9 provided with conically shaped first and second outer raceways for a first row 10 and a second row 11 of rolling bodies comprising tapered rollers. The bearing further comprises a movable ring provided with first and second inner rings or movable rings 12, 13 arranged axially one above the other and provided with conically shaped first and second inner raceways for the first and second roller rows 10, 11, respectively. Moreover, the bearing 5 further comprises a first cage 14 and a second cage 15 for holding the rollers of the first and second roller sets, respectively. Typically, the cages may be formed from segments that abut each other in the circumferential direction.In order to provide the required rigidity and to ensure a long service life, the bearing is prestressed. The axial position of the movable rings 12, 13 relative to the stationary ring 9 is adjusted so that the first and second roller sets 9, 11 have a negative internal play.In one variant, the bearing is not prestressed.In the illustrated bearing, at least one of the rolling elements in one of the first and second roller rows 10, 11 is replaced by the sensor rolling element 7. The shaft 4 is surrounded by and fixed to the movable rings 12, 13.The rolling bearing 5 comprises tapered rollers.In another embodiment, the rolling bearing 5 may comprise other types of rolling elements, e.g. cylindrical rollers or pendulum rollers. The rolling bearing 5 may also include only one row of rolling elements or more than two rows of rolling elements, wherein the number of cages is determined according to the number of rows.The rolling bearing 5, which comprises a series of rolling elements, has a single inner ring.In another embodiment, the outer ring 9 is the movable ring and the inner rings 12, 13 are the stationary rings.FIG. 3 schematically shows an example of the sensor rolling element 7.The sensor rolling element 7 comprises a rolling element 16 comprising a central bore 17 and a sensor unit 18 within the central bore 17 which extends through the rolling element 16.The sensor unit 18 comprises a housing 19 formed of two semi-cylindrical housings which are secured together by means of first and second end caps 20, 21 screwed onto respective first and second threaded portions 22, 23 at opposite axial ends of the housing. The housing of the sensor unit as a whole is shaped to fit in the roller bore 17 and is fixed to and arranged in the bore 17 by means of first and second sealing elements 24, 25.The sensor unit 18 further comprises a load sensor 26 for measuring the load distribution over the sensor rolling element 7.The sensor unit 18 may further comprise a speed sensor 27 for measuring the rotational speed of the sensor rolling element 7 in the bearing 5 and may further comprise a temperature sensor 28 for measuring the temperature of the sensor rolling element 7.The sensor unit 18 comprises a wireless transmitter 29 for transmitting measurement sets of the sensors 26, 27, 28, a scanner 30 for scanning the signals supplied by the sensors and a battery 31 for supplying the sensors 26, 27, 28 and the wireless transmitter.FIG. 4 schematically shows an example of the processing module 8.The processing module 8 comprises receiving means 32 connected to an antenna 33 of the processing module 8, first determining means 34, second determining means 35, third determining means 36, storage means 37 and comparing means 38.The receiving means 32 receives via the antenna 33 a real-time signal which is transmitted from the wireless transmitter of the sensor unit 18 and comprises sets of measurements of the sensors 26, 27, 28.The storage means 37 stores an evaluation life model MODEL of the bearing 5, may store a table TAB, and may further store a look-up table TAB 2.The first determining means 34 are intended to receive the temporal continuous signal comprising a set of measurements of the sensors 26, 27, 28, and are intended to determine the lifetime score for each measurement of the set of measurements at least from the load values of the measurement and from the evaluation lifetime model MODEL.The second determining means 35 is adapted to determine the updated statistical lifetime value USL from the lifetime evaluation values provided by the first determining means 34.The second determination means 35 comprise calculation means 39 implementing a Palmgren-Miner rule algorithm ALGO.An evaluation life model is a deterministic model that determines, based on input of application data, the number of revolutions that one of the two concentrically rotating rings of the bearing or disks of the bearing makes with respect to the other ring or disk before the first signs of fatigue develop in the material of one of the two rings or in the material of one of the disks or in the material of one of the rolling elements.The evaluation lifetime model MODEL may include the basic evaluation lifetime model defined in ISO 281, which includes a relationship between the load value P and the basic lifetime evaluation value L 10 i of a measurement i, the relationship being equal to: wherein:L 10i: the baseline evaluation lifetime score with a probability of 90% in millions of revolutions,C: the dynamic load bearing number in kN,P: the equivalent dynamic load of the bearing in kN determined from the load distribution measured by the load sensor 26; andp: a geometric constant (3 for ball bearings, 10 / 3 for roller bearings).In one variant, the evaluation lifetime model MODEL may take more than just the load into account. The evaluation life model MODEL may take into account, for example, features of a lubricant of the bearing 5 including the lubrication state of the bearing 5 and the contamination of the bearing 5, and geometric features of the bearing 5.The evaluation lifetime model MODEL may include the modified evaluation lifetime model defined in ISO 281, which includes a relationship between the modified evaluation lifetime model value L nm, the basic lifetime evaluation value L 10 i, a lifetime modification factor a 1 for reliability, and a lifetime modification factor a ISO that is equal to: where L nm is the modified evaluation lifetime value at a probability of n in millions of revolutions.a 1 is the Fife reliability modification factor.The life modification factor a ISO is equal to: where the factors e c and κ take into account features of the lubricant of the bearing 5 including the contamination and the lubrication state of the bearing 5, and C u is a fatigue load limit defined as the load at which the fatigue stress limit is just reached in the most heavily loaded raceway contact.The factor κ is equal to the kinematic viscosity of the lubricant of the bearing 5 divided by the reference kinematic viscosity of the lubricant.The factor κ is determined from the rotational speed of the bearing n i, the geometric features of the bearing 5 including the pitch circle diameter of the bearing 5, and the temperature of the bearing 5.The temperature of the bearing 5 is supplied from the temperature sensor 28.The bearing rotational speed n i, which is equal to the rotational speed of the shaft 4, is determined from the rotational speed of the sensor rolling element 7 measured by the speed sensor 27 of the sensor rolling element 7 and geometric features of the bearing 5 according to the following equation: wherein:n R: rotational speed of the sensor rolling element 7,d m: pitch diameter of the roller set in mm,D: diameter of the rolling element 5 in mm, andα: operating contact angle of the rolling element 5 in degrees,where d is m, D and α is geometric features of the bearing 5.In a variant, the evaluation lifetime model MODEL may further take into account the misalignment value between the stationary ring raceway and the movable ring raceway from the load distribution.In another embodiment, the evaluation lifetime model MODEL may include the modified reference evaluation lifetime model defined in ISO / TS 16281. In the modified reference evaluation lifetime model, the misalignment is described by a sipe model.The look-up table TAB2 determines the misalignment from the load distribution provided by the load sensor 26.The look-up table TAB2 is prepared from, for example, a simulation.The modified reference evaluation lifetime model is such that: wherein:L nmr: the modified baseline evaluation lifetime value at a probability of n in millions of revolutions,n s: is the number of lamellae,k: is the k-lamella,q kci: is the basic dynamic load bearing coefficient of the k-plate of the first and second inner rings 12, 13,q kce: is the basic dynamic load bearing coefficient of the k-plate of the outer ring 9,q is kei: the dynamically equivalent load on a k-blade at the inner rings 12, 13, andq kee: which is the dynamically equivalent load on a k-plate on the outer ring 9.q kci and q kce are determined from the number n s of the blades, the basic radial load bearing number and the features of the bearing 5.q kei and q kee are determined from the number of rolling elements, the load on each k-blade, and a stress function approximating the stress concentration on the raceway of the inner ring and the outer ring.In a variant, the modified reference evaluation lifetime model defined in ISO / TS 16281 may be implemented without considering the misalignment between the stationary ring raceway and the movable ring raceway.In another variation, the MODEL evaluation lifetime model may include, for example, a Generalized Bearing Life Model (GBLM) or an Advanced Fatigue Calculation Model (AFC).The sensor rolling element 7, the evaluation life model MODEL of the bearing 5, the first determination means 34, and the second determination means 35 constitute a device for determining the USL value of the rolling bearing 5 in the engine 1.The device for determining the USL value of the rolling bearing 5 in the machine 1 may further comprise the third determining means 36, the storing means 37 and the comparing means 38.When the machine 1 comprises the sensor 6 and the processing device 8 comprises the third determination means 36 and the table TAB, the third determination means 36 are intended to determine a machine value V1, Vn of the parameter representative of the operating conditions of the machine 1 provided by the sensor 5 associated with each measurement, and the storage means 37 are intended to store, for each measurement, the lifetime evaluation value LR1, LRn determined by the evaluation lifetime model MODEL and the associated machine value V1, Vn in the table TAB.FIG. 5 schematically shows an example of a method for determining the USL of the bearing 5 in the machine 1.The method implements the device for determining the USL value of the rolling bearing 5 in the machine 1.During a step 40, the sensor rolling element 7 determines a set of measurements.Each measurement includes at least load values of the load distribution measured by the load sensor 26 of the sensor rolling element 7.When the sensor rolling element 7 comprises the speed sensor 27 and the temperature sensor 28, each measurement further comprises a rotational speed value of the sensor rolling element 7 and a temperature value of the sensor rolling element 7.A set of measurements may comprise between forty and two thousand measurements, for example.When the machine 1 comprises the sensor 6, the third determination means 36 determine the machine value V1, Vn of the parameter representative of the operating conditions of the machine associated with each measurement.During a step 41, the first determining means 34 determines, for each measurement of the set of measurements, the lifetime evaluation value LR1, LRnfrom the load values of the load distribution of the measurement and from the evaluation lifetime model MODELcomprising the basic evaluation lifetime model defined in equation (1).When the sensor rolling element 7 includes the speed sensor 27 and the temperature sensor 28, the first determination means 34 determines, for each measurement of the set of measurements, the life evaluation value LR 1, LRnfrom the load values of the load distribution of the measurement, the temperature value of the measurement, and the rotational speed of the measurement, from the modified evaluation life model defined in Equations (2), (3), and Equation (4).When the sensor rolling element 7 includes the speed sensor 27 and the temperature sensor 28, the first determination means 34 determines, for each measurement of the set of measurements, the life evaluation value LR 1, LRnfrom the load values of the load distribution of the measurement, the temperature value of the measurement, and the rotational speed of the measurement, from the modified reference evaluation life model defined in Equations (3), (5), and Equation (4).In a variant, for each measurement of the set of measurements, the first determination means 34 determine the lifetime evaluation value LR 1, LRnfrom the load values of the load distribution of the measurement, the temperature value of the measurement, the rotational speed of the measurement and the misalignment, from the modified reference evaluation lifetime model defined in equations (3), (5) and equation (4).In one variation, the MODEL evaluation life model may include, for example, a Generalized Bearing Life Model (GBLM) or an Advanced Fatigue Calculation Model (AFC).Further, when the third determining means 36 determines the machine value V1, Vn of the parameter representative of the operating conditions of the machine associated with each measurement, the storing means 37 stores, for each measurement of the set of measurements, the life evaluation value LR1, LRn of the measurement and the machine value V1, Vn associated with the measurement, in step 40.The storage means 37 may store the life evaluation value LR1, LRn of the measurement and the machine value V1, Vn associated with the measurement in the table TAB or a database.During a step 42, when the life evaluation value LR1, LRn of each measurement of the set of measurements is determined by the first determining means 34 in step 41, the second determining means 35 determines the USL value of the bearing 5 from the life evaluation values determined by the first determining means 34.The calculation means 39 implement the Palmgren-Miner rule algorithm ALGO to determine the updated statistical lifetime value Ln, where n is an index related to the probability of failure, e.g. 1, 10, 50. wherein:j: index for each load case, andU j: duty cycle (percentage of occurrence of load case)LRj: Lifetime evaluation value determined from equation (1), (2) or (5).The duration between two successive measurements may be the same or different and may be, for example, four hours.In order to have an accurate USL value, when the storage means comprise the table TAB in which a plurality of machine values V1, Vn associated with the life evaluation values LR1, LRn are stored, the third determination means 36 determine at least one actual machine value from the measurements provided by the sensor 6 between two successive measurements of the set of measurements provided by the sensor rolling element 7. The comparing means 38 compares the actual machine value with the stored machine values in the table TAB to find a stored machine value equal to the actual machine value. The calculation means 39 implement the Palmgren-Miner rule algorithm ALGO in order to determine the updated statistical lifetime value Ln from the machine values determined by the comparison means 38 and stored machine values.The updated statistical lifetime is an indicator that allows the operating application conditions to be compared to the originally assumed or estimated application conditions and thus to identify critical application conditions that may result in damage or accelerated damage accumulation, to increase the operating time of the bearing and to reduce unscheduled down times of the machine.The USL determined with the method for determining the USL can be determined continuously, since the measurements are carried out continuously. The USL makes it possible to determine the trend of the bearing life of the bearing 5. If the USL deviates, countermeasures may be initiated on the application to extend the bearing life of the bearing 5.
Claims
A method for determining an updated statistical lifetime value of a rolling bearing (5) in a machine (1), said rolling bearing comprising a stationary ring (9) and a movable ring (12, 13) suitable for rotating concentrically relative to each other, and at least one row of rolling elements (10, 11) interposed between a first raceway and a second raceway respectively provided on said first and second rings, at least one of said rolling elements (10, 11) being a sensor rolling element (7) comprising at least one load sensor (26) measuring the load distribution across said sensor rolling element (7), said method comprising: - determining a set of measurements, each measurement comprising at least load values of the load distribution measured by said load sensor (26) of said sensor rolling element, - determining a lifetime evaluation value (LR1, lrn) for each measurement at least from the load values of the measurement and from an evaluation lifetime model (MODEL) of the bearing (5), and - determining the updated statistical lifetime value at least from the lifetime evaluation values (LR1, LRn).The method according to claim 1, wherein the sensor rolling body (7) further comprises a temperature sensor (28) measuring the temperature of the sensor rolling body (7) and a speed sensor (27) measuring the rotational speed of the sensor rolling body (7), each measurement further comprising a temperature value and a rotational speed value, wherein the life evaluation value (LR1, LRn) of each measurement is further determined from the temperature value of the measurement, the rotational speed value of the measurement, geometric features of the bearing (5) and features of a lubricant of the bearing and the evaluation life model (MODEL).The method of claim 2, further comprising determining the misalignment value between the stationary ring (9) raceway and the movable ring (12,13) raceway from the load distribution, wherein the life evaluation value of each measurement is further determined from the misalignment value.Method according to any one of claims 1 to 3, further comprising: - determining a machine value (V1, Vn) of at least one parameter representative of the operating conditions of the machine (1) associated with each measurement, and - for each measurement, storing the lifetime score value and the associated machine value (V1, Vn).The method according to claim 5, further comprising - determining an actual machine value of the parameter representative of the operating conditions of the machine (1), and - comparing the actual machine value and the stored machine values (V1, Vn) to find a stored machine value equal to the actual machine value, wherein the updated statistical lifetime value is determined from the lifetime evaluation values and the stored lifetime evaluation value (LR1, LRn) associated with the stored machine value equal to the actual machine value.Method according to any of claims 1 to 5, wherein the machine (1) is a wind turbine.Device for determining the updated statistical lifetime value of a rolling bearing (5) in a machine (1), said rolling bearing comprising a stationary ring (9) and a movable ring (12, 13) suitable for rotating concentrically relative to each other and at least one row of rolling elements (10, 11) interposed between a first raceway and a second raceway respectively provided on said first and second rings, said device further comprising: - a sensor rolling element (7) replacing a rolling element of said row of rolling elements (10, 11), said sensor rolling element (7) comprising at least one load sensor (26) configured to measure the load distribution over said sensor rolling element, said load distribution comprising load values, - an evaluation lifetime model (MODEL) of said bearing (5), - first determination means (34) configured to:, for each measurement, a lifetime evaluation value (LR1, LRn) at least from the load values of the load distribution of the measurement and from the lifetime evaluation model (MODEL) of the bearing (5), and second determination means (35) configured to determine the updated statistical lifetime value at least from the lifetime evaluation values.The device according to claim 7, further comprising: - third determination means (36) configured to determine a machine value (V1, Vn) of at least one parameter representative of the operating conditions of the machine associated with each measurement, and - storage means (37) configured to store, for each measurement, the lifetime assessment value (LR1, LRn) and the associated machine value (V1, Vn).The apparatus according to claim 8, wherein the third determining means (36) is further configured to determine an actual machine value of the parameter representative of the operating conditions of the machine (1), wherein the apparatus further comprises comparing means (38) configured to compare the actual machine value and the stored machine values (V1, Vn) to find a stored machine value equal to the actual machine value, and wherein the second determining means (35) is further configured to determine the updated statistical lifetime value from the lifetime evaluation values and the stored lifetime evaluation value (LR1, LRn) associated with the stored machine value equal to the actual machine value.Wind turbine (1) comprising a rolling bearing (5), said rolling bearing comprising a stationary ring (9) and a movable ring (12, 13) suitable for rotating concentrically relative to each other, and at least one row of rolling elements (10, 11) interposed between a first raceway and a second raceway respectively provided on said first and second rings, and a device according to claims 7 to 9.