Method for determining the reliability of a bearing

Abstract

The invention relates to a method for determining the reliability of a bearing, consisting of determining the geometric, material, and residual stress parameters, as well as the motor parameters, for a given bearing, and then performing a plurality of combinations of said parameters. In a second step, bearing damage models are used to determine a service life for each of said parameter combinations. Finally, from these service lives, a failure rate is established and compared to an acceptable failure rate. Abstract figure: Figure 2

Description

Title of the invention: Method for determining the reliability of a bearing technical field

[0001] The present invention relates to a method for determining the reliability of a bearing Previous technique

[0002] In the aeronautical field, bearings, such as ball or roller bearings, are used to enable the rotation of components such as compressor and turbine rotors. A bearing is typically evaluated according to a criterion known as the L10 criterion, developed by Lundberg and Palmberg [Lundberg G, Pamgre, A. Dynamic capacity of rolling bearings. J Appl Mech 1949; 16(2):165-72], which assesses the time after which 10% of the tested bearings have failed. However, such a failure rate is unacceptable in the aeronautical field, where the failure rate must be on the order of 10⁷, meaning one failure occurrence per ten million flight hours. Furthermore, the L10 criterion requires recalibration through testing, which would necessitate one hundred million hours of testing to achieve a failure rate on the order of 10⁷.

[0003] Thus, currently, an empirical determination of the bearing sizing parameters and materials is used, based on the engine on which they are intended to be installed. This relies on charts and the technical knowledge of operators, which prove difficult to use when the dimensional and material parameters of the bearings and / or the operating parameters of the engine are modified outside the pre-established ranges in the database.

[0004] There is therefore a need to allow validation of the suitability of the dimensional and material parameters of a bearing with the operating parameters of the engine on which it is intended to be installed. Summary

[0005] A method for testing the reliability of a bearing for an engine, such as a turbomachine engine, is thus proposed, comprising the following steps:

[0006] El)

[0007] - Determine >5 geometric, material and residual stress parameters of bearing PRj necessary to perform a bearing equilibrium calculation, j being an integer index varying between 1 and $ and designating one of said parameters, and

[0008] - Obtain A values ​​PRj. i for each of the $ parameters PRj, i being an index ranging from 1 to N and denoting a value of a parameter PRj,

[0009] E2)

[0010] - Determine R engine parameters PMk necessary to perform a calculation of equilibrium bearing, & being an integer index varying between 1 and R and denoting one of said R parameters, and

[0011] - Obtain A PMjfj values ​​for each of the R PMk parameters, i being an index ranging from 1 to N and denoting a value of a parameter PMk,

[0012] E3) Randomly associate a series of PRj.t values ​​with a series of PMu values in order to obtain N pairs of series Ca of values ​​of the parameters PRkj / PMjj,

[0013] E4) For each of the A pairs of series Cü, determine a series of values ​​of output parameters of a bearing balance calculation,

[0014] E5) Establish a damage model of a sublayer of the components unit bearing components, namely the outer ring, the inner ring and the rolling body, then determination of N minimum values ​​DDVSCnùn^ of sublayer service life,

[0015] E6) Establish a surface damage model of the unit components of the bearing, namely the outer ring, the inner ring and the rolling body, then determination of N minimum surface life values ​​DDVSmitij,

[0016] E7) Determine a global lifetime value DDV - global, of the minimum among DDVSCmini and DDYSmi^

[0017] E8) Compare each of the N values ​​of DDV - globab to the target lifetime

[0018] E9) Determine a failure rate.

[0019] In our method, we will use a data-driven approach, combined with bearing physics and a Monte Carlo methodology, to accurately evaluate the reliability of shaft line bearings. This involves combining a deterministic approach and a statistical Monte Carlo methodology to accurately estimate the reliability of bearings on a shaft line of a turbomachine, for example. It should be noted that this approach could be used in fields other than aeronautics, with the benefits described here.

[0020] Step El may include:

[0021] a. Determination of S bearing parameters PRj necessary for carrying out a bearing equilibrium calculation, j being an integer index varying between 1 and S,

[0022] b. Determination of a variation law for each of the PRj,

[0023] c. Generation of A PRj.i values ​​for each of the 5 PRj parameters using the variation law obtained in the previous step.

[0024] Step E2 may include:

[0025] a. Determination of R motor parameters PMk necessary for carrying out a bearing equilibrium calculation, k being an integer index varying between 1 and R,

[0026] b. Determination of a variation law for each of the motor parameters PMk,

[0027] c. Generation of N PM^ values ​​for each of the R PMk parameters using the variation law obtained in the previous step.

[0028] Step E4 can be performed by a bearing equilibrium calculation to obtain:

[0029] i. the contact pressure of the rolling body on the tracks of the inner and outer rings, in MPa

[0030] ii. the PV product which corresponds to the pressure multiplied by the sliding speed of the rolling body and the raceways of the inner and outer rings: unit in W / mm2,

[0031] iii. the surface stress tensor,

[0032] iv. the sublayer stress tensor,

[0033] v. the tensile stress related to the shrink-fit and the centrifugal force on the inner and outer rings in MPa, and

[0034] vi. the thickness of the oil film, denoted hO, between the rolling body and the tracks of the inner and outer rings, in microns

[0035] Step E5 may include:

[0036] a) The realization of an estimation of the sub-layer life for each of said bearing components from the sub-layer damage model and output parameters of a bearing equilibrium calculation for each unit component of the bearing, namely the outer ring, the inner ring and the rolling body respectively denoted BE_D^ BI_D{ and CR_Di, namely:

[0037] 1. DDVSC-B^ corresponding to the sub-layer lifetime for the inner ring,

[0038] 2. DDVSC- BEj corresponding to the sub-layer lifetime for the ring external,

[0039] 3. DDVSC-CR- corresponding to the sub-layer lifetime for the body of rolling,

[0040] In order to obtain N triplets of values ​​[ DDVSC-BIr DDVSC-BEp DDVSC-CR^,

[0041] b) determine the minimum DDVSCmin of each triplet of values ​​so as to obtain N minimum values ​​DDVSCminj of sublayer lifetime.

[0042] Step E6 may include:

[0043] a) The calculation of a surface life estimate for each of said bearing components from the sub-layer damage model and output parameters Dü of a bearing equilibrium calculation for each unit component of the bearing, namely the outer ring, the inner ring and the rolling element respectively denoted BE_D^ BIDt and CRDj, namely:

[0044] 1. DDVS-BIj corresponding to the surface life for the inner ring,

[0045] 2. DDVS-BEi corresponding to the surface life for the outer ring,

[0046] 3. DDVS - CRi corresponding to the surface life for the rolling body,

[0047] In order to obtain N triplets of values ​​[ DDVS-BI? DDVS-BE}, DDVS-CR;],

[0048] b) determine the minimum DDVSmin of each triplet of values ​​so as to obtain N minimum surface lifetime values ​​DDVSminj

[0049] The process may further include: - Provision of a maximum bearing failure rate (Tmux) - Definition of parameters P±, Pi of a Monte Carlo numerical simulation allowing the evaluation of said maximum failure rate Tmax, where: • P} corresponds to a number N of series pairs Cü of possible parameter values ​​PR for said bearing and PM for said motor, where ' is an integer index between 1 and N, • P2 corresponds to a target service life to be achieved for said bearing

[0050] The parameters P1 and P2 can be determined such that:

[0051] P]XP2> Number of simulated hours

[0052] Where Nb simulated hours = with ^max representing the maximum bearing failure rate

[0053] The target lifetime may be equal to at least 20,000 hours, preferably equal to 20,000 hours. Brief description of the drawings

[0054] Other features, details and advantages will become apparent upon reading the detailed description below, and upon analysis of the accompanying drawings, on which:

[0055] [Fig.1] [Fig.1] illustrates a turbomachine of a known type;

[0056] [Fig.2] [Fig.2] illustrates the flowchart of the process according to the this document;

[0057] [Fig.3] [Fig.3] illustrates the fourth step E4 of the process in this document;

[0058] [Fig.4] [Fig.4] illustrates the fifth step E5 of the process in this document;

[0059] [Fig.5] [Fig.5] illustrates the fifth step E6 of the process in this document;

[0060] [Fig. 6] [Fig. 6] illustrates the last three steps E7, E8 and E9 of the present process document ;

[0061] [Fig. 7] [Fig. 7] illustrates an example of a damage law for a component unit of a bearing for one of the defects such as sub-layer or surface defect, this curve establishing the correspondence between the number of cycles to failure and a given stress. Description of the implementation methods

[0062] Figure 1 represents a turbomachine 10 of a known type, comprising, from upstream to downstream (i.e., along the direction of airflow within the turbomachine), a blower 12 with a fan wheel that accelerates the incoming airflow. This airflow splits into a primary annular airflow and a secondary annular airflow surrounding the primary airflow. The primary annular airflow passes through a low-pressure and then high-pressure compressor 14, a combustion chamber 16, and a high-pressure and then low-pressure turbine 18.

[0063] The compressor 14 and the turbine 18 comprise rotors, the rotation of which is guided by means of bearings of various types, such as roller or ball bearings. Typically, each bearing comprises an inner annular ring and an outer annular ring, one of the inner and outer rings being fixed to a rotor and the other of the inner and outer rings being fixed to a stator component or to another moving part when the bearing is arranged between two moving parts rotating at different speeds and / or in different directions.

[0064] A turbomachine has many bearings, and it is easy to understand that controlling their lifespan, i.e., reliability, is essential for the proper functioning of the turbomachine.

[0065] During operation, two major types of defects can occur on a bearing or on its components. The first defect is deep spalling, which consists of sub-layer defects. In practice, spalling is observed, meaning a deep cracking within the part. The second defect is deep spalling initiated at the surface, which consists of spalling or cracking created in the vicinity of a defect caused by an indentation. An indentation is a defect resulting from the passage of one or more particles within the bearing between the rolling element and the inner and outer rings.

[0066] Mainly, the two aforementioned defects are observed on the inner ring, the outer ring and the rolling body, i.e. the rolling body between the inner ring and the outer ring.

[0067] As mentioned previously, the determination of the dimensioning parameters and materials of the bearings is carried out with a methodology not adapted to the desired service life conditions in the aeronautical world.

[0068] To this end, a method is proposed for determining the dimensioning and material parameters of a bearing.

[0069] The process is illustrated by the sequence of successive steps represented in [Fig.2].

[0070] The process comprises nine steps E1, E2, E3, E4, E5, E6, E7, E8 and E9 which are not not necessarily successive according to the successive sequence from one to nine. Thus, it must be understood that the term "step" in relation to a given number "X" does not mean that said step must necessarily be carried out after step X1 and before step X+1.

[0071] More specifically, as will become apparent from reading the description:

[0072] - Steps E1 and E2 are steps that can be carried out simultaneously or one after the other. The data obtained at the end of these steps E1 and E2 are used to carry out step E3. Thus, it must be understood that steps E1 and E2 must be carried out prior to step E3.

[0073] - Step E4 is carried out after step E3 and before steps E5 and E6.

[0074] - Steps E5 and E6 can be carried out simultaneously or one after the other the other. The data obtained at the end of steps E5 and E6 are used to carry out step E7, this last step E7 therefore being carried out after steps E5 and E6.

[0075] - Steps E7, E8 and E9 are carried out successively one after the other and in this order.

[0076] Prior to the implementation of steps E1 to E9, as illustrated in [Fig.2], the process comprises:

[0077] - Provision of a maximum bearing failure rate T}nax

[0078] - Definition of parameters P, Py of a Monte Carlo numerical simulation allowing the evaluation of said maximum failure rate Tmi!X, where: • Pi corresponds to a number A of pairs of series Cü with values ​​of possible PRi parameters for said bearing and possible PMt parameters for said motor, where ' is an integer index between 1 and N, • P2 corresponds to a target life to be achieved for said bearing

[0079] These parameters P1 and P2 are parameters that can be used in a Monte Carlo simulation.

[0080] P [ and P2 are determined such that:

[0081] Pi x P2 > Number of simulated hours [Equation 1]

[0082] Where simulated hours = with 9ui represents the maximum bearing failure rate,

[0083] By way of example, when aiming for a maximum failure rate Tmax of 10⁷, the number of simulated hours, which is then equal to 10⁹, cannot exceed the product P₁ x P₂ in order to verify the equation above. Thus, if we fix the target lifetime P2 to be achieved at 20000 hours, then it is appropriate to have a parameter P] which must be at least 50000 pairs of series Cü.

[0084] We will now describe steps E1 and E2.

[0085] Step El thus consists of: - Determine all the -S geometric and rolling material parameters PRj necessary to perform an equilibrium calculation, j being an integer index varying between 1 and S and denoting one of said parameters, and - Obtain N PRj values. i for each of the -S PRj parameters, * being an index ranging from 1 to N and designating a value of a PRj parameter.

[0086] A person skilled in the art is well acquainted with the geometric, material and residual stress parameters necessary to carry out a bearing equilibrium calculation which provides the output pressure parameters.

[0087] By way of example, for a ball bearing application, the geometric, material and residual stress parameters may include: the number of balls, the nominal diameter of each ball, the mean diameter of the bearing calculated from the center of the bearing to the center of a ball, the diametral clearance, the curvature of the radially external face of the inner ring, the curvature of the radially internal face of the outer ring of the bearing, the rotational regime of the inner ring.

[0088] By way of example, for a roller bearing application, the geometric, material and residual stress parameters may include: the number of rollers, the external diameter of the cylindrical part of each roller, the total length of each roller, the radii of connection of the cylindrical part of each roller to the flanks of the roller, the length of the cylindrical part of the roller, the calculated mean diameter from the center of the bearing to the center of a roller, the curvature of the radially external face of the inner ring, the curvature of the radially internal face of the outer ring of the bearing, or even the Young's modulus, Poisson's modulus, the residual stresses.

[0089] This step El comprises the following substeps: a. Determination of S geometric parameters, materials and residual rolling stress PRj necessary to perform a rolling equilibrium calculation, j being an integer index varying between 1 and 5, b. Determination of a variation law for each of the parameters PRj, c. Generation of N PRj i values ​​for each of the 5' PRj parameters in using the variation law obtained in the previous step.

[0090] Step b) above is carried out by collecting N values ​​of the PRj parameters. Thus, in relation to the example given previously of a failure rate of 107, for a given parameter such as, for example, the number of balls for a ball bearing, It will be necessary to collect at least N=50000 distinct values ​​of each number of marbles.

[0091] It is thus understood that it will be necessary to establish a list of N values ​​for each of the parameters PRj. The data obtained can be stored in a table having the The following general form, the table also being exemplified for a ball bearing: PRu (e.g., 1 represents the number of marbles) PRSi (e.g., S represents the nominal diameter of each marble) i = 1 ii = N (e.g., N = 50000)

[0093] Step E2 thus consists of: - Determine R motor parameters PMk necessary to perform a bearing balance calculation, where k is an integer index varying between 1 and R and designates one of said R parameters, and - Obtain N PM^ values ​​for each of the R PMk parameters, i being an index varying from 1 to N and designating a value of a PMk parameter,

[0094] The person skilled in the art is well aware of the PMk motor parameters necessary to carry out a bearing balance calculation allowing the pressure parameters to be obtained as output.

[0095] By way of example, for a ball bearing or roller bearing application, the motor parameters may include for example: for the operating point(s) considered the rotational speed of the inner ring, the rotational speed of the outer ring, the axial load permissible by the bearing, the radial load permissible by the bearing.

[0096] This step E2 comprises the following substeps: a. Determination of R, the motor parameters PMk necessary to perform a bearing balance calculation, where Σ is an integer index varying between 1 and R. b. Determination of a variation law for each of the motor parameters PMk, c. Generation of N PM^ values ​​for each of the R PMk parameters using the variation law obtained in the previous step,

[0097] Step b) of the paragraph above is carried out by collecting N values ​​of the PMk parameters. Thus, in relation to the example given previously of a failure rate of 107, for a given parameter such as, for example, the rotation speed of the inner ring, it will be necessary to collect at least N=50000 distinct values ​​of the rotation speed of the inner ring.

[0098] It is thus understood that a list of N values ​​for each of the PMk parameters must be established. The data obtained can be arranged in a table having the following general form, the table also being exemplified for a ball bearing:

[0099] In practice, there are as many tables as there are mission points. A technique called rainflow could be used to obtain a single table PMU (e.g., 1 represents the axial force) PMkj PMNj (e.g., S represents the radial force) 1=1 i iN (e.g., N=50000)

[0100] After obtaining the data concerning the bearings and relating to the operation of said bearings in the motor, the method consists of carrying out a step E3 in which a series of PRjj values ​​is randomly associated with a series of PM, j values ​​in order to obtain N pairs of series Cü of values ​​of the parameters PRkj / PMji.

[0101] In a step E4, for each of the N series pairs C^, a bearing equilibrium calculation is performed by solving the bearing equilibrium equations as illustrated in Figures 2 and 3, which allows the output parameters of said bearing equilibrium calculation to be obtained, namely i. the pressure between the rolling elements and the tracks ii. the PV product which corresponds to the pressure multiplied by the speed between the rolling elements and the tracks, iii. the surface stress tensor, iv. the sublayer stress tensor, v. the tensile stress related to the shrink-fit and centrifugal force, and vi. the thickness of the oil film, denoted hO, between the rolling elements and the raceways

[0102] Thus, each series of input parameters Cü is associated with a series Dj of output parameters (i to v above) for each use case ' which varies from I to A and up to 50000 in the example given previously ([Fig.3]).

[0103] It should be noted that the equilibrium equations of the bearing as well as the mathematical principle of balancing a bearing are described in the book Rolling Bearing Analysis, 5th Edition, by Tedric A. Harris & Michael N. Kotzalas.

[0104] The output data can be presented in the form of the following table (see also [Fig.3]): Pressure Product PV Surface stress tensor Sub-layer stress tensor Tensile stress related to shrinkage and centrifugal force Oil film thickness denoted h0 Di Di dn (ex:N=50000)

[0105] It should be noted that the method can draw upon the user's knowledge, allowing them to also use their empirical knowledge to estimate the output parameters. For example, it can be assumed that the column headings in the table immediately above vary according to a particular normal distribution, so that estimating the N values ​​of each parameter can be done more quickly. This method, however, proves to be less precise than calculating the parameters through a bearing equilibrium calculation, but faster.

[0106] The steps D1, E2, E3 and E4 described above are carried out for each of the unit components of said bearing, namely the inner ring BI, the outer ring BE and the rolling body CR. This gives A parameter values ​​D for the ring

[0107]

[0108]

[0109]

[0110] [YES]

[0112]

[0113]

[0114] internal denoted BI_D^ N parameter values ​​D for the outer ring denoted BE_Di and N parameter values ​​D for the rolling body denoted CR_Dt as illustrated in [Fig.4], To calculate the service life of each individual component of the bearing assembly—namely, the inner ring, the outer ring, and the rolling element—a damage model is established based on the first defect described previously: a subsurface defect. A subsurface damage model is established for each of the inner ring, outer ring, and rolling element. A damage model, either subsurface or surface damage, is created beforehand. For this purpose, a series of at least S bearings, where SS 40 is obtained, is produced. For each bearing, a contact fatigue test is performed, which is defined as a failure or material removal due to crack propagation caused by an alternating stress field close to the surface. During this test campaign, for each unit component of the bearing, namely the outer ring, the inner ring and the rolling body, the following parameters are measured or calculated: - The residual stress in the rolling direction and the orthogonal direction, - The stress resulting from the shrink-fitting of the inner and outer rings, - The pressure, and - The sublayer (or surface) stress tensor A person skilled in the art can use the following two formulas to first calculate the total stress and then the equivalent Tresca stress. Regarding the total stress for damage to the sub-layer, it is given by the following equation: / rrContact °U rrContact u 12 rtContact \ "13 a Total ~ ^Contact "12 srContact "22 rrContact "23 çyContact ,-rContact a23 rrContact i "33 / 1 ^Hoop "he 0 0\ 0 0\ + 0 0 0 + 0 0 \ 0 0 0 / 0 0 0 / [Equation 1] Where 0 represents the stress tensor expressed in MPa. The first part of the equation above corresponds to the stress generated by the contact problem, the second part corresponds to the stress resulting from the shrink fitting of the inner and outer rings, the third corresponds to the residual stress.

[0115] Regarding the total stress with respect to surface damage, This is given by the following equation:

[0116] / ^Contact irContact °I2 çyContMt ' 'ÏPh^ 0 0\ / —Hoop u 11 0 0) Total ~ (^Contact rrCmitact ^22 (^Contact 0 0 0 + 0 0 0 + si-Contact \ai3 rrContact °23 ^Contact a33 \ 0 0 0 / \ 0 0 0^

[0117] 1 0 0\ [equation 2] + 0 < 7^ 0 0 0 0 /

[0118] Where 0 represents the stress tensor expressed in MPa,

[0119] hb is the bead height,

[0120] hO the oil film thickness, and

[0121] being the coefficient of friction

[0122] The first part of the above equation corresponds to the stress generated by the contact problem, the second part corresponds to the contribution of the indentation, the third part to the stress resulting from the shrink fitting of the inner and outer rings, the fourth corresponds to the residual stress.

[0123] By tensor convention, index 1 corresponds to the circumferential direction of rolling, index 2 corresponds to a perpendicular direction of rolling and index 3 corresponds to the radial direction perpendicular to the first and second directions.

[0124] The Tresca equivalent stress equation (common to sublayer damage models and surface damage models) is obtained according to:

[0125] ° Tresca = ««X ^7 ' ^11 b I ^IH ' ^11 h! ' ^IHI ) [eqUaÜ°n 31

[0126] It will be noted that the Tresca equivalent stress allows us to obtain a scalar value from the stress tensor

[0127] For each unit component of the bearing among the S bearings tested, the number of cycles to failure is determined, which makes it possible to obtain a damage law or model associated with each unit component. For example, for the inner ring, the damage law is obtained by determining, for a given stress value, the number of cycles after which failure occurs. The number of cycles corresponding to failure corresponds to a stress frequency of the unit component at a given stress. Each damage law can be improved as the test campaigns progress.

[0128] The damage law takes the form of a curve having the following shape represented in [Fig.7]. It is understood that as the stress increases, the number of failure cycles is decreased.

[0129] Consequently, having established an underlayer damage model for each of the inner ring BI, the outer ring BE and the rolling body CR, it is possible to determine the underlayer life for each of said bearing components as illustrated in [Fig.4] through step E5a.

[0130] We thus obtain: 1. DDVSC - BL corresponding to the sub-layer lifespan for the inner ring, 2. DDVSC - BE { corresponding to the underlayer lifespan for the ring external, 3. DDVSC -CR, corresponding to the underlayer service life for the rolling body, In order to obtain N triplets of values ​​[ DDVSC-BI,, DDVSC-BE{, DDVSC-CR^

[0131] In a step E5b, the minimum DDVSCmin of each triplet of values ​​is determined so as to obtain N minimum sublayer lifetime values ​​DDVSCmin'.

[0132] Similarly, having established a surface damage model for each of the inner ring BI, the outer ring BE and the rolling body CR, it is possible to determine the surface life for each of said bearing components as illustrated in [Fig.5] through step E6a.

[0133] This gives us: 1. DDVS - BIj corresponding to the surface life for the inner ring, 2. DDVS - BEt corresponding to the surface life for the ring external, 3. DDVS - CRt corresponding to the surface life for the rolling body, In order to obtain N triplets of values ​​[ DDVS-BI^ DDVS-BE}, DDVS-CR,],

[0134] In a step E6b, the minimum DDVSmin of each triple of values ​​is determined so as to obtain N minimum values ​​DDVSmin' of surface lifetime.

[0135] In a step E7 illustrated in Figure 6, N overall lifetime values ​​are determined according to: DDVS - Overall: = DDVSCmin., DDVSmin. (step E7, [Fig.6]). I.J.

[0136] Each of the N DDVS-Global values ​​is compared to a target lifetime recorded in the database (step E8, figure 6) and a list of N positive (yes) or negative (no) failure values ​​is established (step E9, [Fig.6]).

[0137] Next, reliability is obtained by determining the ratio of the number of failures to the number of hours corresponding to the target service life. In the case of an aircraft engine, the target service life is at least 20,000 hours.

[0138] In practice, to carry out the simulation, the following will be performed: - Provision of a maximum bearing failure rate (Ttnax), - Definition of parameters Pj, ^2 of a Monte Carlo numerical simulation allowing the evaluation of said maximum failure rate Tmax, where: • P y corresponds to a number N of pairs of series Cü of values ​​of geometric, material and residual stress parameters PR, possible for said bearing and PM parameters, possible for said motor, where ' is an integer index between 1 and N, • P2 corresponds to a target service life to be achieved for said bearing The parameters P] and P2 can be determined such that:

[0139] P]XP2^Nb simulated hours

[0140] Where Nfr simulated hours = with Tmax representing the maximum bearing failure rate

[0141] While the method described above can be implemented using only the two models of surface damage and sub-layer damage, it is understood that other damage modes could be added, such as surface-initiated spalling. However, it should be noted that in aeronautics, the two damage modes mentioned above are the most important and must therefore be taken into account in a study and definition of the reliability of a new bearing.

Claims

Claims

1. A method of testing the reliability of a bearing for an engine, such as a turbomachine engine, comprising the following steps: E1) - Determine S geometric, material and residual bearing stress parameters PRj necessary to carry out a bearing balance calculation, j being an integer index varying between 1 and $ and designating one of said parameters, and - Obtain V PRj values, j for each of the PRj parameters, i being an index varying from 1 to V and designating a value of a PRj parameter, E2) - Determine R PMk engine parameters necessary to carry out a bearing balance calculation, k being an integer index varying between 1 and R and designating one of said R parameters, and - Obtain V PM values ​​for each of the R PMk parameters, i being an index varying from 1 to V and designating a value of a PMk parameter, E3) Randomly associate a series of PRjj values ​​with a series of PMk i values ​​so as to obtain N pairs of series Q of values ​​of the parameters PR^i / PMji, E4) For each of the V pairs of series Cü, determine a series of values ​​of output parameters Du of a balance calculation of the bearing, E5) Establish a damage model of a sub-layer of the unit components of the bearing, namely the outer ring, the inner ring and the rolling body then determine N minimum DDVSCtm^ values ​​of sub-layer life, E6) Establish a surface damage model of the unit components of the bearing, namely the outer ring, the inner ring and the rolling body, then determine N minimum DDVSmini values ​​of surface life, E7) Determine an overall lifetime value DDV - global of the minimum among DDVSCmini and DDVSnûni E8) Compare each of the N values ​​of DDV - global, to the target lifetime E9) Determine a reliability rate obtained by comparison with a target lifetime.

2. Method according to one of the preceding claims, in which step E1 comprises: a. Determination of S rolling parameters PRj necessary for carrying out a rolling balance calculation, j being an integer index varying between 1 and b. Determination of a variation law of each of the PRj, c. Generation of IV values ​​PRj. î for each of the $ parameters PRj using the variation law obtained in the previous step.

3. Method according to one of the preceding claims, in which step E2 comprises: a. Determination of R PMk engine parameters necessary for carrying out a rolling balance calculation, & being an integer index varying between 1 and R, b. Determination of a variation law for each of the PMk engine parameters, c. Generation of IV PM^ values ​​for each of the R PMk parameters using the variation law obtained in the previous step.

4. Method according to one of the preceding claims, in which step E4 is carried out by a calculation of the balance of the bearing making it possible to obtain: i. the contact pressure of the rolling body on the tracks of the inner and outer rings, in MPa ii. the product PV which corresponds to the pressure multiplied by the sliding speed of the rolling body and the tracks of the inner and outer rings: unit in W / mm2, iii. the surface stress tensor, iv. the sub-layer stress tensor, v. the tensile stress linked to the hooping and to the centrifugal force on the inner and outer rings in MPa, and vi. the thickness of the oil film denoted h0 between the rolling body and the tracks of the inner and outer rings in microns

5. Method according to one of the preceding claims, in which step E5 comprises: a) Carrying out an estimate of the sub-layer life for each of the said bearing components from the sub-layer damage model and output parameters Dü of a bearing balance calculation for each unit component of the bearing, namely the outer ring, the inner ring and the rolling body respectively noted BE_Dh BI I), and CR_Di, namely:

1. DDVSC - BI{ corresponding to the sub-lifetime layer for the inner ring, 2. DDVSC - BE; corresponding to the sub-life layer for the outer ring, 3. DDVSC - CRt corresponding to the sub-life layer for the rolling body, In order to obtain N triplets of values ​​[DDVSC-Bli, DDVSC-BE^ DDVSC-CR^ b) determine the minimum DDVSCnùn of each triplet of values ​​in order to obtain N minimum values ​​DDVSCmini of sub-layer lifetime.

6. Method according to one of the preceding claims, in which step E6 comprises: a) Carrying out an estimate of the surface life for each of the said bearing components from the sub-layer damage model and output parameters Du of a bearing balance calculation for each unit component of the bearing, namely the outer ring, the inner ring and the rolling body respectively noted BE_Dh BI_Dé and CR_Di, namely:

1. DDVS-BIj corresponding to the surface life for the inner ring, 2. DDVS-BE{ corresponding to the surface life for the outer ring, 3. DDVS - CR; corresponding to the surface life for the rolling body, In order to obtain N triplets of values ​​[ DDVS -BI^ DDVS-BEj, DDVS-CR^ b) determine the minimum DDVSmn of each triplet of values ​​so as to obtain N minimum values ​​DDVSmi^ of surface life

7. Method according to one of the preceding claims, in which it comprises: - Providing a maximum failure rate Tmax of the bearing - Defining parameters P^, P2 of a Monte Carlo numerical simulation making it possible to evaluate said maximum failure rate Tmax, where: • P\ corresponds to a number N of pairs of series P a of possible parameter values ​​PRi for said bearing and possible parameters PM{ for said motor, where ' is an integer index between 1 and N, • P2 corresponds to a target lifetime to be achieved for said bearing

8. Method according to the preceding claim, in which the parameters P{ and P2 are determined so that: P] x P2 > Nb simulated hours Where Nb simulated hours = 7^ with which represents the maximum failure rate of the bearing

9. Method according to one of the preceding claims, in which the target lifetime is equal to at least 20,000 hours, preferably equal to 20,000 hours.

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