Method for designing and manufacturing an aeronautical part including a geometric accident

Abstract

Method for designing and manufacturing an aeronautical part comprising a geometric accident. One aspect of the invention relates to a method for designing an aeronautical part comprising a geometric accident (3), comprising the following steps: Estimation of a stress concentration coefficient from a nomogram of aeronautical geometric accidents developed by the following steps, for each geometric accident (3): Definition of a numerical model; Definition of a mesh (10) comprising a fixed portion (1) and a moving portion (2); Definition of one or more variants of the geometric accident (3), and for each variant: Adaptation of the moving portion (2); Calculation of a reference stress concentration coefficient; Determination of a lifetime of the aeronautical part from the stress concentration coefficient; and Design of the aeronautical part comprising said geometric accident (3).Figure to be published with the abbreviation: Figure 3.

Description

Title of the invention: Method for designing and manufacturing an aeronautical part comprising a geometric accident TECHNICAL FIELD OF THE INVENTION

[0001] The technical field of the invention is that of the design and machining of aeronautical parts.

[0002] The present invention relates to a method for designing and manufacturing an aeronautical part comprising a geometric accident. TECHNOLOGICAL BACKGROUND OF THE INVENTION

[0003] In a mechanical part, a geometric accident is a sudden and very localized discontinuity of the geometry, which may be desired, for example a drilling or a boss, or unwanted, such as a notch or a tear following an impact.

[0004] It is considered that if the overall behavior, for example in deformation or displacement, of the structure without the accident is the same as the behavior with the accident, then the geometric accident is "small". Generally speaking, it is considered that these geometric accidents are of sufficiently small dimensions, for example between 1 / 10th and 1 / 100th of the size of a structure which accommodates the mechanical part, and do not modify the behavior of the part during its use but can alter, or even degrade, its fatigue resistance and therefore its service life. It is therefore necessary to have tools in order to check that the geometric accident present, whether desired or not, does not degrade the service life of the part.

[0005] Three main tools are known from the literature for determining the impact of geometric accidents on the fatigue resistance of the part: • By a numerical analysis of the part taking into account all the geometric and mechanical properties of the geometric accident, • By reading an abacus of geometric accidents of mechanical parts and simplified numerical analysis of the mechanical part, • By load test on a specimen including a reproduction of the geometric accident.

[0006] The approach by numerical analysis of the complete part including the geometric accident makes it possible to remove doubts about the fatigue resistance of the part since all the properties of the geometric accident are taken into account. However, the implementation of this approach is difficult to envisage in a context of mass production or control, since it requires a significant amount of computer resources. Indeed, the reliability of the calculation depends intrinsically the accuracy of the calculation, and therefore the resources involved. This approach is mainly used occasionally for specific studies.

[0007] Since a geometric accident is small compared to the dimensions of the part, it is possible to model it, in a numerical analysis tool, by a stress concentration coefficient rather than taking into account its geometric shape and its complete mechanical properties. Indeed, taking into account a geometric accident can increase the computing cost by several orders of magnitude if it is represented completely. It is therefore preferable to take into account the geometric accident by representing it by a coefficient that will be equivalent to it. This allows for a simplified numerical analysis to be carried out more quickly and just as reliably as if the entire geometric accident had been taken into account. To do this, the stress concentration coefficient is determined by reading a geometric accident chart, such as the Peterson chart (Peterson's Stress Concentration Factors, 4th Edition, Walter D. Pilkey, Deborah F.Pilkey, Zhuming Bi, John Wiley & Son, 2020). This coefficient has the advantage of being simple and quick to determine since it involves a simple reading of the graph corresponding to the accident in question. Thus, if we know the geometric and loading characteristics of the geometric accident, it is possible to determine the associated stress concentration coefficient. Although this method is simple and quick to implement, the data available in these charts are not necessarily transposable to all industrial applications. This is particularly the case in aeronautics where the so-called "atypical" machining and use conditions of mechanical parts, such as turbine parts, are often beyond the data provided in the charts, which concern so-called "classic" manufacturing and use conditions of the parts.For example, in high pressure and low pressure turbines, some parts have multiple perforations and / or complex shapes of small dimensions (slots, disruptors, etc.) such as high pressure distributors, high pressure mobiles, low pressure distributors or low pressure mobiles. We can also mention the combustion chamber which includes multiple perforations. In addition, the use of an abacus is restricted by the very nature of the abacus, where the data are presented on two-dimensional graphs. In an aeronautical context, geometric accidents can depend on more than two parameters, which makes the use of such an abacus incompatible with the desired application.

[0008] Finally, subjecting a test piece to a load test is very time-consuming since the manufacture of a test piece requires a significant amount of time, but has the advantage of overcoming the limitations of charts. Indeed, it is possible to precisely define, depending on the application concerned, the desired geometry. of the specimen and the load test parameters in order to reproduce the geometric accident and evaluate its fatigue resistance. The disadvantage is that this method requires knowledge of the loading applied to the specimen for the formation of the geometric accident, which is not always the case either in the design or manufacturing phase for a desired accident, or in the control phase for an undesired accident. In addition, if several different geometric accidents are to be manufactured or controlled, it will be necessary to provide a specimen for each of the accidents, making the approach tedious, and all the more complex, to implement.

[0009] Thus, there is a need for a means of controlling the fatigue resistance of a mechanical part comprising a geometric accident which is compatible with the contexts of design, manufacture and control of an aeronautical part. Summary of the invention

[0010] The invention offers a solution to the problems mentioned above, by proposing a method for designing an aeronautical part comprising a geometric accident whose dimensioning satisfies the requirements of a specification associated with said aeronautical part.

[0011] A first aspect of the invention relates to a method of designing a part aeronautics including a geometric accident, comprising the following stages: • Estimation of a stress concentration coefficient from properties of the geometric accident and an aeronautical geometric accident chart, the aeronautical geometric accident chart comprising a set of reference stress concentration coefficients and being developed by the following steps: • For each reference geometric accident of a plurality of reference geometric accidents, each reference geometric accident of the plurality of geometric accidents being of a different type, • Definition of a digital model of the reference geometric accident; • Definition of a mesh comprising a fixed portion and a mobile portion, the mobile portion being circular in shape and being included in the fixed portion; • Definition of one or more variants of the reference geometric accident, the variant(s) comprising at least one geometric variant, at least one mechanical variant being associated with the at least one variant geometric, and at least one of the mechanical variants being a stress direction variant; • For each at least one geometric variant of the reference geometric accident: • Adjustment of the mobile portion of the mesh defined according to the geometric variant of the reference geometric accident; • Adaptation of the mobile portion adjusted according to at least one mechanical variant of the direction of constraint of the geometric variant; • Calculation of the reference stress concentration coefficient using a numerical solver and from the numerical model of the reference geometric accident as well as the adjusted and adapted mesh; • Determination of a lifetime criterion for the aeronautical part using a dedicated computer program and from a digital model of the aeronautical part where the geometric accident is replaced by the estimated stress concentration coefficient; and • Design of the geometric accident and of the aeronautical part comprising said designed geometric accident, provided that the determined lifespan criterion of the aeronautical part is greater than or equal to a desired lifespan criterion.

[0012] Thanks to the invention, it is possible to design an aeronautical part which comprises a desired geometric accident so that the aeronautical part complies with design and / or manufacturing and / or use requirements. For example, these are requirements in the specifications of said part, in particular concerning its fatigue resistance. The fatigue resistance is evaluated by estimating the service life of the part with a view to its intended use. The invention therefore makes it possible to estimate the impact in terms of damage of the geometric accident on the aeronautical part.

[0013] Advantageously, the design of the aeronautical part is based on the aeronautical geometric accident chart which is specifically developed for aeronautical parts and machines. The chart lists as exhaustively as possible the geometric accidents encountered in aeronautical applications and allows, from knowledge of the properties of a geometric accident, to estimate a stress concentration coefficient. The advantage of estimating such a coefficient is that it is possible to simulate, in a numerical solver, typically in finite element solving software, the geometric accident by the stress concentration coefficient. This coefficient then serves as a quantity equivalent to the geometric accident. It is therefore not necessary to fully model the geometric accident for the numerical solver to be able to estimate the service life of the aeronautical part which includes said geometric accident. In this case, the geometric accident is not drawn in the numerical model of the aeronautical part, but is represented by the stress concentration coefficient.

[0014] In particular, the development of the abacus is quick to implement since it is based on a mesh of which a portion is mobile. This mobile portion makes it possible to easily and quickly adapt the mesh to each variant of the geometric accident considered. Such a mesh, easy to adapt, makes it possible in particular to do without calculating a new mesh for each variant of each geometric accident to be studied. This mobile mesh therefore allows a significant saving of time to develop the abacus because only a few meshes are necessary, of the order of ten or a few tens, instead of hundreds or even thousands of meshes for each geometric accident.

[0015] In addition to the characteristics which have just been mentioned in the preceding paragraph, the method according to the first aspect of the invention may have one or more complementary characteristics among the following, considered individually or according to all technically possible combinations.

[0016] In one embodiment, the method further comprises a step of manufacturing said designed aeronautical part comprising the designed geometric accident.

[0017] In one embodiment: • At the estimation stage, a plurality of stress concentration coefficients are estimated from the known properties of the geometric accident and a tolerance margin on unknown properties; • In the life criterion determination step, a life criterion is estimated for the aeronautical part for each stress concentration coefficient of the plurality of stress concentration coefficients; and • At the design stage, the geometric accident is designed whose stress concentration coefficient, from the plurality of concentration coefficients, whose determined lifespan criterion is greater than or equal to the desired lifespan criterion.

[0018] Thanks to this embodiment, it is possible to design the geometric accident which is the most suitable, according to one or more criteria, for the aeronautical part and the use which will be made of it. In this case, the criterion(s) may relate to design and / or manufacturing and / or use requirements of said part, and more particularly to requirements of the specifications. It is in particular possible to design such a geometric accident by estimating the impact of several variants of the geometric accident on the lifetime of the designed part and to choose to design the variant of the geometric accident which best satisfies the criterion(s). Preferably, these are criteria such that the geometric accident is simple to produce, compatible with the manufacturing process of the aeronautical part and / or makes it possible to maximize the fatigue resistance of said part.

[0019] In one embodiment, the method further comprises a step of verifying the geometric accident on the manufactured aeronautical part, the verification step comprising the sub-steps: • Measurement of at least one dimension of the geometric accident on the manufactured aeronautical part; • Comparison of the dimension and data of the geometric accident with the aeronautical geometric accident chart to determine a final stress concentration coefficient; • Verification of the geometric accident by comparing a life criterion of the manufactured part with the desired life criterion, the life criterion of the manufactured aeronautical part being calculated by means of a dedicated computer program and from the digital model of the aeronautical part where the geometric accident is replaced by the final stress concentration coefficient.

[0020] Thanks to this variant, it is possible to use the aeronautical geometric accident chart so as to verify that the geometric accident of the manufactured part complies with the specifications, in particular in that it respects the desired service life required for said part. This variant makes it possible to detect whether the geometric accident has been correctly manufactured or whether it must be modified in order to meet the fatigue resistance requirements. This variant also makes it possible to know whether the part must be remanufactured, which may prove necessary if an anomaly appeared during the manufacture of the part.

[0021] In one embodiment, the method further comprises a step of validating the conformity of the aeronautical part to the occurrence of an undesired geometric accident, the undesired geometric accident resulting from the manufacture or use of said aeronautical part, the validation step comprising the sub-steps: • Measurement of at least one dimension of the unwanted geometric accident on the manufactured aeronautical part; • Comparison of the dimension and data of the unwanted geometric accident with the aeronautical geometric accident chart to determine a coefficient of alteration stress concentration; • Calculation of a lifespan criterion for the manufactured aeronautical part using a digital solver and from the digital model of the aeronautical part where the geometric accident is replaced by the alteration stress concentration coefficient; and • Validation of the conformity of the manufactured part by comparing the lifespan criterion of the manufactured part with the desired lifespan criterion.

[0022] Thanks to this embodiment, the geometric accident chart can also be used to detect a modification, in particular a degradation, of the fatigue strength of the mechanical part by the appearance of an undesired geometric accident. It is then possible to trigger an operation of modification of said part in order to restore its conformity to the fatigue strength requirements, in particular concerning its service life. If a modification does not make it possible to restore the integrity of the aeronautical part, then the manufacture of a new part can be triggered.

[0023] In one embodiment the defined mesh comprises a plurality of nodes and wherein the stress concentration coefficient is determined for each node of the plurality of nodes of the mesh.

[0024] In one embodiment the stress concentration coefficient determined for each node of the plurality of nodes of the mesh is different.

[0025] Thanks to this embodiment, it is possible to define a stress concentration coefficient gradient. It is therefore possible to simulate the mechanical impact of the geometric accident with greater precision and reliability.

[0026] In one embodiment, the aeronautical geometric accident chart is a multidimensional database comprising a subspace for each type of reference geometric accident, each subspace comprising each variant of the geometric accident with which the subspace is associated.

[0027] Thanks to this embodiment, it is possible to easily read and manipulate the aeronautical geometric accident chart since, in this case, the chart behaves like an analytical function which, for properties of one or more geometric accidents at the input, produces one or more stress concentration coefficients at the output.

[0028] In one embodiment in the step of calculating the reference stress concentration coefficient, the reference stress concentration coefficient is calculated from a maximization of a reference loading tensor, the reference loading tensor being estimated by the numerical solver.

[0029] Thanks to this embodiment it is possible to have a stress concentration coefficient which is simple, since it is a scalar, and which is representative of the mechanical impact of the geometric accident.

[0030] In one embodiment the calculation of the reference stress concentration coefficient for each variant of each reference geometric accident of the plurality of reference geometric accidents is distributed over a distributed computing infrastructure.

[0031] Thanks to this embodiment, it is possible to reduce the time required to develop the aeronautical geometric accident chart.

[0032] A second aspect of the invention relates to a computer program product comprising instructions which, when the program is executed on a computer, cause the latter to implement the steps of the method according to the first aspect of the invention.

[0033] A third aspect of the invention relates to a computer-readable recording medium comprising instructions which, when executed by a computer, cause the computer to implement the steps of the method according to the first aspect of the invention.

[0034] The invention and its various applications will be better understood upon reading the following description and examining the accompanying figures. BRIEF DESCRIPTION OF THE FIGURES

[0035] The figures are presented for information purposes only and in no way limit the invention. • [Fig. 1] is a block diagram illustrating the sequence of steps of the method according to the invention. • [Fig.2] is an example of a mesh according to the invention comprising a fixed portion, a mobile portion and a disc. • [Fig.3] is a simplified representation of the mesh according to the invention, comprising the fixed portion, the mobile portion and the disc. • [Fig.4] is a simplified representation of the mesh according to the invention, where the mobile portion and the disc are rotated. DETAILED DESCRIPTION

[0036] Unless otherwise specified, the same element appearing in different figures has a single reference.

[0037] The invention, according to a first aspect, relates to a method for designing an aeronautical part comprising a geometric accident. The design is implemented with the support of a geometric accident chart, comprising a set of coefficients of reference stress concentration. The use of this chart makes it possible to estimate a stress concentration coefficient for the geometric accident to be designed on the aeronautical part. The stress concentration coefficient then makes it possible to estimate the fatigue resistance of the part in the presence of the geometric accident and, if the fatigue resistance indicates a service life of the part compatible with a specification, the design of the geometric accident on the part is implemented.

[0038] [Fig.l] is a schematic representation of the sequence of steps of a method 100 for designing an aeronautical part comprising a geometric accident according to the invention. The method comprises three successive steps numbered 101 to 103.

[0039] Step 101 of the method 100 according to the invention is a step of estimating a stress concentration coefficient, noted in the following KT, associated with the geometric accident to be designed. The coefficient KT is notably estimated from properties of the geometric accident and from an abacus of aeronautical geometric accidents.

[0040] A geometric accident is understood to mean a sudden and local discontinuity in the geometry of the aeronautical part. A geometric accident may be desired, for example a drilling or a boss, and will then result from a design and, possibly, from machining. A geometric accident may also be undesired, for example a notch or a snag, and is linked to a manufacturing defect or an unforeseen event during its use or handling, such as a shock with another part.

[0041] The mechanical impact of geometric accident on the fatigue strength of a mechanical part, or of a structure on which the part is assembled, is governed by scale-independent properties, such as dimensional ratios or stress loading.

[0042] By way of example, in the embodiment described here, it is considered that the geometric accident is desired and that it is a cylindrical drilling in a direction orthogonal to a surface of the part. The drilling is carried out by sinking electroerosion (in English "Electrical Discharge Machining" - EDM). In this case, it is considered here that the aeronautical part is a blade to replace a defective blade on a turbomachine shaft. In another example, the part is mounted new and does not replace a defective part. The drilling is carried out on a wall connecting the exterior and the interior of the part, and allows the passage of the colder internal air to the warmer exterior of the part, thus cooling the wall.

[0043] The properties of the geometric accident are physical quantities characterizing the specific mechanical and / or geometric dimensions of the geometric accident to be designed. These properties differ from one type of geometric accident to another and Each geometric accident can be characterized by a number of different physical quantities, each of which has a different nature. For example, a cylindrical hole is characterized at least by the hole diameter and the hole angle, while a notch is characterized by its width, length and depth in the part material.

[0044] These properties can be defined upstream of the design according to specifications of the aeronautical part to be designed, for example according to requirements or constraints of design, manufacturing, assembly and / or use of the part. For example, the thickness of the material to be drilled is known since it is necessary to pass through the entire material of the blade at one of the ends, while the drilling diameter is determined according to the ventilation constraints, in particular the circulation flow rate and the overpressure rate ensuring the flow in the desired direction.

[0045] Furthermore, one or more of the physical quantities of the properties of the geometric accident may support a tolerance margin in the design of the geometric accident. The tool thus makes it possible to estimate a tolerance on the mechanical impact of the geometric accident, but especially on the geometric properties of the accident, or the loading to which it will be subjected. In this case, the design may be implemented from one or more threshold values ​​not to be exceeded, for example in the form of an interval of values, a maximum value or a minimum value. For example, the diameter to be applied to the geometric accident must not exceed a maximum diameter and a minimum diameter imposed by the specifications. The properties of the geometric accident therefore contain the maximum diameter and the minimum diameter admissible for drilling.Alternatively, these thresholds can be defined according to constraints of use of the device to carry out the geometric accident or by properties of the material of the part, such as its stiffness, its density, its hardness, etc.

[0046] The properties of the geometric accident are then compared with the data from the aeronautical geometric accident chart to estimate the KT coefficient.

[0047] The geometric accident chart can be developed in a paper format. The comparison is then carried out by reading one or more graphs associated with the desired type of geometric accident, here the cylindrical drilling orthogonal to the surface of the part. Each graph can include one or more curves representing the evolution of the KT coefficient as a function of one or more physical quantities characterizing the geometric accident. For example, a graph can include one or more curves representing the variation of the KT coefficient as a function of the drilling diameter. Thus, the estimation of the stress concentration coefficient is obtained quickly by simply reading a graph or by cross-reading several graphs from the aeronautical geometric accident chart.

[0048] The geometric accident chart can also be developed in a digital format, such as a database, for example in the form of a database recorded on a non-volatile memory. The advantage of using a digital format is that the reading and / or comparison with the chart can be carried out automatically. For example, the reading of the chart is carried out by means of a control interface which makes it possible to enter one or more physical quantities of the properties of the accident in order to automatically obtain the associated coefficient Kt, by means of an automatic computer search tool. Furthermore, in a digital format, the chart can be interpolated or regressed. In this case, the regression or interpolation works in a similar way to an analytical function which will estimate the coefficient KT as a function of the properties entered in the search tool.Interpolation / regression can, furthermore, be implemented using a machine learning algorithm.

[0049] Several geometric accident charts are known from the state of the art, the reference in this field being the Peterson chart (Peterson's Stress Concentration Factors, 4th Edition, Walter D. Pilkey, Deborah F. Pilkey, Zhuming Bi, John Wiley & Son, 2020). However, in the case of aeronautical parts, these charts are difficult to use since they list geometric accidents of parts for so-called "classic" cases, of design and use, whose properties can be synthesized in a paper format (i.e. by means of two-dimensional curves), which is not the case for geometric accidents in aeronautics which are characterized by more than two parameters. Indeed, most of the data available in these charts come from an accumulation of knowledge over several decades on geometric accidents encountered in the industry as a whole.However, aeronautical parts are designed for so-called "atypical" applications that differ from conventional parts in their context of use. For example, the parts of a turbomachine are subjected to very high stresses due to the high pressures linked to the operation of the engine. These engines also operate at very high speeds, following often brutal transient operating modes. These operating conditions being specific to aeronautics, the classically known charts cannot be easily used for these applications. Furthermore, in aeronautics, there are many variants of the same geometric accident that are very different from each other due to the high variability of the properties of this accident in such a context. Thus, even if a geometric accident is listed in the Peterson chart, all the variants of this accident encountered in an aeronautical context. would not be found there, since this abacus does not contain enough special cases to cover all the variants.

[0050] The invention therefore solves this problem by developing a geometric accident chart for aeronautical parts which lists a value of the coefficient KT for each of the reference geometric accidents of a plurality of reference geometric accidents and for each of the variants of a plurality of variants of each of the reference geometric accidents of the plurality of reference geometric accidents.

[0051] The abacus can be constructed according to one or more of the following methods: • By analytical resolution of mathematical equations allowing, from the properties of the reference geometric accident, to obtain the stress concentration coefficient; • By an empirical, experimental or numerical study.

[0052] The analytical approach has the advantage of providing complete data for each type of reference geometric accident concerned. The disadvantage is that this approach is only feasible for accidents with few characteristic physical quantities, typically two to three. It can therefore be used for certain simple geometric accidents, but is not feasible for developing the most exhaustive possible chart also listing geometric accidents characterized by a large number of physical quantities.

[0053] The empirical approach, on the contrary, makes it possible to obtain KT coefficients despite a large number of physical quantities characteristic of the accident. An experimental study allows an almost exact estimation of the KT coefficient, to the detriment of the implementation time since it is necessary to produce a large number of test specimens, one for each variant of each reference geometric accident. A numerical study, for its part, makes it possible to estimate a large number of KT coefficients independently of the type of the reference accident, the number of reference accidents and the number of variants of each accident.

[0054] The term "variant of a geometric accident" means a geometric accident of a specific type, for example a drilling, of which at least one of the characteristic physical quantities is different from that of another geometric accident of the same type. A geometric accident therefore comprises one or more variants, each different from the others. Preferably, the properties of the geometric accident are dimensionless and a variant of the geometric accident is characterized by a specific ratio between its properties. For example, this may be the diameter / thickness ratio for a drilling, which, for example, takes values ​​between 0.1 and 2.

[0055] Two types of variants can be distinguished: geometric variants and mechanical variants. Geometric variants are all variants of the geometric accident that only concern differences in the shape or dimensions of said accident. For example, a drilling with a larger or smaller diameter with a more or less acute drilling angle are geometric variants of the drilling. In a complementary manner, mechanical variants are variants that only concern differences in the non-geometric properties of the geometric accident. A mechanical variant can therefore relate to a temperature, a loading, a stress direction, etc.

[0056] In order to be sufficiently exhaustive, the abacus must therefore list a value of the coefficient KT for each of the reference geometric accidents of a plurality of reference geometric accidents, the reference geometric accidents being of different types from each other, and for each of the variants of a plurality of variants of each of the reference geometric accidents of the plurality of reference geometric accidents. To take the previous example of a reading of graphs from the abacus, the curves of the graphs must each include enough points to allow interpolation / regression to variants that will not have been studied.

[0057] The term "point of a curve" means the association of a value of the KT coefficient with the value of at least one of the physical quantities characteristic of the reference geometric accident for a given variant. The objective is therefore to develop the abacus from a sufficiently large number of variants of each type of reference geometric accident to allow a robust estimation of the KT coefficient.

[0058] Alternatively, the geometric accident chart can be interpreted as a multidimensional database comprising a plurality of multidimensional subspaces, each of the subspaces being associated with a reference geometric accident type and representing the multiplicity of variants of the reference accident type. Each subspace is defined by one or more dimensions which therefore each correspond to one of the physical quantities of the characteristic properties of the reference geometric accident. Each subspace therefore makes it possible to associate a coefficient KT with each combination of values ​​of the physical quantities characterizing the reference accident. In this case also, each subspace must include enough points to allow interpolation / regression to variants which have not been studied. Interpolation / regression can also be implemented using a machine learning tool, a network of neurons or a kernel machine. The interpolation / regression then forms an interpolated or regressed subspace of the KT coefficients for each geometric accident.

[0059] In the example of cylindrical drilling, five physical quantities can be used to characterize the geometric accident: a ratio of the drilling radius to the drilling thickness, a drilling angle, a stress direction, a biaxial stress ratio and a temperature. It can be considered, to ensure robust interpolation / regression at points not studied for this geometric accident, that 7 values ​​are required for the ratio of the drilling radius to the drilling thickness, 6 values ​​for the drilling angle, 6 values ​​for the stress direction, 18 values ​​for the biaxial stress ratio and 3 values ​​for the temperature. This therefore corresponds to a total of 13608 points, which are as many variants to be studied of the accident.

[0060] It therefore appears that an experimental empirical study is not feasible to study each of the reference geometric accidents of the plurality of reference geometric accidents of different types. Thus, a numerical empirical study is preferred for the completeness of the aeronautical geometric accident chart.

[0061] The aeronautical geometric accident chart is developed by implementing six successive steps numbered from 110 to 160. Steps 110 to 130 are implemented for each of the reference geometric accidents of the plurality of reference geometric accidents of different types. Steps 140 to 160 are implemented for each of the variants of the plurality of variants of each of the reference geometric accidents. For each variant, a coefficient KT is thus determined.

[0062] Step 110 is a step of defining a digital modeling of each of the reference geometric accidents. Preferably, each of the reference geometric accidents is modeled by computer-aided design or by a digital drawing interface. For example, the digital model is defined by means of computer-aided design software such as Solidworks™ or CATIA™.

[0063] The digital model is for example drawn by an operator or created automatically by the computer-aided design software based on the properties of the reference geometric accident. Preferably, the digital model is drawn based on geometric physical quantities which characterize the reference geometric accident.

[0064] The advantage of using digital modeling software is that, once the model has been defined, it is possible to apply variations to some of the dimensions of the reference geometric accident. For example, in the case of drilling, it is possible to define the drilling angle as a variable physical quantity so as to create, from the same digital model, several variants of the reference geometric accident, each having a different drilling angle. In the same way In this way, the thickness of the pierced material can be the variable physical quantity to produce several variants of the reference geometric accident, each to pierce a different thickness of material.

[0065] Step 120 is then a step of defining a mesh for each reference geometric accident of the plurality of reference geometric accidents. This mesh will be used by numerical analysis software to study the reference geometric accident. Preferably, the mesh is defined to be used by numerical resolution software based on the finite element method. The mesh is, for example, defined using meshing software, such as ANSA™ software.

[0066] The mesh comprises a set of nodes. The arrangement of the mesh nodes delimits geometric shapes in the mesh, called elements. The number and position of the nodes, and therefore of the elements, of the mesh depend on the reference geometric accident to be studied, and in particular on its geometric dimensions and variations and the desired calculation precision. These nodes and elements can also be defined according to the professional knowledge of the operator wishing to study the reference geometric accident.

[0067] If the definition 110 of a digital model is easily automated, the automatic definition 120 of a mesh is more delicate. Indeed, it is known from the state of the art that automatic meshing tools have fairly poor performance on objects whose geometric shapes are small, irregular and / or non-uniform, and produce results that are not very robust and not very reliable.

[0068] In the case of drilling, only the temperature and the biaxial stress ratio have no impact on the choice of the mesh when defining it. On the contrary, the ratio of drilling radius to drilling thickness, drilling angle and stress direction have an impact on the definition of the mesh. In the case of drilling, at least 252 meshes are necessary to study enough variants for this reference geometric accident. The problem that arises then is that the production of 252 meshes for the sole case of drilling is far too time-consuming to be achievable in a reasonably short time.

[0069] The present invention therefore provides a solution to this problem by proposing a dynamic mesh. The mesh 10 is illustrated in [Fig.2] and [Fig.3]. [Fig.2] is a modeling of the mesh 10 in a digital meshing tool and [Fig.3] is a schematic representation of said mesh 10. In these figures, the geometric accident 3 is a drilling.

[0070] The mesh 10 comprises a fixed portion 1, also called box 1. The mesh 10 also comprises a mobile portion 2, also called ring 2. The ring 2 is included in the box 1 and is preferably circular in shape. The center of ring 2 can be the center of box 1. Box 1 is preferably parallelepiped in shape and can be centered on the reference geometric accident 3. Ring 2 comprises an internal region 2a called a disk. Box 1 comprises a part of the nodes and elements of mesh 10 and ring 2 comprises the other part of the nodes and elements of mesh 10.

[0071] The dimensions of the disk 2a depend on the reference geometric accident 3 and on business criteria. The disk 2a is of dimensions large enough to contain the entire reference geometric accident 3 and to allow the elements of the mesh 10 of the disk 2a, from the surface of the geometric accident 3 to the edge of the ring 2, to be of gradually increasing size, without unnecessarily complicating the mesh 10 with very small elements around the geometric accident 3. This thus makes it possible to reduce the weight of the mesh 10. In the case of drilling, the diameter of the disk 2a is, for example, between 10 and 40 times larger than the diameter of the drilling. Indeed, it is necessary to ensure that the disc 2a is at least as large as the largest variant of the geometric accident 3 and can include a margin to allow the application of the mesh 10. In this case, the drilling angle strongly influences the projected length of the drilling.Alternatively, the diameter of the disc 2a is slightly larger than the diameter of the drilling cylinder, for example it is at least 1 mm larger.

[0072] The disc 2a is also defined by a thickness which depends on the geometry of the reference geometric accident 3. Preferably, the thickness of the disc 2a is defined as a function of a thickness of the reference geometric accident 3. For example, in the case of drilling, the thickness of the disc 2a corresponds to the thickness of the drilled material.

[0073] “Conformal mesh” means a mesh arranged so that the intersection of two distinct elements is: • The empty set; or • A common simplex, such as a knot, an edge or a triangle.

[0074] The mesh is therefore not conformal if, in the intersection, there is a volume or one or more non-common simplices.

[0075] The ring 2 is mobile, that is to say that it can be set in motion in the box 1. In this case, the ring 2 can be set in rotation around its center in the box 1. Preferably, the ring 2 is meshed so that the elements of the ring 2 located at the interface between the ring 2 and the box 1 ensure the continuity and conformity of the mesh 10 from the ring 2 to the box 1, without breaking the mesh. There is therefore no discontinuity between the fixed portion 1 and the mobile portion 2. There is also coincidence between the nodes of the ring 2 and the nodes of the box 1 at the interface between the ring 2 and the box 1. The elements of the ring 2 at the interface between the ring 2 and the box 1 therefore ensures the continuity of the mesh 10 and supports rotations according to a previously selected angular step, allowing the desired discretization in the loading direction.

[0076] The dimensions of box 1 are fixed, that is to say that the dimensions of box 1 are invariant whatever the studied variant of the reference geometric accident 3. In other words, the outer perimeter of the box and the interface between ring 2 and box 1 are the same for all the variants of a given reference geometric accident 3. In addition, box 1 is meshed by a fixed mesh, that is to say that this mesh is unchanged whatever the studied variant of the reference geometric accident 3. For example, for a drilling of 3 mm diameter and 4 mm diameter, box 1 is the same: it has the same nodes and the same elements with the same characteristic dimensions and the same positions.The mesh of box 1 is defined by parameters, such as a number of nodes or a maximum distance between two consecutive nodes, which can be defined by the operator based on business knowledge or by an automatic meshing tool. Preferably, the mesh of box 1 is regular and homogeneous. Furthermore, the nodes of the mesh of box 1 located at the interface between ring 2 and box 1 are regularly spaced along this interface by a fixed distance. This value can be set based on business parameters and / or the desired fineness of the mesh at this interface. The elements of the mesh of box 1 at this interface form a ring mesh of conformity box 1a.

[0077] The adaptability of the mesh 10 therefore lies in the mobility of the ring 2. The ring 2 comprises an internal dimension and an external dimension. The internal dimension is delimited by the presence of the geometric accident 3. The internal dimension is therefore variable depending on the variant studied. The external dimension is delimited by the interface between the ring 2 and the box 1. The external dimension is therefore fixed, due to the immobility of the mesh of the box 1, whatever the variant studied.

[0078] The mesh of ring 2 is adapted so that the nodes which are located at the interface between ring 2 and box 1 coincide with the nodes of the mesh of box 1 located on the same interface. For example, the nodes of ring 2, as well as the nodes of box 1, can be regularly spaced at the interface between ring 2 and box 1 by the same predefined distance. This makes it possible to maintain the coincidence of the nodes of ring 2 with the nodes of box 1 at the interface between ring 2 and box 1. This distance can be predefined according to business parameters and / or a desired fineness of the mesh 10 at this interface. The elements of ring 2 at this interface form a ring mesh of disc conformity 2b. The ring mesh of disc conformity 2b can therefore be considered a boundary condition between ring 2 and box 1, distant from the geometric accident.

[0079] The number of nodes included in the mesh of ring 2 depends on the desired precision. This precision can be defined by the operator according to business criteria. The number of nodes in the mesh of ring 2 is the same for all variants of the reference geometric accident 3 studied.

[0080] The arrangement of the nodes, including the nodes of box 1 and ring 2, makes it possible to form the elements in the mesh 10. These elements may be of different shapes or types. Preferably, the elements of the mesh of box 1 are of the same type and shape. Respectively, the nodes of the mesh of ring 2 are of the same type and shape.

[0081] Preferably, the elements of the ring 2 and of the conformity box ring mesh 1a are of ordered tetrahedral shape, of quadratic type. The elements of the mesh of the ring 2 are preferentially arranged so that, as shown diagrammatically in [Fig.2], each edge of each triangular element is placed opposite the same edge of another triangular element.

[0082] It is possible to define a load to be applied to the outer faces of the box 1. For example, the load can be applied to the upper surface and the lower surface of the box 1, or to the side surfaces of the box 1.

[0083] Step 130 is then a step of defining the variant(s) of the reference geometric accident 3. Each reference geometric accident 3 is therefore assigned one or more variants, the number of variants being dependent on the desired precision for the study of each reference geometric accident 3. The precision of the study defines the number of points necessary for each curve of each graph of the abacus in order to have an interpolation / regression which is reliable. It is therefore a question of defining a number of variants which is sufficiently large so that the interpolation / regression is reliable, but which is sufficiently small so as not to make the numerical study long to implement.

[0084] Preferably, the variants defined in step 130 comprise at least one geometric variant and one mechanical variant. The mechanical variant is preferably a constraint direction variant. The geometric variant and the mechanical variant may be included in the same variant. The geometric variant and the mechanical variant are compatible with each other. In the case where several geometric variants are defined, each of the geometric variants may be associated with one or more mechanical variants, preferably one or more constraint direction variants. All or part of the associated mechanical variants may differ or be identical from one geometric variant to another.

[0085] Furthermore, the number of variants can be defined as a function of the number of physical quantities characteristic of each geometric accident 3 and as a function of the nature of each of the physical quantities. The number of variants can thus be defined according to a number of values ​​of each physical quantity of the properties of the reference geometric accident 3. In this case, the number of variants is the number of possible combinations of the different values ​​of each physical quantity. For example, in the case of drilling, defining 7 points for the ratio of the drilling radius to the drilling thickness, 6 points for the drilling angle, 6 points for the direction of the stresses, 18 points for the biaxial stress ratio and 3 points for the temperature requires defining 13608 variants to be studied.

[0086] Alternatively, if we consider the abacus as a multidimensional database and each reference geometric accident 3 as a subspace whose dimensions are the physical quantities of the properties of the accident, it is possible to define a number of variants to be distributed in each subspace. The number of variants is then defined so as to sample the subspace to allow reliable and robust interpolation / regression, via interpolation or regression. Interpolation / regression can also be implemented using the machine learning tool, the neural network or the kernel machine. In such a case, the number of variants is not necessarily defined as a function of the number of values ​​studied for each physical quantity of the properties of the reference geometric accident 3.For example, the distribution of variants can be implemented using a sampling algorithm, such as Latin hypercube sampling.

[0087] Step 140 is then implemented for each of the geometric variants of the reference geometric accident 3, defined in the previous step. Step 140 is a step of adjusting the mesh 10 to the geometric variant studied. Preferably, the adjustment of the mesh 10 is an adjustment of the ring 2. The adjustment of the ring 2 consists of adjusting the ring 2, in particular the disc 2a, to the geometric dimensions and particularities of the geometric variant. The objective is to ensure the continuity and conformity of the mesh 10 from the geometric accident 3 to the box 1, taking into account the specificities linked to the geometric variant in question.

[0088] Step 150 is a step of adapting the mesh 10 to the mechanical variant, the mechanical variant being a constraint direction variant. Preferably, the adaptation of the mesh 10 is implemented by adapting the mobile portion 2 of the mesh 10. The adaptation is, for example, the rotation of the ring 2.

[0089] Indeed, the mobility of the ring 2 is ensured by the fact that the ring 2 is circular in shape. The disc conformity ring mesh 2b and the box conformity ring mesh 1a being furthermore regular and whose nodes coincide two by two, it is possible to apply a rotation to the mesh of the ring 2 around the center of ring 2, while box 1 remains stationary. The mesh can thus be adapted to each mechanical variant, associated with the studied geometric variant of the reference geometric accident 3. The interest is then to be able to quickly and simply define a mesh 10 for the mechanical variant(s) of the reference geometric accident 3 from a first mesh 10, for example defined by an operator.

[0090] Figure 4 illustrates the rotation of the ring 2 in the box 1. Preferably, in order to maintain the conformity of the mesh from one mechanical variant to another, the rotation of the ring 2 is carried out according to an angular step V' which depends on the distance between two nodes of the disc conformity ring mesh 2b at the interface with the box 1. More precisely, the angular step of rotation is equal to an angular difference between two nodes of the disc conformity ring mesh 2b at the interface with the box 1. The angular difference between two nodes is here the angle formed between two consecutive nodes of the disc conformity ring mesh 2b at the interface with the box 1 relative to the center of the ring 2. For example, in the case of a drilling, the nodes of the disc conformity ring mesh 2b at the interface with the box 1 are arranged so that v> = 2.5 °.The interest is then to be able to define a mesh 10 for one or more mechanical variants of the reference geometric accident 3 without modifying the structure of the first mesh 10. The angular step can be zero or be an integer multiple of the angular step between two contiguous nodes of the disc conformity ring mesh 2b at the interface with the box 1. Thus, the continuity of the mesh 10 is ensured, in particular the continuity of the mesh of the ring 2 with the mesh of the box 1.

[0091] For example, for the 6 values ​​of the loading direction in the case of cylindrical drilling, the operator imposes a rotation by angular step V' — 15 0 in an interval ranging from 0° to 90°.

[0092] In other words, the operator can define a first mesh 10 for one of the geometric variants of the reference geometric accident 3, then define, for each mechanical variant of each geometric variant, a mesh adapted to said mechanical variant by simply applying a rotation of the ring following the angular step V. In the case of drilling, there is no longer any need to define a new mesh for each of the mechanical variants corresponding to the 6 points for the direction of the constraints. It is sufficient to define a rotation of the ring 2 for each of these mechanical variants.

[0093] The advantage of this step 150 of adapting the mesh 10 is that it is no longer necessary to define a different mesh for each variant or for each geometric variant / mechanical variant pair of the reference geometric accident 3. Indeed, the same mesh 10 can be used for several variants different mechanics, by adapting it by a simple rotation of its mobile portion 2. Consequently, in the case of drilling, instead of 252 meshes to define, there is only a need to define 42 meshes 10 (in fact, there remain 7 points for the ratio of the drilling radius by the drilling thickness and 6 points for the drilling angle) and 210 rotations. The meshes 10 to be defined can thus be defined by the meshing software. For example, the 42 meshes 10 of the drilling variants can be defined automatically by the meshing software.

[0094] Preferably, the rotation of the ring 2 is carried out so as to maintain the continuity and conformity of the mesh 10. In particular, the rotation of the ring 2 is implemented so that each node of the disc conformity ring mesh 2b coincides with one of the nodes of the mesh of the box 1 at the interface between the ring 2 and the box 1. The rotation of the ring 2 therefore respects the coincidence of the nodes at the interface between the ring 2 and the box 1. The coincidence can be ensured by means of a connection between the mesh of the ring 2 and the mesh of the box 1. The connection can be carried out automatically by a digital meshing tool, for example by the ANSA meshing software, or by a dedicated script.

[0095] For each geometric variant, the mesh 10 can be defined by the operator or by means of an automatic meshing tool. Preferably, the mesh of each geometric variant is defined by the automatic meshing tool so as to respect mesh precision and conformity criteria.

[0096] Furthermore, a validity of the mesh 10 is estimated by means of a quality criterion of the mesh 10. This validity can be estimated by the meshing tool, for example by the ANSA meshing software, by means of one of its native functions to determine the quality of a mesh. The mesh 10 is validated if the quality of the mesh 10 is greater than or equal to the quality criterion of the mesh 10.

[0097] Optionally, a “bounding box” type method is used in order to gradually control the precision of the elements of the mesh of the ring 2, while controlling the continuity of said mesh 10. This makes it possible to reduce the number of elements in the mesh 10 by gradually optimizing the refinement of the mesh 10 around the geometric accident 3 up to the interface between the ring 2 and the box 1. Thanks to the bounding box, the calculation time of the numerical study is greatly reduced. For example, the “bounding box” can be implemented by defining a mesh within several concentric circles of increasing radius around the geometric accident 3, within the ring 2, each circle having a predefined size of elements or number of elements. In particular, the size of the elements of the mesh of each circle can be proportional to the radius of said circle.This allows for gradually increasing size of elements with their distance from geometric accident 3 towards box 1.

[0098] Furthermore, the mesh of ring 2 can be determined by parameterized equations as a function of the geometric accident 3 considered and the coincidence of the nodes of ring 2 with those of box 1 at the interface between ring 2 and box 1. Thus, the size of the mesh elements is adapted to each type and variant of geometric accidents 3.

[0099] Step 160 is then a step of determining the reference stress concentration coefficient KT for a geometric variant of the reference geometric accident 3. The reference coefficient KT is preferably calculated by means of a numerical solver, which uses the numerical model of the reference geometric accident 3 and the mesh 10 which has been adapted to the variant. Step 160 is therefore implemented for each of the variants of each reference geometric accident 3.

[0100] The numerical solver is a numerical tool that allows solving systems of equations governing the mechanical behavior of the geometric accident 3. For example, the numerical solver is a tool based on a resolution by finite difference, finite elements or finite volumes. Preferably, the numerical solver is a tool based on finite element resolution, such as Abaqus™ or COMSOL™.

[0101] The numerical solver calculates the reference coefficient KT using, as input to the calculation, the values ​​of the physical quantities which characterize each variant of the reference geometric accident 3.

[0102] It is possible to use the principle of superposition of constraints, linked to the linearity of elastic behavior, in order to avoid having to perform a calculation using the numerical solver for each of the variants of the reference geometric accident 3. In particular, in a plane, it is only necessary to calculate two values ​​of monodirectional constraints to construct the points of the abacus. In the case of drilling, it is then no longer necessary to calculate all the variants for the combinations of the 18 loading cases, but only 2 values. That is to say, only two adaptations of ring 2 are necessary to extrapolate the calculation of the coefficient KT to all the loading variants. Indeed, as soon as two constraints are known in a plane, any other constraint will be a linear combination of these two known constraints.In particular, for a given direction, it is necessary to know the stress in the given direction and the stress orthogonal to the given direction in order to then obtain all the loading cases by linear combination. In the case of drilling, it is therefore sufficient to implement 756 calculations and no longer 13608 calculations.

[0103] Preferably, the numerical solver makes it possible to determine, for each accident, a reference stress tensor Kr. In particular, it is possible to determine a reference stress tensor Kt along the x axis and a tensor of ^Tx reference stress KTy along the y axis.

[0104] In an optional step 170, it is then possible to calculate, for each value of the biaxial stress ratio, therefore for each loading case, a reference loading tensor a. This reference tensor (7) is determined by — (yx KTx + rj-jK / 'y °ù is a stress along the x axis, is a stress along the 4 axis'. The constraints ax and CP are defined, for each variant, as a function of the values ​​of the biaxial stress ratio of the variants to be studied. These constraints TX and are therefore comparable to weightings for studying each of the linear combinations of loading cases studied.

[0105] In this optional step 170, the coefficient KT can then be determined by a maximization of the reference tensor. For example, the coefficient KT is determined by a maximization of the dimensionless reference tensor, such that , °ù is the operator of the Von Mises criterion. Kr = max q gr 0 0 ' 0 0 0 /

[0106] For some variants, it may be preferable to keep the reference tensor <7 rather than reducing it to the reference KT coefficient. Indeed, the advantage of the Kt coefficient is that it is a simple scalar which therefore requires few memory resources to be stored in a database. Furthermore, this KT coefficient is representative of the constraints associated with geometric accident 3. On the contrary, the reference tensor 77 provides more complete information than the reference KT coefficient but requires more memory resources for its storage.

[0107] In order to reduce the calculation time for developing the abacus, the calculations of the reference KT coefficient, or of the reference KT tensor, for each of the variants of each of the reference geometric accidents can be implemented on a distributed computing infrastructure, for example on a server or a high-performance computer (HPC or “High Performance Computing”).

[0108] A smart queue module can be implemented to allocate the calculations of the KT coefficient to resources of the distributed computing infrastructure. For this, a number of slots is defined. This number of slots indicates a maximum number of calculations that can be executed at the same time on the distributed computing infrastructure. A minimum number of licenses per calculation is also defined and indicates the minimum number of licenses of the numerical solver that must be available to correctly execute a calculation and not block calculations of other users; below this threshold, it is no longer possible to execute said calculation. Advantageously, defining a high value for this threshold makes it possible to avoid a situation where calculations monopolize almost all licenses. For example, if a calculation requires 8 licenses, setting the threshold value to 40 ensures that other users have priority to use the licenses if they need to make calculations. In particular, this smart queue mechanism is activated when activity is low, at night and on weekends, and allows long calculations (several days) by other users not to find themselves without licenses because of calculations for the abacus. Finally, a number of processors per calculation is defined according to the power of the machine. Alternatively, the number of licenses per calculation is defined according to the number of processors per calculation.

[0109] The smart queue module then regularly checks the number of available numerical solver licenses, the number of free slots (a slot being unavailable when a calculation is being executed, and being released when the execution of the calculation ends), and allocates resources of the distributed computing infrastructure to one or more calculations each time the number of available licenses allows it, and at least one slot is free.

[0110] It is thus possible to make maximum use of the available resources of the distributed IT infrastructure.

[0111] As soon as one of the calculations of the coefficient KT for one of the variants is completed, it is possible to transfer the calculated value of the coefficient KT into a memory dedicated to the development of the geometric accidents chart. Once the value has been transferred, it is possible to clean the resource(s) allocated for the calculation of said value, in particular the memory type resources, and to check that the transfer of the calculated value has been carried out correctly. The interest is then to reduce the time necessary for the development of the geometric accidents chart and to avoid saturating the memory of the calculator with the completed calculations. In this system, the memory is cleaned as and when.

[0112] Similarly, for the calculation of the reference stress tensor KT, it is possible to transfer the calculated reference stress tensor KT into a memory dedicated to the development of the abacus. Once the value has been transferred, it is possible to clean the resource(s) allocated for the calculation of said tensor, in particular the memory type resources, and to verify that the transfer of the calculated tensor has been correctly carried out. The interest is then to reduce the time required to develop the abacus of geometric accidents by compressing the waiting times during the execution of the calculations on the distributed computing infrastructure.

[0113] Step 102 of the method 100 is a step of determining a criterion for the lifespan of the aeronautical part. This criterion is based on professional knowledge and feedback and is representative of the fatigue resistance or the lifespan of the part. In particular, the service life criterion may be a service life that indicates, for example in hours, days, weeks, months or years, a period during which the aeronautical part can be used with minimal risk of an anomaly related to this part occurring. The service life may, in addition, indicate the period of use beyond which the part will require maintenance. The service life criterion may also be fatigue indicated in number of cycles or in equivalent number of cycles.

[0114] The determination of the lifetime criterion is implemented via a dedicated computer program, which solves the damage equations of the material considered. In particular, to calculate the lifetime, such software is executed in two stages: one for initiation and one for propagation.

[0115] Preferably, the service life is determined by a comparison with one or more fatigue criteria. For example, in initiation, a multiplication of the KT coefficient with a stress of the part is compared to the elastic limit of the material, and this value called “criticality” or “reduced stress” is compared to reference data. Then, in propagation, the gradient of the KT coefficient is multiplied by the stress of the part, and the result, which represents the evolution of the stress as a function of the distance, is compared to references of propagation and / or non-propagation of the geometric accident 3. The interest here is to take into account conditions of propagation of the geometric accident 3, in particular if it is undesired, for example a crack, which depend mainly on distant stresses, unlike the conditions of appearance of the geometric accident 3 which depend essentially on local stresses.

[0116] Advantageously, the dedicated computer program is based on the numerical model calculated using the numerical solver. The specificity of this numerical model is that the geometric accident 3 is not modeled therein. On the contrary, the geometric accident 3 in the numerical model is taken into account by applying the stress concentration coefficient KT at the location of the geometric accident 3 not shown. The numerical solver used here may be the same numerical solver used in step 160 of calculating the coefficient KT.

[0117] The digital model is therefore an equivalent representation of the aeronautical part where the geometric accident 3 is modeled by the stress concentration coefficient KT. The advantage of such an equivalent representation is that the calculation of the service life is implemented quickly since there is no need to have great calculation precision in order to model the geometry, potentially complex, of the geometric accident 3 which is much smaller than the part aeronautics. The fatigue resistance of the aeronautical part is therefore estimated easily, quickly and reliably using the method 100 according to the invention.

[0118] Step 103 of the method 100 is then a step of designing the geometric accident 3 and the aeronautical part comprising said designed geometric accident 3. This design step 103 is implemented on the condition that the determined lifespan criterion of the aeronautical part is compatible with a specification of said mechanical part.

[0119] In other words, in step 103, the determined lifetime criterion is compared to a specification of the aeronautical part. This specification includes at least one desired lifetime criterion of the aeronautical part. In particular, if the criterion is the lifetime, the aeronautical part comprising the geometric accident 3 is compatible with fatigue resistance requirements of the specification if the determined lifetime is equal to or greater than the desired lifetime. In this case, the design of the aeronautical part comprising the geometric accident 3 is implemented. The design can be implemented using a computer-aided design or digital drawing tool, for example CATIA™ or Solidworks™. In this design, the geometric accident 3 is fully designed, respecting its exact geometry. For example, the designed blade includes the cylindrical bore.

[0120] The method 100 may further comprise a step 104 of manufacturing said aeronautical part comprising the geometric accident 3. The manufacturing may be carried out by molding, machining, welding, forging, additive manufacturing, etc. The manufactured aeronautical part then comprises the geometric accident 3, for example the cylindrical drilling.

[0121] In an alternative, the reference KT coefficient is determined for each node of the mesh 10. That is to say that the numerical solver used to develop the abacus produces at the output of the calculation a reference KT coefficient for each of the nodes of the mesh 10. The reference KT coefficient can thus be different from one node to another. The interest is to be able to take into account a distribution or a variation of the reference KT coefficient in the modeling of the geometric accident 3.

[0122] Preferably, the reference stress tensor KT is determined for each node of the mesh 10. That is to say that the numerical solver used to develop the abacus produces at the output of the calculation a reference stress tensor KT for each of the nodes of the mesh 10. The reference stress tensor KT can thus be different from one node to another. The interest is to be able to take into account a distribution or a variation of the reference stress tensor KT in the modeling of the geometric accident 3. In this case, the numerical solver makes it possible to determine, for each node of the mesh 10, a reference stress tensor KTx along the x axis and is a reference stress tensor KT along the axis Optional step 170 is then implemented in order to determine, for each mesh node 10, the stress concentration coefficient KT of each node. For example, the coefficient KT can be determined by a maximization of the loading tensor <7 of dimensionless reference of each of the nodes, such that K r ^^'knots I aViJa) lax 0 0\ \ \0 0 0 / / where °vm is the Von Mises criterion operator.

[0123] In this case, the aeronautical geometric accident chart includes, for each variant of each geometric accident 3, a stress concentration coefficient KT for each node of the mesh 10. In addition, it is possible to interpolate or to make a regression of the values ​​of the coefficients KT determined for each node in order to obtain a distribution function of the coefficients KT for each variant of each geometric accident 3. The advantage is to interpolate an estimate of the value of the coefficient KT at any point of the geometric accident 3 and the surrounding surface. The interpolation / regression can also be implemented by means of a machine learning algorithm.

[0124] Consequently, the digital model used to determine, in step 102, the duration of the aeronautical part comprises a mesh of the part comprising a plurality of nodes. At least one of the nodes of the mesh of the part is assigned a reference coefficient Kt of one of the nodes of the mesh 10 included in the aeronautical geometric accident chart. Preferably, the reference coefficient KT assigned to at least one of the nodes of the mesh of the part is obtained by interpolation / regression of the values ​​of the reference coefficients KT. The mesh of the part may, furthermore, comprise part or all of the mesh 10 of the geometric accident 3. The mesh of the part may alternatively comprise a mesh different from the mesh 10.

[0125] In an alternative, during step 102 of determining the lifetime criterion of the aeronautical part, each node of the mesh of the part is associated with one of the reference KT coefficients or with one of the reference KT tensors.

[0126] In an alternative, at least one of the properties of the geometric accident 3 is not predefined. For example, the non-predefined property is not subject to a requirement in the specifications as to its value. On the contrary, a tolerance margin can be defined for this property.

[0127] In this case, step 101 of estimating the coefficient KT is further implemented taking into account the tolerance margin for said non-predefined property. It is therefore a question of estimating the KT coefficient for several variants resulting from the tolerance margin on the non-predefined property. The estimation step 101 then produces a plurality of KT coefficients, each associated with a different variant located within the tolerance margin. The number of estimated KT coefficients is sufficiently large so that the plurality of different KT coefficients is representative of the variability of the KT coefficient as a function of the value of the non-predefined property. The number of different estimated KT coefficients is for example greater than or equal to 3. This number may depend on the defined tolerance margin as well as a criticality of this property. The term "critical property" means a property in which a small variation results in a large variation of the KT coefficient.

[0128] Step 102 of determining the lifespan criterion is then implemented for each of the variants resulting from the tolerance margin. Step 102 therefore produces a plurality of lifespans of the aeronautical part, each being associated with one of the variants.

[0129] In step 103 of designing the aeronautical part, the geometric accident 3 included in the aeronautical part is designed from a compatible variant belonging to the plurality of variants resulting from the tolerance margin. For example, each lifetime of the plurality of lifetimes is compared to the desired lifetime. A variant of the geometric accident 3 is then chosen from among the variants whose associated lifetime is greater than or equal to the desired lifetime. The choice of the variant can be made according to an imposed criterion. This can be a manufacturing criterion, for example an indication of a functional need, such as the maximum admissible size of a heat-affected zone during drilling, a minimum machining size below which a manufacturing tool cannot operate, constraints of heat pumping, manufacturing cost or minimization of the time for machining the part.It may also be a usage criterion, for example maximizing the part's lifetime or mechanical strength constraints. The part may also be designed to verify tolerances on the manufacturing criterion(s). Finally, the aeronautical part is designed such that it includes the variant of geometric accident 3 which satisfies the imposed criterion.

[0130] The method 100 according to the invention may, in addition, comprise a step 105 of verifying the manufactured geometric accident 3. The verification is implemented by three successive sub-steps, numbered 105a to 105c.

[0131] Step 105a is a step of measuring at least one of the dimensions of the geometric accident 3 manufactured and included in the manufactured part. The measurement is carried out with a dimension measuring tool, such as a ruler or a caliper, and / or by a non-destructive testing tool, such as ultrasonic or X-rays. This involves, for example, measuring a geometric quantity for which the manufacturing process presents an uncertainty as to its conformity with respect to its value in the designed part.

[0132] Step 105b is then a step of comparing the measured dimensions and manufacturing data of the geometric accident 3 with the aeronautical geometric accident chart. The objective is to determine a stress concentration coefficient KT for this manufactured geometric accident 3. The manufacturing data of the geometric accident 3 includes information relating to the manufacturing, in particular parameters entered in one or more machines to carry out the manufacturing. For example, in the case of the drilled blade, this includes, among other things, the composition of the material of the aeronautical part or of the geometric accident 3, the temperature of the material during drilling, dimensions of the zone thermally affected by the EDM drilling, etc.The interest here is to take into account any variability that may have occurred during manufacturing in order to verify the conformity of the manufactured geometric accident 3 with the designed geometric accident 3. In addition, it is possible to take into account manufacturing uncertainties, for example related to the control of the manufacturing machine. For example, it is possible to take into account the fact that the accuracy of EDM drilling is subject to a certain percentage of uncertainty, for example 1% uncertainty.

[0133] The comparison 105b of the measured dimensions and the manufacturing data of the geometric accident 3 with the aeronautical geometric accident chart makes it possible to obtain a final stress coefficient KTf, associated with the manufactured geometric accident 3. This comparison is carried out in the same way as for the estimation of the coefficient KT in step 101.

[0134] Finally, step 105c is a step of verifying the manufactured geometric accident 3. A lifetime criterion of the manufactured aeronautical part is estimated by the numerical solver from the numerical model of the designed aeronautical part. In this numerical model, in the same way as for the design step 103, the geometric accident 3 is replaced by the final stress concentration coefficient KTf. The lifetime criterion of the manufactured part is then compared to the desired lifetime criterion. The geometric accident 3 is then verified if the lifetime criterion of the manufactured part is greater than or equal to the desired criterion, for example, if the lifetime of the manufactured part is greater than or equal to the desired lifetime.

[0135] If the geometric accident 3 is not verified, the method may further comprise a step 106 of correcting the geometric accident 3. In this case, the manufactured aeronautical part is machined so that the geometric accident 3 is verified, and therefore that the duration of the manufactured aeronautical part complies with the specifications.

[0136] The method according to the invention may, finally, comprise a step 107 of validating the conformity of the aeronautical part to the appearance of an undesired geometric accident 3. The aeronautical geometric accident chart according to the invention was previously used in the context of desired geometric accidents, but it may also be used for undesired geometric accidents. Indeed, one or more undesired geometric accidents may appear in the part during its manufacture or during its use. The verification step 107 comprises four successive steps, numbered from 107a to 107d.

[0137] Step 107a is a step of measuring at least one of the dimensions of the unwanted geometric accident 3. The measurement is carried out with a dimension measuring tool, such as a ruler or a caliper, and / or by a non-destructive testing tool, such as ultrasonic or X-ray inspection. Preferably, a plurality of dimensions are measured in order to describe the geometry of the unwanted accident accurately and completely.

[0138] Certain unwanted geometric accidents may be regularly found on certain parts and may be difficult to prevent. In this case, we speak of typical geometric accidents. For these typical cases, it is possible to determine all of the typical geometric accidents expected according to criteria of professional knowledge and feedback. If all of the expected cases are acceptable according to these criteria, then the typical geometric accident 3 may be authorized by default, which avoids the measurement and verification step. On the contrary, if certain variants are unacceptable, for example due to one or more specific characteristics, it is possible to implement step 107a in order to measure only dimensions associated with these specific characteristics, which makes it possible to reduce the number of measurements required.

[0139] Step 107b is then a step of comparing the measured dimensions with the aeronautical geometric accident chart. The comparison is used to obtain one or more stress concentration coefficients KTa of alteration.

[0140] To the extent that the properties of the undesired geometric accident 3 are not all known, it is possible to define tolerance margins for one or more unknown physical quantities of the properties of the undesired geometric accident 3. These error margins make it possible to obtain a plurality of KTa alteration coefficients and therefore to provide information on a trend in the mechanical behavior of the geometric accident 3 as a function of the unknown physical quantities.

[0141] In some cases, some of the properties of the unwanted geometric accident 3 are known, and it is possible to compare the measured dimensions and the properties known with the aeronautical geometric accident abacus to obtain the KTa alteration coefficient(s). This comparison is carried out in the same way as for the estimation of the KT coefficient in step 101.

[0142] Step 107c is then a step of determining a lifetime criterion of the manufactured aeronautical part comprising the undesired geometric accident 3. The lifetime criterion is estimated by the dedicated computer program from the digital model of the designed aeronautical part. In this digital model, in the same way as for the design step 103, the undesired geometric accident 3 is replaced by the stress concentration coefficient KT a of alteration.

[0143] Step 107d is then a step of validating the lifetime criterion of the aeronautical part. The validation is implemented by comparing the lifetime criterion of the aeronautical part with the desired lifetime criterion. The lifetime is validated if the lifetime criterion of the manufactured part is greater than or equal to the desired criterion, for example, if the determined lifetime is greater than or equal to the desired lifetime. In this case, the conformity of the manufactured aeronautical part is validated.

[0144] The method 100 according to the invention may, optionally, comprise a step 108 of correcting the aeronautical part. The objective of the correction is to modify the undesired geometric accident 3 or the aeronautical part so that the lifetime criterion satisfies the desired lifetime criterion, for example, so that the lifetime criterion of the manufactured part is greater than or equal to the desired criterion, and in particular if the lifetime of the part is greater than or equal to the desired lifetime. The modification may be implemented by removing or adding material, such as machining or reinforcement.

[0145] Alternatively, if a correction of the part is not able to improve its fatigue resistance, that is to say that the service life criterion does not satisfy the desired service life criterion, for example its service life would be less than the desired service life, then a new aeronautical part not comprising the undesired geometric accident 3 would be manufactured. For this, steps 101 to 104 of the method 100 can be implemented to design and manufacture said part. In addition, if the aeronautical part is already designed, it is sufficient to implement step 104 of manufacturing said part.

[0146] Correction step 108 may occur in the context of maintenance of a system on which the aeronautical part is assembled.

[0147] In an alternative, the reading of the abacus is carried out by means of the control interface, which makes it possible to enter one or more physical quantities of the properties of the accident in order to automatically estimate the associated KT coefficient. The control interface therefore allows the operator to consult one or more particular cases geometric accidents and / or variants of geometric accidents, based on the properties of the geometric accident(s) that he has provided. The estimation of the KT coefficient is implemented using the automatic search computer tool.

[0148] The control interface further allows the operator to consult the sensitivity and impact of the coefficient KT as a function of the properties of one or more variants of said geometric accident 3. The control interface then generates, for one or more physical quantities designated by the operator, one or more impact curves and / or one or more sensitivity curves of the coefficient KT for these designated physical quantities, for said geometric accident 3. The impact curve(s) are, for example, iso-rest curves of the designated physical quantity(s).

[0149] Furthermore, the control interface allows searching for a KT envelope. In this case, the user enters the tolerance margins for one or more of the physical quantities of the properties of the geometric accident 3. The operator can also enter a maximum value for the KT coefficient that the geometric accident 3 must not exceed. The control interface then produces the KT envelope as output in the form of intervals for each of the physical quantities associated with one of the tolerance margins. Additional constraints can be entered in the control interface to reduce or expand the KT envelope. Preferably, the intervals are as large as possible.

[0150] In an alternative, the position of the geometric accident 3 on the aeronautical part is not imposed. It is then possible to define a plurality of variants of position of the geometric accident 3, then to implement step 102 of determining the lifetime criterion of the aeronautical part for each of the variants of the plurality of variants of position of the geometric accident 3. It is then possible to compare these different lifetimes with each other and to design, in the design step 103, the variant of position of the geometric accident 3 so that said variant of position best satisfies the desired lifetime criterion, for example by maximizing the lifetime of said aeronautical part. The objective is therefore to minimize the impact of the geometric accident 3 on the fatigue resistance of said part.

Claims

1. Claims Method (100) for designing an aeronautical part comprising a geometric accident (3), comprising the following steps: - Estimation (101) of a stress concentration coefficient from properties of the geometric accident (3) and an aeronautical geometric accident chart, the aeronautical geometric accident chart comprising a set of reference stress concentration coefficients and being developed by the following steps: • For each reference geometric accident (3) of a plurality of reference geometric accidents, each reference geometric accident (3) of the plurality of geometric accidents being of a different type, • Definition (110) of a digital model of the reference geometric accident (3); • Definition (120) of a mesh (10) comprising a fixed portion (1) and a mobile portion (2), the mobile portion (2) being circular in shape and being included in the fixed portion (1); • Definition (130) of one or more variants of the reference geometric accident (3), the variant(s) comprising at least one geometric variant, at least one mechanical variant being associated with the at least one geometric variant, and at least one of the mechanical variants being a stress direction variant; • For each at least one geometric variant of the reference geometric accident (3): • Adjustment (140) of the mobile portion (2) of the mesh (10) defined according to the geometric variant of the reference geometric accident (3); • Adaptation (150) of the mobile portion (2) adjusted according to the at least one mechanical variant of direction of constraints of the geometric variant; • Calculation (160) of the reference stress concentration coefficient using a numerical solver and from the numerical model of the reference geometric accident (3) as well as the adjusted and adapted mesh (10); Determination (102) of a lifespan criterion of the aeronautical part by means of a dedicated computer program and from a digital model of the aeronautical part where the geometric accident (3) is replaced by the estimated stress concentration coefficient; and Design (103) of the geometric accident (3) and of the aeronautical part comprising said designed geometric accident (3), on the condition that the determined lifespan criterion of the aeronautical part is greater than or equal to the desired lifespan criterion; Manufacture (104) of said designed aeronautical part comprising the designed geometric accident (3).

2. Method (100) according to the preceding claim, wherein: - In the estimation step (101), a plurality of stress concentration coefficients is estimated from the known properties of the geometric accident (3) and a tolerance margin on unknown properties, each stress concentration coefficient being associated with a different variant of the geometric accident lying within the tolerance margin; - In the determination step (102) of the lifespan criterion, a lifespan criterion is estimated for the aeronautical part for each stress concentration coefficient of the plurality of stress concentration coefficients, the determined lifespan being associated with one of the variants of the geometric accident; and - In the design step (103), the geometric accident (3) is chosen whose determined lifespan criterion is greater than or equal to the desired lifespan criterion.

3. Method (100) according to one of the preceding claims, further comprising a step of verifying (105) the geometric accident (3) on the manufactured aeronautical part, the verification step comprising the sub-steps: - Measurement (105a) of at least one dimension of the geometric accident (3) on the manufactured aeronautical part; - Comparison (105b) of the dimension and data of the geometric accident (3) with the aeronautical geometric accident chart to determine a final stress concentration coefficient;- Verification (105c) of the geometric accident (3) by comparison of a life criterion of the manufactured part with the desired life criterion, the life criterion of the manufactured aeronautical part being calculated by means of a dedicated computer program and from the digital model of the aeronautical part where the geometric accident (3) is replaced by the final stress concentration coefficient.;

4. Method (100) according to one of the preceding claims, further comprising a step of validating (107) the conformity of the aeronautical part to the appearance of an unwanted geometric accident (3), the unwanted geometric accident (3) resulting from the manufacture (104) or use of said aeronautical part, the validation step (107) comprising the sub-steps: - Measurement (107a) of at least one dimension of the unwanted geometric accident (3) on the manufactured aeronautical part; - Comparison (107b) of the dimension and data of the unwanted geometric accident (3) with the aeronautical geometric accident chart to determine a coefficient of alteration stress concentration; - Calculation (107c) of a lifetime criterion of the manufactured aeronautical part by means of a numerical solver and from the numerical model of the aeronautical part where the geometric accident (3) is replaced by the coefficient of alteration stress concentration;and - Validation (107d) of the conformity of the manufactured part by comparison of the life criterion of the manufactured part with the desired life criterion.;

5. Method (100) according to one of the preceding claims, wherein the defined mesh (10) comprises a plurality of nodes and wherein the stress concentration coefficient is determined for each node of the plurality of nodes of the mesh (10).

6. Method (100) according to the preceding claim, wherein the stress concentration coefficient determined for each node of the plurality of nodes of the mesh (10) is different.

7. Method (100) according to one of the preceding claims, in which the aeronautical geometric accident chart is a multidimensional database comprising a sub-space for each type of reference geometric accident (3), each sub-space comprising each variant of the geometric accident (3) with which the sub-space is associated.

8. Method (100) according to one of the preceding claims, wherein in the step of calculating (160) the reference stress concentration coefficient, the reference stress concentration coefficient is calculated from a maximization of a tensor of

9. reference loading, the reference loading tensor being estimated by the numerical solver. Method (100) according to one of the preceding claims, wherein the calculation (160) of the reference stress concentration coefficient for each variant of each reference geometric accident (3) of the plurality of reference geometric accidents is distributed over a distributed computing infrastructure.

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