NON-DESTRUCTIVE INSPECTION METHOD FOR A PART

Abstract

A non-destructive testing method (100) comprising at least the following steps: - (Step 1) Perform a tomography scan of a part; - (Step 2) Generate a first surface mesh of the tomography scan; - (Step 3) Acquire a second surface mesh of a reference model of the manufactured part; - (Step 4) Calculate modes of a Beltrami Laplacian on the first surface mesh and modes of a Beltrami Laplacian on the second surface mesh; - (Step 5) Compare the modes of the Beltrami Laplacian calculated in Step 4; - (Step 6) Construct a third surface mesh by morphing the paired nodes of the first and second surface meshes; - (Step 7) Determine the functional performance of the part; - (Step 8) Mark the part. Figure to be published with the abbreviation: Fig. 1

Description

Title of the invention: METHOD for non-destructive testing of a part technical field

[0001] The invention relates to the field of non-destructive testing of geometric variations of manufactured aeronautical parts. STATE OF PRIOR ART

[0002] It is known that aeronautical parts such as the ceramic cores of high-pressure turbine blades are manufactured in several stages: injection molding, firing, and finishing. Geometric variations can occur at these different stages and can be generated by various causes (temperature, material composition, human impact, etc.). Furthermore, when the turbine blades are cast, these cores are subjected to high pressures and temperatures exceeding 1500°C, causing further geometric variations. This results in discrepancies between the turbine blade actually manufactured and its CAD (Computer-Aided Design) definition drawn in the design office. These variations can appear in different forms (local over / under thickness, position of drilling points and axes, etc.). One possible solution for capturing these geometric deviations is to perform tomography on the manufactured parts.Tomography allows for the reconstruction of a three-dimensional (3D) part in a tensor where the value of the points depends on the density and absorption factor of the material.

[0003] Today, finite element numerical simulations are performed on theoretical geometric data derived from CAD. The variability present in production is not taken into account. Furthermore, the theoretical geometry may differ significantly from the actual geometry, and thus the calculated values ​​may be quite far from reality. To perform physical simulations of a real part, a three-dimensional mesh (Tomo) obtained from tomography is relevant, but a set of boundary conditions must be applied. The difficulty lies in the fact that defining these boundary conditions is very costly in terms of time and computing resources. For example, more than two hundred boundary conditions are defined when calculating the lifespan of a blade.

[0004] Furthermore, techniques for characterizing and representing geometries using modal approaches are used in the field of image registration or mesh morphing.

[0005] The document “Functional metrology by 3D imaging and digital twin learning: application to thermo-mechanical fatigue in superalloys” The article "Monocrystalline" published by A. Aublet proposes a mesh morphing algorithm, that is, a mesh deformation algorithm. This algorithm is very relevant for accounting for geometric variations due to the manufacturing process, but the method has some drawbacks. In particular, this method has only been tested on relatively simple geometries and not on real parts. One of the limitations of this method is the matching of nodes in the CAD mesh and the tomography mesh in the case of large geometric variations or the presence of thin walls in the geometry. Indeed, node matching is calculated by a "nearest neighbor" algorithm between the nodes of the CAD mesh and those of the tomography mesh that have been registered relative to the initial (CAD) mesh.The "nearest neighbor" algorithm between the two meshes fails when the part has a thin wall, which is generally the case for turbine blades. A node on the outer wall of the geometry obtained from the tomography may have a corresponding node, using the "nearest neighbor" algorithm, on an inner wall of the CAD model. This error is due to the use of the Euclidean or Cartesian metric, since the Euclidean distance between the inner and outer walls is very small.

[0006] Another drawback of the "Mesh morphing" method proposed in the document "Functional metrology by 3D imaging and digital twin learning: application to thermo-mechanical fatigue in single-crystal superalloys" is the use of the graph's Laplace operator, since it depends on the density of the mesh on which it is calculated. In general, the actual part is meshed much more finely than the CAD digital model, so it is not possible to consider the same modal basis for both meshes.

[0007] In this context, it is necessary to provide a method for performing simulations on the manufactured parts, in order to validate the parts. [Disclosure of the invention]

[0008] To this end, according to a first aspect, a non-destructive testing method is proposed for measuring a manufactured part against the corresponding measurements of a reference model of the part. The method is implemented by a non-destructive testing device comprising electronic circuitry adapted to implement the method. The method comprises at least the following steps: - (Step 1) Perform a tomography of a manufactured part to measure the manufactured part in three dimensions. - (Step 2) Generate a first surface mesh of the tomography; - (Step 3) Acquire a second surface mesh of a reference model of the manufactured part; - (Step 4) Calculate modes of a Beltrami Laplacian operator on the first surface mesh and modes of a Beltrami Laplacian on the second surface mesh; - (Step 5) Compare the modes of the Beltrami Laplacian calculated in step 4 to match nodes of the first surface mesh and nodes of the second surface mesh; - (Step 6) Construct a third surface mesh by morphing the paired nodes of the first surface mesh and the second surface mesh; - (Step 7) Determine the functional performance of the manufactured part using the third surface mesh, by mechanical, thermal or thermomechanical simulations on the third mesh obtained by morphosis; - (Step 8) Sanction the piece by keeping the piece or rejecting the piece.

[0009] According to a particular arrangement, step 4 of calculating the modes of a Beltrami Laplacian on the first surface mesh and on the second surface mesh includes correcting the sign of each mode of the Beltrami Laplacian on the first surface mesh according to a sign of a corresponding mode of a Beltrami Laplacian on the second surface mesh.

[0010] According to a particular provision, the sign correction of step 4 comprises the following sub-steps: - (Substep 4.1) Calculate a grey level image of a mode of the Beltrami Laplacian on the second mesh, mode_CAO, with a single color channel; - (Substep 4.2) Calculate a grey level image of a mode of the Beltrami Laplacian on the first mesh, mode_Tomo, with a single color channel; - (Substep 4.3) Calculate a mask by [ 1 in the intersection (mode_CAD, mode_Tomo); l 0 otherwise - (Sub-step 4.4) Calculate a first difference DI between the two images in the mask; - (Substep 4.5) Repeat substeps 2 and 3 with a negative sign for the tomographic mode mode_Tomo and calculate a second difference D2 between the two images in the mask; - (Substep 4.6) If D2 <D1 alors changer de signe pour le mode tomographique mode_Tomo.

[0011] According to a particular arrangement, step 5 comprises the following substeps for pairing the nodes: - (Substep 5.1) Select a predetermined number k of Pi points on the second surface mesh using eigenvectors of the Beltrami VCAO Laplacian operator; - (Substep 5.2) Find for each point P; selected a corresponding point, tomoj of the first surface mesh by minimizing a distance which takes into account Cartesian coordinates and spectral coordinates Vcao or ^Tomo of the nodes of the first surface mesh and the second surface mesh.

[0012] According to a particular provision, step 4 further includes the following substep: - (Substep 5.3) Apply weights to the Cartesian and spectral coordinates of the nodes of the surface meshes to define a metric for matching the nodes of the two meshes.

[0013] According to a particular arrangement, step 6 of constructing the third mesh is carried out using a Tikhonov regularization method to remove measurement noise and filter details from the first surface mesh and the second surface mesh.

[0014] According to a particular arrangement, step 6 comprises the following substeps: - (Substep 6.1) Search for X coordinates of the third surface mesh such that: minXTLX and AX = b With b = XQ[F] where F are the indices of the medoids selected during step 5, b the coordinates of their corresponding nodes on the surface mesh obtained from the tomography, A is the diagonal matrix containing 1 or 0 so as to have: AX -b^ X0[F] = b, L the Laplacian matrix and XG the coordinates of the second surface mesh. - (Substep 6.2) Apply a Tikhonov regularization such that min\\AX-b\\l+ ||X-X0^ with P = - (Substep 6.3) Solve X = X„+ {A^A + L^A^Çb-AX^ to determine the coordinates of the third surface mesh.

[0015] According to another aspect, a non-destructive testing device is proposed comprising electronic circuitry adapted to implement the non-destructive testing process which includes at least the following steps: - (Step 1) Perform a tomography of a manufactured part to measure the manufactured part in three dimensions. - (Step 2) Generate a first surface mesh of the tomography; - (Step 3) Acquire a second surface mesh of a model of reference of the manufactured part; - (Step 4) Calculate modes of a Beltrami Laplacian operator on the first surface mesh and modes of a Beltrami Laplacian on the second surface mesh; - (Step 5) Compare the modes of the Beltrami Laplacian calculated in step 4 to match nodes of the first surface mesh and nodes of the second surface mesh; - (Step 6) Construct a third surface mesh by morphing the paired nodes of the first surface mesh and the second surface mesh; - (Step 7) Determine the functional performance of the manufactured part using the third surface mesh, by mechanical, thermal or thermomechanical simulations on the third mesh obtained by morphosis; - (Step 8) Sanction the piece by keeping the piece or rejecting the piece.

[0016] According to another aspect, a computer program product is proposed comprising program code instructions for executing the process when said program is run on a computer.

[0017] According to another aspect, a non-transient storage medium is proposed on which is stored a computer program comprising program code instructions to execute the process according to the invention, when said instructions are read from said non-transient storage medium and executed by a processor. Brief description of the drawings

[0018] The features of the invention mentioned above, as well as others, will become clearer upon reading the following description of at least one exemplary embodiment, said description being made in relation to the accompanying drawings, among which:

[0019] [Fig. 1] schematically illustrates the process of a non-destructive testing procedure;

[0020] [Fig.2] schematically illustrates a computer system adapted to implement the process.

[0021] DETAILED DESCRIPTION OF IMPLEMENTATION METHODS

[0022] Non-destructive testing method

[0023] With reference to [Fig. 1], according to a first aspect, a 100 process is proposed non-destructive testing of measurements of a manufactured part against the corresponding measurements of a reference model of the part.

[0024] The process is implemented by a non-destructive testing device 200 comprising electronic circuitry adapted to implement the process. The device 200 will be described in more detail below.

[0025] The process comprises at least the following steps: - (Step 1) Perform a tomography of a manufactured part to measure the part in three dimensions. - (Step 2) Generate a first surface mesh of the tomography; - (Step 3) Acquire a second surface mesh of a model of reference of the manufactured part; - (Step 4) Calculate geometric modes of a Beltrami Laplacian operator on the first surface mesh and geometric modes on the second surface mesh; - (Step 5) Compare the modes of the Beltrami Laplacian calculated in step 4 to match nodes of the first surface mesh and nodes of the second surface mesh; - (Step 6) Construct a third surface mesh by morphing the paired nodes of the first surface mesh and the second surface mesh; - (Step 7) Determine the functional performance of the manufactured part using the third surface mesh, by mechanical, thermal or thermomechanical simulations on the third mesh obtained by morphosis; - (Step 8) Sanction the piece by keeping the piece or rejecting the piece.

[0026] Steps 1, 2 and 3

[0027] The first three steps of the process allow the acquisition of the first surface mesh and the second surface mesh which are used in the process.

[0028] According to a particular arrangement, the second surface mesh can be obtained from a design file and meshing software.

[0029] The first mesh can be created using tomography meshing methods.

[0030] It is specified that a mesh is a two- or three-dimensional representation of an object by means of elements, representing the elementary cells of the tiling. The elements consist of nodes representing points in space and edges, in order to construct the elements in space. Thus, a mesh is represented by a set of node coordinates and an association table between the nodes to define the elements.

[0031] Depending on a particular arrangement, an object can also be viewed as a graph, very similar to a mesh. A mesh is a sampling of the object by its cells (representing small volumes). A graph is an object with a higher level of abstraction because it is simply composed of nodes and links. Meshes use notions of quality (solution accuracy) and density (local refinement) that are not useful in the context of a graph.

[0032] Step 4 - Calculation of modes

[0033] As previously stated, the method 100 then includes calculating modes of a Beltrami Laplacian on the first surface mesh and modes of a Beltrami Laplacian on the second surface mesh.

[0034] The Beltrami Laplace operator A is a second-order differential operator defined on a Riemannian manifold such that:

[0035] to.~div(grad)

[0036] The eigenvalue problem of the Beltrami Laplacian can be written as: Av = xv

[0037] With 2 an eigenvalue of the operator and v its associated eigenvector (mode).

[0038] The operator A is positive semi-definite, we denote in ascending order:

[0039] 0 = 20^2^22^23^.,.

[0040] The modes of the Beltrami Laplacian calculated on a mesh of a part are a spectral signature which allows the geometry of the part to be represented and the mesh to be decomposed into a modal basis.

[0041] It is noteworthy that CAD and tomographic models can be very similar. Consequently, their spectral signatures are close, and the comparison between these two models can be made using their spectral modes.

[0042] According to a particularly advantageous arrangement, in step 4, low-frequency modes of the Beltrami Laplacian represent global deformations of the part and high-frequency modes of the Beltrami Laplacian represent local surface details of the part.

[0043] According to a particular arrangement, the nodes are matched according to the low-frequency modes of the Beltrami Laplacian, so that the matched nodes correspond to surface correspondences of the first surface mesh and the second surface mesh.

[0044] According to a particular arrangement, step 5 of calculating the modes of a Beltrami Laplacian on the surface mesh of the tomography and on the surface mesh of the reference model includes correcting the sign of each mode of the Laplacian Beltrami on the first mesh as a function of a sign of a corresponding mode on the second surface mesh.

[0045] In a particularly advantageous way, the correction of the sign of each mode of the Beltrami Laplacian makes it possible to match the signs of the modes of the Beltrami Laplacian of the first surface mesh to the signs of the modes of the Beltrami Laplacian of the second surface mesh.

[0046] According to a particular provision, the sign correction of step 4 comprises the following sub-steps: - (Substep 4.1) Calculate a grey level image of a mode of the Beltrami Laplacian on the second mesh, mode_CAO, with a single color channel; - (Substep 4.2) Calculate a grey level image of a mode of the Beltrami Laplacian on the first mesh, mode_Tomo, with a single color channel; - (Substep 4.3) Calculate a mask by [ 1 in the intersection (CAD_mode, Tomo_mode) Otherwise - (Substep 4.4) Calculate a first difference DI between the two images in the mask. - (Substep 4.5) Repeat substeps 2 and 3 with a negative sign for the tomographic mode mode_Tomo and calculate a second difference D2 between the two images in the mask. - (Substep 4.6) If D2 <D1 alors changer de signe pour le mode tomographique mode_Tomo.

[0047] Substep 4.3 corresponds to a mask calculation; it involves finding the intersection zone between the CAD image and the tomographic image. This mask allows the geometric intersection of the two CAD and tomographic parts to be found.

[0048] We then compare the modes, i.e. the images of the modes of the CAD and the tomographic only in the areas of geometric intersection.

[0049] In substep 4.4, we first calculate the difference between the image in CAD mode and the image in Tomographic mode, denoted DI.

[0050] Next, the modes are defined up to a sign, and we want the CAD mode to correspond to the Tomographic mode. We look at the image of the Tomographic mode with a negative sign in substep 4.5, and a second difference is also calculated, denoted D2. In substep 4.6, if the second calculated difference is smaller than the first, this means that the image of the Tomographic mode with the negative sign corresponds to the CAD mode with the correct sign.

[0051] Step 5 - Node Matching

[0052] Step 5 comprises the following substeps for pairing the nodes: - (Substep 5.1) Select a predetermined number k of points P, on the second surface mesh using eigenvectors of the Laplacian Beltrami V cao operator; - (Substep 5.2) Find for each point P, selected a corresponding point, tomOj of the first surface mesh by minimizing a distance which takes into account Cartesian coordinates and spectral coordinates Vcao or Vrotna of the nodes of the first surface mesh and the second surface mesh.

[0053] According to a particular provision, step 5 may include the following substep: - (Substep 5.3) Apply weights to define a chosen metric for matching.

[0054] Step 6 - Construction of the third mesh

[0055] Step 6 of constructing the third mesh which corresponds to the results of the matching of step 5 (Mesh morphing in English) is carried out using a Tikhonov regularization method which allows to have an optimal position for all the surface nodes of the CAD mesh.

[0056] Step 6 comprises the following substeps: - (Substep 6.1) Search for X coordinates of the third surface mesh such that: minXTLX and AX = b With 6 = X0[F] where F are the indices of the medoids (the cluster centers calculated by spectral clustering) selected during step 5, b the coordinates of their corresponding nodes on the surface mesh from the tomography, A is the diagonal matrix containing 1 or 0 so that we have: AA = b Xo[ F ] -b^L the Laplacian matrix (We can for example take L=K which is the stiffness matrix from the discretization of the Beltrami Laplace operator by a finite element method) and Xo the coordinates of the second surface mesh. - (Substep 6.2) Apply a Tikhonov regularization such that min\\AX-b\\l+ ||X-X0^ with P = - (Substep 6.3) Solve X = X0+ (ATPA + LYiATP(b-AX<)) to determine the coordinates of the third surface mesh.

[0057] Computer program product

[0058] According to another aspect, a computer program product is proposed comprising program code instructions for executing the detection method, when said program is executed on a computer

[0059] Storage medium

[0060] According to another aspect, a non-transient storage medium is proposed on which is stored a computer program comprising program code instructions to execute the detection process 100, when said instructions are read from said non-transient storage medium and executed by a processor.

[0061] Non-destructive testing device

[0062] According to another aspect, a non-destructive testing device is proposed comprising electronic circuitry (computer system 200) adapted to implement a process 100.

[0063] As schematically shown in [Fig.2], the computer system 200 may include, connected by a communication bus 210: a processor 201; a random access memory 202; a read-only memory 203, for example of type ROM (“Read Only Memory”) or EEPROM (“Electrically-Erasable Programmable Read Only Memory”); a storage unit 204, such as a hard disk drive (HDD) or a storage media reader, such as an SD card reader (“Secure Digital”); and an input / output interface manager 205.

[0064] The processor 201 is capable of executing instructions loaded into RAM 202 from ROM 203, external memory, a storage medium (such as an SD card), or a communication network. When the computer system 200 is powered on, the processor 201 is capable of reading instructions from RAM 202 and executing them. These instructions form a computer program enabling the processor 201 to implement process 100.

[0065] All or part of the process 100 can thus be implemented in software form by executing a set of instructions by a programmable machine, for example a DSP (Digital Signal Processor) or a microcontroller, or be implemented in hardware form by a dedicated machine or component, for example an FPGA (Field Programmable Gate Array) or ASIC (Application-Specific Integrated Circuit). Generally, the computer system 200 includes electronic circuitry adapted and configured to implement, in software and / or hardware form, the process in relation to the computer system 200 in question.

Claims

Demands

1. A method (100) for non-destructive testing of measurements of a manufactured part against corresponding measurements of a reference model of the part, the method being implemented by a non-destructive testing device comprising electronic circuitry adapted to implement the method, the method being characterized in that it comprises at least the following steps: - (Step 1) Perform a tomography scan of a manufactured part to measure the manufactured part in three dimensions. - (Step 2) Generate a first surface mesh of the tomography scan; - (Step 3) Acquire a second surface mesh of a reference model of the manufactured part; - (Step 4) Calculate modes of a Beltrami Laplacian operator on the first surface mesh and modes of a Beltrami Laplacian on the second surface mesh;- (Step 5) Compare the modes of the Beltrami Laplacian calculated in step 4 to match nodes of the first surface mesh and nodes of the second surface mesh; - (Step 6) Construct a third surface mesh by morphing the matched nodes of the first and second surface meshes; - (Step 7) Determine the functional performance of the manufactured part using the third surface mesh, through mechanical, thermal, or thermomechanical simulations on the third mesh obtained by morphing; - (Step 8) Deem the part acceptable by keeping it or rejecting it.

2. A method according to claim 1, wherein step 4 of calculating the modes of a Beltrami Laplacian on the first surface mesh and on the second surface mesh comprises correcting the sign of each mode of the Beltrami Laplacian on the first surface mesh as a function of a sign of a corresponding mode of a Beltrami Laplacian on the second surface mesh.

3. A method according to claim 2, wherein the sign correction of step 4 comprises the following substeps: - (Substep 4.1) Calculate a grayscale image of a Beltrami Laplacian mode on the second mesh, mode_CAO, with a single color channel; - (Substep 4.2) Calculate a grayscale image of a Beltrami Laplacian mode on the first mesh, tomographic mode mode_Tomo, with a single color channel; - (Substep 4.3) Calculate a mask by 1 in the intersection (mode_CAO, mode_Tomo); 0 otherwise; - (Substep 4.4) Calculate a first difference DI between the two images in the mask; - (Substep 4.5) Repeat substeps 2 and 3 with a negative sign for the tomographic mode mode_Tomo and calculate a second difference D2 between the two images in the mask; - (Substep 4.6) If D2 <D1 alors changer de signe pour le mode tomographique mode_Tomo.

4. A method according to any one of the preceding claims, wherein step 5 comprises the following substeps for matching the nodes: - (Substep 5.1) Selecting a predetermined number k of points P( on the second surface mesh using eigenvectors of the Laplacian Beltrami Vcao operator; - (Substep 5.2) Finding for each selected point Pi a corresponding point, toniOj qu first surface mesh by minimizing a distance that takes into account Cartesian coordinates and spectral VCAO coordinates or nodes of the first surface mesh and the second surface mesh.

5. A method according to claim 4, further comprising the following substep: - (Substep 5.3) Apply weights to the Cartesian and spectral coordinates of the nodes of the surface meshes to define a metric for matching the nodes of the two meshes.

6. A method according to any one of the preceding claims, wherein step 6 of constructing the third mesh is carried out using a Tikhonov regularization method to remove measurement noise and filter details from the first surface mesh and the second surface mesh.

7. A method according to claim 6, wherein step 6 comprises the following substeps: - (Substep 6.1) Search for X coordinates of the third surface mesh such that: min(XTLX) and XX = b, with b - X(j[F]), where F are the indices of the medoids selected in step 5, b the coordinates of their corresponding nodes on the surface mesh obtained from the tomography, A is the diagonal matrix containing 1 or 0 such that AX - b^XQ[F\ - b^Li is the Laplacian matrix, and Xo the coordinates of the second surface mesh. - (Substep 6.2) Apply a Tikhonov regularization such that min^AX - b\2p + ||X-Xo||| with P = maxdiaglL} - (Substep 6.3) Solve X = Xo + (ATPA + LÿATP(b-AXa)) To determine the coordinates of the third surface mesh.

8. A non-destructive testing device comprising electronic circuitry adapted to implement the non-destructive testing process which includes at least the following steps: - (Step 1) Perform a tomography scan of a manufactured part to measure the manufactured part in three dimensions. - (Step 2) Generate a first surface mesh of the tomography scan; - (Step 3) Acquire a second surface mesh of a reference model of the manufactured part; - (Step 4) Calculate modes of a Beltrami Laplacian operator on the first surface mesh and modes

9. of a Beltrami Laplacian on the second surface mesh; - (Step 5) Compare the modes of the Beltrami Laplacian calculated in step 4 to match nodes of the first surface mesh and nodes of the second surface mesh; - (Step 6) Construct a third surface mesh by morphing the paired nodes of the first surface mesh and the second surface mesh; - (Step 7) Determine the functional performance of the manufactured part using the third surface mesh, by mechanical, thermal or thermomechanical simulations on the third mesh obtained by morphosis; - (Step 8) Sanction the piece by keeping the piece or rejecting the piece. Product computer program comprising program code instructions to execute the method (100) according to any one of claims 1 to 7, when said program is executed on a computer.

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