Method and apparatus for determining the dimensional stability of a product manufactured according to a given manufacturing process

Abstract

Method (30) for determining a structural strength (11) of a product manufactured according to a manufacturing process (12) with given parameters, characterized by the following features: - a prediction (21) regarding the structural strength (11) is made based on a database (10) of comparison products, - the accuracy (29) of the prediction (21) is checked (22) by comparing the parameters with the corresponding parameters of the comparison products, - if the accuracy (29) falls below a required minimum level (34), the structural strength (11) is tested (23), - if the accuracy (29) reaches the minimum level (34), a deviation (31) of the prediction (21) from the actual structural strength (11) is estimated (24) using the comparison products most similar to the product. - based on the deviation (31) a number (32) of tests (18) required to determine the structural strength (11) is calculated (25) and - the prediction (21) is refined by the experiments (18) (26).

Description

[0001] The present invention relates to a method for determining the dimensional stability of a product manufactured according to a given manufacturing process. The present invention further relates to a corresponding device, a corresponding computer program, and a corresponding storage medium. State of the art

[0002] In materials science and mechanical engineering, fatigue strength refers to the deformation and failure behavior of materials under cyclic loading. According to current technology, fatigue strength is measured using a S-N test, the results of which can be used to construct the so-called S-N curve. This curve indicates the number of load cycles that can be withstood until the expected fatigue failure, depending on the stress, and is typically divided into short-term fatigue strength, long-term fatigue strength, and endurance limit.

[0003] The fatigue strength of a specific component is also referred to as structural strength.

[0004] DE 10 2015 008 933 A1 relates to a method for determining the fatigue strength of a component, wherein a notch radius is determined on the component, wherein a burst test is carried out to determine a static strength of the component, wherein at least one centrifugal test is carried out on a component to determine a fatigue strength in order to determine at least two S-N curves with respective fatigue strength curves for different failure probabilities, wherein a fatigue strength curve of a censored S-N curve is placed between the fatigue strength curves of the determined S-N curves, and wherein a fatigue strength curve of the censored S-N curve is placed horizontally through an intersection of the fatigue strength curve of the censored S-N curve with a predetermined number of load cycles.

[0005] Methods from data analytics and machine learning for predicting the fatigue strength of steels are known from AGRAWAL, Ankit [et al.]: Exploration of data science techniques to predict fatigue strength of steel from composition and processing parameters. In: Integrating Materials and Manufacturing Innovation, Vol. 3, 2014, pp. 1-19. and from SHIRAIWA, Takayuki; MIYAZAWA, Yuto; ENOKI, Manabu: Prediction of Fatigue Strength in Steels by Linear Regression and Neural Network. In: Materials Transactions, Vol. 60, 2018; No. 2, pp. 189-198. Disclosure of the invention

[0006] The invention provides a method for determining the dimensional stability of a product manufactured according to a given manufacturing process, a corresponding device, a corresponding computer program and a corresponding machine-readable storage medium according to the independent claims.

[0007] The proposed approach is based on the premise that a conventional experimental determination of the S-N or S-N curve begins with sequential cyclic loading of fatigue specimens or components at different stress amplitudes or stress sequences, with the aim of determining the stress-dependent lifetime and its scatter up to a specific limiting number of load cycles. In this procedure, the functional representation of the lifetime and its aleatory scatter at different stress amplitudes or a specific series of stress sequences constitutes the S-N or S-N curve.

[0008] The method described here is further based on the understanding that material and process parameters (MPP) in component manufacturing conventionally contribute only to a limited extent to determining stress resistance and are not systematically recorded. Therefore, according to the state of the art, a new S-N curve determination is regularly required when one of the MPPs is changed.

[0009] One advantage of this solution is the low cost and time expenditure, as results from previously conducted tests can also be taken into account outside the respective project when designing similar design elements.

[0010] The measures listed in the dependent claims enable advantageous further developments and improvements of the basic concept stated in the independent claim. For example, prediction can be based on a S-N curve. Using the WPP (presumably a specific method or technique), a preliminary, machine learning (ML)-supported estimation of the S-N curve parameters is performed, which is then refined by further targeted fatigue tests with optimally selected loads. This use of prior knowledge, along with cost-optimized load selection during trials, can contribute to a reduction in the number of test specimens without compromising accuracy.

[0011] Furthermore, for metallic products, the recorded parameters can relate to the material, shape, cutting, heat treatment, or finishing of the product. This enables efficient prediction of the cyclic stress resistance of metallic, smooth, or notched design elements and rapid optimization of materials with regard to their stress resistance. Overall, the stress resistance determination of metallic design elements is accelerated in this way or can be eliminated entirely, which significantly reduces the associated development costs. Brief description of the drawings

[0012] Exemplary embodiments of the invention are shown in the drawings and explained in more detail in the following description. It shows: Fig. 1. The schematic representation of the testing process according to the state of the art and after the implementation of the proposed hybrid model. Fig. 2 the flowchart of the proposed procedure. Fig. 3 the relationship between the deviation of the estimated to the actual Wöhler curve parameters and the number of experiments required to determine them. Fig. 4. The application of Bayes' theorem to increase the prediction accuracy of candidate S-N curves by means of fatigue tests. Embodiments of the invention

[0013] Fig. Figure 1 illustrates a hybrid development process for design elements. By systematically recording material and process parameters as well as the associated experimentally determined S-N curve in a database (10) and subsequently systematically evaluating them using machine learning methods, a prediction made during the design of the design elements (19) can be validated or refined through experiments in the testing phase (28), which requires higher accuracy. The results from these S-N tests (18) are stored in the database (10) and used for further, similarly “hybrid” predictions (21).

[0014] The steps of the procedure used for this purpose (30) are now described in relation to Fig. 2 examined in detail.

[0015] First, based on the input WPP, e.g., using a regression model based on the material database (10), a prediction regarding the fatigue strength (11) is made in the form of a Wöhler curve, which will subsequently be referred to as the “candidate Wöhler curve” (process 21). This candidate Wöhler curve W→ This is described, for example, using terms such as inclination, corner point, fatigue strength and scatter.

[0016] Based on this, it is assessed to what extent the input WPP differs from parameters present in the material database (10) (process 22). For example, it can be checked whether the input WPP lies within the convex hull of the parameter points contained in the database (10).

[0017] If - referring to Fig. 3 - If the accuracy (29) of the candidate S-N curve (33) falls below this minimum value (34), the experiments required to test the structural strength (11) are carried out in full (Process 23). If, however, the required minimum level (34) of accuracy (29) is achieved, the deviation (31) of the individual parameters of the candidate S-N curve from those of the actual S-N curve is estimated using the most similar data sets in the material database (10) – i.e., those comparison products whose S-N curves exhibit the smallest possible deviation from those of the product at hand (Process 24). The candidate S-N curve is then used as the basis for further experimental validations, which may be more or less complex depending on the deviation (31).

[0018] Based on the estimated parameter deviation (31), and using the existing test data, the number (32) of tests (18) required to precisely determine the structural strength (11) is calculated (process 25). The number (32) of test points defined in this way can be generated from the parameter distribution of the candidate S-N curve using the inversion method.

[0019] In accordance with Bayes' theorem, the candidate-speak curve with the defined number of trial points (see Fig.4) an a priori distribution (36) with a defined variance of the parameters (35). Additional Wöhler trials (18) on test subjects with the same WPP represent a plausibility or likelihood distribution (39), which reduces the inaccuracy of the parameters of the candidate Wöhler curve (35) by including additional information. The so-called marginal likelihood P(X), i.e., the expected value of the likelihood function (39) with respect to the a priori distribution (36) of the parameters of the candidate Wöhler curve (35), weights the influence of both distributions.

[0020] By means of a tool trained through active learning (AL) (20), an optimal voltage amplitude or sequence is selected for each of the trials (18).

Claims

[1] Method (30) for determining the structural strength (11) of a product manufactured according to a manufacturing process (12) with given parameters, characterized by the following characteristics: - a prediction (21) regarding the structural strength (11) is made based on a database (10) of comparison products, - the accuracy (29) of the prediction (21) is checked (22) by comparing the parameters with the corresponding parameters of the comparison products, - if the accuracy (29) falls below a required minimum level (34), the structural strength (11) is tested (23), - if the accuracy (29) reaches the minimum level (34), a deviation (31) of the prediction (21) from the actual structural strength (11) is estimated (24) using the comparison products most similar to the product. - based on the deviation (31) a number (32) of tests (18) required to determine the structural strength (11) is calculated (25) and - the prediction (21) is refined by the experiments (18) (26). [2] Method (30) according to claim 1, characterized by the following characteristics: - the experiments (18) are Wöhler experiments (18) and - the prediction (21) is made using a Wöhler curve. [3] Method (30) according to claim 2, characterized by , that the Wöhler curve is described by at least one of the following: - a tendency, - a key point, - a fatigue strength and - a dispersion. [4] Method (30) according to any one of claims 1 to 3, characterized by that the parameters relate to at least one of the following: - Starting materials of the manufacturing process (12) and - Process steps of the manufacturing process (12). [5] Method (30) according to any one of claims 1 to 4, characterized by that the products are metallic and the parameters relate to at least one of the following: - a material (13) of the product, - a shaping (14) of the product, - a cut (15) of the product, - a heat treatment (16) of the product or - a surface treatment (17) of the product. [6] Method (30) according to any one of claims 1 to 5, characterized by the following characteristic: - each load (27) of the product in the experiments (18) is optimized by active learning (20). [7] Method (30) according to any one of claims 1 to 6, characterized by the following characteristic: - the refinement (26) of the prediction (21) is carried out by calculating an A Posteriori distribution (37) of the structural strength (11) from an A Priori distribution (36) corresponding to the prediction (21) according to a Bayes formula (38), whereby the tests (18) are weighted according to a plausibility function (39). [8] Computer program configured to execute the method (30) according to any one of claims 1 to 7. [9] Machine-readable storage medium on which the computer program according to claim 8 is stored. [10] Device (10) configured to perform the method (30) according to any one of claims 1 to 7.

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