A method for parameter calibration of cemented carbide discrete element method based on BP neural network

Abstract

The present invention relates to the field of mechanical processing technology, and discloses a method for calibrating cemented carbide discrete element parameters based on BP neural network, comprising the following steps: constructing a discrete element constitutive model according to material physical property parameters; setting parameters and ranges to be calibrated; performing combined experimental design (DOE) according to the parameters and ranges to be calibrated; importing the results of DOE combined with experimental design as input data into the discrete element constitutive model for discrete element simulation; obtaining sufficient training samples; establishing a training set with data; obtaining an approximate model between the parameters to be calibrated and the output data of the discrete element simulation; calibrating the parameters to be calibrated with actual mechanical properties as the target, and then comparing the simulation results with the physical test results. The technical solution of the present invention solves the problems of difficulty in obtaining existing cemented carbide particle parameters and low measurement accuracy, and provides an effective technical means for determining BPM bonding bond parameters in cemented carbide particle numerical simulation tests.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical processing, and in particular to a parameter calibration method of cemented carbide powder bonding bonds based on a discrete element method (DEM). Background Art

[0002] With the advancement of powder metallurgy technology and the increasing requirements for advanced machining processes, especially modern metal powder 3D printing, which integrates mechanical engineering, CAD, reverse engineering technology, layered manufacturing technology, CNC technology, material science, and laser technology, powder metallurgy product technology has become a modern comprehensive technology across more disciplines. Therefore, it is necessary to use advanced numerical simulation methods to study the physical and mechanical properties of metal powders.

[0003] Discrete element method (DEM) is widely used to simulate the interaction between particles. DEM uses the Lagrangian method to model the whole system, which is regarded as composed of discrete rigid particles. According to Newton's second law of motion, the collision between particles or between particles and the wall is calculated. It is used to analyze discrete discontinuities and continua composed of particles, analyze and solve the motion laws and mechanical properties of complex discrete systems, heat transfer, bonding and breaking of chemical bonds between particles, and constitutive behavior in response to changes in external fields. It is widely used in geotechnical, mining, agriculture, food, chemical, pharmaceutical and environmental fields. Its advantage is that it does not need to consider grid division, is particularly suitable for analyzing the contact between two objects, does not consider the deformation of the object, and has a fast calculation speed. It can clearly reflect the real movement of the reaction particles and solve their stress conditions. Moreover, the physical properties of metal powder particles, which are the basis of numerical simulation of powder metallurgy technology, are the basic basis for numerical simulation research. It plays a vital role in the numerical simulation of metal powder metallurgy, so accurate and reasonable powder particle model parameters are a necessary condition to ensure the high accuracy of numerical simulation results.

[0004] At present, establishing the connection between the virtual bond micro-parameters and the macroscopic mechanical response of the material model is still an ongoing challenge. For the material object to be studied, the parameters of the bond still need to be calibrated according to the actual mechanical properties of the material. For the ubiquitous irregularly arranged particle aggregates, the calibration process of the bond micro-parameters can adopt the trial and error method, parameter inversion, or some statistical methods to improve the calibration process, such as the response surface method. However, there is a complex nonlinear relationship between the bond parameters and the macroscopic mechanical response. When there are many parameters to be calibrated, the use of the above-mentioned single calibration method has problems such as low efficiency and the relative error of the simulated mechanical response cannot be guaranteed. In addition, few literatures explore the significance of the influence of bond parameters on the macroscopic mechanical response, which is crucial for the regulation strategy of the parameters to be calibrated. Blindly regulating the parameters to be calibrated not only reduces the efficiency, but also reduces the accuracy of the calibration. In order to improve the accuracy of DEM simulation results, researchers have tried many methods to calibrate parameters, but none of them have developed a standardized parameter calibration process. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a cemented carbide discrete element parameter calibration method based on BP neural network. To achieve this purpose, the present invention adopts the following technical solutions:

[0006] A method for calibrating parameters of cemented carbide discrete element based on BP neural network comprises the following steps:

[0007] S1: The compressive modulus and compressive strength are obtained through uniaxial compression test, and the bending strength is obtained through three-point bending test. The uniaxial compression physical test results of the cemented carbide sample to be simulated are determined. The test formula is as follows:

[0008] ;

[0009] Among them, CS is compressive strength, CM is compressive modulus, BS is flexural strength, F c is the peak axial force, F b is the bending failure load, L is the span, b is the width, h is the thickness, A t is the cross-sectional area of ​​the specimen, σ is the axial stress in the linear portion, and ε is the axial strain in the linear portion.

[0010] The compressive modulus and compressive strength of the uniaxial compression test are used as the preliminary calibration values ​​of the bond micro-parameters in the discrete element model, and the flexural strength of the three-point bending test is used as the final calibration value of the bond micro-parameters in the discrete element model.

[0011] S2: Construct a discrete element model and use the commercial discrete element software EDEM to establish a uniaxial compression specimen bonded particle model BPM. Considering the computational efficiency, the particle size and geometric area in BPM are simultaneously enlarged by the same multiple h compared with the original model to obtain an accurate scaled model of the system. The scaled model is a cylinder with a height-to-diameter ratio of 2. The height of the cylindrical scaled model is 100μm and the diameter is 50μm. The radius of the particle is set to 2μm, the contact radius is 2.2μm, the filling rate of the particle is 0.6, and the radius R of the Bond bond is set to 2μm, which is consistent with the particle radius. A DEM virtual model corresponding to the uniaxial compression and three-point bending of the actual test is established.

[0012] S3: Setting the parameters and ranges to be calibrated, wherein the parameters to be calibrated are microscopic parameters of the bonding bond, including normal stiffness per unit area, tangential stiffness per unit area, normal critical force and tangential critical force; using Plackett-Burman design to identify the significance of the impact on the response by comparing the differences between the high and low levels of the microscopic parameters of the bonding bond, normal stiffness per unit area, tangential stiffness per unit area, normal critical force and tangential critical force, and listing the high and low level values ​​of the parameters to be calibrated, and the value range is obtained through preliminary debugging.

[0013] S4: In order to consider the interaction between the parameters to be calibrated to refine the training sample network, a Box-Behnkendesign test was performed. For each parameter factor to be calibrated, three levels -1, 0, and +1 were selected, and the single-factor test value was taken to design an experimental matrix. The experimental matrix included all possible combinations of each parameter to be calibrated and the level to provide sufficient response information.

[0014] S5: DEM virtual experiment, the design matrix of the single factor test and Box-Behnken test is numerically imported into the discrete element model to obtain the corresponding CS and CM.

[0015] S6: Sample interpolation, establishing training set, test set, validation set and training BP neural network.

[0016] S7: Verify the BP neural network. If it fails, return to step S6 to adjust the structure of the neural network and continue training the BP neural network.

[0017] S8: Using genetic algorithm parameter inversion, the trained BP neural network model is used as the fitness function of the genetic algorithm, and the experimentally measured uniaxial compression physical test results CS and CM are set as the optimization targets of the genetic algorithm to optimize the four bond micro parameters to be calibrated.

[0018] S9: Calibrate material parameters according to the output results of the genetic algorithm.

[0019] Furthermore, the BP neural network of step S6 comprises an input layer, a hidden layer and an output layer, wherein the number of neurons n in the input layer is set to 4, the number of neurons m in the output layer is set to 2, and the number of neurons k in the hidden layer is determined by the following formula:

[0020] ;

[0021] Where n and m are the number of neurons in the input layer and output layer respectively, and l is an integer in the interval [1,11].

[0022] Furthermore, the calculation formula of the interpolation is:

[0023] ;

[0024] In the formula, A, B, C, D are coefficients, k = 0, 1, … , n-2.

[0025] Furthermore, the samples in steps S4, S5, S6 and S7 are divided into three parts: training set, test set and validation set according to the ratio of 0.7:0.15:0.15.

[0026] Furthermore, in step S9, the MATLAB neural network toolbox is used to establish a BP neural network. The input vectors are the physical quantities monitored by the normal stiffness per unit area, the tangential stiffness per unit area, the normal critical force and the tangential critical force. The output vectors are the compressive modulus and compressive strength of the actual mechanical properties of uniaxial compression. The input and output vectors are normalized using the MATLAB built-in function mapminmax. Before training the neural network, the learning rate, the maximum number of training times, the training error and the training algorithm must be determined.

[0027] Furthermore, in step S9, the trained network model is used as the fitness function of the genetic algorithm, and the optimization target of the genetic algorithm is set according to the uniaxial compression physical test result in step S1. The parameters to be calibrated are optimized and compared with the corresponding stress-strain curves of the uniaxial compression virtual test and the physical test.

[0028] Compared with the prior art, the present invention has the following advantages:

[0029] 1. Based on the discrete element theory and method, the present invention establishes the BPM constitutive model of uniaxial compression specimens and three-point bending specimens, and numerically simulates the mechanical properties of M08 cemented carbide specimens. The CM (compressive modulus) and CS (compressive strength) obtained from the actual uniaxial compression experiment are used as BP neural network correction and evaluation indicators to optimize the BPM model parameters of M08 cemented carbide, thereby overcoming the problem of difficulty in determining the parameters of the existing conventional BPM model and providing a new method for the calibration of the BPM bonding bond parameters of cemented carbide particles.

[0030] 2. The BP neural network method adopted in the present invention, by combining experimental design (DOE) including single factor test and Box-Behnken test, obtains a large number of training samples by sample interpolation while considering the interaction between the parameters to be calibrated, so as to refine the training of BP neural network. In addition, in order to eliminate the influence of different dimensions between input and output, accelerate the convergence speed of the training process, and normalize the training sample data, it has the advantages of fast calculation speed, high credibility of numerical test results, and high stability.

[0031] 3. The present invention solves the key problem that the existing BPM model parameters of cemented carbide particle numerical simulation are difficult to calibrate, and provides reliable particle model parameters for cemented carbide DEM numerical simulation research.

[0032] In summary, the technical solution of the present invention solves the problems of difficulty in calibrating the existing cemented carbide particle BPM model parameters and low measurement accuracy, and provides an effective technical means for determining the BPM bonding bond parameters of cemented carbide particles in numerical simulation tests. The technical solution of the present invention can be used to calibrate the BPM model parameters of cemented carbide particles simply, quickly and accurately, with the advantages of high accuracy, wide application range and high efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0034] Attached Figure 1 This is a schematic diagram of a method for calibrating bonding parameters of a BPM model of M08 cemented carbide particles based on a discrete element method according to the present invention;

[0035] Attached Figure 2 This is a numerical simulation test diagram of the uniaxial compression BPM model of the present invention;

[0036] Attached Figure 3 This is the numerical simulation test diagram of the three-point bending BPM model;

[0037] Attached Figure 4 The BP neural network topology structure adopted by the present invention;

[0038] Attached Figure 5 is the cubic spline curve of the present invention;

[0039] Attached Figure 6 This is the MSE value output result diagram of the model training of the present invention;

[0040] Attached Figure 7 It is a cubic spline interpolation diagram of a single-factor test of a uniaxial compression virtual test of the present invention;

[0041] Attached Figure 8 This is the BP neural network structure training process of the present invention;

[0042] Attached Fig. 9 It is a regression analysis diagram of the BP neural network structure of the present invention;

[0043] Attached Fig.10 A stress-strain curve comparison diagram of the uniaxial compression virtual test and the physical test of the present invention;

[0044] Attached Fig.11 A diagram showing a key stress concentration area according to an embodiment of the present invention;

[0045] Attached Fig.12 FIG. 4 is a diagram showing a bond breaking concentration area according to an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The technical solution of the present invention is further described below with reference to the accompanying drawings and through specific implementation methods.

[0047] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on this patent; in order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0048] As attached Figure 1 This embodiment provides a parameter calibration method for the M08 cemented carbide discrete element BPM model based on BP neural network. The cemented carbide material is composed of a high-hardness, high-brittle carbide hard phase and a relatively soft metal bonding phase, and the two phases are combined by a powder metallurgy process. As a composite metal-ceramic material, cemented carbide has the characteristics of high hardness, wear resistance, and high temperature resistance. It is widely used in the field of CNC machining tools. This embodiment selects tungsten-cobalt cemented carbide rods (M08, cobalt content 8%) produced by Zhuzhou Huarui Precision Tools Co., Ltd. as the object, and performs the following technical means:

[0049] S1: The compressive modulus and compressive strength are obtained through uniaxial compression test, and the bending strength is obtained through three-point bending test. The uniaxial compression physical test results of the cemented carbide sample to be simulated are determined. The test formula is as follows:

[0050] ;

[0051] Among them, CS is compressive strength, CM is compressive modulus, BS is flexural strength, Fc is the peak axial force, F b is the bending failure load, L is the span, b is the width, h is the thickness, A t is the cross-sectional area of ​​the specimen, σ is the axial stress in the linear part, and ε is the axial strain in the linear part;

[0052] S2: A discrete element constitutive model is constructed based on the physical properties of the material. Furthermore, the bonded particle model (BPM) of the uniaxial compression specimen is established using the commercial discrete element software EDEM (2021). Figure 2 As shown, the uniaxial compression specimen is a cylinder with a height-to-diameter ratio of 2. The height of the BPM original specimen model is 100μm and the diameter is 50μm, where the particle radius is 2μm, the contact radius is 2.2μm, the particle filling rate is 0.6, and the radius R of the bonding bond is set to 2μm, which is consistent with the particle radius. The original model is scaled to a scaled model by the magnification factor h. A pressure plate is placed on the top and bottom of the BPM model, where the lower pressure plate is fixed as a loading platform, and a specified vertical velocity is applied to the upper pressure plate to simulate the quasi-static compression process. The vertical velocity is specified to be 10mm / s. Similarly, the three-point bending specimen is as follows Figure 3 As shown, the span is 100 μm and the compression vertical speed is specified as 5 mm / s.

[0053] A specified vertical velocity is applied to the upper platen to simulate the quasi-static compression process. The vertical velocity is specified to be 10 mm / s. 24 All virtual tests were performed on a Dell PowerEdge T640 workstation, which uses an Intel® Xeon® Silver 4214 CPU with a main frequency of 2.20GHz and a memory of 128.0GB. The simulation was stopped when the BPM specimen was crushed, and the simulation file was saved every 0.0001s. The time step (Δ t ) is set to 20% of the Rayleigh time step (Δtc) to balance the simulation accuracy and simulation time. According to equation (7) and the DEM parameters in Table 2, it is calculated that Δt = 3.425×10 -9 s.

[0054] ;

[0055] Where R is the particle radius, G is the shear modulus of the particle, γ is the Poisson's ratio of the particle, and ρ is the particle density.

[0056] S3: Perform single factor test on the parameters to be calibrated and set the range and level.

[0057] It should be noted that the parameters to be calibrated include normal stiffness per unit area (NSPUA), tangential stiffness per unit area (SSPUA), normal critical force (CNS) and tangential critical force (CSS). As shown in Table 1, the high and low levels and range values ​​of the single factor test are listed. The Plackett-Burman design is used to compare the differences between the high and low levels of the microscopic parameters of the bond bond normal stiffness per unit area, tangential stiffness per unit area, normal critical force and tangential critical force to identify the significance of the impact on the response, and the high and low level values ​​of the parameters to be calibrated are listed. The value range of the parameters to be calibrated is obtained through preliminary debugging.

[0058] Table 1

[0059]

[0060] S4: In order to consider the interaction between the parameters to be calibrated to refine the training sample network, a Box-Behnkendesign test was performed. For each parameter factor to be calibrated, three levels -1, 0, and +1 were selected (see Table 1), and the single-factor test value was taken to design an experimental matrix, which included all possible combinations of each parameter to be calibrated and the level to provide sufficient response information.

[0061] It should be further explained that Table 2 is the test matrix of the single factor test, and the corresponding CS and CM values ​​measured by the uniaxial compression virtual test are also given.

[0062] Table 2

[0063]

[0064] S5: Conduct a DEM virtual experiment and perform sample interpolation based on the design matrix of the single-factor test and the CS and CM values ​​measured by the corresponding uniaxial compression virtual test.

[0065] S6: Sample interpolation, establish training set, test set, validation set and train BP neural network. The topological structure of BP neural network is shown in the attached Figure 4 .

[0066] It should be noted that the present invention uses a cubic spline curve with good smoothness to interpolate the original data in Table 2. Cubic spline interpolation is a very effective and computationally efficient interpolation method with a wide range of applications. Cubic spline interpolation uses a cubic polynomial to fit two adjacent known data points. Figure 5 The piecewise cubic polynomial function g(x) used for interpolation consists of nl cubic polynomials g defined in the interval [xk,xk+1] k Composition, g k The definition of is shown in formula (8). In addition, for the unknown function f (x), it is known thatx 0 to x n-1 common n The value of a point f ( x k ). In the interval x 0< x 1<…< x k <…< x n-1 On, need to ensure g ( x ) satisfy g ( x k ) = f ( x k ).

[0067] ;

[0068] In the formula, A, B, C, D are coefficients, k = 0, 1, …, n-2.

[0069] The original samples of NSPUA (A), SSPUA (B), CNS (C) and CSS (D) are segmented by cubic spline, see Appendix Figure 7-8 There are 9 interpolation points between two adjacent data points on the cubic spline interpolation curve. After interpolation, a total of 41 groups of sample data are obtained, and a total of 164 groups of sample data are obtained for the four factors.

[0070] The Box-Behnkendesign (BBD) test is performed on the parameters to be calibrated.

[0071] It should be noted that the single-factor test cannot take into account the influence of the interaction between factors. In order to consider the interaction between the parameters to be calibrated and to refine the sample network used to train the BP neural network, a BBD experimental design was carried out on the four microscopic parameters to be calibrated, namely NSPUA (A), SSPUA (B), CNS (C) and CSS (D), to determine the influence of more than three factors and their interactions on the response.

[0072] It should be further explained that after determining the factors, three levels (-1, 0, +1) need to be selected for each factor. The values ​​shown in Table 1 are taken and the design matrix is ​​shown in Table 3. The corresponding CS and CM values ​​measured by the uniaxial compression virtual test are also given.

[0073] Table 3

[0074]

[0075] In order to eliminate the influence of different dimensions between input and output and speed up the convergence of the training process, the training sample data is normalized. Similarly, the prediction inversion results of the neural network also need to be denormalized. The linear transformation function is used to normalize and denormalize the sample data, as shown in the following formula. The distribution interval of the processed data is [0,1].

[0076] ;

[0077] In the formula, X norm is the normalized value, X is the original sample value, X max and X min are the maximum and minimum values ​​of the original samples respectively; Y norm is the normalized value of the predicted inversion data, and Y is the denormalized value of the predicted inversion data.

[0078] S7: Establish training set, test set and validation set according to the single factor test interpolation sample and BBD test sample.

[0079] The construction and training of a BP single hidden layer neural network is implemented based on the Matlab R2021b platform. The network training uses the Levenberg-Marquardt algorithm, and the mean square error (MSE) is used as the performance function. The target MSE of the training is set to 0.00001, and the maximum number of training iterations is 1000. It can be seen from the previous text that the number of hidden layer neurons k is 4~13. Through repeated tests, the best value of k is 5. The MSE values ​​corresponding to the training set, test set, and validation set during the model training process are output. The results are as follows Figure 6 As shown. It can be seen that with the increase of training iterations, the mean square error of the network structure decreases, indicating that it is constantly learning. With the increase of training times, the mean square error tends to be stable. Due to the small sample size, the best verification performance is obtained when the number of iterations is 6, and the MSE value is 0.00051632. When the number of iterations is 12, the model has reached a convergence state and the network training is completed.

[0080] The trained network model is used as the fitness function of the genetic algorithm, and the uniaxial compression physical test results (CS, CM, Table 2) measured in the previous article are set as the optimization target of the genetic algorithm to optimize the four bond parameters to be calibrated. The optimal parameters are shown in Table 4, and the corresponding stress-strain curves of the uniaxial compression virtual test and the physical test are compared. Fig.10As shown in the figure, it can be seen that the simulation results are consistent with the actual ones. The comparison results of the corresponding BPM simulated mechanical properties and the actual mechanical properties are shown in Table 5. The relative errors of CM and CS are 2.523% and 1.008%, respectively. The errors are all within the acceptable range, indicating that the constructed BPM effectively reflects the mechanical behavior of M08 cemented carbide.

[0081] Table 4

[0082]

[0083] Table 5

[0084]

[0085] It should be noted that the above-mentioned single factor test interpolation samples and BBD test samples obtained a total of 193 groups of sample data. Figure 3 For the training of the BP neural network structure, the sample data is divided into three parts: training set, test set and validation set according to the ratio of 0.7:0.15:0.15. Therefore, the number of samples in the training set is 135, and the number of samples in the test set and validation set is 29 respectively.

[0086] S8: Perform neural network training according to the training set to obtain an approximate model between the parameters to be calibrated and the output data of the discrete element simulation.

[0087] It should be noted that, in order to establish the mapping relationship between the bonding parameters and the macroscopic mechanical response, the BP neural network topology used in the present invention is as shown in the attached figure. Figure 4 As shown in Figure 1, it includes an input layer, a hidden layer, and an output layer. The number of neurons in the input layer is set to 4 (n=4), including the bonding parameters to be calibrated (NSPUA, SSPUA, CNS, CSS), and the number of neurons in the output layer is set to 2 (m=2), which is the macroscopic mechanical properties CM and CS obtained by the uniaxial compression test.

[0088] Using a single hidden layer structure, the number of neurons k in the hidden layer is determined by the following formula:

[0089] ;

[0090] In the formula, n and m are the number of neurons in the input layer and the output layer respectively, l is an integer in the interval [1,11]. The number of neurons in the hidden layer k is calculated to be 4 ~ 13.

[0091] It should be further explained that in order to eliminate the impact of different dimensions between input and output and speed up the convergence of the training process, the training sample data needs to be normalized. Similarly, the prediction inversion results of the neural network also need to be denormalized.

[0092] S9: Verify the BP neural network. If it fails, adjust the structure of the neural network and return to step S7 to continue training the neural network.

[0093] It should be noted that MSE is used to evaluate the performance of the network training process. MSE can measure the average error of the data according to the degree of change of the data. The smaller its value, the better the accuracy of the model in describing the test results. Figure 7-8 It can be seen that at the beginning of training, with the increase of the number of training iterations, the mean square errors of the training set, test set and validation set of the network structure all decreased, indicating that the network structure is constantly learning. With the increase of the number of training times, the mean square errors tend to be stable. Due to the small sample size of the present invention, the best validation performance was obtained when the number of iterations was 6, and the MSE value was 0.00051632. When the number of iterations was 12, the model had reached a convergence state, indicating that the network training was completed.

[0094] It should be further explained that through the above training, a neural network structure with excellent performance is obtained. The regression performance of this network structure is shown in the attached figure. Fig. 9 The results show that the correlation coefficients R of the training set, validation set, and test set data are all greater than 0.99, the data distribution is relatively uniform, and has a good linear relationship, indicating that there is a good correlation between the predicted and actual data, and the effect of the trained neural network structure is relatively good.

[0095] S8: Genetic algorithm parameter inversion.

[0096] It should be noted that after the network model is trained, the trained network model is used as the fitness function of the genetic algorithm, and the actual measured uniaxial compression physical test results (CS, CM) are set as the optimization target of the genetic algorithm. The four microscopic parameters of the bond to be calibrated, namely, the normal stiffness per unit area (NSPUA), the tangential stiffness per unit area (SSPUA), the normal critical force (CNS) and the tangential critical force (CSS), are optimized. The optimal parameters are: the normal stiffness per unit area (NSPUA) is 1.51632×10 14 N / m3, tangential stiffness per unit area (SSPUA) is 3.24037×10 13 N / m3, normal critical force (CNS) is 1.46076×10 9 MPa, tangential critical force (CSS) is 9.5×10 8 MPa, and the corresponding stress-strain curves of the uniaxial compression virtual test and the physical test are shown in the attached figure. Fig.10 As shown, it can be seen that the simulation is consistent with the actual situation.

[0097] It should be further explained that the bonding bond parameters were preliminarily calibrated through the uniaxial compression virtual test. In order to better meet the material properties of the actual M08 cemented carbide material, the three-point bending virtual test can be continued on the basis of the preliminarily calibrated bonding bond parameters.

[0098] Specifically, the comparison between the CM, CS and BS obtained by the virtual test and the actual measured values ​​is shown in Table 6. It can be seen that the relative deviations between the CM, CS and BS values ​​obtained by discrete element simulation and the actual test values ​​of M08 cemented carbide material are all within 5%, indicating that the calibrated bonding bond parameters can be used to construct the BPM discrete element model of M08 cemented carbide material.

[0099] Table 6

[0100]

[0101] See attached Figure 11-12 During the DEM virtual test of uniaxial compression, the axial stress-strain data saved every 0.0001s are displayed, and the fracture of the bonding bond during the compression process is counted. The broken bonds are evenly distributed in the BPM to consider the possible defects of the actual specimen. In the initial stage of compression (axial strain: 0~0.006), as the pressure plate continues to press down, see the attached Fig.11 The particle stress and the normal force of the bonding bond gradually increase. Fig.12 It can be seen that the number of bond fractures remains basically unchanged, indicating that the maximum stress on the bond is still below its critical stress and the bond between particles remains intact. At this time, the axial stress-strain curve is linear, and the BPM elastically deforms under axial compression. In the crack extension stage (axial strain: 0.006~0.010), as the pressure plate presses down, the bond between particles begins to break, but due to Fig.11 From the axial stress-strain curve, we can see that the BPM is still in the elastic deformation stage, which means that the bond fracture is in the stable expansion stage and will not cause macroscopic damage to the BPM. In the macroscopic damage stage (axial strain: 0.010~0.013+), as the downward pressure continues to be applied, the number of bond fractures increases sharply, and the axial stress reaches its peak value. Fig.11 The key stress concentration area shown in the figure shows that the crack grows rapidly in this area and forms Fig.12 The bond fracture concentration area shown in Figure 1 eventually leads to the brittle fracture of the BPM. Subsequently, the extensive fracture and extension of the bonding bonds lead to the macroscopic destruction of the BPM, and the brittle failure is transformed into ductile failure.

[0102] Based on the physical test of uniaxial compression and DEM virtual test, the present invention combines the Single-factor test, sample interpolation and BBD test to construct training samples and train a BP neural network with good results. The PB design is used to explore the significance of the influence of bonding parameters on the macroscopic mechanical response of BPM. Through the trained network model, the optimal bonding parameter combination is inverted with the measured mechanical properties of cemented carbide as the target. The following conclusions are obtained through the scheme of the present invention:

[0103] NSPUA, SSPUA, CNS and their interactions have significant effects on the macroscopic mechanical properties CS and CM, while CSS has no significant effects on both CS and CM. During the calibration process, it is possible to consider fixing CSS at an intermediate level to improve the calibration efficiency.

[0104] By combining the methods of Single-factor test, cubic spline interpolation and BBD Test, sufficient training samples can be obtained more conveniently and the calibration efficiency can be improved.

[0105] The regression performance of the trained network structure shows that the correlation coefficients R of the training set, validation set, and test set data are all greater than 0.99, indicating that there is a good correlation between the predictions of this method and the actual data, and the network structure has a good fitting effect.

[0106] When the normal stiffness per unit area (NSPUA) of the bond is 1.51×10 14 N / m 3 , tangential stiffness per unit area (SSPUA) is 3.24×10 13 N / m 3 , the normal critical force (CNS) is 1.46×10 9 MPa, tangential critical force (CSS) is 9.50×10 8 MPa, the relative errors of CM and CS with the actual values ​​were 2.523% and 1.008%, respectively. The errors were within the acceptable range, indicating the effectiveness of the calibration method.

[0107] It should be noted that the above specific implementations are only preferred embodiments of the present invention and the technical principles used. Those skilled in the art should understand that various modifications, equivalent substitutions, changes, etc. can be made to the present invention. However, as long as these changes do not deviate from the spirit of the present invention, they should be within the scope of protection of the present invention. In addition, some terms used in the specification and claims of this application are not restrictive, but are only for the convenience of description.

Claims

1. A cemented carbide discrete element parameter calibration method based on BP neural network, characterized in that: The steps include: S1: The compressive modulus and compressive strength are obtained through uniaxial compression test, and the bending strength is obtained through three-point bending test. The uniaxial compression physical test results of the cemented carbide sample to be simulated are determined. The test formula is as follows: ； Among them, CS is compressive strength, CM is compressive modulus, BS is flexural strength, F c is the peak axial force, F b is the bending failure load, L is the span, b is the width, h is the thickness, A t is the cross-sectional area of ​​the specimen, σ is the axial stress in the linear part, and ε is the axial strain in the linear part; The compressive modulus and compressive strength of the uniaxial compression test are used as the preliminary calibration values ​​of the bond mesoscopic parameters in the discrete element model, and the flexural strength of the three-point bending test is used as the final calibration value of the bond mesoscopic parameters in the discrete element model. S2: Construct a discrete element model and use the commercial discrete element software EDEM to establish a uniaxial compression specimen bonded particle model BPM. Considering the computational efficiency, the particle size and geometric area in BPM are simultaneously enlarged by the same multiple h compared with the original model to obtain an accurate scaled model of the system. The scaled model is a cylinder with a height-to-diameter ratio of 2. The height of the cylindrical scaled model is 100 μm and the diameter is 50 μm. The radius of the particle is set to 2 μm, the contact radius is 2.2 μm, the filling rate of the particle is 0.6, and the radius of the Bond bond is R It is set to 2 μm, consistent with the particle radius, and a DEM virtual model corresponding to the uniaxial compression and three-point bending of the actual test is established; S3: setting the parameters and ranges to be calibrated, wherein the parameters to be calibrated are microscopic parameters of the bonding bond, including normal stiffness per unit area, tangential stiffness per unit area, normal critical force and tangential critical force; identifying the significance of the impact on the response by comparing the differences between the high and low levels of the microscopic parameters of the bonding bond, normal stiffness per unit area, tangential stiffness per unit area, normal critical force and tangential critical force, and listing the high and low level values ​​of the parameters to be calibrated, wherein the value range of the parameters to be calibrated is obtained by trial and error; S4: In order to consider the interaction between the parameters to be calibrated to refine the training sample network, a Box-Behnken design test was performed. For each parameter factor to be calibrated, three levels -1, 0, and +1 were selected, and the single-factor test value was taken to design an experimental matrix. The experimental matrix included all possible combinations of each parameter to be calibrated and the level to provide sufficient response information; S5: DEM virtual experiment, the design matrix of the single factor test and Box-Behnken test is numerically imported into the discrete element model to obtain the corresponding CS and CM; S6: Sample interpolation, establishing training set, test set, validation set and training BP neural network; S7: Verify the BP neural network. If it fails, return to step S6 to adjust the structure of the neural network and continue to train the BP neural network. S8: Using the genetic algorithm parameter inversion, the trained BP neural network model is used as the fitness function of the genetic algorithm, and the experimentally measured uniaxial compression physical test results CS and CM are set as the optimization targets of the genetic algorithm to optimize the four bonding bond micro parameters to be calibrated; S9: Calibrate material parameters according to the output results of the genetic algorithm.

2. The method for calibrating cemented carbide discrete element parameters based on BP neural network according to claim 1, characterized in that: The BP neural network in step S6 comprises an input layer, a hidden layer and an output layer, wherein the number of neurons in the input layer is n Set to 4, the number of neurons in the output layer m Set to 2, the number of neurons in the hidden layer k Determined by the following formula: ； In the formula, n , m are the number of neurons in the input layer and the output layer respectively, l It is an integer in the interval [1,11].

3. A cemented carbide discrete element parameter calibration method based on BP neural network according to claim 1 or 2, characterized in that: The calculation formula of the interpolation is: ； In the formula, A, B, C, D are coefficients, k = 0, 1, … , n-2.

4. A cemented carbide discrete element parameter calibration method based on BP neural network according to claim 1 or 2, characterized in that: The samples in steps S4, S5, S6 and S7 are divided into three parts: training set, test set and validation set according to the ratio of 0.7:0.15:0.

15.

5. The method for calibrating cemented carbide discrete element parameters based on BP neural network according to claim 3, characterized in that: In step S9, the MATLAB neural network toolbox is used to establish a BP neural network. The input vectors are the physical quantities monitored by the normal stiffness per unit area, the tangential stiffness per unit area, the normal critical force and the tangential critical force. The output vectors are the compressive modulus and compressive strength of the actual mechanical properties of uniaxial compression. The input and output vectors are normalized using the MATLAB built-in function mapminmax. Before training the neural network, the learning rate, the maximum number of training times, the training error and the training algorithm must be determined.

6. A cemented carbide discrete element parameter calibration method based on BP neural network according to claim 1 or 2, characterized in that: In step S9, the trained network model is used as the fitness function of the genetic algorithm, and the optimization target of the genetic algorithm is set according to the uniaxial compression physical test result in step S1. The parameters to be calibrated are optimized and compared with the corresponding stress-strain curves of the uniaxial compression virtual test and the physical test.

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